ORNL-3411.txt

AR
3 4456 D3L5240 1
ORNL-3411

UC-4 = Chemistry
TID-4500 (20th ed., Rev.)

 

REVIEW OF ELECTRONIC ABSORPTION
SPECTRA OF MOLTEN SALTS

G. P. Smith

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OAK RIDGE NATIONAL LABORATORY
? operated by

UNION CARBIDE CORPORATION
for the

U.S. ATOMIC ENERGY COMMISSION

 
ORNL-3411

Contract No. W-7405-eng-26

METALS AND CERAMICS DIVISION

REVIEW OF ELECTRONIC ABSORPTION SPECTRA OF MOLTEN SALTS

G. P. Smith

DATE ISSUED

AUG 13 1963

 

OAK RIDGE NATIONAL LABORATORY
Oak Ridge, Tennessee
operated by
UNION CARBIDE CORPORATION
for the
U.S. ATOMIC ENERGY COMMISSION

AR

3 4456 03k5240 1

 

 

 

 

 
L.

II.

II.

Iv.

 

CONTENTS

....................................................................................................................................

Nomenclature and Phenomenological Laws ..o

AN SIEION="METAL JOMIS ittt ettt et e e e e et s e be st et e ee s e e vaessesennsensansennsasaneseresnasnnans

1. Some Theoretical ReSULLS ..ottt e e s e s e se e e er s srar e
Atomic Energy Levels .ot et
Ligand-Field EffeCts .o et ettt e e b e ce s e seaeee s
Cubic F1elds it s e s s e
Low=Symmetry Fields ..o et e s
Spin=Orbit Coupling

e I EEIISIEY e ettt ettt et e e e e st e et ee e n e e nenne

----------------------------------------------------------------------------------------------------------

MHOOw

2. Results for Molten=Salt SOIULIONS ....iveicviiiiiiiiievie e rrrrerre s verre s raeeerenrann e e aas e serereeereeeseannnees
I ETOAUCEION ettt e et ettt e et e et e eeees s e ma e statn sttt e bbbt esbeetaeaeaeatasaeats
Titanium(IID), 31 oottt et
Vanadium(IV), 341
Vanadium(III), 347
Vanadium(II), 3d7 ....oovvieeivereeieeeeeeeceenesseessesmes s ssss s es e et s
Chromium(III), 347
Chromium(II), 3d4 ..............................................................................................................
Manganese(Il), 3d5
Iron(III), 34°
TEON(IE), 3@ oot
COBALLIIY, 3@ oot et e ese s ees s eea e st es st ess s s s s e
NECKEIIL), B3 oot e e e ee e ee e ee s s ee e ee e e s ese s neeeteeereeeerenes
Copper(Il), 3d’

............................................................................................................

............................................................................................................

............................................................................................................

..........................................................................................................

......................................................................................................................

SR 20T mY 0w

..................................................................................................................

3. Charge~Transfer SPECIIA ...ttt e e e e s s e
A INEEOAUCEION et ei i ii sttt ie v eetar et sstertasrestr b asesasassasansssstrnssnsaresssnnssnnnnnensarterinrentennnrenns
B. TheoretiCal ReSULLS i ccre vt ee it se e e e e et e ee s saease s s seaet s eeeanaanse s s e e e eesesnnanns
C. Experimental Results ..o s e e e

Lanthanide Metal Ions

L. INErOAUCEION oot iiiiei ittt e e e e e ettt e e e e e e ets sara s an s e te e e s e e siat b e ae s e s e s
NOLES 0N TREOIY .eiiiiiiriiiiis ettt e e et b e b e s e s bbb e e e e

2.
3. Survey of Results
4.

Band ASSIZNMENTS iiiiiiiiiieiiiiiee st et e e e a et e

AcCtinide MeEtal IOmS iiiuiiieiiiiiiiecierii e ettt s s s e r e st s s s e e e s e s b s shabesee s e e s e r e nrens
1. Introduction
2. Uranium(III)
3. Uranium(IV)
4, Uranium(VI)
5

..............................................................................................................................
..............................................................................................................................
..............................................................................................................................

..............................................................................................................................

AN SUL AN LU LOM S ttntietniteeeesaeseesssaesasie ensesensasassrssssrasssssssssnsssssissensosassesnssressresnsatsnssnsesrnsassraseness

111
iv
Ve Metals 10 MoOLten Salts oottt e e e e eeeereveresevasaesasnsssssntassesrassesssrasseserrnsseresaresiees 46
VIL. NOBMELALLIC LOMS 1ottt st s e reeeeresatsee st s e maeae e saems naeseneesneassnaaeesesnnnesennessnsressnnrserns 47
L HaAlIAE 0D tairitiiiiiee ettt e e e e e e e e e e e e ae e s e eeenare s eamsnarasesarersraresseenresrrssrnerereraes 47
2o NIELATE LOM oo et e s ere st e see s anae s e aesareeeseeasnn e et et e aes et e e aeeenseemesieeeesereeeeeneans 48
A IOt AUCTION oeiieiiiiis ettt ettt e et se e e e ee et aeeseeemeseeseanresesssnsssssraressessssarnsssssesntaseereins 48
B. Band-Energy COIelatiOns ...iciciiiiiiiiiiiiiiiiieiieciene et est et et et eae e beamneses aeresbeensaens 50
C. LCAO-MO Model for NITTate IOM cuoiveuuiriiseieeiieteriererereeesssesesesssssasaseseesseaaeessssreesnrons 51
D. Theories of the Band=Energy Shift......ccccoeiiiiiiiiiniiiiineeiiee i et 52
E. Oscillator Strength Correlation ....ccoooiiiniiiiirciie e 56
3. Other NonmMeETallic Loms oottt ettt e ee s e eraveasesessseseasse s aeeesesmesssmssrmesnsesemessesssen 57
ACkNOWIEdZMENT ..ot e e e ettt et e et ee e ene s eeeae s et eeeeeeanes 57

BiblIOGIAPRY oo e e ettt e et e et ee et e r et enenes 58

 
REVIEW OF ELECTRONIC ABSORPTION SPECTRA OF MOLTEN SALTS*

G. P. Smith

ABSTRACT

The results of investigations of electronic absorption spectra of molten salts
are reviewed with the primary aim of providing a guide to the literature for those
doing experimental research. The period covered is 1916 through mid-1962, with,
however, most of the research concentrated on the period since 1956. Literature
citations number 160 and include a large number of references to theoretical ar-
ticles.

The kinds of chromophores treated include transition-metal ions, lanthanide-
metal ions, actinide-metal ions, halide ions, oxy-anions, and solutions of metals
and halogens in molten salts. Typical spectra are illustrated.

The results of background theory necessary for interpretation of experimental

results are given.

. INTRODUCTION

Spectroscopy serves physical chemistry both as a means of chemical analysis and as a stim-
ulus and testing ground for theories of molecular structure and interactions. In the study of salt
melts, spectroscopy gives promise of fulfilling these functions well, although it is not quite the
universal tool that some of its mote ardent prophets suggest.

This material reviews results of investigations of electronic absorption spectra of molten
salts with the primary aim of providing a guide to the literature for those doing experimental re-
search. Although a fused-salt spectrum was published by Schaefer in 1916 (129),** only a few
electronic spectra were reported during the next 40 yr; therefore this review is concerned almost
entirely with publications from 1957 through mid-1962. No attempt is made to accord historical
priorities or to describe experimental technique. The latter subject is covered in (12, 47, 48, 102,
103, 144, 156).

The results of background theory underlying the interpretation of molten-salt spectra are given
as needed, and references are provided to articles and books wherein these results are developed.
Some readers may regret that the theory is not developed here. Since, however, the transition
types in molten-salt spectroscopy not only cover a wide range but also have been considerably
advanced in theory during the past decade, it is not reasonable to develop relevant background
theory in a brief and specialized review.

In this review the subject matter is divided according to types of chromophoric ions, and an

initial section defines the nomenclature in terms of elementary phenomenological laws.

 

*This report is to be presented as a chapter in Selected Topics in Molten-Salt Chemistry (ed. by M.
Blander), Interscience, New York (scheduled for publication in 1963).

**See Bibliography.

 
II. NOMENCLATURE AND PHENOMENOLOGICAL LAWS

The elementary phenomenclogical laws of absorption spectroscopy are presented here through
the introduction of the nomenclature used in subsequent sections. More complete treatments of
different systems of nomenclature are given in (17, 37, 51, 61, 118), and more complete treatments
of the phenomenological laws are given in (97, 123).

We are concerned with the rectilinear transmission of monochromatic light through a homoge-
neous medium confined between plane, smooth, parallel windows. It is an exact law of absorption
that the radiant power in passing through the medium decreases logarithmically with distance.
That is, if P, is the radiant power which enters the medium and P is the radiant power transmitted
through a distance b of the medium, then log (PO/P) is proportional to . This behavior is known
as Lambert’s law. The distance b is commonly referred to as the ‘‘path length.”’ Because of the
logarithmic attenuation, log (PO/P) is of special importance and for pure materials is called the

*‘absorbance’ or “‘optical density,” denoted A:

A =log (P,/P) . (IL.1)

The absorption by solids is often reported as the absorption constant k (or a), where

k=(1/b) In (P /P)=2.303 A/b . (I1.2)
In the study of solutions the interest generally is in absorption by the solute apart from ab-
sorption by the solvent. It is conventional in this case to redefine the absorbance A by subtract-

ing the logarithmic absorption of the solvent from that of the solution to give

A=log(P_ . /P_.), (11.3)

solv soln

where P is the radiant power transmitted through a given thickness of solution and P is
soln solv

that transmitted through the same thickness of solvent when both solution and solvent are irradi-

ated with the same incident power. In some systems of nomenclature different names and symbols

are given to the different quantities defined by Eqs. (II.1) and (II.3), but this commendable prac-

tice has never been popular.

For dilute solutions, A/b is often proportional to the concentration ¢ of the light-absorbing
species to within a good approximation. For this reason it is useful to define the absorptivity or

extinction coefficient a as
a=A/ch . (I1.4)

If & is in centimeters and ¢ equals M (moles/liter), it is a common convention to change the sym-

bols and write
€ =A/Mb , (I1.5)

where € is the molar absorptivity or molar extinction coefficient. When dealing with pure fused
salts, it is often possible to associate the absorption over some finite wavelength range with a
particular constituent ion. In this case it is useful to define the molar absorptivity of the chromo-

phortic ion by letting M in Eq. (II.5) equal the number of gram-ions of chromophore per liter of melt.

 
Each of the quantities A, k, a, and € as a function of wavelength may be regarded as an ab-
sorption spectrum. The absorptivity, @ or €, is a differential photon cross section with the dimen-
sions of area per specified quantity of chromophore.

There are two important laws of ideal behavior: Beer’s law or the Lambert-Beer law, which
states that at a fixed wavelength 2 and € are constants independent of concentration; and the law
of additive absorbancies, which states that in a solution of several light-absorbing species each

species contributes additively to the absorbance. That is,

A/b=(1/B)S,A, =5 a.c,, (11.6)

where A is the absorbance of the whole solution, and AI., a, and c, are, respectively, the absorb-
ance, absorptivity, and concentration of the ith species, with A, and a. determined at the concen-
tration ¢ .

Only a few studies have been made to check Beer’s law in a precise way for solutions in
melts. In one instance Boston and Smith (12) measured the visible spectrum of NiCl2 in the
fused LiCl-KCl eutectic at seven concentrations, ranging from 0.01 to 0.4 M. Beer’s law was ac-
curately obeyed at all wavelengths.

Modest deviations from the ideal laws generally indicate interparticle interactions. These
may be interactions between chromophoric ions or between chromophoric ions and the ions of a
second solute which is not itself light-absorbing. Drastic deviations generally indicate the pres-
ence of more than one solute species. An example of the latter behavior is given in Sec VI.

A conventional measure of the integrated absorption of a single electronic band is the oscil-

lator strength or [ number (93, 105):

mc 2 e mc? (In 10) oo 0 oo
f=—s kdv=——5——10° € dv =4.32x 10~ € dv, (I1.7)
e N J, Te"N, 0 0

 

where m is the electronic mass, e the electronic charge, ¢ the velocity of light, N the number of
chromophoric particles per cubic centimeter, N, Avogadro’s number, and v the wave number in
cm™!. Asa practical matter the integral is, of course, taken over only the range of v values for
which € is appreciable. The oscillator strength defined in this way is an empirical quantity
closely related but not identical to the oscillator strength of dispersion theory, because Eq. (II.7)
does not take into account the effect that the medium has on the properties of the incident light
wave (24). Usually the difference between empirical and theoretical oscillator strength is ignored

because the best theoretical calculations of oscillator strength are exceedingly rough. The oscil-

lator strength is a dimensionless quantity proportional to the integrated photon cross section.

1il. TRANSITION-METAL IONS

The spectra of transition-metal ions with partially filled d shells consist of broad weak bands

in the near-infrared and visible regions and of much stronger bands in the ultraviolet region. The

 
weak bands arise from d - d transitions, that is, from transitions between energy levels of d” elec-
tronic configurations. These transitions are the primary subject of discussion here. The strong

bands in the ultraviolet are attributed to so~called ‘‘charge-transfer’’ transitions, which are dis-

cussed in Sec III.3.

1. Some Theoretical Results

Elementary theoretical results that deal largely with the classification of energy levels and
the assignment of optical transitions are compiled here not to serve as an introduction to the
theory of transition-metal ions but to refresh the memory of the reader.

The relevant theory is known, in variant forms, as crystal-field theory and ligand-field theory.
For a qualitative introduction to the spectroscopic aspects of theory, the reader is referred to the
article by Manch and Fernelius (95). For more detailed and quantitative discussions the reader is
referred to the review articles by Bleaney and Stevens (I1), Dunn (28), Moffitt and Ballhausen
(98), Hartmann (55), McClure (89), and Runciman (I24) and to the books by Griffith (41), J#rgensen
(74), Ballhausen (2), and Orgel (111).

The transition-metal 10ons thus far studied in salt melts are confined to the first transition-
metal series and have electronic configurations that consist of closed electron shells (the argon
core), plus an incomplete 34 shell. In this section we are concerned with only the 4 -+ d transi-
tions and therefore are interested in only those energy levels that arise from 34" electronic con-
figurations.

In refined theory the wave functions associated with d » 4 transitions of complex ions need
not be combinations of pure nd orbitals but may contain admixtures of (n + 1)s, (n + 1)p, etc., and
ligand orbitals that have the same symmetry properties as the pure nd orbitals. Thus, strictly
speaking, a d » 4 transition is one between states with the symmetry properties of 4 orbitals.

A. Atomic Energy Levels. — For an atomic ion in field-free space the energy levels of the 3d
electrons are arranged in a sequence of groups. Each group is called a ‘‘term’’ or “‘multiplet
term.”” The energy separation between terms is a consequence of the electrostatic repulsions be-
tween 3d electrons. Different terms are characterized by their different values of the total orbital
angular momentum (quantum number L) or of the total electronic spin (quantum number §).

The terms that arise from the various d” electronic configurations are listed in Table IIl.1.
They are specified by a capital letter designating the quantum number L according to the scheme
0,1,2,...=85,P,D, F, G, H, I, and by a superscript numeral giving the spin degeneracy or mul-
tiplicity 7, where 7 = 2§ + 1 and § is the spin quantum number. Hence 4F (read ‘‘quartet F”’) sig-
nifies a term with L = 3, r =4, and § = 3/2

The lowest-energy or ground term for each configuration is denoted in Table III.1 by bold type
and may be derived from Hund’s rule that the term of lowest energy is that of largest L among
those of highest multiplicity.

dlo—n

The configurations 4" and give rise to the same system of terms because 10-n elec-

trons in a d shell behave like those of a closed & shell of 10 electrons plus n positrons or electron

 
 

Table 11L.1. Terms for the 4" Electronic Configurations

 

 

Configurations Terms
R 2p
P, & 3¢, 3p 1 1p, 1s
3, d ‘e, 4p 2y 26 2F, 2p, 2p, 2p
at, & °D 3y, 36, 3F, 3F, 3p, 3P, 3p I, 16, 16, 'F, 'p, D, s, 15
d° bg 4G, 4F, 4p, 4p 21 2n, %6, %G, %F, %F, 2p, 2D, ?p, 2p, %5

 

“*holes.” The electrostatic forces between holes are the same as the electrostatic forces between
electrons.

If . and § for a given term are not zero, the magnetic moment due to electronic spin interacts
with the magnetic moment generated by electronic orbital motion in such a way as to separate the
component energy levels of a term by an amount which is relatively small for 3d electrons. This

y

magnetic interaction is known as ‘‘spin-orbit coupling,’” and the small separation of multiplet

components is known as “'spin-orbit splitting.”

The strength of spin-orbit coupling increases
with increasing atomic number over the first transition series.

Each component of a term is characterized by a different value of the total angular momentum
(quantum number ), and when it is necessary to specify a specific component, the appropriate |
value is appended to the term symbol as a subscript. The possible values of | for a term are

4F 4F

J=L+S§S L+5~-1,...,L~§, sothat the components of the term AF are 4F 7720 s /2>

and 4F

9/2°
3/2°

B. Ligand-Field Effects. — Electrons in the 34 shell are poorly shielded by the outer elec-
trons of the ion, so that their energy states are very sensitive to the fields of surrounding ions
and molecules. The perturbing influence of the surroundings shifts the relative positions of the
free-ion terms and splits them into components with an energy separation that may be of the mag-

nitude of the separation of free-ion terms, that is, on the order of 10* cm™!. This effect is called

3 t

“‘crystal-field’’ or “‘ligand-field splitting.”” For historical reasons the term ‘‘crystal field"’ is
sometimes reserved to refer to a particular theoretical approximation used in deducing the effect
of the field, irrespective of whether the surroundings constitute a crystal lattice, while the term
““ligand field’’ is applied to a better approximation. In this report ligand field is used in an inel-
egant way to refer to the field produced by the ligands irrespective of theoretical approximations.
Spin-orbit coupling splits the ligand-field components by a relatively small amount, just as
was the case for the free-ion terms, and is therefore ignored as a small effect that can be added
after the general features of the much larger ligand-field splitting of the orbital degeneracy have

been described.

 
 

The number of levels into which a given multiplet term splits in a ligand field depends on the
orbital angular momentum of the term and on the symmetry of the perturbing field.

As was noted, the orbital angular moment of electrons on an atom in field-free space or in a
spherically symmetric field is denoted by the quantum numbers s, p,d, f, ... =0,1, 2,3, ....
When the atom is contained in a molecule or molecule ion, other sets of quantum numbers are used
that specify the orbital angular moment in relation to symmetry properties of the molecule. For a
linear molecule the symbols o, 77, §, ¢, ... =0, 1, 2, 3, ... indicate the magnitude of the com-
ponent of orbital angular moment along the internuclear axis. For nonlinear configurations the
symbols d, b, e, t, g, and b are used and have the following meaning: @ means that the molecular
wave function does not change sign under a rotation of 277/n about the molecular n-fold rotational
axis of symmetry, while b means that it does change sign; e, ¢, g, and » mean that the wave func-
tion is, respectively, twoe, three-, four-, or fivefold degenerate. The quantum numbers g and 5
occur only for isosahedral configurations.

The subscripts g and z designate that the wave functions are even or odd, respectively, with
regard to inversion at a center of symmetry, while the subscripts 1, 2, 3, ... designate that they
are odd or even with respect to reflection in some specified plane of symmetry.

The above definitions are equivalent to saying that a-type wave functions have a component
of angular momentum which is a multiple of 7 along the n-fold axis, while b-type wave functions
have a similar component which is an odd multiple of /2. Conversely, e-, t-, g=, and b-type wave
functions are not multiples of n/2 about some n-fold axis.

C. Cubic Fields. — The high-symmetry fields produced by octahedral and tetrahedral configu-
rations of ligands are of basic importance since a great many complexes have configurations which
approximate these or may be regarded as being derived from them by simple distortions. Octahe-
dral and tetrahedral configurations and their fields are said to belong, respectively, to the octabe-
dral symmetry group, designated 0,, and the tetrabedral symmetry group, designated T ; Both
symmetry groups are members of the cubic symmetry class and are referred to collectively as
cubic. In the following discussion the classification of energy levels formed by cubic field split-
ting is described, with some consequences of distortions from cubic symmetry considered cur-
sorily.

The component energy levels formed by ligand-field splitting of multiplets are labeled accord-
ing to the symmetry properties, or species, of the wave functions. For the d” configurations in
cubic fields five symmetry species are possible. They are conventionally denoted by the symbols
listed in Table III.2. In this review Mulliken’s symbols will be used. Some authors use F in
place of Mulliken’s T, and a few reverse T, and T2. In the case of octahedral fields the subscript
g is appended to denote even parity. Tetrahedral fields, which have no inversion center, do not
preserve the even parity of the 3d wave functions. The multiplicity may be denoted, as in the
case of term symbols, by a prefixed superscript.

The energy levels formed by cubic-field splitting of terms with L values of S, P, D, ..., I are
given in Table II[.3. Thus an § term does not split but gives rise to a single level of species A,

while an H term splits into four components, two of which have the same species, Tl'

 
Table 111.2. Correlation of Symmetry Symbols Used to Designate
Energy Levels in Cubic Fields

 

 

Mulliken (104) Bethe (10) Degeneracy
A Fl 1
A, FZ 1
E Iy 2
T, r, 3
T, r, 3

 

Table 11}.3. Species of Levels Arising from Splitting of Terms
in Cubic Fields

 

 

Terms Species
S Ay
P T,
D E T,
F A, T, T,
G AL E Ty, T2
H E, T,, T, T,
! A Ay E T, T, T,

 

The information in Tables IIl.1 and III.3 may be combined to give the total number of orbital
energy levels formed by a d™ configuration in cubic fields. It will be seen that d* and d° configu-
rations each have but one term, which splits into two energy levels, that 4% and 4% configurations
yield eleven levels, and that the greatest number, 43 levels, is formed by d.

The spectra resulting from these many levels would be much more complex were it not that
many of the transitions are forbidden by the spin selection rule, which specifies that transitions
involving a change in multiplicity may not occur. Although this rule applies alike to electric-
dipole, electric-quadrupole, and magnetic-dipole transitions, it is exact only for vanishing spin-
orbit coupling and holds less and less rigorously as spin-orbit coupling increases. Thus spin-
forbidden transitions may occur for 3d” configurations but generally will be very much weaker than
spin-allowed transitions.

For example, of the sixteen energy levels for the configurations d? and d in cubic fields, four
are quartets, derived from the quartet terms, and twelve are doublets. In weak ligand fields the

ground state -is a quartet, and so there are three spin-allowed transitions to the three excited

 
quartet states and twelve spin-forbidden transitions. It is a rule that in weak fields the ground
state always has the maximum multiplicity, and it may be verified from Tables III.1 and 3 that the
number of spin-allowed transitions is either 0, 1, or 3 for all the d” configurations. These few
spin-allowed transitions dominate the spectra of most transition-metal ions in molten salts. In
strong fields, as is discussed later, it is possible for the ground state of certain d” configurations
to become a low-multiplicity term with a consequentincrease in the number of spin-allowed transi-
tions.

Energy-level diagrams for d' and 4° configurations are shown in Fig. III.1, where energy is
plotted as a function of the cubic crystal-field parameter Dg. The 2D multiplet term is split into

the two levels °E and T, with an energy separation defined to be 10| Dg|. In an octahedral

27
field the ground state of a d! ion is 2T28 and the excited state is 2Eg. The broad absorption
band at 20,300 em™ ! for aqueous solutions of Ti(Ill) has been assigned (62) to the 2ng - 2Eg
transition with a Dg value of 2030 em™ L.

The electronic configurations of the energy levels are denoted in the margins of the diagrams
in terms of the one-electron orbitals t, {or zzg) and e (or eg). In other systems of nomenclature
these orbitals are designated, respectively, as y, and y,, or d,. and d,y. Lower-case symbols are
generally used to specify the symmetry properties of one-electron orbitals, while upper-case sym-
bols are used to specify the symmetry properties of wave functions for a multielectronic configura-
tion.

Since a tetrahedral configuration has only four ligands while an octahedral configuration has
six, the crystal-field splittings achieved by tetrahedral complexes are decidedly smaller than
those achieved by octahedral complexes of similar ligands. Elementary crystal-field theory sug-

gests that Dg for a tetrahedral complex of a given kind of ligand is ~ 4/9 of Dg for an octahedral

complex of the same ligand. Various factors not anticipated in elementary theory could modify the

UNCLASSIFIED
CORNL-LR-DWG 72509

 

 

 

 

5 a
29 %
%%
+) Og 0 -\Dg
Fig. Ill.1. Energy Levels of 4V and d° Configurations
g in Cubic Fields. The lower diagram applies to the d!

configuration, The right side of each diagram shows
the splitting of the 2p multiplet by octahedral fields
(Ob symmetry) and the left side shows the splitting by

ENERGY ———— =

oo tetrahedral fields (Td symmetry}. The marginal notation

 

gives the electronic configurations of the levels. The

 

 

 

 

10g o *10g separation of the energy levels is 10|Dq|. The sign of

TETRAHEDRAL FIELD ~OCTAHEDRAL FIELD Dgq is indicated in parentheses.

 
number 4/9

erally valid.

considerably, but experimental evidence suggests that a value of about one-half is gen-

Figure III.1 shows that the sequence of orbital levels for term splitting is inverted in going
from d' to d° and from octahedral to tetrahedral fields. This is true for all d"—d!%~" configura-
tional pairs as a result of electrons and holes having opposite charge and so interacting with neg-
ative ligands in symmetrically opposite ways and an octahedral configuration of negative charges
having the same qualitative effect as a tetrahedral configuration of positive charges.

Configurations with more than one d electron or hole have more than one free-ion term. As the
ligand-field strength increases and the term splitting becomes greater, the energy levels arising
from different terms may cross over one another, so that the order of energy levels is not the same
in fields of high strength as it is in fields of low strength. If the crystal field is relatively weak
so that the splitting of individual terms is small compared with the energy separation of different
terms, one speaks of '‘weak-field splitting.”” If, however, the crystal field is so strong that the

splitting of individual terms is substantially greater than the energy separation of different terms,

¢ ¥

one refers to “'strong-field splitting.’”’ The latter is achieved when the crystal field is strong
enough to overcome the electrostatic repulsions between 34 electrons which determine the separa-
tion of terms in a free ion. The intermediate region, in which the interelectronic repulsions and
crystal-field forces are comparable and in which the levels cross, is called ‘‘intermediate split-
ting.”” In practice, intermediate splitting is quite common.

The effect of cubic fields on the energy levels of d? and d® configurations is schematically
illustrated in Fig. III.2. The solid curves represent energy levels that are predominantly triplet
states and that, in weak fields, represent the splitting of the 3F and P terms. The dashed
curves represent energy levels that are predominantly singlet states. This figure is intended pri-
marily to show the correlation between weak-field and strong-field levels. It gives the qualitative
sequence in which these energy levels occur, but not the quantitative energy separations. In the
margins of the figure are electronic configurations in terms of the one-electron orbitals ¢, (or tzg)
and e (or eg) for the three configurations formed in the strong-field limit.

It will be noted from Fig. III.2 that a wiplet level is always the ground state, irrespective of
field strength, and that there are three excited triplet levels. Hence three spin-allowed transi-
tions are possible, and they provide the most prominent bands in the visible and infrared spectra
of d° and d® ions with approximately octahedral or tetrahedral arrangements of ligands.

As an example, 1n a d8-configuration ion, such as Ni(Il), in a weak tetrahedral field the three
spin-allowed transitions in the order of increasing energy are 3T1(F) > 3T2(F), BTI(F) > 3A2(F),
and 3T1(F) > 3T1(P)’ with the free-ion terms from which the energy levels arise in weak fields in-
dicated in parentheses.

The only strong-field situation encountered thus far with d? and d® jons in melts is that of
V(III) in octahedral fields (51). For this case the three spin-allowed transitions in the order of
Increasing energy are 3T1g(t2) > 3ng(i‘e), 3'Tlg(t.'z) > 3’Tl(t.'e), and 3Tlg(lz) > 3A28(ez), where the
electronic configurations from which the states arise in the strong-field limit are indicated by an

abbreviated notation in parentheses.
UNCL ASSIFIED
ORNL ~LR-DWG 7251

 

 

 

 

 

i
4 _q
‘29 %9
>
g f5 6’3
w 2g ¢
=
wl
I f_fgegz
4
to (+) Dg 0 (=) 0g -

 

ENERGY

 

 

 

 

- (=) 0g 0 (+) Og +
STRONG-FIELD TETRAHEDRAL  SPHERICAL-SYMMETRY OCTAHEDRAL STRONG - FIELD
LiMIT FIELD FIELD FIELD LIMIT

Fig. I11.2. Schematic Energy Levels of 42 and 2% lons Showing the Correlation Between Weak
and Strong Cubic Fields. The lower diagram applies to 4° and the upper diagram to &P, The
central portion of each diagram shows the crystal-field splitting of free-ion levels, The sides
show the exchange splitting of the strong-field levels. To the right is the splitting by octahedral
fields (Ob symmetry), and to the left the splitting by tetrahedral fields (Td symmetry). Levels
with primarily triplet character are shown as solid lines, and those with primarily singlet character
as dashed lines., At the median line Dg has the value zero, while at the margins it has the value

infinity,

 
11

The configurations d?, d3, d’, and d® all have F and P as terms of maximum multiplicity.

Consequently, in weak cubic fields d> and d’ ions give a pattern of three spin-allowed transitions
much like that described above for 4% and 4% ions. The 41, d4, d6, and d° configurations all have
a D term as the term of maximum multiplicity and all give but a single spin-allowed transition in
weak cubic fields. In strong cubic fields, however, the situation may be quite different. The be-
havior of the quartet levels and of the lowest-energy doublet level for d? in a tetrahedral field and
for d’ in an octahedral field is shown (qualitatively) in Fig. IlI.3. The pattern of quartet levels
is the same as that for d° in octahedral fields and for 4% in tetrahedral fields. The lowest-energy
doublet level, however, decreases in energy as Dg becomes more negative, until it eventually
drops below all the quartet levels and becomes the ground state. In strong fields therefore it is
the doublet-doublet transitions that are spin-allowed and not the quartet-quartet transitions.

This change from the ground state given by Hund’s rule to a different ground state in strong
fields occurs for 43, d4, d>, and d® in tetrahedral fields and for d4, ds, d6, and 47 in octahedral
fields.

Since the multiplicity and hence the total electronic spin always decreases in these cases in
going from weak fields to strong fields, one refers to ‘‘high-spin’’ complexes when the ground
state is given by Hund’s rule and to “‘low-spin’’ complexes when the ground state violates Hund’s

rule.

UNCLASSIFIED
ORNL~LR-DWG 72508

 

Fig. E1l.3. Schematic Energy-Level Diagram Show-
ing the Quartet Levels and the Lowest Doublet Level £
for @3 lons in Tetrahedral Fields or d’ lons in Octa-
hedral Fields. In both cases Dg has negative values.
Not shown are five additional doublet terms which lie

at higher energies.

 

7~ IN 7;, \\ 7,
7
N O \
d y \
\\
\ 2

 

 

 

-Dg

 
12

The configuration d° is a special case. It has 65 as the only free-ion term of maximum multi-
plicity, and an § term is not split by crystal fields. Consequently there are no spin-allowed tran-
sitions in weak fields; all the observed bands are due to very feeble, spin-forbidden transitions.
The energy-level diagram ts the same for both tetrahedral and octahedral fields.

Quantitative energy-level diagrams for the multielectron 4" configurations in cubic fields are
available and provide a basic guide in the assignment of bands and the estimation of Dg values.
Among the most useful of these diagrams are the diagrams of Tanabe and Sugano (149), which
cover all the multielectron d” configurations in octahedral fields and which are also reproduced
with discussion in the reviews by McClure (89) and Dunn (28). More exact diagrams, which in-
clude spin-orbit coupling, have been reported by Liehr (80) for d' and 4° complexes, by Liehr and
Ballhausen (84) for V(III), configuration d2, and for Ni(II), configuration d®, in both octahedral and
tetrahedral fields; and by Liehr (81) for Cr(IIl), configuration d3, and for Co(lD), configuration d’,
in both octahedral and tetrahedral fields. In using these diagrams, one must keep in mind that the
theory upon which they are based is an approximation and also that ligand fields need nothave
cubic symmetry.

Jorgensen (74) gives tables of spectral assignments for a large number of transition-metal

complexes that provide useful comparisons for the assignment of molten-salt spectra.

D. Low-Symmetry Fields. — Ligand fields of low symmetry will, in general, split free-ion mul-
tiplet terms into a greater number of components than are obtained with cubic fields. In many in-
stances a low-symmetry field may be regarded as having been achieved by continuous distortion
of a cubic field. In such cases the possible energy levels may be obtained by considering how
the distortion splits the cubic-field levels.

The maximum splitting of the five kinds of cubic-field levels is given by the orbital degen-
eracy values listed in Table III.2, where the spin-orbit fine structure is neglected. Thus A, and
A, are not split by low-symmetry fields, E may be split into two levels, and T, and T, are split
into a maximum of three each. For example, the cis-isomers of ions such as (MxéYz)iy are of
sufficiently low symmertry to split all degeneracies.

Among the most common examples of noncubic fields are those belonging to the tetragonal
symmetry class, which includes the symmetry groups D, and D,,. A tetragonal field is formed,
for example, when two trans-ligands of an octahedral complex differ in some nontrivial respect
from the remaining coplanar four; for example, the bond length might differ or the complex might be
a lrans-isomer of (MX4Y2)iy.

Tetragonal distortions of cubic fields split the doubly degenerate E state into two nondegen-
erate states and split the triply degenerate 7| and T, states into one nondegenerate and one
doubly degenerate state.

If an octahedral configuration of ligands is tetragonally deformed by changing relative bond
lengths, two limiting cases are obtained: the removal of two trans-ligands to infinity leaves a
square-planar configuration, whereas the removal of four coplanar ions to infinity leaves a sym-

metrical linear complex. A square-planar configuration may also be formed by a tetragonal dis-

 
13

tortion in which a tetrahedron is flattened. Some complexes referred to as ‘‘square”’

are actually
intermediate between tetrahedral and planar.

The splitting of a multiplet term by a cubic field is quantitatively described by a single pa-
rameter Dg, which may usually be evaluated from spectroscopic measurements. If the field is dis-
torted to tetragonal symmetry, three parameters are required, while in fields of still lower sym-
metry four are required. Experimental data seldom permit an unambiguous evaluation of three or
four parameters for solution spectra at ordinary and elevated temperatures.

The theory of 4! and d” configuration ions in tetragonally distorted octahedral fields has been
considered by Ilse and Hartmann (62), by Belford, Calvin, and Belford (9), and by Weakliem (I54).
Liehr (80) has computed the spin-orbit coupling for d' and 47 ions in tetragonal and trigonal
fields. The influence of tetragonal distortions on the octahedral-field energy levels of the 4! con-
figuration in the absence of spin-orbit coupling is shown schematically in Fig. II1.4. When the
figure is inverted, it applies to the d° configuration. It will be seen that the Eg and ng levels
each split into two new levels, making three absorption bands possible. If the splitting is small,
one of these bands will lie in the far-infrared region, and the other two may overlap so as to give
a single broadened and possibly skewed band. If the distortions are large, the upper component

of T, may lie near the lower component of E.

UNCLASSIFIED
ORNL-LR-DWG 72540

Fig. IH.4. Schematic Diagram of the Splitting of
Energy Levels of the 4l Configuration in an Octa-
hedral Field Subjected to Tetragonal Distortion.
When the diagram is inverted, it applies to the d’

configuration. The two energy levels deriving from

the multiplet term 2D in a field of rigorous octa-

hedral symmetry are at the center line of the dia-
gram, The right side of the diagram shows the
splitting caused by moving two opposite ligands
further away than the other four, and the left side
shows the splitting caused by moving four coplanar

ligands further away than the other two.

  

. g |
2 i
ng \

|

LINEAR OCTAHEDRAL SQUARE PLANAR

X,y Z
EXPANSION EXPANSION
14

Complexes of dl and d° configuration ions may be distorted from cubic symmetry by the Jahn-
Teller effect, but it is very difficult in a given instance to decide whether a distortion is caused
by simple coulombic forces or by the Jahn-Teller effect (83).

Theoretical treatments of multielectronic d” configurations in fields of less than cubic sym-
metry include d2 and 48 (3, 95, 115, 119, 154), d° and d’ (3, 4, 141, 142, 154), d* and d° (3, 6, 8),
and 4 (3, 109).

E. Spin-Orbit Coupling - Spin-orbit coupling splits many of the crystal-field energy levels
into fine-structure components. In most instances the energy separation of these components is
too small to be resolved in the optical spectra of complexes at ordinary and elevated temperatures,
and therefore the details are of no great interest here. The most favorable circumstances for spin-

orbit splitting to be observed in spectra are for transitions involving the T, Tlg’ T,, and T2g

23
orbital levels, which show the greatest splitting, and for the higher atomic-number ions, such as
Ni(Il), which have the greatest spih-orbit coupling. For example, the 3z"izg(F) - 3Tlg(F) transi-
tion of the octahedral hexaquo Ni(II) complex gives rise to a double peak with maxima near 15,000
cm™ !, which Liehr and Ballhausen (84) ascribe to transitions to spin-orbit split components of
’T, [(F).

F. Intensity. — The overall intensity of visible and near-infrared spectra is generally much
greater for tetrahedral ligand configurations than for octahedral configurations. This fact has
been much used as a criterion for distinguishing between these two configurations in melts. The
difference is associated with the operation of Laporte’s selection rule.

Laporte’s rule requires that electric-dipole transitions always take place between energy
states with wave functions of opposite parity. A wave function has even parity (denoted by sub-
script g) if it remains unaltered upon inversion through the center of symmetry, that is, the metal
nucleus, and it has odd parity {(subscript «) if it changes sign upon inversion. In the absence of
external perturbations all states of the same configuration have the same parity, so that electric-
dipole transitions between them are Laporte-forbidden. Thus 4 - 4 transitions, which occur be-
tween different states of a d” configuration, are always weak and secure their intensity from inter-
actions with surrounding ions and molecules.

When the field due to the surroundings retains an inversion center among its symmetry ele-
ments, as is the case for an exactly octahedral field, the parity of the wave functions is unaf-
fected by the field and Laporte’s rule remains rigorously operative. However, distortions of a
centrosymmetric field that destroy the inversion center will mix small components of odd-parity
orbitals with the even 34 wave functions and permit feeble transitions to occur. The necessary
distortions may be accomplished by odd vibrations, in which case the transitions are designated

as '‘vibronic "’

Generally this mechanism leads to a change in intensity with changing tempera-
ture because of a change in population of the various ground-state vibrational levels. Holmes and
McClure (60) have observed such intensity changes in some hydrated transition-metal ioans.

The intensity of vibronic transitions depends on the extent to which the vibrations distort the

electronic wave functions. In general the intensity increases with the vibrational amplitude but

never becomes very strong,

 
15

Permanent distortions of octahedral fields will contribute to transition intensity only to the
extent that they destroy the center of symmetry. Thus pure tetragonal distortions, which do not
affect the center of symmetry, leave the transitions Laporte-forbidden.

A tetrahedral field, of course, has no center of symmetry, and so absorption bands for tetra-
hedral complexes are generally much stronger than those for octahedral complexes. The mecha-
nism by which intensity is gained in the case of tetrahedral complexes is theoretically treated by
Ballhausen and Liehr (5, 85) and by Carrington and Schonland (16). It involves a mixing of 4p and

ligand orbitals with the 34 orbitals.

2. Results for Molten-Salt Solutions

A. Introduction. — It has been possible to classify many spectra of molten-salt solutions as
octahedral-like or tetrahedral-like. In some instances this classification is quite accurate; the
molten-salt spectra either closely resemble the spectra of known cubic complexes, or, where data
for comparison are unavailable, they fulfill the predictions of cubic crystal-field theory. An ex-
ample is Ni(I) in fused pyridine hydrochloride with a spectrum like that of Ni(II)-doped CszZnCl4
(tetrahedral).

In many instances, however, the spectra of molten-salt solutions depart in various ways from
the anticipated norms for simple cubic configurations. It is generally supposed (50, 51, 52, 143)
that these deviations represent ligand configurations that can be reasonably described as small
distortions from simple cubic geometry, so that classification into octahedral or tetrahedral cate-
gories is an approximate and useful description.

Most of the departures from typical cubic spectra consist of band splittings, but in several in-
stances molten-salt spectra have been classified as octahedral although they have an unexpectedly
high intensity by comparison with other octahedral spectra of the same ions. Examples include
V(II) (51) and V(ID) (51) in the LiCI-KCl eutectic at 400°C and Ni(II) (50) in the LiNO}s-KNO3 eu-
tectic.

The intensity of spectra for octahedral fields is discussed at the end of the preceding section.
On the basis of the vibronic mechanism the intensity should increase substantially in going from
25°C to the temperature of the melt, but Gruen and McBeth (51) have pointed out that this mecha-
nism alone is insufficient to account for the very large increase observed. In the case of V(i)
solutions in LiCl-KCl at 400°C they invoked the Holmes-McClure (60) model to show that the
vibronic mechanism is expected to produce an increase in [ number of 10 to 30% in going from 25
to 400°C, whereas the observed increase is by a factor of about 10. They concluded that the
hexacoordinated complex must be distorted from simple octahedral geometry in such a way as to
destroy the center of symmetry.

B. Titanium(lll), 34'. — The spectrum of Ti(Ill) was measured by Gruen and McBeth (52) in
the LiCl-KCl eutectic at temperatures from 400 to 1000°C and in molten CsGaCl, at temperatures
from 600 to 900°C. The spectrum underwent large changes when either the solvent salt or the

temperature was changed. These changes were attributed to an equilibrium between tetrachloro

 
16

and hexachloro Ti(Ill) ions in which TECIGS" predominated in LiCl-KCl and TiCl4_ predominated
in CsGaCl,, while with increasing temperature the equilibrium shifted to favor TiCl,™ in both
solvents.

In LiCl-KCl at 400°C, where TiC163" was believed to predominate, the spectrum consisted of

! with molar absorptivities of somewhat less

two maxima at approximately 10,000 and 13,000 cm™
than 5 and a combined oscillator strength of about 104, These bands were attributed to transi-
tions to the two energy levels formed by tetragonal splitting of the 2T2g excited state of an octa-
hedral complex. By averaging the energies of the two bands, a value of about 1150 cm™! was
chosen for the cubic crystal-field parameter Dg. A similar splitting of the excited state is known
for hexaquo Ti(IIl) (71) and is attributed to the Jahn-Teller effect (3, 58).

In molten CsGaCl, at 900°C, where TiCl,” was believed to predominate, a band maximum
was found near 8000 cm™! (¢ = approximately 50) with shoulders at both higher and lower fre-
quencies. This band group was assigned to the 2E - 2T2 transition of a somewhat distorted tet-

rahedral complex with a Dg value of about —800 cm™!. The intensity seems rather low for a tet-

rahedral complex, but the Dg value is reasonable.

C. Vanadium(lV), 34'. — The spectrum of V(IV) was measured in the fused LiCl-KC! eutectic
by Gruen and McBeth (51) and by Molina (99). It consists of a broad band with a peak at 739 mu
and an oscillator strength of 5.9 x 10~ %, There is a suggestion of a shoulder at roughly 650 mpu.
The V(IV) solutions were prepared in the presence of oxygen, and the spectra appear, by compar-
ison with aqueous solutions (34, 79), to be due to the vanadyl ion VO?".

The theory of the vanadyl ion VO?* has been developed by Furlani (33), J#rgensen (71), and
Ballhausen and Gray (2a).

The vanadyl ion VO?" always occurs coordinated to other groups both in the solid state and
in solution with a coordination number of five or six for vanadium. A typical example is
[VO(H20)5]2+ in which the six groups coordinated to vanadium lie in a tetragonally-distorted octa-
hedral array, which may be described by an expansion along two of the fourfold axes. The appro-
priate energy-level scheme is given by the left side of Fig. IIl.4 at a position between the central
line (octahedral) and the point at which zEg and 2Blg cross. Actually, the two trans-ligands are
not equidistant from vanadium. Hence the g must be dropped from the symmetry symbols. Three
transitions are predicted, 282 5 2(E, B,, A)). Observed bands in the aqueous spectrum are as-
signed as follows: 13,000 cm™! to ’B, - *E and 16,000 cm ™! to B, > °B,. The ’B, - ‘A band
is presumed to be hidden by a broad charge-transfer band at higher energies.

Similar results were obtained for solutions of V(III) in molten pyridine hydrochloride at 160°C
(O1).

The 400°C spectrum of V(III) in LiCIl-KCl is quite similar, except for intensity, to the spectra
of various hexacoordinated V(III) ions of the oxo type (34, 56, 57, 88, 119). These oxo-ions are
trigonally distorted. The field over the space of the V(III) ion in LiCl-KCl probably has an even

greater distortion, as indicated by the enhanced intensity in the melt (see Sec II1.2.A).

 
17

D. Vanadium(lll), 3¢2. — The spectrum of V(III) has been measured by Gruen and McBeth (52)
for solutions in molten KAICl, and by several groups (51, 32, 59, 99) for solutions in the LiCI-
KClI eutectic.

In KAICI, at 700°C the V(III) spectrum consisted of two band groups, one centered near 15,000
cm™! (€ = approximately 250) and the other centered near 9000 em™! (€ = approximately 190).
This spectrum was attributed (52) to VCI,~ with a distorted tetrahedral structure on the basis of
a comparison with the spectrum of a solid solution of V(III) in crystalline CsAICl, (46).

In LiCl-KCl at 400°C the spectrum of V(III) was attributed (51) to hexachloro V(III) with an
approximately octahedral structure. Two bands were found, one at 18,020 em™! (€ =35.8, f =
6.4 x 10"4) and one at 11,000 em™! (€ =13.0,/=2.0x 10"4). These bands may be assigned in
the order of increasing energy to BTIg(tz) - 3T2g(te) and 3T1g(t2) - 3Tlg(.te'), with the third tri-
plet-triplet transition presumably obscured by the strong charge-transfer absorption (see Fig. 1I1.2
for a schematic energy-level diagram). A Dg value of 1200 cm~! is obtained by fitting these bands
to the Liehr-Ballhausen energy-level curves (84).

The intensity of the spectrum for the solution in LiCl-KCl at 400°C is appreciably greater
than that for octahedral V(III) complexes at ordinary temperatures. Consequently it is to be pre-
sumed that the configuration of chloride ions about V(III) departs from centrosymmetry in some
significant way. This anomalous intensity is discussed near the end of Sec III.2.A.

In LiCI-KCl as the temperature is increased, the V(III) spectrum progressively changes. At
1000°C it has features that are intermediate between the spectrum in the same solvent at 400°C
and the spectrum in KAICI, at 700°C. For this reason Gruen and McBeth (51, 52) propose that in
LiCl-KCl solutions an equilibrium exists between the configurations VC163_ and VCI, ™ that
favors the tetrachloro species at low temperatures.

E. Vanadium(ll), 34%. — The spectrum of V(II) has been reported by Gruen and McBeth (52)
for solutions in molten CSZZnC14 and by Gruen and McBeth (51, 52) and Molina (99) for solutions
in the LiCl-KCl eutectic. In several ways the results parallel those for V(III) in KA1C14 and LiCl-
KCl as described in the preceding section.

The spectrum of V(II) in molten Cs,ZnCl, at 900°C consists of a strongest band at about
15,000 cm™! (€ = approximately 75), a weaker band near 11,000 cm~!, and three shoulders be-
tween 10,000 and 4000 cm™!. The interionic configurations responsible for this spectrum cannot
be identified with any certainty, but Gruen and McBeth (52) assumed all the V(II) ions to be sur-
rounded by four chloride 1ons with a low order of symmetry.

The spectrum of V(II) in the LiCIl-KCl eutectic is shown in Fig. IIL.5. At 400°C there are
three bands and they lie close to the positions of the bands found for V(II) dissolved in the hex-
agonal modification of crystalline CstC13 at 25°C (52). In the latter substance vanadium ions
presumably substitute for cadmium ions, which are surrounded by an octahedral configuration of
chloride ions. Hence the three bands for the melt are attributed to the octahedral species VC164_
and assigned to transitions from the 4A28(F) ground state to excited states as follows: 4Tlg(F)
at 7200 cm ™! (€ = 8.1), *T, (F) ac 12,020 cm™ ! (¢ = 12.4), and *T | (P) at 19,050 cm™" (€ = 17.5).

This spectrum can be fitted to Liehr’s energy-level curves (81) with a Dg value of 700 cm™ L.

 
18

 

€

 

MOLAR ABSORPTIVITY,

 

 

 

 

O300 400 500 600 700 800 900 (000 1100 1200 1300 1400 1500 1600 !700 180G

WAVELENGTH IN mp

Fig. 11l.5. Temperature Variation of the Absorption Spectrum of V(l1) Dissolved in the LiCl-
KCl Eutectic. A, 400°C; B, 600°C; C, 800°C; D, 1000°C. [From D. M. Gruen and R. L. McBeth,
J. Phys. Chem. 66, 57 (1962).]

The intensity of the spectrum for solution in LiCl-KCl at 400°C is substantially greater than
that for the hexaquo V(II) ion in aqueous solution at 25°C (60). This difference is taken to sig-
nify that the interionic configurations in the melt are appreciably distorted from octahedral in such
a way as to destroy the inversion center (discussed in Sec III.2.A).

At temperatures above 400°C, as shown in Fig. III.5, the spectrum changes in substantial
ways. Gruen and McBeth (51) propose that these changes are attributable to the formation of some

tetrachloro V(II) ions at the higher temperatures.

F. Chromium(lll), 323. — The spectrum of Cr(III) has been measured by Harrington and Sund-
heim (59) and by Gruen and McBeth (52) in the LiCl-KCl eutectic, by Young and White (157) in the
LiF-NaF-KF eutectic, and by Harrington and Sundheim (59) in molten KSCN together with cyanide
additions.

The spectrum of Cr(III) in LiCl-KCl has been attributed (59) to octahedral CrC163_ ions. It
consists of two bands assigned as follows: 12,500 em~ ! to 4A2g(F) - 4T2g(F), and 18,500 em™ !
to 4A2g(F) - 4T1g(F)' A Dg value of 1250 em™ 1 is reported (52). Different values of the molar
absorptivity have been given by different groups, but the value for the high-energy band seems to
lie between 45 and 55 at 400°C, with the low-energy band being slightly weaker.

The spectrum of Cr(IIl) fluoride dissolved in the LiF-NaF-KF eutectic at 650°C is like that
for the chloride solvent described above, except that it is shifted to shorter wavelengths, the two

bands occurring at 14,600 and 22,300 cm™ 1.

 
19

Solutions of CrCl_:5 in molten KSCN have been examined (59) between 400 and 660 mu. In addi-
tion to an absorption edge near the shortswavelength limit, a band was found at 16,700 em™1. Ad-
ditions of KCI to the melt had no effect on the spectrum, but additions of KCN up to a CN/Cr mole
ratio of 1.49 progressively shifted the band toward shorter wavelengths.

G. Chromium(ll), 344. — Gruen and McBeth (49, 52) studied the spectrum of Cr(II) in the LiCl-
KCl eutectic and found a single broad band at 9800 cm™!, which was rather temperature insensis
tive up to 1000°C and which they presumed to arise from a STZ(D) 5 °E(D) type of transition. The
chloride-chromium configuration responsible for this spectrum is unidentified.

H. Manganese(ll), 34°. — Spectra of Mn(II) have been measured by Sundheim and Kukk (148)
for solutions in the molten LiCl-KCl and LiBr-KBr eutectics at temperatures near 450°C. Both
spectra are similar, with each consisting of two very weak bands lying in the 300- to 500-mpu
range. These spectra undoubtedly belong to the weak-field case in which the ground state is de-
rived from the °S state of the free ion. However, all the excited states are either quartets or dou-
blets, so that all transitions are spin-forbidden. This accounts for the very low intensities of the
observed bands in the neighborhood of 0.3 molar absorptivity unit for LiCl-KCl solutions and 1.0
molar absorptivity unit for LiBr-KBr solutions.

From a consideration of Tanabe and Sugano’s calculations (149) and previous assignments of
Mn(II) spectra (69, 107, 140), the band in halide melts with a peak between 400 and 450 my and the
band with a peak near 350 my may be assigned, respectively, to the s 5 4G and °S » 4D cransi-
tions, which are split by the ligand field into unresolved multiplet components. This pattern of
energy levels gives no clue to the ligand configuration. However, Sundheim and Kukk (148) draw
attention to the fact that in other media molar absorptivities for tetrahedral Mn(II) range from about
0.1 to 2.5 but for octahedral Mn(II) they range from about 0.01 to 0.07. Thus the intensities of the
strongest bands of Mn(II) in fused halides lie in the “‘tetrahedral range.”” It seems reasonable to
conclude from this that the ligand configuration does not possess a center of symmetry, but little
else can be said.

. lIron(lll), 34°. — The spectrum of Fe(IIl) has been measured in the LiCl-KCl eutectic by
Harrington and Sundheim (59), in the MgCl,-KCl-NaCl eutectic by Silcox and Haendler (134), and
in the LiNO,-KNO, eutectic by Gruen (43). Gruen states only that there is strong absorption at
wavelengths below 400 mu. In the chloride eutectic a strongly absorbing shoulder is found below
400 mp on the side of an absorption edge which rises steeply at about 250 mu. The absorption
edge is marked by faint ripples in the case of the MgCl,-KCl-NaCl eutectic. These results are
inconclusive with regard to the chloride-iron configuration, as pointed out by Harrington and
Sundheim (59).

J. lron(ll), 3. — The spectrum of Fe(Il) dissolved in the LiCl-KCI eutectic, which has been
reported by Gruen and McBeth (52, 53), consists of a single band, which shifts from 4800 cm™ ! at
400°C to 6000 cm™! at 1000°C with a simultaneous decrease in intensity. It was postulated that
the 400°C spectrum is that of a tetrahedral FeCl42— ion, while the 1000°C spectrum is that of a

less symmetrical FeCI42— ion.
EXTINCTION COEFFICIENT, €

20

K. Cobals(ll), 347. — Absorption spectra have been measured for solutions of Co(Il) in the
following chloride melts: LiCl-KCl eutectic (44, 52, 53, 59, 148), MgClz-CaCl2 eutectic (143),
pyridine hydrochloride (43, 44), and mixtures of nitrates containing chloride salt additions (43,
150). In each instance a distinctive band with three peaks was found at approximately the same
wavelength position. Typical spectra are shown in Fig. III.6, curves B, C, and D. In LiCI-KCI
solution at 400°C the three peaks lie at 14,080, 14,930, and 16,400 cm~!. For all solutions the
maximum molar absorptivity lies between 200 and 600. It was shown (52), by a comparison with
the spectra of known cobalt complexes, that this characteristic spectrum is due to the tetrahedral
C0C142" ion. Therefore the two most intense peaks may be identified as transitions to the 4T(P)
excited state, and the weak peak as a transition to a level arising from the 2G term (4, 52, 110,
116, 154). Spectra measurements on LiCl-KCl solutions were extended into the near-infrared re-
gion by Gruen and McBeth (52), and the 4AZ(F) - 4T1(F) transition was observed at 5600 cm L.
These measurements yielded a Dgq value of approximately 350 em™ L,

Large temperature changes had a marked and rather unique effect on the specttum of Co(Il) in
LiCl-KCl. When the temperature was increased from 400 to 1000°C, the oscillator strength of the
visible band decreased from 4500 to 3200 but the band energy changed very little. Gruen and
McBeth (52) applied the intensity model of Ballhausen and Liehr (5) to this change in oscillator

 

600 -

I
i
P
! i
500 [ ! i -
! !
! !
!
!
Yl
400 | \ : - Fig. Hl,6. Visible Absorption Spectra of Molten
nog \'I Salt Solutions of Colll). A, Co(NO3)2 in the
,;“'\. 'y £ 'l LiN03-KNO3 eutectic at 160°C; B, Cr:;CI2 in the
I f : LiCI-KCl eutectic at 400°C; C, CoCl2 in the
300 — [\/ ' n NH4N03-LiNO3-NH4C| eutectic  with  odded
! ! NH,Cl at 160°C; D, CoCl, in pyridine hydro-
i i chloride at 160°C. [From D. M. Gruen et al,
i
I'- \. Proc. U.N. Intern. Conf. Peaceful Uses At En-
200 ! ]
[i \ ergy, 2nd, Geneva, 1958 12, 112-19 (1958).]
i

oo | /] |

 

 

 

TN |
/ /\.’ i
/ N \\
/ foN A
7 //./ \5\ \%
0 —— __,,—-A"" | N e \_
400 500 600 700

800
WAVELENGTH, mu

 
21

strength and concluded that an increase in temperature caused a corresponding increase in the
tonicity of the Co~Cl bond.

The visible spectrum of CoBr, dissolved in LiBr-KBr eutectic melt was found by Sundheim
and Kukk (148) to be very similar to the corresponding chloride spectrum except that the band
group was shifted to somewhat lower frequencies.

Johnson and Piper (63) measured the spectrum of CoSO4 in the Li2SO4-NaZSO4-KQSO4 eutectic
melt at 550°C. A broad band with two peaks and a shoulder was found in the visible spectrum,
followed by a much weaker, featureless absorption in the infrared out to the limit of measurement
at about 5000 cm™!. The peaks were located at 17,100 and 19,000 cm~! with molar absorptivities
of 93.5 and 83, respectively, while the shoulder was estimated to be at 16,100 cm™!. The investi-
gators attributed this spectrum to a tetrahedral arrangement of four sulfate oxygens about each
Co(Il) ion.

The visible absorption spectrum of CoF, dissolved in the LiF-NaF-KF eutectic at 500°C, as
measured by Young and White (157), is closely similar, except for intensity, to the sulfate spec-

1 with a maximum molar

trum described above. The two maxima occurred at 17,200 and 19,600 cm™
absorptivity estimated to lie between 10 and 20. Because of the low intensity the melt configura-
tion is probably not tetrahedral, but it may be approximately octahedral. Many octahedral Co(II)
complexes are known, and they commonly have a double-peaked band in the visible spectrum cor-
responding to the transition (4, 60) 4T1g > 1Azg(F’) at about 16,000 to 18,000 cem™ ! and to
4713(1:) 5 4T1g(P) at about 20,000 to 21,000 cm™!.

In the LiNOB-KNO3 eutectic the visible spectrum of Co(Il) was measured by Tananaev and
Dzhurinskii (I 50) and by Gruen et al. (43, 44). As shown in Fig. III.G, curve A, it consists of a

! and a molar absorptivity of about 102. Gruen

single smooth band with maximum near 18,000 cm™
attributed this spectrum to a cubic field formed by 12 nitrate oxygens, while Tananaev and
Dzhurinskii supposed the arrangement to be octahedral. The molar absorptivity is quite large for
a centrosymmetric configuration, but, as noted in other sections of this review, anomalously in-
tense bands are not uncommon for octahedral-like spectra in fused salts.

Additions of chloride salts to a solution of Co(II) in nitrate melts yield the C0C142' spectrum
at sufficient chloride concentrations (43, 150). Tananaev and Dzhurinskii (I150) measured the
change in spectrum as KCl was added to solutions of Co(ID) in molten LiNO,~KNO, up to a KCl/
CO(N03)2

ton associations containing 1, 2, 3, and 4 chloride ions.

mole ratio of 1160. They found evidence for the successive formation of chloride-cobalt

The visible spectrum of Co(SCN)2 dissolved in molten KSCN, measured by Harrington and
Sundheim (59), consists of a composite band with a maxtmum at 16,000 cm~! and a molar absorp-
tivity of 86. The investigators suggested that this might be the spectrum of a four-coordinate
complex, based on a comparison with aqueous thiocyanate solutions, but pointed out that there

were uncertainties in the interpretation of the aqueous spectrum.

L. Nickel(ll), 348. — The spectra of Ni(II) have been extensively studied in molten-salt sys-

tems as well as in non-molten-salt media. The spectra of some molten-salt solutions of Ni(II) are

 
22

in accord with the predictions of cubic crystal-field theory and strongly resemble the spectra of
Ni(II) complexes known to have approximately cubic geometry. In such instances the configura-
tion of nearest-neighbor ions about nickel in the molten salt can be assigned with some confidence
as being approximately tetrahedral or approximately octahedral. There are, however, other in-
stances in which the spectra of Ni(II) molten-salt solutions depart in substantial ways from the
norm of simple cubic-field behavior.

General features of the spectrum of octahedral Ni(II) complexes in various non~molten-salt
media are well known on the basis of a large number of studies [for example, see the list in (28),
p 288], and these results confirm the predictions of theory. Assignments of the triplet » triplet
transitions are beyond doubt, and assignment of some triplet - singlet transitions is probable.

The well-known spectrum of the hexaquo Ni(Il) ion in dilute aqueous solution is shown in Fig.
III.76. At the bottom of the figure is a diagram of the triplet-state energy levels, including spin-
orbit fine structure for a value of the cubic crystal-field-splitting parameter Dg equal to ~850
cm™!, This is the value appropriate for the spectrum of the hexaquo Ni(II) ion. The energy levels
were read from the energy-level curves for octahedral Ni(II) given in the paper by Liehr and Ball-
hausen (84). The 3Tlg(F) level is spin-orbit split by a sizable amount, and Liehr and Ballhausen

(84) attribute the double peak near 15,000 cm™! to a partial resolution of this splitting.*

 

*Jprgensen's explanation (67) of this double peak is that the transition lies near the crossing of the

1Eg(D) and 3T1g(F) levels, so that transition to the singlet state is intensified by single-triplet mixing.

UNCL ASSIFIED
ORNL-LR-0OWG 70342R
WAVELENGTH {mu}
350 400 450 500 600 800 1000 2000 5000

T T LT T T 0 T
40 - : . . . . T :

  

20 -

O—;_— e Fig. 1ll.7. Spectra of Ni(ll) in Octahedral Fields.
‘ ‘ (@) Triplet-state energy levels (84) for fields of Ob
symmetry at Dg equal to — 850 cm_]; (b) spectrum of
hexaquo Ni(ll) in woter [taken from the data in (35)];
. J {c) spectrum of Ni{ll) in the LiNOB-KNO:3 eutectic
T T {taken from the data in (50)]; (d) spectrom of Ni(ll) in
‘ the Li250 -NC!2SO4-K2$O4 eutectic [taken from the

data in {63)].

 

 

¢, MOLAR ABSORPTIVITY

 

30,000 20,000 10,000 0
WAVE NUMBERS {(em~!)

w 1 1 |

3 3
B ”

 

3p 3F

 
23

Figure III.7c shows the spectrum of Ni(Il) in LiNO;-KNO, eutectic as measured by Gruen and
McBeth (50). This spectrum is very similar to the hexaquo Ni(II) spectrum except that the inten-
sity is decidedly greater. Johnson and Piper (63) envisage Ni(Il) ions as being surrounded by
three nitrate ions acting as bidentate ligands to give a sixfold coordination of nickel to nitrate
oxygens. In the nitrate melt the 3Tlg(P) and 3T1g(F) excited states lie, respectively, at 23,700
and 12,900 cm ™! above the 3Azg(F) ground state to yield an estimated value of —820 cm™? for
Dg.

The spectrum of NiF, dissolved in the LiF-NaF-KF eutectic, measured by Young and White

(157), appears to be that of an octahedral complex. Two bands were reported, one at 23,000 em™ !

with a molar absorptivity of approximately 7 at 500°C, and a much weaker one at 11,800 em™ !

Figure IlI.7d shows the spectrum of Ni(Il) in the Li2804-Na2804-K2804 eutectic as measured
by Johnson and Piper (63). This spectrum somewhat resembles the hexaquo Ni(II) spectrum but
also shows noteworthy differences: the highest-energy maximum is skewed so as to indicate at
least two overlapping bands with a significant energy separation, and the molar absorptivities are
about five times greater. This spectrum has been regarded (63) as signifying a distorted octa«
hedral complex formed by three sulfate ions acting as bidentate ligands abour Ni(II).

1

The maxima in the sulfate melt at 550°C occur, respectively, at 22,000 and 10,400 cm™ " and

may be firted to the Liehr-Ballhausen diagram (84) for octahedral symmetry at a Dg value of ap-

proximately =660 cm™ 1.

Johnson and Piper (63) arrived at a different value for Dg by fitting two
parameters in a highly simplified secular equation to the two transition energies.

Harrington and Sundheim (59) measured the spectra of NiCl, and NiBr, dissolved in molten
KSCN and observed a weak, broad band (¢ = ~4) with a maximum in the neighborhood of 725 mp
and an absorption edge at wavelengths somewhat shorter than 500 my. Johnson and Piper (63) at-
tribute this spectrum to octahedrally coordinated Ni(II).

The existence of tetrahedral Ni(II) complexes was not definitely established until recently
[see, for example, the introduction in (38)], and therefore the positive identification of the tetra-
hedral NiCl42- spectrum in molten salts by Gruen and McBeth (50) in 1959 was an accomplish-
ment of general importance to transition-metal chemistry. In the past few years rapid progress has
been made in the spectroscopic study of these tetrahedral complexes in various media (20, 21, 38,
54, 115, 154), resulting in many data with which to compare molten-salt results.

A schematic energy-level diagram of Ni(Il) in cubic fields is shown in Fig. II[.2 and discussed
in Sec III.1.C. The spectra for tetrahedral and octahedral ligand configurations are similar since
three regions of spin-allowed absorption are predicted for the visible and near-infrared spectra of
both configurations. However, there are two characteristics which distinguish them. First, the
crystal-field splitting is only about half as great for a tetrahedral complex as for the correspond-
ing octahedral complex, which means that an absorption band should occur in the 4000~ to 5000-
cm™! region for tetrahedral fields but not for octahedral fields. Unfortunately, the spectra of
Ni(II) complexes do not often include this diagnostic region. The second distinguishing feature

is that the intensity of the tetrahedral spectrum should be much greater than that of the octahedral

 
24

spectrum because of the absence of an inversion center among the symmetry elements of a tetra-
hedral field.

Figure III.8c shows the spectrum of a dilute solid solution of Cs,NiCl, in a crystal of
CSzan14 at room temperature as measured by Weakliem (I154). In this solid solution, nickel ions
substitutionally replace zinc ions, which are tetracoordinated to chloride ions with a slightly
distorted tetrahedral geometry. The bands of the three triplet-triplet transitions are easily as-
signed from the energy-level diagram of triplet states shown in Fig. III.84. Each of the triplet
states except 3A2 is split into a group of levels by spin-orbit interaction. This diagram was con-
structed from the energy-level curves of Liehr and Ballhausen (84) at a Dg value of 370 cm™ 1,
which approximately fits the spectra shown in Fig. III.85 and c. [Weakliem (I54) reported that at
77°K Ni(I)-doped Cszan14 has a Dg of 385 em~ 1] In Fig. III.8c there are two very weak ab-
sorptions, which are assigned to transitions from the 3TI(F) ground state to unresolved compo-
nents of the D and !G terms.

Figure III.8b shows the spectrum of Ni(Il) chloride dissolved in molten CsCl at 800°C as
measured by Boston and Smith (data to be published). The 3T1(F) - 3TI(P) band in this spectrum
was first studied by Gruen and McBeth (50) and has a molar absorptivity of about 110. This is in
accord with intensity values for a large number of tetrahedral Ni(II) complexes (20, 21, 38, 54).
The close similarity between the spectrum in the melt and the spectrum of Cs,NiCl-Cs,ZnCl
solid solutions is evident.

The spectrum of Ni(II) chloride in molten KCI has also been measured by Boston and Smith

(data to be published) down to 4000 cm~ ! and closely resembles that for molten CsC] solvent,

UNCLASSIFIED
ORNL-LR-DWG 70763

WAVELENGTH (mu)
400 500 700 1000 2000 5000 o

 

- o T

Fig. {l1l.8. Spectra of Ni{ll) in Tetrahedral Fields.
(a) Triplet-state energy levels (84) for fields of T,
symmetry at Dg equal to 370 cm-]; () spectrum of
Ni(ll). in fused CsCl (from data to be published by
Boston and Smith); (¢) spectrum of Ni(ll) in a single
_y Ni)Cl,, where y ¥ 0.1,
oriented with [001] normal to the light beam, which

 

 

crystal of Csz( Zn i

was forepolarized. [from H. A, Weakliem, J. Chem,
Phys. 36, 2117 (1962).]

ABSORBANCE (arbitrary units)

 

 

20,000 10,000 0
WAVE NUMBERS (cm™)

I 1l

3P e —

 

 
25

The visible spectra of Ni(II} solutions in melts of pyridine hydrochloride and CszZnCl4 measured
by Gruen and McBeth (50) are very similar to the 3T1(F) - 3TI(P) band in Fig. III.8c. All these
spectra undoubtedly arise from Ni(II) surrounded by an approximately tetrahedral array of chloride
tons.

The spectrum of NiCl, dissolved in the LiCI-KCl eutectic was measured as a function of tem-
perature by Boston and Smith (12) with the results shown in Fig. III.9. The systematic changes
in the spectrum with changing temperature were attributed to changes in the ratio of two nickel
complexes in equilibrium. J@grgensen (72) proposed these species to be hexachloro-Ni(II) and tet-
rahedral tetrachloro-Ni(II) ions. He assigned the band at 20,000 em™! to the 31";25,(13') - 3T1(P)
wansition of NiCl,*~, and the other bands to the >T(F) » ?T,(P) transition of NiCl,*~. Anal-
ternative explanation of this spectrum was proposed by Sundheim and Harrington (59, 147), who
gave theoretical reasons for supposing that the entire spectrum may be attributed to tetracoordi-
nated nickel ions with a distortion from tetrahedral symmetry which increases with decreasing
temperature. In this paper several energy-level curves have been mislabeled in such a way that
the theoretical arguments are not relevant to the data. Gruen and McBeth (50) also suppose the
entire spectrum to be that of a distorted tetrahedral NiCl42— ion, while Dunn [(28), p 289] ques-
tions whether any of the spectrum is attributable to NiC142_.

The spectra of NiCl2 dissolved in LiCl melts (50) and in the CaClZ»MgCl2 eutectic (143) are
similar to the spectrum in the LiCl-KCl eutectic at 364°C, as shown in Fig. III.9, except that the
band near 20,000 cm ™! (500 my) progressively increases in intensity for the series of solvents
LiCl-KCl, LiCl, and CaClz-MgC12.

Several studies have been reported (12, 43, 44, 50) in which the complexation of Ni(II) was
changed by the addition of alkali-metal chloride to a solution of Ni(Il) in a fused nitrate, but the
results have not been quantitatively analyzed.

M. Copper(ll), 34%. — The spectrum of Cu(Il) in the LiCl-KCl eutectic consists of two strong
bands (¢ = up to 1500) at 38,500 and 27,000 cm~! in the ultraviolet (59), due to charge-transfer
transitions, and of a single weak band (¢ = ~100) at 9500 in the near-infrared (52), due to a d-
shell transition. This d » 4 band lies intermediate between the positions expected for tetrahedral
and octahedral copper complexes. Pappalardo (113) and Pappalardo and Dietz (I14) measured the
spectra of copper with different known ligand configurations obtained by copper doping of single
crystals of different structures. For a tetrahedral environment the d » d absorption was found in
the neighborhood of 6000 cm™ !, and for an octahedral environment it was roughly 12,000 em™ 1.
(The exact values depended, of course, on the makeup of the complex.)

The spectrum of copper in LiCI-KCl was attributed (52, 59) to the species CuCl42— with a
highly distorted tetrahedral configuration. It is not known whether this description is sufficiently
broad to encompass the correct (but unknown) configuration. Four-coordinated Cu(II) complexes
are known to exist in other media, and the CuC142_ ion has been postulated to be nearer to square
planar than to tetrahedral (1, 66, 86).

The visible spectrum of Cu(Il) in the LiNO3-KN03 eutectic (43) consists of a single band at
about 11,800 em™ L.

 
WAVE LENGTH {(my)

 

UNCLASSIFIED
ORNL~LR—DWG 72950

 

 

 

 

 

 

 

 

3
(x 107) 250 300 350
T T T T 1T 1T T [ +.T1T T 11
4 |
3 }—
Y-245623
WAVE LENGTH (my)
50 400 450 500 550 800 650 700 750
€ 100 T T T T T T T

2 |

80

v
m
so} 540 1 v
494°
€ \ 446

'r 3gs’

40 364°

20}
0 1 | i | 0 1 1 1 1 1 1 1 1 1 i 1 1 1 1 i 1 1

e 5 4 3.5 30 2.5 2.0

ENERGY (electron volis)

Fig. ll1.9. Influence of Temperature on the Spectrum of Ni(ll} in the
and the diagram at the right shows the bands of 4 d transitions. [From

ENERGY (electron voits)

LiCl-KC1 Eutectic. The diagram at the left shows a charge-transfer band
C. R. Boston and G. P. Smith, J. Phys. Chem. 62, 409 (1958).]

9¢
27

3. Charge-Transfer Spectra

A. Introduction. — Transition-metal complexes always have very strong bands in the ultra-

‘*charge-transfer’ bands. Experimental data on these bands

violet region, loosely referred to as
are sparse, and their electronic origins are understood only in general terms. Nevertheless, it ap-
pears likely that these important spectra will be intensively studied during the coming decade.
Charge-transfer processes involving transition-metal ions are reviewed by Jgrgensen (74),

McClure (89), Orgel (106), and Ballhausen (2). Some molecular-orbital energy-level diagrams for
typical complex ions are given by Liehr (82, 83). The molecular-orbital theory of tetrahedral ions
has been developed from different points of view by Wolfsberg and Helmholz (155) and by Ball-~
hausen and Liehr (5) with results which lead to different assignments of spectral bands. The as-

signment of charge-transfer bands in CrBr, crystals is discussed by Dillon, Kamimura, and

Remeika (27).

B. Theoretical Results. — The theory of chargestransfer transitions is in a rudimentary state,
and considerable more experimental data will be required before theory can be pushed forward with
confidence. Nonetheless, qualitative theoretical results based on elementary LCAO-MO theory
give valuable insight into the electronic origins of the spectra of complex ions, and so some of
these results are outlined here.

A molecular-orbital energy-level scheme for an octahedral complex with monatomic ligands is
shown in Fig. II1.10. The orbitals were constructed from atomic s and p orbitals on the ligands
and from atomic nd, (n + 1)s,and (n + 1)p atomic orbitals on the central metal atom according to
symmetry considerations, which are illustrated in Figs. III.11 and 12.

The orbitals up through 1z, are filled, while the 2t§g and SeE orbitals may be partially filled,
depending on the number of d electrons present. The d - 4 transitions, described previously, take
place by the jump of electrons from 2t;g into 362. The orbitals from lalg through 27, contain the
o= and 77-bonding electrons. The orbitals lalg and leg are O bonding, ltzg is 77 bonding, and 1¢,
and lt2g are both ¢ and 7 bonding. In some complexes 1z, may be predomirantly ¢ bonding,
while ltzg is predominantly 7 bonding, but in other complexes it is possible that each of these
orbitals has equal o and 7 character.

The electronic charge density in the bonding orbitals may reside largely on ligand atoms or be
more nearly equally distributed between ligands and the central metal atom, depending on the de-
gree of covalency in bonding. The orbitals 2a1g, Zeg, and 3¢, are approximately nonbonding or-
bitals and lie largely on the ligands. The orbitals ltlg and 12, , for symmetry reasons, reside
exclusively on the ligands. They are slightly antibonding between ligands but completely non-

bonding in metal-ligand directions and hence are referred to as “‘nonbonding.”” The orbitals Zt;g
through 4:¥ are antibonding orbitals that contain electrons that belong primarily to the metal atom
or may be shared by the metal and ligands. It is expected that the highest antibonding orbitals

and the lowest bonding orbitals, both largely of the o type, involve the greatest electron sharing

 
28

UNCLASSIFIED
ORNL-LR-DWG 74602

   
 

w
[
<1
r
(n+Vp 1 [ ] Y
w
o
w
O
{nt+d)s he w
x| e
eg E:J
=
wl o w
G 19 3
EfJ ‘—'_'—'—l: o
fld zZ
w
&
w
0

DEGENERATE

LONE
I BONDS 7-BONDS PAIRSJ

g

 

PRIMARY ATOM  MOLECULAR ORSBITALS LIGAND MOLECULAR
ORBITALS OF THE COMPOUND ORBITALS

Fig. 111.10. Schematic Diagram of Energy Levels for an Octahedral Covalent Complex. The
orbitals are pictorially represented in Fig. I11,11. The energy sequence of orbitals is based on
qualitative principles and is subject to change when theory renders more exact criteria. The
prefix numbers on the orbitals specify the sequence in which orbitals of a given symmetry species
occur, and should not be confused with the principal quantum number. This correlation diagram is

taken from A. D. Liehr, J. Chem. Educ. 39, 135 (1962).

between the metal atom and ligands, whereas 77 orbitals are often less covalent and their elec-
trons may reside largely on ligands (bonding 77 orbitals) or on the metal atom (antibonding 77 or-
bitals). However, no firm rule can be made, and the extent of electron sharing in different com-
plexes can be quite different. In some complexes even the 7 and 7* orbitals may be highly

covalent.

It may be deduced from what has been said that bonding - antibonding transitions sometimes
involve a transfer of electronic charge from the ligands to the central atom. The most likely ex-
amples of this charge-transfer process are transitions of the 7 - 77* type, such as 2t - 2!’5g,
3e;. On the other hand, antibonding - antibonding transitions of the 7* » o* type, namely 2t§g,
392 » 4tF , may transfer charge from the metal atom to the ligands. However, in any of the above
transition types there may be little or no charge transfer, depending on the relative covalency of
the orbitals involved. The most likely examples of the latter situation are the ¢ » o* transitions
lalg, leg > 4t7 . Nonbonding -~ antibonding transitions always transfer charge from ligands to the
metal atom. Among these the four transitions 3¢, ,1t, - 2t§g, 362 are the most probable assign-

ments for the lowest-energy ultraviolet bands. Bonding - bonding and nonbonding » nonbonding

 
29

transitions are impossible, because these orbitals are filled, while transitions that involve no
change in parity (g » g, ¥ » u) are forbidden by the rule of Laporte and so are very weak.

A given electronic configuration gives rise to many states because the orbitals are degen-
erate. Thus, when the degeneracy is removed, electron jumps between any two orbitals may yield
a number of absorption bands, only a few of which will usually be strong. An example is the elec-
tronic transition 1z, - 2t;g in an octahedral complex that contains no 4 electrons. The ground

configuration and ground state are

4 4,6 6 6 1
..Zegszlultlgeru, A

lg

while the excited configuration and excited states are

4 7,6 6 5 *¥1 1,3
..2€g Squlzlg 1t2u 2t2g, (A1u+Eu+T1u+T2u).
Of the eight possible electronic transitions,
1 1 3 1 3 1 3 1 3
Alg_) Alu’ Alu’ Eu’ Eu’ Tlu’ Tlu’ T2u’ T2u’

only lAlg - ITI

The four singlet » triplet transitions are forbidden by the spin rule. The remaining three transi-

tions, IAlge AL E T

, is electronically allowed and it alone may be expected to give an intense band.

2u’

involves first-harmonic vibronic interactions and should be so weak as to be imperceptible.

are vibronically allowed and are therefore weak, but lAlg > lAu

Several kinds of ultraviolet bands are not represented by electronic jumps on the orbital
energy-level diagram in Fig. II[.10. Polyatomic ligands, such as the thiocyanate ion, may have
internal electronic transitions that are only mildly perturbed by complex formation. Such transi-
tions are observed in the spectrum of the complex and are called *‘intraligand’’ bands. Further-
more, it is expected that there will be a series of energy levels leading to ionization of an elec-
tron. At low energies the members of this energy-level series will give charge-transfer transitions
of types already discussed, but at higher energies the orbitals occupied by the excited electron
will be successively larger and will deeply penetrate the surrounding medium. Electron jumps
from a given ground level to this series of high-energy levels produce what are called ‘‘Rydberg’’
spectra by analogy to atomic spectra that involve a change in principal quantum number.

C. Experimental Results. — The well-known chromate spectrum is a typical example of a
charge-transfer spectrum. Smith and Boston (I35) measured the spectra of dilute solutions of
Cr0,*~ in LiNO,, KNO,, CsNO;,

Two of them are shown in Fig. III.13, together with the spectrum of CrO42_ in alkaline aqueous

and the LiCI-KCl eutectic. All these spectra are very similar.

solution. It is evident from the spectra that Cr042- preserves its identity in the salt melts.

Other measurements of charge-transfer spectra in molten salts include MnO, ™, MnO42—, and
Mn043_ in fused hydroxides reported by Lux and Niedermater (86); NiCl2 in the LiCl-KCl eutectic
reported by Boston and Smith (12); NiCl, and CuCl, in LiCl-KCl reported by Harrington and Sund-
heim (59); VO3" in LiCl-KC! by Molina (99); and CuCl, and NiC12 in the MgClz-KCI-NaCl eutectic
by Silcox and Haendler (134).
30

Fig. Iil.11a=e. Construction of Molecular Orbitals of an Octahedral Complex from
Atomic Orbitals. These diagrams schematically illustrate the symmetry properties and
construction of o bonding, 7 bonding, and occupied nonbonding melecular orbitals on an
octahedral complex composed of a central metal atom and six monatomic ligands. The
arrangement of atoms relative to the coordinate axes is given in Fig. l1l.12, and an
energy-level diagram of the orbitals is given in Fig. 1{1.10. The orbital pictures display
the angular orientation of the atomic orbitals from which the molecular orbitals are con-
structed, but not their size and radial nodes. Positive and negative phases of the atomic
orbitals are represented by white and black lobes respectively.

 
31

UNCLASSIFIED
CHRNL-LR-CWG /463848

 

t1u‘px) ttu(py) tiu[pz)

 

TEg(dxy,

Fig. [Il.11a. Atomic Orbitals of the s, p, and d Types on the Central Metal Atom. The symmetry proper-

ties of these orbitals assign them to the a1gt g Nt and th species of the octahedral symmetry group.

 
UNGLASS'FIED
ORNL-LR-DWG 74605A

 

 

 

 

 

 

fy

u

Fig. 11116, Ligand Molecular Orbitals Constructed from Atomic pO Orbitals. The po orbitals are
those ligand p orbitals which lie along the bond directions of the complex., Unoccupied ligands are denoted
by small black spheres.

If ligand s orbitals are included, they form ligand molecular orbitals of the same symmetry species as
). Hence the s orbitals will mix with po orbitals to some extent to form

shown above (a e , and ¢

F:3 lu
atomic sp hybrid orbitals, which need not have equal s and p character. One such set of ligand orbitals
formed from sp hybrids will be virtually nonbonding and will correspond to the chemist's lone-pair electrons.
These orbitals are not illustrated here but they are constructed like the A1t €t and Ly orbitals shown

above. In Fig. IH.10 they are designated 2a]g, 2eg, and BI]u.

 
33

UNCLASSIFIED
ORNL-LR-DwWG 745984

 

 

 

Fig. 111.11c. Ligand Molecular Orbitals Constructed from Atomic pr Orbitals. The pm orbitals are those

ligand p orbitals which are perpendicular to bond directions. Only one of the three partners is shown for

each of these triply degenerate orbitals. Each of the other partners for t]g and t2g may be generated by

rotating the forms shown by 90° about the x and z axes respectively. The partners for i and Loy, ™OY be

produced by rotations about the x and y axes. The s, p, and d orbitals on the central atom do not have

Therefore as long as only these types of central-otom orbitals are used in the con-

2u

t]g or | symmeftry.
struction of molecular orbitals, the ligand orbitals of species t]g and Lo will not combine with central

atom orbitals to form bonds.
34

UNCLASSIFIED
ORNL-LR-DWG 74604A

 

 

I Hw i Hw
( PURE o BONDING) (MIXED & AND 7 BONDING )

Fig. 11.114. T-Bonding Molecular Orbitals. These orbitals are numbered according to the system used
in Fig. H1.10. They are constructed from the ligand O orbitals and central-atom orbital s of the same sym-
metry species. Since there are three ligand O orbitals, three O-bonding orbitals, 'Ia] ’ 'leg, and “]u‘ are
obtained by in-phase overlap of central atom and ligand orbitals, and three antibonding O orbitals (O*
orbitals), 3a* , 3e*, and 4zlu' by out-of-phase overlap. Of the antibonding orbitals only 3a’i’g is shown.

The relative sizes of ligand and central-atom orbitals for Ia] are given to schematically represent the
case in which charge density resides much more on ligands than on the central atom. This situation jorces
charge density in the 3a’]" orbital to reside primarily on the central atom as shown., Were the bonding more

covalent, the diagrams for ]a]g and 3a’ig would appear very similar except for the phase difference.

(NOTE: Caption for Fig. Il.11d Continues at Top of Next Page.)

 
35

One of the three partners of “]u is shown in two formulations. On the left is the molecular orbital con-
structed of pure C-bonding components. However, this orbital will mix to some extent with the 7 orbital of
ty, Symmetry, and such a mixed configuration is schematically indicated on the right.

The collection of three G-bonding orbitals will accommodate six electron pairs to form six O bonds
directed symmetrically ot the six ligands. These molecular orbitals contain the central-atom s, p, and d
orbitals in the ratio sp3d2 as required by valence-bond theory; but molecular orbital theory, unlike valence-

bond theory, does not require that these central-atom orbitals have equal bonding power.

UNCLASSIFIED
ORNL-LR-DWG 746034

 

J
2ty 2ty
{PURE 7 BONDING ! UMIXED 7 AND o BONDING)
Fig. Ill.11e. m-Bonding Molecular Orbitals. These diogroms illustrate one of the three partners for

each of the two m-bonding orbitals ond one of the antibonding 7 orbitals (7*). Two vorionts of the 2t1u
orbital aore shown. The one on the left is constructed of purely m-bonding orbitals, while the one on the

right includes a small odmixture of the L O-bonding orbital.

 
UNCLASSIFIED
ORNL-LR-DWG 745994

 

36

Fig. H1.12, Geometrical Positioning of Atoms in an Octahedral
Complex (Symmetry Group Ob)' The ligand nuclei lie on the
axes and are equidistant from the nucleus of the central metal
atom. The orientation of axes relative to ligands is the same
as that chosen for the construction of orbitals illustrated in

Fig. 1. 11.

UNCLASSIFIED
ORNL-LR-DWG 36274R2

PHOTON ENERGY (ev)

 

50 4.5 40 35 3.0 25
4800 p —t— o i ?7-3»— [t
; ! . :
= e e

3600

2400 +

1200

 

  
 

\__IN WATER (GIBSON) |
o V\:[%k S
|

IN KNO 7i B 7‘
3 2°¢ ¢

LIN LiCl- KCt EUTECTIC
p— 70

 

 

 

WAVE LENGTH (mg)

Fig. I11.13. Spectra of Dilute Solutions of I(,‘_,Cr(')4 in Alkaline Water, Fused KNO3, ond Fused
LiCl-KC| Eutectic. Aqueous spectrum plotted from data given by Gibson (36); other spectra from
G. P. Smith and C. R. Boston, Ann. N.Y. Acad. Sci. 79, 930 (1960).

 
37
IV. LANTHANIDE METAL IONS

1. Introduction

The lanthanide metals constitute the first rare-earth metal group in the periodic table of ele-
ments. They commonly occur as tripositive ions, and it is only in this valence state that they
have been studied in molten~salt solutions.

The spectra of lanthanide ions consist of relatively sharp, weak bands over the wavelength
range from the near-infrared through the near-ultraviolet. Further in the ultraviolet region the
bands are strong and diffuse, but in the case of molten salts have been observed only as absorp-
tion edges. In most instances the spectrum of a lanthanide ion in a molten-salt solution is very
similar to that in aqueous solutions and other media. Neodymium(III), shown in Fig. IV.l, is a
typical example. Spectrum A in this figure is for a solution of NA(III) in the LiCl-KCl eutectic
melt at 400°C. Spectrum B is for a solution of Nd(III) in 1 N HCIO at 25°C. In most respects
these two spectra (7) are quite similar, with their band groups occurring at approximately the same

wavelengths.

2. Notes on Theory

The theory of lanthanide spectra is reviewed by Dunn (28), McClure (89), Runciman (124), and
J#rgensen (74). A few essential results from this theory are outlined here.

The weak, sharp bands in lanthanide spectra arise from f - { transitions, that is, transitions
between different energy levels of the 4/” electronic configurations. These energy levels are in-
fluenced only very weakly by the surroundings, being predominantly determined by the forces
present in the free ions. Only two need be considered here — the electrostatic repulsions between
4/ electrons and the spin-orbit coupling.

Spin-orbit coupling for 4f electrons follows the Russel-Saunders approximation fairly closely.
Thus the system of energy levels for an ion consists of a sequence of multiplec terms, which differ
in having different quantum numbers L or § while the / values for individual electrons remain un-
changed. The multiplet levels are split by a weak spin-orbit coupling into components with dif-
ferent values of the quantum number J. (For a review of the terminology applicable to atomic
energy levels see Sec III.2.)

The 4/ orbitals lie well inside the ions and are strongly shielded from the fields of surround-
ing ions or molecules by the 5s? and 5p° electrons. This accounts for the strong similarity be-
tween the spectra of molten salt and aqueous solutions and for the relative sharpness of the bands.
The ions or molecules of the medium are regarded as producing an electrostatic field over the
space of the 4f orbitals. This field produces a complete or partial Stark splitting of the compo-

nents of the multiplet levels by the magnitude of 100 em™ L,

This small ligand-field splitting is
easily observed in crystals, where the absorption lines are very sharp, and is the basis for using

spectra to study interactions between lanthanide ions and the surrounding medium. Since lines

 
 

UNCLASSIFIED
ORNL— LR—DWG 72948

 

 

 

 

 

12 = T T T T x T T T T T T T T I
|O — —
8 — —
€ — A —
6 - ]
4 [ —
0 | MJ/kL | b, 1 |
250 300 350 400 450 500 550 600 650 700 750 800 850 900
T T T T T 1 T T T T T T T ¥
6 —
—_ B —4
.
]
e A L 1 L I

 

 

450 500 350 600 650 T00 750 800 850 800
WAVELENGTH ( MILLIMICRONS)

Fig. IY.1. Spectra of Nd(Ill). (A) Solution in LiCl-KCIl eutectie at 400°C; (B) solution in aqueous 1 N HC!O4 at 25°C. [From C. V. Banks,
M. R. Heusinkveld, and J. W. O’Laughlin, Anal. Chem. 33, 1235 (1961).)

8¢
39

are much broader in salt melts than in crystals, groups of lines overlap to form bands and cause
the details of ligand-field splitting to be lost.

The absorption lines are weak because transitions between the multiplet levels of a single
configuration are forbidden by Laporte’s rule, which applies to electric-dipole transitions in the
free ion. The reason that the transitions occur at all is a consequence either of the electric-quad-
rupole or magnetic-dipole mechanism or of deviations from centrosymmetry, which result from per-
turbations by neighboring ions or molecules in the medium. In addition to the sharp, weak bands
of / » [ transitions, the lanthanide ions also display bands that are much stronger and broader and
that are sensitive to the ionic environment. These strong bands could be caused by charge-trans-
fer transitions or by transitions of the 4/ » 47~ 54 Rydberg type (70, 73), which we denote [ - d.
Since they are not Laporte-forbidden, their oscillator strengths are of the order of 0.1. The 54 or-
bitals are very much more sensitive to the surroundings than are the 4/ orbitals, and therefore the
[ - d transitions, although they have not been measured in molten-salt media, may be an effective
tool for probing the interactions between lanthanide ions and molten-salt environments.

Bands due to [ » 4 transitions occur in the Ce(Ill) spectrum above 35,000 cm™ L. They should
not be difficult to measure in fused alkali chloride solvents. The divalent samarium i1on has a
large number of / » & bands in easily accessible regions of the spectrum. They have been studied
for solid solutions of SmCl2 in BaCl2 and SrCl2 (89), and analogous studies for the molten chlo-
rides should provide an interesting comparison. Similar statements may be said about Eu(Il) and

Y b(II).

3. Survey of Results

Literature references to the spectra of lanthanide ions in molten-salt solutions are cataloged
in Table IV.1.

The /- { bands in the salt melts at elevated temperatures are generally shifted toward longer
wavelengths and lower absorptivities compared with the same bands in aqueous soluttons at room
temperature. Inasmuch as the bands are generally broader in the melts, it is not always certain
that a decrease in absorptivity is accompanied by a decrease in oscillator strength, Furthermore,
there are several distinct iastances in which a band has greater absorptivity in the melr than in
aqueous solutions; note, for example, the band that lies between 550 and 600 my in Fig. IV.1.
Carnall and Fields (I15) suggested that these effects may be due to the difference in population of
ground-state Stark levels at different temperatures. As the temperature increases, the higher
energy Stark levels become more heavily populated. This tends to decrease the mean transition
energy and to broaden the bands.

In some of the first published spectra of lanthanide ions in molten salts, a number of bands
that occur in aqueous solutions were not found. This raised speculations about the '‘quenching’
of / » f transitions by molten-salt environments. More recently, however, at least a part of the

missing bands have been found.

 
40

Table 1V.1. Reported Spectra of Lanthanide Metal lons in Molten<Salt Solvents

 

 

Ion Solvent Bibliographical Reference

Pr(I1D) LiF (158)
LiF-NaF-KF (157)
LiCl-KCl (7)
LiNO;-KN, (14, 15, 43)

Nd(III) LiF (158)
LiCl-KCl (7, 146)
LiNO;-KNO, (14, 15, 43)

Sm(III) LiF (158)
LiCl-KCl (7
Li1\103-1<1\103 (14, 15)

Eu(IID) LiCl-KCl (7)
LiNOa-KNoa (14, 15, 146)

Gd(IID) LiCl<KCl (7

Th(III) LiCl-KCl (7
LiNOa-KNos (14)

Dy(III) LiCl-KCl (7
1_11\103-1@\103 (14)

Ho(IID) LiCl-KCl (7)
LiNOa—KNoa (14)

Er(IID) LiCl«KCl] (7)
LiNO,-KNO, (14)

Tm(III) LiCl-KCl! (7)
LiNO;=KNO, (14)

Y b(III) LiCl-KCl (7)
L1N03-KN03 (14)

Lu(IID% LiCl-KCl (7)

 

a .
Measurement reported but no absorption found.

4. Band Assignments

The assignment of / - f transitions in molten salts may be made for those bands which have

been identified in crystals. For most lanthanide ions the crystal assignments are by no means

complete, despite a great deal of research, because of the extraordinary complexity of the spectra.

 
41

The terminal ions of the tripositive lanthanide series, La(IIl) with the configuration 4/% and
Lu(Ill) with the configuration 4/14, have no multiplet levels and their spectra are devoid of [ > /
bands.

Cerium(IIl) with one electron, configuration 4/1, and Yb(III) with one electron hole, configura-
and

tion 4/13, each have a single multiplet level, 2F, which splits into the components 2p

2
F'/'

5/2

/2" In Ce(IID) 2F5/2 is the ground state and in Yb(III) 2F7/2 is the ground state. In each in-
stance the only /- / transition is between these two 2F states.

Cerium(IIl) has not been investigated in molten salts, but the 2F5/2—2F separation 1s

7/2
about 2240 cm™! and hence no absorption is expected in the visible region (71?). This ion has
strong, diffuse bands in the ultraviolet but they are not due to / » / transitions.

The spectrum of Yb(III) in LiCl-KCI eutectic at 400°C consists of a pronounced band maxi-
mum near 975 mp with very broad shoulders that spread from about 900 to 1025 mp (7). The spec-
trum of solid YbCla-GHZO consists principally of two sharp lines near 975 mu plus a number of
fainter lines (25). The two lines near 975 my are assigned to components of the 2[3_/,/2 - 2F5/2
transition split by the crystal field. The maximum near 975 my in the melt is undoubtedly the
same transition, The broad shoulders on the 975-myu band in the melt presumably correspond to
the faint lines in the crystal. Inasmuch as the faint crystal lines are probably caused by lattice
vibrations, one must suppose that the broad shoulders are caused by interionic vibrations in the
melt.

Praseodymium(IIl) with two electrons, configuration 4/2, and Tm(III) with two electron holes,
configuration 4/12, are the simplest lanthanide ions with more than one multiplet level. The
Pr(III) spectrum has been measured in a variety of molten-salt media, and the Tm(IIl) spectrum has
been measured in the LiCl-KCl eutectic (see Table IV.1). These spectra are relatively simple,
and the energy-level diagrams given by McClure (89) are known fairly well. Two spectra of Pr(III)
are shown in Fig. IV 2 (15). The solid line represents the spectrum in a deuterated perchlorate
solution at 25°C, and the dashed line the spectrum in the LiNO,-KNO, eutectic melt at 150°C.
The 25°C spectrum does not extend below about 1500 my because of solvent absorption. The
group of three bands near 450 my is a prominent feature of all the spectra of Pr(III) in molten
salts. These bands correspond to spin-allowed transitions from the 3H4 ground state to the multi-

plet components 3.Po, ’p ., and 3P2' The band near 600 my is the 3H4 - 1D2 transition, and the

17
very weak absorption at 1000 my is the 3H4 - 1G4 transition.

The energy-level systems of the remaining tripositive lanthanide ions are exceedingly complex
because of the large number of multiplet levels. In most instances only the low-energy transitions
can be assigned with any certainty. The Nd(III) spectrum in Fig. IV.] is a good example of the
band-rich spectra that these lanthanides generally yield. Only a few assignments are considered
here.

The Nd(III) band at 860 my, shown in Fig. IV.1, has been carefully investigated (26, 126) and

may be assigned to 419/2 S AR Carnall and Fields (14, 15) report two bands at shorter wave-

3/2°
lengths for the spectrum of NA(IIl) in the LiNO,-KNO, eutectic, which are probably transitions be-

tween components of the A multiplet: 4 54 at 2500 mu and 4I S 4 at 1700 my..
P P 9/2 13/2 t 9/2 15/2 -

 
42

 

0.8 t-

OPTICAL DENSITY

0.4

 

 

 

 

| N -2

_I_Jr
OOA\ 0.45 05 055 06 065 1.0

 

 

WAVE LENGTH (p)

Fig. 1V.2. Spectra of Pr(lll). Selid line: solution in 0.4 N DCIO4 at 25°C; dashed line: solution
in the LiN03-|'(N‘.':)3 eutectic at 150°C. [From W. T. Carnall and P. R. Fields, *'The Visible and
Near Infrared Absorption Spectra of Some Trivalent Actinide and Lanthanide Elements in DCIO
and in Molten Nitrate Salts,”’ in Developments in Applied Spectroscopy, vol 1 (ed. by W. D. Ashby),
Plenum Press, New York (to be published in 1962).]

Despite the large number of terms for Eu(III), configuration 4/°, the spectrum in the visible
region has relatively few bands because the ground-state multiplet, ’F, lies well below the other
terms. Carnall and Fields (I15) report that calculations for this ion predict the 7'.Fé level to lie
near 2080 my. Their measurements on this ion in the LiNO,-KNO, eutectic show a double band
with maxima at 2030 and 2167 mu. A possible assignment of these absorptions is 7.FO - 7F6 and
'F, > "F, where the "F_ term is regarded as being populated by thermal excitation.

The 8§ ground state of Gd(III), configuration 4/7, lies far below the other terms, with the result
that this ion has no absorption in the visible or near-infrared regions. Judd (76) and Jgrgensen
(64) calculated the lowest-energy excited multiplet, °P, to lie about 31,000 cm™! above the
ground state. This agrees with the results of Banks, Heusinkveld, and O’Laughlin (7) for Gd(III)

in the LiCI-KCl eutectic, where the first significant absorption band was found near 320 mp.

Y. ACTINIDE METAL IONS

1. Introduction

The actinide metals constitute a group of rare-earth elements characterized by buildup of the
5/ electronic shell. The group begins with actinium, atomic number 89, and is completed by law-

rencium, atomic number 103. The radioactive half-lives of the various isotopes generally decrease

 
43

with increasing atomic number, making them progressively more difficult to prepare and study.
The elements beyond einsteinium, atomic number 99, do not appear to have isotopes sufficiently
long-lived to be isolated in weighable quantities. Spectral measurements on molten-salt solutions
of actinide ions have been restricted to the five elements from uranium through curium.
Theoretical understanding of f » { transitions in actinide spectra is very incomplete, and the
principles to be used in the assignment of observed absorptions is a subject of controversy.
]flrgensen (73, 74) and Conway (I9) interpret actinide spectra in a manner quite analogous to that
for lanthanide spectra, whereby composite bands or line groups are identified with multiplet levels
of the free ion. On the other hand, Satten, Young, and Gruen (127) propose that the composite
bands of actinide ions correspond to transitions that are entirely different from those in lanthanide
spectra.
Laporte-allowed Rydberg transitions of the 5/ - 5/"~1 6d type are well known (68, 70, 73)

and have oscillator strengths ranging from about 10~ for U(III) to about 10~2 for Am(III).

2. Uranium(il)

The spectrum of U(III) was measured in the LiCl-KCI eutectic by Gruen and McBeth (49) and
by Gruen, Fried, Graf, and McBeth (44), who note the similarity between this spectrum and that of

U(IID) in concentrated HCI solution.

3. Uranium(lV)

Morrey (101) measured the spectra of the molten compounds UCl, and Cs,UCl  and also those
of dilute solutions of U(IV) in NaCl, KCl, CsCl, ZrCl,, KCI-AICI,, and CsCl-AICI,.

The spectrum of molten Cs,UCl, was almost identical with the spectra of solutions of U(IV)
in KCI-AICl; and CsCl-AICL; with a mole ratio MCl/AlCl3 greater than unity. These spectra were
deduced to be attributable to an octahedral configuration of chloride ions about U(IV) on
the basis of a comparison with the spectrum of crystalline Cs,UCIl, at various temperatures up to
near its melting point and also with the spectra of [(C,H,),N],UCL, and [(n-C4H,,);NH],UCI¢
dissolved in organic solvents. An example of this UC162" spectrum in a melt and its small varia«
tion for large temperature changes is shown in Fig. V.1.

The spectra of dilute solutions of UCl, in melts of NaCl, KCl, and CsCl are shown in Fig.
V.2, With CsCl as the solvent the spectrum of U(IV) is similar to that of molten CszUCIG, but
there are also significant differences which become accentuated successively in the solvents KCI
and NaCl. These differences were attributed to the presence of a second species, in addition to
uct, 2~

The spectrum of UCl, in molten ZnCl, is shown in Fig. V.3. It is very similar to the spectrum
of the high-temperature crystalline modification of UCl, and also to the spectrum of a UCl melt.

Reasons were advanced for supposing all these spectra to be those of tetrahedrally coordinated

U(Iv).

 
44

The spectra of U(IV) in KC1~AIC13 and CsCl-AlCl3 melts with the mole ratio MCI/AICI3 less
than unity showed large variations for changes in both temperature and solvent compositions.
These variations were attributed to competitive reactions involving complex ions.

The spectra of U(IV) in the LiCI-KCl eutectic and in fused pyridine hydrochloride are reported
by Gruen and McBeth (49). In pyridine hydrochloride the U(IV) spectrum is closely similar to the
spectra assigned to UC162_, while in the LiCl-KCl eutectic the spectrum is similar to that of
UCl, in ZnCl, solutions, shown in Fig. V.3.

Young and White (157) measured the spectrum of UF, dissolved in the LiF-NaF-KF eutectic
and found it to be similar to the UC162" spectrum but with the composite bands less well re-

solved.

UNCLASSIFIED
ORNL-LR-DWG 69585
2o T T T T T T T T T T T T T T

 

ABSORBANCE

 

 

 

 

WAVELENGTH, MICRONS

Fig. VY.1. Spectrum of UC|4 in a KCI-A!CI3 Melt with the Mole Ratio KCI/AICI_, Equal to
1.047. (1) 400°C; (2) 500°C; (3) 700°C. [From J. R. Morrey, Inorg. Chem. 2, No. | (1963).f

UNCLASSIFIED
ORNL-LR-DWG 69586

 

 

 

 

 

T T l T T T T I T T T 1 1 T T 1 { T T T T ] 1
1.0
w I i
w
z | .
<
@
x 05|
o
* i
a |
<
- ] Fig. VY.2. Solutions of UC|4 in Alkeli Chloride
- , Melts at 825°C. (a) Selution in NaCl; (b) solution
0 T T Tt T in KCI; (¢) solution in CsCl. [From J. R. Morrey,

0.5 1.0 1.5 2.0 2.5
WAVELENGTH, MICRONS Inorg. Chem. 2, No. 1 (1963).]

 
45

4. Uranium(VI)

All the spectra reported for U(VI) in fused salts appear to be attributable to the uranyl ion
U022+. The measurements were made on solutions in the eutectics LiCl-KCl, LiNOa-KNOB, and
LiNOB-KNOS-NH4Cl by Gruen and McBeth (49) and in pyridine hydrochloride by Gruen, Graf, and
Fried (45).

5. Transuranium lons

Spectra have been reported for molten-salt solutions of the ions of several transuranium ele-
ments: Np(III} in LiCl-KCl (44); Np(IV) in LiCIl-KCl (44) and in pyridine hydrochloride (44, 45);
Np(V) in LiCIl-KClI (44) and in LiNO;-KNO, (44, 45); Pu(Ill) in LiCI-KCI (54); Pu(IV) in LiCI-KCl
(54) and in pyridine hydrochloride (45); Pu(VI) in LiNOB-KNO3 (44, 45); Am(III) in LiCI-KCl (54)
and in LiNO;-KNO; (15, 44, 45); and Cm(1II) in LiNO,-KNO, (15).

The spectrum of Am(III) nitrate in the LiNO3-KNO3 eutectic at 150°C and of Am(III) perchlo-

rate in deuterated perchloric acid solution at 25°C is shown in Fig. V.4

UNCLASSIFIED
ORNL-LR-DWG 69584

 

 

 

 

1.0 i
W o8 f— - = Loy :
Fig. V.3. Spectrum of UC|4 in Fused ZnCl2 at 30.6 L
575°C. [From J. R. Morrey, Inorg. Chem. 2, No. 1 §0_4k
(1963).] 302
0

 

500 1000 1500 2000 2500
WAVELENGTH (mp)

UNCLASSIFIED
ORNL-LR-DWG 69589

— At e
ai28
T
rabTETe

 

ABSORBANCE

 

 

 

   

 

 

 

~ !
%.35 04 045 05 05507 1.0 LS 2.0 2.5

WAVE LENGTH ()

Fig. V.4. Spectra of Am{lll). Solid line: solution in deuterated perchloric acid at 25°C;
dashed line: solution in LiNOB-KNO3 eutectic at 150°C. [From W. T. Carnall and P. R. Fields,
““The Visible and Near Infrored Absorption Spectra of Some Trivalent Actinide and Lanthanide
Elements in DC|O4 and in Molten Nitrate Salts,’" in Developments in Applied Spectroscopy,
vol 1 (ed. by W. D. Ashby), Plenum Press, New York (to be published in 1962).]
46

Vi. METALS IN MOLTEN SALTS

Very dilute solutions of metals in molten halides are intensely colored, while more concen-
trated solutions are opaque and in some instances may be metallic in appearance. Absorption
spectra have thus far been reported only for dilute solutions of bismuth metal in molten BiCl,
(13), and an unpublished study by Boston and Smith has been completed on bismuth dissolved in
BiBr3. Despite the paucity of spectroscopic work on salt-metal melts, there have been a vast
number of spectroscopic studies of alkali metals dissolved in crystals of their halides (39, 131),
and it is not likely that melts of these important systems will long remain uninvestigated.

There has been much debate over whether bismuth metal dissolved in its molten halides forms
a single solute species or whether there are several solute species in equilibrium in which the
species are presumably of the form (Bi_) tm, Spectrophotometric measurements lend strong support
to the multispecies model.

Typical spectra of Bi-BiCl, melts at several concentrations of solute bismuth and at 264°C

are shown in Fig. VI.I. The quantity €y is equal to A/bM where M. 1s the total molar concen-

Bi’
tration of solute bismuth. At low concentrations a strong band is found which diminishes in molar
absorptivity with increasing M. until it is almost indistinguishable against the background of a

diffuse absorption edge. Figure VI.2 shows the manner in which A/b varies with M. at 264°C.

UNCLASSIFIED
ORNL- LR -DWG 69557

 

1 : 4 : 264°C|
6 . . . [ _

   

Fig. VI.1. Spectra of Bismuth Metal in Fused 2
BiCl3 at 264°C and Several Concentrations. (A)
0.0027 M; (B) 0.0341 M; (C) 0.113 M; (D) 0.696 M.

 

 

 

 

[From C. R. Boston and G. P. Smith, J. Phys. 0 —- : '
450 500 550 600 650 700 750
Chem. 66, 1178 (1962).] WAVELENGTH (my)
UNCLASSIFIED
(x10) ORNL~LR-DWG 69588
8 7 |
! -
/ —
& o

 

t :
/’ /

 

 

 

 

 

 

 

 

 

 

 

A / -
7 / /o/
/ /o/
/ /'.
2 ll/=' S e Fig. VI.2. Beer's Law Plotted for Solu-
40. tions of Bismuth Metal in Molten BiC|3 ot
0§ 264°C. A/b determined at 560 mii. [From
o 0. 0.2 0.3 0.4 0.5 06 07 C. R. Boston and G. P. Smith, J. Phys.

Chem. 66, 1178 (1962).}

 
47

The portion of the curve near the origin, from 0.003 to 0.014 M, is accurately known. It closely
approximates the dashed straight line and hence obeys Beer’s law. At higher concentrations the
curve breaks away from the line for Beer’s law to give a deviation from ideality that increases
with increasing concentration until, at the highest concentration studied, it is exceedingly large.
A quantitative analysis of the spectra based on the law of additive absorbances showed that the
spectral profile changes in the way to be expected for a solution of two light-absorbing species.
Boston and Smith have made a spectroscopic study (to be published) of bismuth metal dis-
solved in fused bismuth tribromide, and obtained results qualitatively like those described above

for solutions of bismuth in bismuth trichloride.

Vil. NONMETALLIC IONS

1. Halide lons

The alkali-metal halides occupy a position of special importance in the study of molten salts,
but their spectra, which are very intense and extend into the vacuum ultraviolet, are difficult to
measure. The lowest-energy transition of a halide ion surrounded by rare-gas-configuration cat-
ions should be of the charge-transfer type that may be described very approximately as the transfer
of a p electron on a halide ion into an expanded orbital confined by the surrounding cations and
leaving behind a halogen atom in either the 2P3/2 or “ZPI/2 state. The lowest-energy transition
should be followed closely by a series of higher-energy transitions. Reviews of this type of
charge transfer in various media are given by Rabinowitch (120) and Orgel (106). A discussion of
recent attempts to describe the orbital of the lowest-energy excited state for solution spectra is
given by Griffiths and Symons (42). Fine structure in the spectra of alkali halide crystals is
treated by Overhauser (112).

Absorption edges of the charge-transfer band in pure molten-halide compounds have been
measured by Mollwo (100) and by Sundheim and Greenberg (145). Absorption bands attributed to
charge-transfer transitions were reported by Greenberg and Sundheim (40) for I” and Br™ dissolved
in molten chlorides. The molar absorptivities of these bands may be calculated from the data to
have unexpectedly low values, which lie between 10 and 102. However, recent measurements (to
be published by Boston and Smith) indicate that, at least in the case of I~ dissolved in the LiCl-
KCl! eutectic, € is of the order of 104, a value in accord with measurements of the I” spectrum in
other media, and that the band maximum lies at substantially shorter wavelengths than was re-
ported by Greenberg and Sundheim.

Recently, Zarzycki (I59) measured the Faraday effect and refractive indices for a variety of
molten salts and called attention to the possibility of using the results to obtain information on
charge-transfer absorption in fused halides. The Faraday effect refers to the rotation of the plane
of polarization of linearly polarized light by the action of a magnetic field on a transparent me-

dium. It has been found that a = VHb, where a is the angle of rotation, & is the path length, H is

 
48

the magnetic field strength in the direction of propagation, and V is the Verdet constant, a propor-
tionality factor. The units of V are generally taken to be minutes of arc per gauss-centimeter.

The Faraday effect, like the refractive index of a transparent medium, is related to the exist-
ence of strong, electronic absorption bands in the ultraviolet, and the theoretical connection be-
tween the two is made by way of dispersion theory. The classical theory of the Faraday effect
(122), which is still much used, is based on the classical theory of the Zeeman effect and the re-
lated theorem of Larmor, treating the effect of a magnetic field on the classical motion of elec-
trons. This classical theory is at best a very approximate treatment. The quantum mechanical
theory of the Faraday effect (132, 151) is derived from the general theory of dispersion, 1n which
account is taken of the effect that magnetic fields have on the energy levels of atoms and mole-
cules.

If the i1ons of a molten salt are assumed to contain electronic oscillators of a single frequency
v, then classical dispersion theory predicts a relation between vy and the Verdet constant, and

between 1, and the refractive index (122). This frequency is traditionally identified with the

0
lowest-energy charge-transfer band, and, experimentally, v, for alkali halide crystals is close to
the first absorption maximum in the ultraviolet.

Zarzycki reports (159) that he measured the Verdet constants and refractive indices of the
following salts in the fused state: LiF, NaF, KF, LiCl, NaCl, KCl, LiBr, NaBr, KBr, LiNO3,
NaNO,, KNO,, Li,SO,, Na,50,, K,S0,, Na,WO,, and Na,;AlF .. From a detailed study of NaCl
in the range 20 to 850°C he concluded that measurements of the Verdet constant and refractive in-

dex provide an indirect method of studying the ultraviolet spectrum of molten salts and of measur-

ing the shift of the ultraviolet absorption maximum upon fusion.

2. Nitrate lon

A. Introduction. — The spectra of nonmetallic ions as a class have not been systematically
studied in salt melts, but the spectrum of the nitrate ion as a representative of that class has
been intensively studied (I&, 121,125, 129, 135, 136, 137, 145).

Recent interest in the nitrate spectrum in molten salts stems from the fact that the peak of the
lowest-energy band shifts in energy in a very systematic way when the cationic composition or
temperature of the melt is changed. This phenomenon — which is not well understood, although
different theories (reviewed in Sec VII.2.C) have been proposed — is a consequence of the inter-
action of nitrate ions with surrounding ions in a melt and is analogous to the ‘‘solvent effects”
observed (90) for organic molecules dissolved in different solvents. The importance of this phe-
nomenon lies in the expectation that, when better understood, it may become a tool for the direct
measurement of molecular interactions.

Smith and Boston (136) reviewed early measurements, which gave only approximate informa-
tion, and related them to the results described here. Sakai (7125) reported wavelength values for
absorption edges of RbNO3, CsNO,, and NH NO, from room temperature to above their melting

points. Sundheim and Greenberg (145) measured absorption edges for the fused nitrates of lithium

 
49

and potassium. These absorption-edge measurements are easily rationalized with the spectral
profiles of the nitrates but are much less revealing. Schaefer (129) determined the approximate
ultraviolet spectrum of molten KNO, with results that agree favorably with recent measurements.
The *‘log mm”’ scale used by Schaefer equals —log € plus an unknown constant.

The low-energy end of the absorption spectra of fused lithium, sodium, and cesium nitrates
(136) is shown in Fig. VII.1. These spectra are qualitatively like the characteristic spectrum of
the nitrate ion in other media. There is a weak absorption band (¢ < 20) with a maximum near
300 myu overlapped by the steeply rising absorption edge of a strong band. Substantial changes
are observed in wavelength position and in the intensity of the lowest-energy band when one goes
from cesium to lithium nitrate. Much smaller but important changes occur when the temperature
level is varied.

The profiles of the alkali nitrate spectra have been studied in detail by numerical methods

(136). They are accurately given by the equation

e(A) = g, exp [=(A = Ay/a)] + exp (w— vA)

where €, and A are the coordinates of the maximum of the low-energy absorption band, 0 i1s a
bandwidth constant, and w and v are constants that specify the exponential absorption edge. The
first term in this equation is a gaussian function that is symmetric on a wavelength scale but

skewed on an energy scale. It was shown that this skewness properly represents the shape of the

UNCLASSIFIED
ORNL—LR-DWG 50229

 

 

 

  
 
 
  

£ (ev)
50 44 40 36 32
20— S
| | | i
(5l . oo LiNO, AT 273°C | !

——o—tm NaNO4 AT 314°C ;
—o—o—o- CsNOy AT 425°C ‘

 

10—

Fig. VIL.1. Typical Spectra of Molten Alkali 3 _...T..A,h.
Nitrates over the Wavelength Range of the 05 o ot
Lowest-Energy Absorption Band. [From G. P. o
Smith and C. R. Boston, J. Chem. Phys. 34, - o
1396 (1961).]

—Q5 -

 

240

 
50

band. The oscillator strength of the low-energy band may be obtained from the parameters in the

profile equation by means of the series

f=0.07653(e, 0 /A Y, (o/2A,)((2r + D1/r1] .

=0

Convergence of this series depends on the ratio of o to 2A;. For the nitrate spectrum this ratjo
is always in the neighborhood of 0.04 and the series converges very rapidly.

B. Band-Energy Correlations. — The shift in energy for the low-energy band in nitrate melts
correlates in a strikingly simple way with cationic composition. A summary of resules (136, 137,
and data to be published by Smith and Boston) is shown in Fig. VII.2. The ordinate of this figure
1s the photon energy of the band maximum (hv)_ . in electron volts. The abscissa is the sum
over all species of cations of the cationic charge-to-radius ratios (z/ro)i (with o in A units), each
multiplied by its concentration expressed as the cationic electrical equivalent fraction )_(:, given

by the expression

x::zin;/;s; z].n;, (VIL.1)

+ + . . . . .
where n, and n; are the numbers of gram-atoms of cations of species i and j, respectively.
For pure alkali-metal nitrates, denoted by squares in the figure, the abscissa reduces to l/ro,
the reciprocal of cationic radius. Binary mixtures of alkali-metal nitrates are represented by tri-

angles, and binary and ternary mixtures of alkali-metal nitrates with a nitrate of the polyvalent

UNCLASSIFIED
ORNL-LR-DWG 69114

 

44 | }

  

Fig. VII.2. Correlation Between (b;)mux

 

 

3 Cs-Li and a Weighted Average of the Cationic Po-
2 {:2:? tentials (z/ro)i for Alkali-Nitrate Mixtures.
g L -K o The weighting fucfcls are the electrical
§ Ba-K equivalent fractions X!. of the cations, The
g?:k' units of ry are A. The nitrate mixtures are

’ gg:ti—K listed on the figure according to their cati-

~— | [te-Li-K - l onic constituents. Points corresponding to

the pure alkali-metal nitrates and the LiNO3-
I'(NO3 eutectic oare individually labeled,
[From date to be published by G. P, Smith
_ i and C. R. Boston; G. P, Smith and C. R.
o ] Boston, J. Chem. Phys. 34, 1396 (1961);
i.5 20 G. P. Smith and C. R. Boston, Discussions
Faraday Soc. 32, 14 (1962).]

 
51

cation Ba®*, Sr2*, Ca®* or La?" are represented by circles. The various two- and three<compo-
nent systems studied are listed on the figure according to their metallic constituents. All data
were either measured at or extrapolated to 360°C.

It is evident from the figure that there is a close correlation between the position of the band

maximum and ¥ (z/7,), )—(: The straight line about which the data cluster is given by
z

(#7)__ =034 ¥ (2/rp) X} + 3.81 . (VIL2)

It has been found that nitrate mixtures which contain Mg2+ and Y7 do not conform to this cor-
relation. These cations have greater z/ro values than any represented in Fig. VII.2.

A special correlation is provided by the trio of cations Ba®* K*, and Li*. The barium ion
has approximately the same radius as the potassium ion and approximately the same charge to
radius ratio as the lithium ion. The (b;)max values for Ba(N03)2 + KNO3 mixtures lie quite close
to those for LiNO3 + KNO3 when compared at the same electrical equivalent fraction. Further-
more, the addition of Ba(N03)2 to LiNO3 changes (b;)max of the latter by only a small amount. In
both instances Ba’* and Li* behave alike when compared on an equal electrical-equivalent basis.

Cleaver, Rhodes, and Ubbelohde (18, 121) measured the effect that a change in temperature
has on (bi_/)max over the range from room temperature to above the melting point. They found that
(b'i/')max correlates quite well with thermal expansion for nitrate crystals and melts except in the
vicinity of phase transitions and that as the nitrate expands, (bl—/)max decreases. This effect is
quite small, of the order of —2 cal/deg (I136).

C. LCAO-MO Model for Nitrate lon. — The energy-level schemes for molecules and ions are
generally treated by molecular-orbital methods. These methods have been applied most exten-
sively to organic molecules, and there is a great deal of literature on this subject. The funda-
mentals are given in several texts on quantum chemistry such as those by Eyring, Walter, and
Kimball (31) and by Daudel, Lefebvre, and Moser (23), and in reviews by Mulliken (104).

The electronic transition that produces the lowest-energy band of the nitrate ion is adequately
described for present purposes in terms of the linear combination of atomic orbital—molecular
orbital (LCAOQ-MQ) model of electronic configurations. Sayre (128) specifies the LCAO-MO or-
bitals that may be constructed from the 2s and 2p atomic orbitals of the constituent atoms. Three
different assignments have been proposed for the lowest-energy transition (32, 91, 92, 128, 139,
I55), and in terms of the D,, symmetry of an isolated nitrate ion are the symmetry-forbidden tran-
sitions Al’ - Al" (n » 77*) and Al’ - Aé'(n - o*) and the symmetry-allowed transition Al' - E’

(71 > 7%).

The two highest-energy one-electron orbitals that are filled and the two lowest-energy one-
electron orbitals that are empty are shown schematically in Fig. VII.3. On the right side of this
figure is an energy-level diagram showing the relative order of the levels on a schematic energy
scale. There is some debate over the relative positions of the az”(’/T*) and al' {(o*) orbitals. The

positions shown in Fig. VII.3 were chosen according to an elementary consideration of relative

 
52

destabilization due to repulsive overlap. The three assignments proposed for the lowest-energy
transition are designated by vertical arrows. To the left side of each energy level is a diagram
showing the orientations of the atomic orbitals on the D, nuclear frame of NO,. Positive and
negative regions of these orbitals are represented, respectively, by light and dark spheres.

The 77-type molecular orbitals in the LCAO-MO approximation are constructed from 2p atomic
orbitals oriented perpendicular to the molecular plane. Three of the four possible 7 orbitals are
shown in Fig. VII.3: the degenerate pair of symmetry species e and the antibonding 77* orbital
5
e ’(77) orbitals are localized exclusively on oxygen atoms.

of symmetry species a.,. Not shown is the bonding counterpart of the 7* orbital. The degenerate
The n-type orbitals are constructed from the 2p orbitals on oxygen atoms that lie in the mo-
lecular plane and perpendicular to the N-O bonds. There are three possible orbitals of this type,
but only one, that of symmetry species a,, is shown in Fig. VII.3. All the n orbitals are localized
on oxygen atoms. The designation of n-type or nonbonding orbitals is somewhat of a misnomer
since the az'(rz) orbital involves a small out-of-phase overlap and is, therefore, slightly antibond-
ing.
L
This is constructed from the 2po orbitals on the oxygen atoms overlapping out of phase with the

The remaining orbital in Fig. VII.3 is the o* (o antibonding) orbital of symmetry species a

2s orbital on the nitrogen atom.

D. Theories of the Band-Energy Shift. — Cleaver, Rhodes, and Ubbelohde (18) postulate that
inasmuch as the orbital of the excited electron is strongly antibonding it is spread out at the pe-
riphery of the nitrate ion and overlaps to some extent the first coordination shell of cations. They
propose therefore that the excitation can be regarded as analogous to the lowest-energy charge-
transfer transition of a halide ion. In such a transition the excited electron may be regarded as

moving in a centrosymmetric orbital, which is defined largely by the potential field of surrounding

UNCLASSIFIED
ORNL—LR—-DWG 62158R

 

K, —— &, Fig. VII.3. Schematic Diagram of Some One-

Electron Orbitals for the Nitrate ton., Shown
are the two highest-energy filled orbitals and

 

the two lowest-energy empty orbitals. On the
Ky —= &} right are energy levels, and on the left the

relative orientations of atomic orbitals from

 

 

 

which the molecular orbitals are constructed in
simple LCAO-MO theory. Spacing of the en-
A £ ergy levels is arbitrary and there has been

some disagreement over whether the #* or the

 

o* orbital is lower. The right partner of the

 

e’ orbital has a node through one oxygen,

which is why no orbital resides there.

 
53

ions and by electronice-repulsion effects. There are two different models of the influence that the
surrounding medium may have on such transitions; they are compared by Griffiths and Symons (42).
One is the ""expanded’’ model of Platzman and Franck (117) in which the orbital of the excited
electron is regarded as invading the surrounding medium quite deeply. The other is the *‘con-
fined’’ model of Smith and Symons (I38) in which the orbital of the excited electron is confined
within the nearest-neighbor shell. Cleaver, Rhodes, and Ubbelohde adopted the confined model,
while Shimoji (133) proposed that the expanded model be used to describe the influenceof environ-
ment on the nitrate spectrum in molten salts.

In order to obtain a rough estimate of the differences between the transition energies for io-
dide ions in various environments, Smith and Symons (I38) describe the retaining force on the
excited electron by an infinite, square-well potential of spherical symmetry and radius R;;. By
analogy with F-centers, they propose that R, may be qualitatively regarded as an effective lattice
parameter. In the case of nitrate melts this would be the sum of the radius of the cavity contain-
ing a nitrate ion and the radius of a cation. These authors derive the following expression for the

temperature derivative of the energy of the band maximum:
d(hv)_ /dT =~(h*/4mR})dRy/dT (VIL.3)

where b is Planck’s constant and m is the electronic mass. Cleaver, Rhodes, and Ubbelohde

equate (3/RO)(dRO/dT) with the cubic coefficient of expansion 3 of an ionic medium so that

dhv) __ /dT =~(h*/12mR)B . (VIL4)

Measured values of d(bi_/)max/dT and 3 were used in Eq. (VII.4) to compute R,. For the crystal-
line alkali-metal nitrates it was found that R is approximately the same as the sum of the cation
radius and the cation-anion distance calculated from crystal structures. For melts of alkali-metal
nitrates, however, considerably higher values of R, were found. It was concluded that a substan-
tial fraction of the thermal expansion of such melts arises from the creation of holes and free
space in the liquid, rather than from an increase in the average distance between anions and cat-
tons, and that therefore Eq. (VII.4) does not apply.

The mechanism suggested by Smith and Boston (136, 137) by which surrounding ions may in-
fluence the lowest-energy nitrate transition is entirely different from the mechanism described
above — namely, the transition is localized on the nitrate ion rather than spread out to encompass
the neighboring ions. The basis of this supposition is the following: Inasmuch as oxygen is more
electronegative than nitrogen, their atomic orbitals will not have equal weights when forming a
molecular orbital. As a consequence, the strongly bonding ¢ and 77 orbitals (not shown in Fig.
VII.3), which are occupied, reside predominantly on the oxygen atoms. This forces the corre-
sponding antibonding orbitals a,’(77*) and a[(0*), which are empty in the ground state, to reside
predominantly on nitrogen. Thus each of the three proposed assignments for the lowest-energy
transition removes an electron from an orbital that is localized on the oxygen atoms, e "’(77) or

az’ (n), and transfers it to an orbital that resides predominantly on the nitrogen atom, az”(’fl) or
54

a{(o*). That is, the transition shifts electronic charge density from the region around oxygen
atoms to the region around the nitrogen atom.

Over the space occupied by a nitrate ton there is an external electrostatic potential, V, which
is established by the Coulomb forces of the other ions in the melt. This potential contributes to

the transition energy in a way approximately described by
o = 2 2
B = B0 + @ [ (W |7 =, [V v (VIL5)

where (hv), represents the transition energy for a nitrate ion separated to infinity and the integral
represents the change in interaction energy between V and the electronic charge cloud of the ni-
trate ion in going from the ground state to the excited state. In this equation lj;gr and ¢y __ are the
total electronic eigenfunctions of the ground and excited states, respectively; therefore ll’bgr‘z and
|¢ex|2 are the electronic density functions, e is the electronic charge, and the integral is over
the volume of the nitrate ion. The eigenfunctions and V are functions of position within the ni-
trate 1on.

In the development of their equations Smith and Boston (I36) introduce repulsive-overlap
forces in a formal way but conclude later that these are not responsible for the observed shift in
(bfi)max. In effect UJ;O) in Eq. (VII.5) must be regarded as containing an energy term due to the
change in repulsive overlap.

If, for simplicity, the correlation shown in Fig. VII.2 and Eq. (VII.2) is extrapolated to include
the pure molten nitrates with polyvalent, rare-gas configuration cations, then the qualitative fea-

tures of this correlation are as follows. With two nitrates having transition energies (h7)

then (bl—/)m

max,l

is an increasing function of (z/7,); ~ (z/7,),. This empirical qualitative correlation may be ra-

and (lnf)max,2 and cationic charge-to-radius ratios (z/ro)1 and {(z/r

ax,l max,?

tionalized in terms of Eq. (VII.5) as described below, which must, however, be regarded as incom-
plete since the problem of relative coordination numbers in different nitrates is ignored.
If V in Eq. (VIL.5) is regarded as arising from pairwise electrostatic interactions between

ions, then for a melt containing N ions

N-1 ¢ pAr.)
Vg )= ), — | ——av, (VIL.G)
NO3 D lr - ! i
i=1 NO i
3
where r 1s the vector position of a volume element (vaO ) in a nitrate ion that becomes ex-

NO
3
cited, r.is the vector position of a volume element dvl_ in the ith ion, pz,(rz,) 1s the charge-density

function of the ith 1on, and D is an effective dielectric constant. The term ’rNO - rz.| is the
scalar distance between vaO3 and dv . ’

The external electrostatic potential V is positive because nitrate is negative. We may imagine
expanding V 1n a multipole series with the singularity at infinity. The first term is a constant and
can contribute nothing to the integral in Eq. (VIL.5), essentially because moving an electrom from
one place to another in a constant potential involves no interaction work. Which of the higher

terms contribute to the interaction integral depends on their symmetry properties and the symmetry
55

properties of the shift in charge density, |¢ ex|2 - ngr| 2. For example, the A] » A[" transition
has a symmetry that is too high to combine with the dipole terms. Actually, as shown later, the
Al - A" transition will not occur unless the nitrate ion is distorted by the medium, in which case
it may combine slightly with the dipole terms.

The dipole and higher terms in V are produced primarily by neighboring ions. Therefore it is
useful to divide the ions of the melt into two groups: those ions which neighbor a given nitrate
ion and those ions which are more remote. The nearest neighbors are cations and are assumed to
have rare-gas electronic configurations. With small polarization terms ignored, these cations can

be represented as point charges and the following change made in Eq. (VIL.G):

C e z,
V(rNO3) ) sl dUN% + V. her » (VIL.7)
i=1 NO3 z
where zZ; is the net charge or electrostatic valence of the 7th cation, (rNO )i is the scalar distance
from the center of the ith cation to the volume element vaO
3
is a term similar to Eq. (VIL.G) but is

of the nitrate ion, the summation is
over the C cations of the nearest-neighbor shell, and V. .
summed from C + 1 through N — 1. The dipole and higher terms in Eq. (VII.7) are of greatest mag-
nitude near the neighbor cations, where they increase as the cationic z/r0 increases. Conse-
quently the interaction-energy integral in Eq. (VIL.5) changes when z/r0 changes.

It is important now to consider whether the sign of this change is positive or negative. The
lowest-energy transition shifts charge density from the neighborhood of oxygens to the neighbor-
hood of nitrogens with a conservation of total charge. Consequently it is possible to divide the
space of a nitrate ion into two regions, one around nitrogen and the other around oxygens, so that
the volume integral of lt,[/exlz - };[/griz has some positive value, «, over the space around nitrogen
and a corresponding negative value, — &, over the space around oxygens. For purposes of qualita-
tive discussion |gbexl2 - {;figrlz is chosen to be a step function with the values a and —a,and Vis
chosen to be a similar step function with the value V{9 over the region around the oxygen atoms

(N

and over the region around the nitrogen atom. Substituting these functions into Eq. (VIL.5)

results in

(BD)_  — (D) = ~(ea) [V — y (O] | (VIL8)

According to this expression the relative magnitudes of V) and v(O) determine whether the Cou-
lomb forces of the melt contribute toward a ‘‘blue shift’’ [(b—fi)max - (lffi)o positive| or toward a
**red shift”’ [(bl_/")max ~ (bv), negative]. The experiments specify that (bl_/)max - (b'i;)o is positive.
Elementary electronic considerations are sufficient to show that nitrogen-oxygen bonds on the
nitrate ion in its ground state are polarized in such a direction that the charge around oxygens
(electrons plus nuclei) is more negative than the charge around nitrogen. Therefore the lowest-
energy configurations in the melt will tend to be those in which nitrogen-oxygen bonds lie along

(0) (N)

directions in which V 1s greater than V According to Eq. (VII.8), this is the condition for

a Coulomb contribution to a blue shift. At a sufficiently low temperature such configurations will
56

predominate. In a melt, of course, there will be configurations which are not energetically favor-
able, and their increasing number with increasing temperature will be manifest in band broadening
and in a decreasing contribution of the Coulomb potential to a blue shift. Qualitatively, this tem-
perature dependence is in the same direction as the observed d(b'f/')max/dT.

E. Oscillator Strength Correlation. — Another important empirical correlation is with regard to
the oscillator strengths of the lowest-energy transition in alkali-metal nitrate melts. These oscil-
lator strengths have been calculated by numerical profile analysis of the alkali nitrate spectra
(136). They are small, of the order of 10~ 4, and change relatively little in going from CsNO; to
RbNO, to KNO;. Then they increase very rapidly in going from KNO, to NaNO; to LiNOa. Simi-
larly, the oscillator strengths increase rapidly on addition of nitrates with polyvalent cations of
rare-gas electronic configurations to molten KNO,.

The development of a mechanism to account for these oscillator strength correlations is seri-
ously restricted by large uncertainties in the band assignment. Proposed assignments are dis-
cussed in Sec VII.2.C and are illustrated in Fig. VIL.3.

If the transition is Al' -~ E’7 (7 » 77*), symmetry considerations impose no restriction on in-
tensity, and there is no ready explanation of the low oscillator strength observed in the melt. It
seems more appropriate, at present, to assign the A/ » E’ transition to the very strong band that
is generally found near 190 my.

For the remaining two assignments that have been proposed, Al' »A['(n > 7*) and Al »
Az'(n - O'*), very approximate considerations of antibonding character in the excited state place
A] > A["(n > 7*) lower in energy. It is possible, nevertheless, that the o* orbital lies lower in
energy than the 77* orbital.

Even if A] » A['(n » 77%) proves to be lower in energy, it may not correspond to the observed
lowest-energy band. In strict D,, symmetry this transition is of an unusual type. It is forbidden
as an electric-dipole, electric-quadrupole, or magnetic-dipole transition and although permitted as
a vibronic transition, requires two vibrational quanta. Very little is known about the intensity of
such transitions but elementary considerations suggest that they are extremely weak. If the ob-
served lowest-energy band is to be assigned to this transition, then the trigonal symmetry of the
A" excited state must be statistically relaxed by some relatively efficient mechanism. Even if
such a mechanism exists, there must be a very strong transition close enough in energy to be a
source of stolen intensity. The observed spectrum shows the nearest strong band to lie about

2 ev away, which seems rather remote for the purpose.

In summary, the oscillator strength of the lowest-energy band of the nitrate ion varies by a
large amount with variation in melt composition, and these variations are roughly correlated. How-
ever, the theory of this transition is not well enough understood to suggest a specific mechanism

to account for the empirical observation.

 
57

3. Other Nonmetallic lons

A few other nonmetallic species have received some study, among them the thiocyanate ion in
molten KSCN, measured by Rhodes and Ubbelohde (121); the nitrite ion in solution in molten po-
tassium nitrate, measured by Smith and Boston (I35); and solutions of halogen gases in molten
alkali-metal halides, measured by Greenberg and Sundheim (40).

The nitrite spectrum in a 2.48 M solution of KNO, in fused KNO, at 342°C is very much like
that in crystalline (96) KNO, and differs only slightly from the nitrite spectrum in dilute aqueous
solutions (130). These spectra consist of a weak lowest-energy band in the ultraviolet and of a
broad minimum followed by an absorption edge at shorter wavelengths. In the melt the band max-
imum occurs at 359 my with an € value of 30.6. In dilute aqueous solutions these values are
366 my and 21.9, respectively, while in crystalline KNO, the band maximum occurs at 360 my.

The spectra of solutions of halogens in halide eutectics were interpreted to show the presence
of trihalide ions. Chlorine dissolved in the LiCI-KCl eutectic and bromine in the LiBr-KBr eu-
tectic each gave spectra that were very similar to the trihalide spectra in aqueous solutions (77,
160). On the other hand, iodine in the Lil-KI eutectic was reported to have three band maxima in
a region where only two were expected. However, the lowest-energy maximum occurred at a wave-
length where absorption of the solvent salt is quite substantial; so this third maximum may be an
artifact of stray light. When iodine was dissolved in molten LiCI-KCl, the spectrum obtained re-

sembled that of IZCI—.

ACKNOWLEDGMENT

It is a pleasure to record my thanks to A. D. Liehr for help with the manuscript; to C. V.
Banks, P. R. Fields, D. M. Gruen, A. D. Liehr, J. R. Morrey, and H. A. Weakliem and Analytical
Chemistry, Annals of the New York Academy of Sciences, Inorganic Chemistry, Journal of Chem-
ical Education, The Journal of Chemical Physics, Journal of Physical Chemistry, and Plenum
Press, Inc., for permission to reproduce figures; to Virginia Hamrick for editing the manuscript;
to W. C. Colwell and his associates for drafting many of the figures; and to my secretary, Wilma

Mason, for assistance in many ways.

 
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(17)
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(28)

(29)

58

BIBLIOGRAPHY

Asprey, L. B., and T. K. Keenan, [. Inorg.. Nucl. Chem. 7, 27 (1958).
Ballhausen, C. J., Introduction to Ligand Field Theory, McGraw-Hill, New York, 1962.
Ballhausen, C. J., and H. B. Gray, Inorg. Chem. 1, 111 (1962).

Ballhausen, C. J., and C. K. Jérgensen, Kgl. Danske Videnskab. Selskab Mat.-Fys. Medd. 29,
No. 14 (1955).

Ballhausen, C. J., and C. K. Jdrgensen, Acta Chem. Scand. 9, 397 (1955).

Ballhausen, C. J., and A. D. Liehr, J. Mol. Spectr. 2, 342 (1958); errata, J. Mol. Spectr. 4,
190 (1960).

Ballhausen, C. J., and W, Moffitt, J. Inorg. Nucl. Chem. 3, 178 (1956).

Banks, C. V., M. R. Heusinkveld, and J. W. O'Laughlin, Anal. Chem. 33, 1235 (1961).
Basolo, F., C. J. Ballhausen, and J. Bjerrum, Acta Chem. Scand. 9, 810 (1955).
Belford, R. L., M. Calvin, and G. Belford, J. Chem. Phys. 26, 1165 (1957).

Bethe, H., Ann. Physik 3, 133 (1929).

Bleaney, B., and K. W, H. Stevens, Rept. Progr. Phys. 16, 108 (1953).

Boston, C. R., and G. P. Smith, J. Phys. Chem. 62, 409 (1958).

Boston, C. R., and G. P. Smith, J. Phys. Chem. 66, 1178 (1962).

Carnall, W. T., Anal. Chem. 34, 786 (1962).

Carnall, W. T., and P. R. Fields, ""The Visible and Near Infrared Absorption Spectra of Some
Trivalent Actinide and Lanthanide Elements in DCIO4 and in Molten Nitrate Salts,’’ in Devel-
opments in Applied Spectroscopy, vol 1 (ed. by W. D. Ashby), Plenum Press, New York (to be
published in 1962).

Carrington, A., and D. S. Schonland, Mol Phys. 3, 331 (1960).

Christiansen, J. A., . Am. Chem. Soc. 82, 5517 (1960).

Cleaver, B., E. Rhodes, and A. R. Ubbelohde, Discussions Faraday Soc. 32, 22 (1961).
Conway, J. G., |. Chem. Phys. 31, 1002 (1959).

Cotton, F. A., O. D. Faur, and D. M. L. Goodgame, J. Am. Chem. Soc. 83, 344 (1961).
Cotton, F. A., and D. M. L. Goodgame, . Am. Chem. Soc. 82, 5771 (1960).

Cotton, F. A., D. M. L. Goodgame, and M. Goodgame, . Am. Chem. Soc. 83, 4690 (1961).
Daudel, R., R. Lefebvre, and C. Moser, Quantum Chemistry, Interscience, New York, 1959.

Dexter, D. L., ""Theory of the Optical Properties of Imperfections in Nonmetals,’’ pp 355—441
in Solid State Physics, vol 6, Academic Press, New York, 1958.

Dieke, G. H., and H. M. Crosswhite, . Opt. Soc. Am. 46, 885 (1956).
Dieke, G. H., and L. Heroux, Phys. Rev. 103, 1227 (1956).
Dillon, J. F., H. Kamimura, and J. P. Remeika, Phys. Rev. Letters 9, 161 (1962).

Dunn, T. M., **The Visible and Ultra-Violet Spectra of Complex Compounds,”’ pp 229~-300 in
Modern Coordination Chemistry (ed. by J. Lewis and R. G. Wilkins), Interscience, New York,
1960.

Elliott, R. J., and K. W. H. Stevens, Proc. Roy. Soc. (London) A215, 437 (1952); A218, 553
(1953); A219, 387 (1953).

 
(30)
(31)
(32)
(33)
(34)
(35)
(36)
(37)
(38)
(39)

(40)
(41)

(42)
(43)
(44)

(45)

(46)
(47)
(48)
(49)
(50)
(51)
(52)

(53)
(54)
(55)
(56)
(57)

(58)
(59)
(60)

59

Englman, R., Mol. Phys. 3, 48 (1960).

Eyring, H., J. Walter, and G. E. Kimball, Quantum Chemistry, Wiley, New York, 1944.
Friend, J. A., and L. E. Lyons, [, Chem, Soc. 1959, 1572.

Furlani, C., Ric. Sci. Riv. 27, 1141 (1957).

Furman, S. C., and C. S. Garner, |. Am. Chem. Soc. 72, 1785 (1950).

Furlani, C., Z. Phys. Chem. (Frankfurt) 10, 291 (1957).

Gibson, K. S., Nat. Bur. Std. (U.S.) Cir. 484, 3—6 (1949).

Gill, N. S., and R. S. Nyholm, [. Chem. Soc. (London) 1959, 3997.

Goodgame, D. M. L., and F. A. Cotton, |. Am. Chem. Soc. 82, 5774 (1960).

Gourary, B. S., and F. J. Adrian, “*Wave Functions for Electron-Excess Color Centers in
Alkali Halide Crystals,’”’ pp 127—247 in Solid State Physics, vol 10, Academic Press, New
York, 1960.

Greenberg, J., and B. R. Sundheim, |. Chem. Phys. 29, 1029 (1958).

Griffith, J. S., The Theory of Transition Metal lons, Cambridge University Press, London and
New York, 1961.

Griffiths, T. R., and M. C. R. Symons, Trans. Faraday Soc. 56, 1125 (1960).
Gruen, D. M., J. Inorg. Nucl. Chem. 4, 74 (1957).

Gruen, D. M., S. Fried, P. Graf, andR. L. McBeth, Proc. U.N. Intern. Conf. Peaceful Uses At.
Energy, 2nd, Geneva, 1958 12, 112—19 (1958).

Gruen, D. M., P. Graf, and S. Fried, '‘Spectrophotometric and Chromatographic Studies of
Actinide lons in Fused Salts,”” pp 319-27 in XVI Congrés International de Chimie Pure et
Appliquée. Memoires Présentés a la Section de Chimie Minérale, Societé D’ Edition D’
Enseignement Supérieur, No. 5, Place de la Sorbonne, Paris, 1958.

Gruen, D. M., and R. Gut, Nature 190, 713 (1961).

Gruen, D, M., and R. L. McBeth, |. Phys. Chem. 63, 393 (1959).

Gruen, D. M., and R. L. McBeth, J. Phys. Chem. 66, 57 (1962).

Gruen, D. M., and R. L. McBeth, J. Inorg. Nucl. Chem. 9, 290 (1959).

Gruen, D. M., and R. L. McBeth, J. Phys. Chem. 63, 393 (1959).

Gruen, D. M., and R. L. McBeth, J. Phys. Chem. 66, 57 (1962).

Gruen, D. M., and R, L. McBeth, **The Coordination Chemistry of 3d Transition Metal Ions in

-

Fused Salt Solutions,’’ Plenary Lecture at Seventh International Conference on Coordination
Chemistry, Stockholm, Sweden, June 25—29, 1962; to be published by Butterworth, London.
The writer is grateful to D. M. Gruen for showing him the manuscript before publication.

Gruen, D. M., and R. L. McBeth, Nature 194, 468 (1962).
Gruen, D. M., R. L. McBeth, J. Kooi, and W. T. Carnall, Ann. N.Y. Acad. Sci. 79, 941 (1960).
Hartmann, H., Z. Elektrochem. 61, 908 (1957).

Hartmann, H., and C. Furlani, Z. Physik. Chem. (Frankfurt) 9, 162 (1956).

Hartmann, H., and H. L. Schlidfer, Z. Naturforsch. 6a, 754, 760 (1951); Angew. Chem. 66, 768
(1954).

Hartmann, H., H. L. Schlédfer, and K. H. Hansen, Z. Anorg. Allgem. Chem. 289, 40 (1957).
Harrington, G., and B. R. Sundheim, Ann. N.Y. Acad. Sci. 79, 950 (1960).
Holmes, O. G., and D. S. McClure, |. Chem. Phys. 26, 1686 (1957).
(61)
(62)
(63)
(64)
(65)
(66)
(67)
(68)
(69)
(70)

(71)
(72)
(73)
(74)

(75)
(76)
(77)
(78)
(79)
(80)
(81)

(82)
(83)

(84)
(85)
(86)
(87)
(88)
(89)

(90)
(91)
(92)
(93)
(94)

60

Hughes, H. K., Anal. Chem. 24, 1349 (1952).

Ilse, F. E., and H. Hartmann, Z. Physik, Chem. (Leipzig) 197, 239 (1951).

Johnson, K. E., and T. S. Piper, Discussions Faraday Soc. 32, 32 (1961).

Jérgensen, C. K., Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 29, No. 11 (1955).
Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 29, No. 7, (1955).
Acta Chem. Scand. 9, 405 (1955).

Jdrgensen, C. K.,
, Acta Chem. Scand. 9, 1362 (1955).

K.
Jdrgensen, C. K.
Jérgensen, C. K.
Jdrgensen, C. K., Acta Chem. Scand. 10, 1503 (1956).
Jergensen, C. K., Acta Chem. Scand. 11, 53 (1957).

K.

Jérgensen, C. Energy Levels of Complexes and Gaseous lons, Gjellerups, Copenhagen,

1957.
Jérgensen, C.

~

Acta Chem. Scand. 11, 73 (1957).
Mol. Phys. 1, 410 (1958).
, Mol. Phys. 2, 96 (1959).

Jgrgensen, C. K., Absorption Spectra and Chemical Bonding in Complexes, Pergamon, London
and New York, 1961.

Judd, B. R., Proc. Roy. Soc. (London) A227, 552 (1955).

Judd, B. R., Proc. Roy. Soc. (London) A228, 120 (1955).

Katzin, L. 1., |. Chem. Phys. 20, 1165 (1952).

Lang, R. J., Can. ]. Research 14A, 127 (1936).

LaSalle, M. J., and J. W. Cobble, J. Phys. Chem. 59, 519 (1955).
Liehr, A. D., J. Phys. Chem. 64, 43 (1960).

Liehr, A. D., in Symposium on Molecular Structure and Spectroscopy, June 12—16, 1961, Ohio
State University, Columbus.

Liehr, A. D., J. Chem. Educ. 39, 135 (1962).

-

-

K.
Jérgensen, C. K.
Jérgensen, C, K.

K.

Liehr, A. D., **The Coupling of Vibrational and Electronic Motions in Degenerate Electronic
States of Inorganic Complexes. Part I. States of Double Degeneracy,”’ pp 281—-314, 314a—f
in Progress in Inorganic Chemistry, vol 3, Interscience; New York, 1962,

Liehr, A. D., and C. J. Ballhausen, Ann. Phys. (N.Y.) 6, 134 (1959).
Liehr, A. D., and C. J. Ballhausen, Phys. Rev. 106, 1161 (1957).
Liehr, A. D., and C. J. Ballhausen, Ann. Phys. (N.Y.) 3, 304 (1958).
Lux, H., and T. Niedermaier, Z. Anorg. Allgem. Chem. 285, 246 (1956).
Low, W., Z. Physik. Chem. (Frankfurt) 13, 107 (1957).

McClure, D. S., **Electronic Spectra of Molecules and Ions in Crystals. Part II. Spectra of
Ions in Crystals,” pp 399-525 in Solid State Physics, vol 9, Academic Press, New York,
1959.

McConnell, H., J. Chem. Phys. 20, 700 (1952),

McEwen, K. L., J. Chem. Phys. 34, 547 (1961).

McGlyan, S. P., and Kasha, J. Chem. Phys. 24, 481 (1956).
Maccoll, A., Quart. Revs. (London) 1, 16 (1947).

Maki, G., J. Chem. Phys. 28, 651 (1958).
(95)
(96)
(97)
(98)

(99)
(100)
(101)
(102)
(103)
(104)
(105)
(106)
(107)
(108)
(109)
(110)
(111)

(112)
(113)
(114)
(115)
(116)
(117)
(118)
(119)
(120)
(121)
(122)
(123)

(124)
(125)
(126)
(127)
(128)
(129)
(130)

 

61

Manch, W., and W. C. Fernelius, [. Chem. Educ. 38, 192 (1961).
Maslakowez, 1., Z. Physik 51, 696 (1928).
Mellon, M. G., Analytical Absorption Spectroscopy, Wiley, New York, 1950.

Moffitt, W. E., and C. J. Ballhausen, '"Quantum Theory,”’ pp 107—36 in Annual Reviews of
Physical Chemistry, vol 7, Annual Reviews, Palo Alto, Calif., 1956.

Molina, R., Bull. Soc. Chim. France 1961, 301.

Mollwo, E., Z. Physik 124, 118 (1947).

Morrey, J. R., Inorg. Chem. 2, No. 1 (1963).

Morrey, J. R., and A. W. Madsen, Rev. Sci. Instr. 32, 799 (1961).
Morrey, J. R., and E. E. Voiland, Spectrochem. Acta 18, 1175 (1962).
Mulliken, R. S., Phys. Rev. 43, 279 (1933); J. Chim. Phys. 46, 497, 675 (1949).
Mulliken, R. S., and C. A. Rieke, Rept. Progr. Phys. 8, 231 (1941).
Orgel, L. E., Quart. Revs. (London) 8, 422 (1954).

Orgel, L. E., J. Chem. Phys. 23, 1284 (1955).

Orgel, L. E., J. Chem. Phys. 23, 1819 (1955).

Orgel, L. E., |. Chem. Phys. 23, 1958 (1955).

Orgel, L. E., J. Chem. Pbys.23,1004(1955)

Orgel, L. E., Introduction to Transition-Metal Chemistry — Liquid Field Theory, Wiley, New
York, 1960.

Overhauser, A. W., Phys. Rev. 101, 1702 (1956).

Pappalardo, R., J. Mol Spectr. 6, 554 (1961).

Pappalardo, R., andR. E. Dietz, Phys. Rev. 123, 1188 (1961).

Pappalardo, R., D. L. Wood, and R, C. Linares, Jr., . Chem. Phys. 35, 1460 (1961).
Pappalardo, R., D. L. Wood, and R. C. Linares, |. Chem. Phys. 35, 2041 (1961).
Platzman, R., and J. Franck, Z. Physik. 138, 411 (1954).

Pohl, R. W., Optik und Atomphysik, pp 146—50, Springer-Verlag, Berlin, 1954.
Pryce, M. H. L., andW. A. Runciman, Discussions Faraday Soc. 26, 34 (1958).
Rabinowitch, E., Rev. Mod. Phys. 14, 112 (1942).

Rhodes, E., and A. R. Ubbelohde, Proc. Roy. Soc. (London) A251, 156 (1959).
Rossi, B., Optics, Addison-Wesley, Reading, Mass., 1957.

Rossotti, F, J. C., and H. Rossotti, The Determination of Stability Constants, pp 270—85,
McGraw-Hill, New York, 1961.

Runciman, W. A., Rept. Progr. Phys. 21, 30 (1958).

Sakai, K., |. Phys. Chem. 61, 1131 (1957).

Satten, R, A., J. Chem. Phys. 21, 637 (1953).

Satten, R. A., D. Young, and D. M. Gruen, J. Chem. Phys. 33, 1140 (1960).
Sayre, E. V., |. Chem. Phys. 31, 73 (1959).

Schaefer, K., Z. Anorg. Allgem. Chem. 97, 285 (1916).

Scheibe, G., and W. Fromel, *‘Molekiilspektren von Lésungen and Fliissigkeiten,”” p 162 in
Hand-und [abrbuch der Chemischen Physik, vol 9, Sec IV, Akademische Verlagsgesellschaft,
Leipzig, 1937.
(131)
(132)
(133)
(134)
(135)
(136)
(137)
(138)
(139)
(140)
(141)
(142)
(143)

(144)
(145)
(146)

(147)
(148)
(149)
(150)
(151

(152)
(153)
(154)
(155)
(156)
(157)
(158)
(159)

(160)

62

i

.
¥
/

Seitz, F., Rev. Mod. Phys. 26, 7 (1954).

Serber, R., Phys. Rev. 41, 489 (1932).

Shimoji, M., Discussions Faraday Scc. 32, 66 (1961).

Silcox, N. W., and H. M. Haendler, |. Phys. Chem. 64, 303 (1960).

Smith, G. P., and C. R. Boston, Ann. N.Y. Acad. Sci. 79, 930 (1960).
Smith, G. P., and C. R. Boston, J. Chem. Phys. 34, 1396 (1961).

Smith, G. P., and C. R. Boston, Discussions Faraday Soc. 32, 14 (1961).
Smith, M., and M. C. R. Symons, Trans. Faraday Soc. 54, 346 (1958).
Strickler, S. J., Ph.D. Dissertation, Florida State University, January 1961.
Stout, J. W., J. Chem. Phys. 31, 709 (1959); 33, 303 (1960).

Sugano, S., and Y. Tanabe, J. Phys. Soc. Japan 13, 880 (1958).

Sugano, S., and I. Tsujikawa, J. Phys. Soc. Japan 13, 899 (1958).

Sundheim, B. R., *‘The Coordination of Metal Ions in Fused Salts,’”’ p 94 in Proceedings of
the Seventh International Conference on Coordination Chemistry, Stockholm and Uppsala,
Sweden, June 25-29, 1962, Almquist and Wiksell, Uppsala.

Sundheim, B, R., and J. Greenberg, Rev. Sci. Instr. 27, 703 (1956).
Sundheim, B. R., and J. Greenberg, J. Chem. Phys. 28, 439 (1958).

Sundheim, B. R., and G. Harrington, Absorption Spectra of Molten Salts, USAEC Report
NYO-7742, March 9, 1959; G. Harrington, Ph.D. Dissertation, New York University, 1958.

Sundheim, B. R., and G. Harrington, J. Chem. Phys. 31, 700 (1959).

Sundheim, B. R., and M. Kukk, Discussions Faraday Soc. 32, 49 (1961).

Tanabe, Y., and S. Sugano, J. Phys. Soc. Japan 9, 753, 766 (1954).

Tananaev, I. V., and B. F. Dzhurinskii, Dokl. Akad. Nauk SSSR 134, 1374 (1960).

Van Vleck, J. H., The Theory of Electric and Magnetic Susceptibilities, Oxford University
Press, London and New York, 1932.

Van Vleck, J. H., J. Chem. Phys. 3, 807 (1935).

Walsh, A. D., J. Chem. Soc. 1953, 2301.

Weakliem, H. A., J. Chem. Phys. 36, 2117 (1962).

Wolfsberg, M., and L. Helmholz, |. Chem. Phys. 20, 837 (1952).
Young, J. P., and J. C. White, Anal. Chem. 31, 1892 (1959).
Young, J. P., and J. C. White, Anal. Chem. 32, 799 (1960).
Young, J. P., and J. C. White, Anal. Chem. 32, 1658 (1960).

Zarzycki, J. ‘‘Faraday Effect in Fused Salts,”’ pp 94-95 in Proceedings of the Seventh
International Conference on Coordination Chemistry, Stockbolm and Uppsala, Sweden, June
2529, 1962, Almquist and Wiksell, Uppsala.

Zimmemman, G., and F. C. Strong, |. Am. Chem. Soc. 79, 2063 (1957).

 
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