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Discrete Variable Representation (DVR) for Rovibrational structure of a closed-shell diatomic molecule

This repository contains code that computes the rovibrational structure of a diatomic molecule in a given closed-shell electronic potential curve. The eigensystem is obtained by using Discrete Variable Representation (DVR).

Overview

The DVR Hamiltonian for a given potential energy curve + rotational structure is implemented using a Fourier basis and an uniform grid approach, it follows reference J. Chem. Phys. 96(3) 1982 (1992). For radial coordinates, the represetation uses eigenfunctions of a particle-in-a-box for a semi-infinite interval and the mass is included explicitly in the kinetic energy operator.

Input

  • Electronic potential energy curve file: it should have two columns, 1st: radial coordinate and 2nd: potential energy
  • Input file: DVR step, reduced mass of the molecule in amu, maximum values of the rotational and vibrational quantum number to be considered.

Output

  • Eigensystem written in an external files.
  • Scalar product of the wavefunctions to check orthonormality.
  • Comparition between the Dumham expation series (only for LiCs) and the eigenenergies obtained.

Main program

The main program rovib.f90 is set to computed the rovibrational structure of a LiCs in the electronic state, with and . The potential energy curve for this state is shown in the figure below:

[Figure]

The main program uses other routines to interpolate the curve values (spline.90) integrate the eigenfunctions to check orthonormality (double_integral.f90) and change measurement units (unit_convertion.f90).

Results folder

This folder has the output files from the LiCs example.

Use for other examples

In order to run other examples, you must supply the potential energy curve file (molecule_PEC.in) and set the input values for your system.

How to run it

It can be run normally as a regular Fortran program after compilation with:

gfortran -w unit_conversion.f90 spline.f90 integration_double.f90 rovib.f90 -o rovib2 -llapack -lblas

Or it can be used in Python running Numpy's f2py with the following command:

python3 -m numpy.f2py -c rovib.f90 spline.f90 unit_conversion.f90 integration_double.f90 /usr/lib/x86_64-linux-gnu/lapack/liblapack.so -m rovibpy

LAPACK needs to be installed in order to run the command above, and you may have to change the location of the liblapack file if it's located in a different place (check its location by running dpkg -L liblapack3).

References

This program was written by Felipe Herrera and modified by Vanessa Olaya as a part of her Master thesis project.