diff --git a/src/api/sirius_api.cpp b/src/api/sirius_api.cpp
index e6f1961c3..c3b1f4aff 100644
--- a/src/api/sirius_api.cpp
+++ b/src/api/sirius_api.cpp
@@ -851,7 +851,7 @@ sirius_set_parameters(void* const* handler__, int const* lmax_apw__, int const*
                 }
                 if (hubbard_full_orthogonalization__ != nullptr) {
                     if (*hubbard_full_orthogonalization__) {
-                        sim_ctx.cfg().hubbard().full_orthogonalization(true);
+                        sim_ctx.cfg().hubbard().hubbard_subspace_method("full_orthogonalization");
                     }
                 }
 
@@ -862,12 +862,17 @@ sirius_set_parameters(void* const* handler__, int const* lmax_apw__, int const*
                 if (hubbard_orbitals__ != nullptr) {
                     std::string s(hubbard_orbitals__);
                     std::transform(s.begin(), s.end(), s.begin(), ::tolower);
+                    bool jump = false;
                     if (s == "ortho-atomic") {
-                        sim_ctx.cfg().hubbard().orthogonalize(true);
-                        sim_ctx.cfg().hubbard().full_orthogonalization(true);
+                        sim_ctx.cfg().hubbard().hubbard_subspace_method("full_orthogonalization");
+                        jump = true;
                     }
                     if (s == "norm-atomic") {
-                        sim_ctx.cfg().hubbard().normalize(true);
+                        sim_ctx.cfg().hubbard().hubbard_subspace_method("normalize");
+                        jump = true;
+                    }
+                    if (!jump) {
+                        sim_ctx.cfg().hubbard().hubbard_subspace_method(s);
                     }
                 }
                 if (fft_grid_size__ != nullptr) {
@@ -2240,8 +2245,29 @@ sirius_set_atom_type_hubbard(void* const* handler__, char const* label__, int co
                 auto& sim_ctx = get_sim_ctx(handler__);
                 auto& type    = sim_ctx.unit_cell().atom_type(std::string(label__));
                 type.hubbard_correction(true);
-                type.add_hubbard_orbital(*n__, *l__, *occ__, *U__, J__[1], J__, *alpha__, *beta__, *J0__,
-                                         std::vector<double>(), true);
+                if (type.file_name().empty()) {
+                    type.add_hubbard_orbital(*n__, *l__, *occ__, *U__, J__[1], J__, *alpha__, *beta__, *J0__,
+                                             std::vector<double>(), true);
+                } else {
+                    // we use a an external file containing the potential
+                    // information which means that we do not have all information
+                    // yet.
+                    //
+                    // let's build the local hubbard section instead
+                    //
+
+                    json elem;
+
+                    elem["atom_type"]               = label__;
+                    elem["n"]                       = *n__;
+                    elem["l"]                       = *l__;
+                    elem["total_initial_occupancy"] = *occ__;
+                    elem["U"]                       = *U__;
+                    elem["J"]                       = *J__;
+                    elem["alpha"]                   = *alpha__;
+                    elem["beta"]                    = *beta__;
+                    sim_ctx.cfg().hubbard().local().append(elem);
+                }
             },
             error_code__);
 }
diff --git a/src/context/config.hpp b/src/context/config.hpp
index a39e43f2b..55a6dcc63 100644
--- a/src/context/config.hpp
+++ b/src/context/config.hpp
@@ -1587,41 +1587,17 @@ class config_t
             : dict_(dict__)
         {
         }
-        /// If true, orthogonalization is applied to Hubbard orbitals.
-        inline auto orthogonalize() const
+        /// Method to use for generating the hubbard subspace. [none] bare hubbard orbitals,  [full_orthogonaliation] use all atomic wave functions to generate the hubbard subspace, [normalize] normalize the original hubbard wave functions, [orthogonalize] orthogonalize the hubbard wave functions
+        inline auto hubbard_subspace_method() const
         {
-            return dict_.at("/hubbard/orthogonalize"_json_pointer).get<bool>();
+            return dict_.at("/hubbard/hubbard_subspace_method"_json_pointer).get<std::string>();
         }
-        inline void orthogonalize(bool orthogonalize__)
+        inline void hubbard_subspace_method(std::string hubbard_subspace_method__)
         {
             if (dict_.contains("locked")) {
                 throw std::runtime_error(locked_msg);
             }
-            dict_["/hubbard/orthogonalize"_json_pointer] = orthogonalize__;
-        }
-        /// If true, all atomic orbitals from all atoms are used to orthogonalize the hubbard subspace
-        inline auto full_orthogonalization() const
-        {
-            return dict_.at("/hubbard/full_orthogonalization"_json_pointer).get<bool>();
-        }
-        inline void full_orthogonalization(bool full_orthogonalization__)
-        {
-            if (dict_.contains("locked")) {
-                throw std::runtime_error(locked_msg);
-            }
-            dict_["/hubbard/full_orthogonalization"_json_pointer] = full_orthogonalization__;
-        }
-        /// If true, normalization is applied to Hubbard orbitals.
-        inline auto normalize() const
-        {
-            return dict_.at("/hubbard/normalize"_json_pointer).get<bool>();
-        }
-        inline void normalize(bool normalize__)
-        {
-            if (dict_.contains("locked")) {
-                throw std::runtime_error(locked_msg);
-            }
-            dict_["/hubbard/normalize"_json_pointer] = normalize__;
+            dict_["/hubbard/hubbard_subspace_method"_json_pointer] = hubbard_subspace_method__;
         }
         /// If true, simplified version of Hubbard correction is used.
         inline auto simplified() const
diff --git a/src/context/input_schema.json b/src/context/input_schema.json
index fb760323b..83018cf89 100644
--- a/src/context/input_schema.json
+++ b/src/context/input_schema.json
@@ -854,20 +854,16 @@
             "type": "object",
             "title": "Hubbard U correction",
             "properties": {
-                "orthogonalize": {
-                    "type": "boolean",
-                    "default": false,
-                    "title": "If true, orthogonalization is applied to Hubbard orbitals."
-                },
-                "full_orthogonalization": {
-                    "type": "boolean",
-                    "default": false,
-                    "title": "If true, all atomic orbitals from all atoms are used to orthogonalize the hubbard subspace"
-                },
-                "normalize": {
-                    "type": "boolean",
-                    "default": false,
-                    "title": "If true, normalization is applied to Hubbard orbitals."
+                "hubbard_subspace_method": {
+                    "type": "string",
+                    "default": "none",
+                    "enum": [
+                        "none",
+                        "full_orthogonalization",
+                        "normalize",
+                        "orthogonalize"
+                    ],
+                    "title": "Method to use for generating the hubbard subspace. [none] bare hubbard orbitals,  [full_orthogonaliation] use all atomic wave functions to generate the hubbard subspace, [normalize] normalize the original hubbard wave functions, [orthogonalize] orthogonalize the hubbard wave functions"
                 },
                 "simplified": {
                     "type": "boolean",
diff --git a/src/hubbard/hubbard_occupancies_derivatives.cpp b/src/hubbard/hubbard_occupancies_derivatives.cpp
index 052cdfc37..276c392f4 100644
--- a/src/hubbard/hubbard_occupancies_derivatives.cpp
+++ b/src/hubbard/hubbard_occupancies_derivatives.cpp
@@ -78,7 +78,7 @@ build_phi_hub_s_psi_deriv(Simulation_context const& ctx__, int nbnd__, int nawf_
                 int offset_in_wf  = atomic_wf_offset__[ia] + type.indexb_wfs().index_of(rf_index(idxr_wf));
                 int offset_in_hwf = hubbard_wf_offset__[ia] + type.indexb_hub().index_of(e.idxrf);
 
-                if (ctx__.cfg().hubbard().full_orthogonalization()) {
+                if (ctx__.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
                     /* compute \sum_{m} d/d r_{alpha} O^{-1/2}_{m,i} <phi_atomic_{m} | S | psi_{jk} > */
                     la::wrap(la::lib_t::blas)
                             .gemm('C', 'N', mmax, nbnd__, nawf__, &la::constant<std::complex<double>>::one(),
@@ -174,7 +174,7 @@ Hubbard::compute_occupancies_derivatives(K_point<double>& kp__, Q_operator<doubl
     std::unique_ptr<la::dmatrix<std::complex<double>>> inv_sqrt_O;
     std::unique_ptr<la::dmatrix<std::complex<double>>> evec_O;
     std::vector<double> eval_O;
-    if (ctx_.cfg().hubbard().full_orthogonalization()) {
+    if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
         ovlp = la::dmatrix<std::complex<double>>(nawf, nawf);
         wf::inner(ctx_.spla_context(), mt, wf::spin_range(0), phi_atomic, wf::band_range(0, nawf), phi_atomic_S,
                   wf::band_range(0, nawf), ovlp, 0, 0);
@@ -231,7 +231,7 @@ Hubbard::compute_occupancies_derivatives(K_point<double>& kp__, Q_operator<doubl
 
         /* compute < d phi_atomic / d r_{alpha} | S | phi_atomic >
          * used to compute derivative of the inverse square root of the overlap matrix */
-        if (ctx_.cfg().hubbard().full_orthogonalization()) {
+        if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
             grad_phi_atomic_s_phi_atomic[x] = la::dmatrix<std::complex<double>>(nawf, nawf);
             wf::inner(ctx_.spla_context(), mt, wf::spin_range(0), *s_phi_atomic_tmp, wf::band_range(0, nawf),
                       phi_atomic, wf::band_range(0, nawf), grad_phi_atomic_s_phi_atomic[x], 0, 0);
@@ -249,7 +249,7 @@ Hubbard::compute_occupancies_derivatives(K_point<double>& kp__, Q_operator<doubl
 
     /* compute <phi_atomic | S | psi_{ik} > */
     std::array<la::dmatrix<std::complex<double>>, 2> phi_atomic_s_psi;
-    if (ctx_.cfg().hubbard().full_orthogonalization()) {
+    if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
         for (int ispn = 0; ispn < ctx_.num_spins(); ispn++) {
             phi_atomic_s_psi[ispn] = la::dmatrix<std::complex<double>>(nawf, kp__.num_occupied_bands(ispn));
             /* compute < phi_atomic | S | psi_{ik} > for all atoms */
@@ -312,7 +312,7 @@ Hubbard::compute_occupancies_derivatives(K_point<double>& kp__, Q_operator<doubl
                 /* from O = <phi | S | phi > we get
                  * O' = <phi' | S | phi> + <phi | S' |phi> + <phi | S | phi'> */
 
-                if (ctx_.cfg().hubbard().full_orthogonalization()) {
+                if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
                     /* <phi | S' | phi> */
                     wf::inner(ctx_.spla_context(), mt, wf::spin_range(0), phi_atomic, wf::band_range(0, nawf),
                               *phi_atomic_tmp, wf::band_range(0, nawf), ovlp, 0, 0);
@@ -463,7 +463,7 @@ Hubbard::compute_occupancies_stress_derivatives(K_point<double>& kp__, Q_operato
     std::unique_ptr<la::dmatrix<std::complex<double>>> inv_sqrt_O;
     std::unique_ptr<la::dmatrix<std::complex<double>>> evec_O;
     std::vector<double> eval_O;
-    if (ctx_.cfg().hubbard().full_orthogonalization()) {
+    if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
         ovlp = la::dmatrix<std::complex<double>>(nawf, nawf);
         wf::inner(ctx_.spla_context(), mt, wf::spin_range(0), phi_atomic, wf::band_range(0, nawf), phi_atomic_S,
                   wf::band_range(0, nawf), ovlp, 0, 0);
@@ -477,7 +477,7 @@ Hubbard::compute_occupancies_stress_derivatives(K_point<double>& kp__, Q_operato
 
     /* compute <phi_atomic | S | psi_{ik} > */
     std::array<la::dmatrix<std::complex<double>>, 2> phi_atomic_s_psi;
-    if (ctx_.cfg().hubbard().full_orthogonalization()) {
+    if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
         for (int ispn = 0; ispn < ctx_.num_spins(); ispn++) {
             phi_atomic_s_psi[ispn] = la::dmatrix<std::complex<double>>(nawf, kp__.num_occupied_bands(ispn));
             /* compute < phi_atomic | S | psi_{ik} > for all atoms */
@@ -508,7 +508,7 @@ Hubbard::compute_occupancies_stress_derivatives(K_point<double>& kp__, Q_operato
             sirius::apply_S_operator_strain_deriv(mt, 3 * nu + mu, bp_gen, bp_coeffs, bp_strain_gen, bp_strain_coeffs,
                                                   phi_atomic, q_op__, *ds_phi_atomic);
 
-            if (ctx_.cfg().hubbard().full_orthogonalization()) {
+            if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
                 /* compute <phi_atomic | ds/d epsilon | phi_atomic> */
                 wf::inner(ctx_.spla_context(), mt, wf::spin_range(0), phi_atomic, wf::band_range(0, nawf),
                           *ds_phi_atomic, wf::band_range(0, nawf), ovlp, 0, 0);
diff --git a/src/k_point/k_point.cpp b/src/k_point/k_point.cpp
index 6c32bb6cd..d15a00cfa 100644
--- a/src/k_point/k_point.cpp
+++ b/src/k_point/k_point.cpp
@@ -238,7 +238,7 @@ K_point<T>::generate_hubbard_orbitals()
         sirius::apply_S_operator<T, std::complex<T>>(mem, wf::spin_range(0), wf::band_range(0, nwf), bp_gen, bp_coeffs,
                                                      *atomic_wave_functions_, q_op.get(), *atomic_wave_functions_S_);
 
-        if (ctx_.cfg().hubbard().full_orthogonalization()) {
+        if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
             /* save phi and sphi */
 
             wf_tmp  = std::make_unique<wf::Wave_functions<T>>(gkvec_, wf::num_mag_dims(0), wf::num_bands(nwf),
@@ -319,7 +319,7 @@ K_point<T>::generate_hubbard_orbitals()
         }
     }
     /* restore phi and sphi */
-    if (ctx_.cfg().hubbard().full_orthogonalization()) {
+    if (ctx_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
 
         wf::copy(memory_t::host, *wf_tmp, wf::spin_index(0), wf::band_range(0, nwf), *atomic_wave_functions_,
                  wf::spin_index(0), wf::band_range(0, nwf));
diff --git a/src/unit_cell/atom_type.cpp b/src/unit_cell/atom_type.cpp
index a7ae92227..5388ce606 100644
--- a/src/unit_cell/atom_type.cpp
+++ b/src/unit_cell/atom_type.cpp
@@ -358,13 +358,15 @@ Atom_type::print_info(std::ostream& out__) const
             }
             out__ << lo_descriptors_hub_[i];
         }
+
+        bool orthogonalize_ = parameters_.cfg().hubbard().hubbard_subspace_method() == "orthogonalize";
+        bool full_orthogonalization_ =
+                parameters_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization";
+        bool normalize_ = parameters_.cfg().hubbard().hubbard_subspace_method() == "normalize";
         out__ << std::endl;
-        out__ << "  orthogonalize                      : " << boolstr(parameters_.cfg().hubbard().orthogonalize())
-              << std::endl
-              << "  normalize                          : " << boolstr(parameters_.cfg().hubbard().normalize())
-              << std::endl
-              << "  full_orthogonalization             : "
-              << boolstr(parameters_.cfg().hubbard().full_orthogonalization()) << std::endl
+        out__ << "  orthogonalize                      : " << boolstr(orthogonalize_) << std::endl
+              << "  normalize                          : " << boolstr(normalize_) << std::endl
+              << "  full_orthogonalization             : " << boolstr(full_orthogonalization_) << std::endl
               << "  simplified                         : " << boolstr(parameters_.cfg().hubbard().simplified())
               << std::endl;
     }
@@ -858,7 +860,7 @@ Atom_type::read_hubbard_input()
         }
     }
 
-    if (parameters_.cfg().hubbard().full_orthogonalization()) {
+    if (parameters_.cfg().hubbard().hubbard_subspace_method() == "full_orthogonalization") {
         this->hubbard_correction_ = true;
         if (lo_descriptors_hub_.empty()) {
             for (int s = 0; s < (int)ps_atomic_wfs_.size(); s++) {
diff --git a/verification/test22/output_ref.json b/verification/test22/output_ref.json
index c15104414..2824f7283 100644
--- a/verification/test22/output_ref.json
+++ b/verification/test22/output_ref.json
@@ -5,35 +5,38 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 32,
-                "fft_mode": "serial",
+                "fft_mode": "parallel",
                 "gen_evp_solver_name": "lapack",
-                "memory_usage": "high",
+                "gvec_chunk_size": 500000,
                 "mpi_grid_dims": [
                     1,
                     1
                 ],
                 "num_bands_to_print": 10,
                 "ortho_rf": false,
-                "print_checksum": false,
+                "output": "stdout:",
                 "print_forces": true,
-                "print_hash": false,
-                "print_memory_usage": false,
                 "print_neighbors": false,
-                "print_performance": false,
                 "print_stress": true,
-                "print_timers": true,
                 "processing_unit": "cpu",
                 "reduce_gvec": true,
                 "rmt_max": 2.2,
-                "spglib_tolerance": 0.0001,
+                "spglib_tolerance": 1e-06,
                 "std_evp_solver_name": "lapack",
                 "use_second_variation": true,
                 "verbosity": 2,
                 "verification": 0
             },
             "hubbard": {
-                "full_orthogonalization": false,
+                "constrained_calculation": false,
+                "constraint_beta_mixing": 0.4,
+                "constraint_error": 1e-06,
+                "constraint_max_iteration": 10,
+                "constraint_method": "energy",
+                "constraint_strength": 1.0,
+                "hubbard_subspace_method": "none",
                 "local": [
                     {
                         "J": 0.0,
@@ -45,9 +48,8 @@
                         "total_initial_occupancy": 8
                     }
                 ],
+                "local_constraint": [],
                 "nonlocal": [],
-                "normalize": false,
-                "orthogonalize": false,
                 "simplified": true
             },
             "iterative_solver": {
@@ -81,6 +83,7 @@
                 "T": 300.0,
                 "kappa": 0.3,
                 "maxiter": 300,
+                "processing_unit": "",
                 "restart": 10,
                 "tau": 0.1,
                 "tol": 1e-09
@@ -97,8 +100,8 @@
                 "gk_cutoff": 6.325,
                 "hubbard_correction": true,
                 "lmax_apw": -1,
-                "lmax_pot": 4,
-                "lmax_rho": 4,
+                "lmax_pot": -1,
+                "lmax_rho": -1,
                 "molecule": false,
                 "ngridk": [
                     4,
@@ -212,6 +215,16 @@
                     ]
                 ],
                 "lattice_vectors_scale": 1.0
+            },
+            "vcsqnm": {
+                "alpha0": 0.01,
+                "eps_subsp": 0.001,
+                "forces_tol": 0.0001,
+                "initial_step_size": -0.1,
+                "lattice_weight": 2.0,
+                "nhist_max": 10,
+                "num_steps": 300,
+                "stress_tol": 1e-05
             }
         },
         "fft_coarse_grid": [
@@ -224,55 +237,66 @@
             1
         ],
         "num_atoms": 4,
-        "omega": 249.33862849999997
+        "omega": 249.3386285
     },
     "counters": {
-        "band_evp_work_count": 5141.447995115001,
-        "local_operator_num_applied": 39628
+        "band_evp_work_count": 6094.895786688399,
+        "local_operator_num_applied": 53141
     },
-    "git_hash": "ce6ae705e2870be0b66928bcce68667b3c0cdf49",
+    "git_hash": "bd14a5684ad99f193820ddeaa5247058e7cc21f4",
     "ground_state": {
-        "band_gap": 0.10974174153770971,
+        "band_gap": 0.10974172760116385,
         "converged": true,
-        "core_leakage": 0.0,
-        "efermi": 0.5246334957773069,
+        "efermi": 0.5246334556620487,
         "energy": {
-            "bxc": -0.21533660045621467,
-            "core_eval_sum": 0.0,
-            "entropy_sum": -2.468095155091394e-16,
-            "enuc": 0.0,
-            "eval_sum": -27.46239309559973,
-            "ewald": -237.8225283083057,
-            "exc": -42.93999555007287,
-            "kin": 114.98833840923253,
-            "scf_correction": -8.543736385036027e-08,
-            "total": -375.38903762575023,
-            "veff": -142.23539490437605,
-            "vha": 246.75254182494697,
-            "vloc": -335.33821793272693,
-            "vxc": -53.6497187965967
+            "bxc": -0.2153364979074735,
+            "entropy_sum": -2.467979438715347e-16,
+            "eval_sum": -27.462395753275004,
+            "ewald": -237.82252835243912,
+            "exc": -42.939995185083696,
+            "kin": 114.98833783810144,
+            "scf_correction": -1.1304166491754586e-09,
+            "total": -375.3890376308642,
+            "veff": -142.23539709346898,
+            "vha": 246.75253646841466,
+            "vloc": -335.3382151243094,
+            "vxc": -53.64971843757389
         },
         "etot_history": [
-            -359.0918985584859,
-            -370.84096812724385,
-            -373.99733375306323,
-            -374.9262348738466,
-            -374.8800418937111,
-            -375.3691863584895,
-            -375.3522202716779,
-            -375.39878595543917,
-            -375.3886962095654,
-            -375.3888452121745,
-            -375.38946907692196,
-            -375.3890395134396,
-            -375.3890169010583,
-            -375.38905486659564,
-            -375.38904996549076,
-            -375.38903472902916,
-            -375.3890366040884,
-            -375.38903725582543,
-            -375.3890376169785,
-            -375.38903762575023
+            -358.4084383387285,
+            -370.87678391559444,
+            -373.82390452188343,
+            -375.11651120379673,
+            -374.94523565019944,
+            -375.321392013332,
+            -375.2291798715251,
+            -375.41123130892936,
+            -375.3925709189242,
+            -375.38716424885126,
+            -375.38898244277743,
+            -375.38886923760765,
+            -375.38907555920605,
+            -375.3890417664653,
+            -375.38905947455726,
+            -375.38905489646515,
+            -375.38902894787884,
+            -375.3890345423415,
+            -375.38903681850707,
+            -375.3890377418872,
+            -375.38903764566606,
+            -375.38903762273264,
+            -375.3890376433061,
+            -375.38903762737544,
+            -375.3890376312384,
+            -375.3890376308435,
+            -375.38903763079304,
+            -375.38903763091844,
+            -375.38903763102815,
+            -375.3890376309063,
+            -375.38903763090457,
+            -375.3890376308841,
+            -375.3890376308776,
+            -375.3890376308642
         ],
         "forces": [
             [
@@ -286,58 +310,73 @@
                 0.0
             ],
             [
-                -2.154001144332873e-27,
-                -1.0771076498589902e-27,
-                1.0770745720121956e-27
+                1.723271577835958e-26,
+                4.3081961752431304e-26,
+                -3.446581809085899e-26
             ],
             [
-                3.231209207364338e-27,
-                -2.1541513909426594e-27,
-                -1.0768558024199293e-27
+                1.7233257927638924e-26,
+                -2.5849479910362307e-26,
+                3.44658629650267e-26
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         ],
-        "num_scf_iterations": 19,
+        "num_scf_iterations": 33,
+        "rho_min": 0.011102112306705672,
         "rms_history": [
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+            2.455305444225234e-10,
+            2.542183283796671e-10,
+            2.45257032120946e-10
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-        "scf_time": 84.010706007,
+        "scf_time": 60.561824894,
         "stress": [
             [
-                -8.490828646799675e-05,
-                8.476751189883732e-06,
-                8.476751189883722e-06
+                -8.489845282177479e-05,
+                8.461485223347476e-06,
+                8.461485223347481e-06
             ],
             [
-                8.476751189883732e-06,
-                -8.4908286467969e-05,
-                8.476751189883722e-06
+                8.461485223347476e-06,
+                -8.489845282180428e-05,
+                8.461485223347475e-06
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             [
-                8.476751189883722e-06,
-                8.476751189883722e-06,
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+                -8.489845282186673e-05
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         ]
     },
     "task": 0,
-    "threads_per_rank": 16
+    "threads_per_rank": 4
 }
\ No newline at end of file
diff --git a/verification/test22/sirius.json b/verification/test22/sirius.json
index 0ed42b70a..31346c395 100644
--- a/verification/test22/sirius.json
+++ b/verification/test22/sirius.json
@@ -68,7 +68,6 @@
                   }
     },
     "hubbard" : {
-        "full_orthogonalization": false,
         "simplified" : true,
         "local" : [
             {
diff --git a/verification/test24/output_ref.json b/verification/test24/output_ref.json
index 07b08c775..248cce92c 100644
--- a/verification/test24/output_ref.json
+++ b/verification/test24/output_ref.json
@@ -5,35 +5,38 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 32,
-                "fft_mode": "serial",
+                "fft_mode": "parallel",
                 "gen_evp_solver_name": "lapack",
-                "memory_usage": "high",
+                "gvec_chunk_size": 500000,
                 "mpi_grid_dims": [
                     1,
                     1
                 ],
                 "num_bands_to_print": 10,
                 "ortho_rf": false,
-                "print_checksum": false,
+                "output": "stdout:",
                 "print_forces": true,
-                "print_hash": false,
-                "print_memory_usage": false,
                 "print_neighbors": false,
-                "print_performance": false,
                 "print_stress": false,
-                "print_timers": true,
                 "processing_unit": "cpu",
                 "reduce_gvec": true,
                 "rmt_max": 2.2,
-                "spglib_tolerance": 0.0001,
+                "spglib_tolerance": 1e-06,
                 "std_evp_solver_name": "lapack",
                 "use_second_variation": true,
-                "verbosity": 2,
+                "verbosity": 1,
                 "verification": 0
             },
             "hubbard": {
-                "full_orthogonalization": false,
+                "constrained_calculation": false,
+                "constraint_beta_mixing": 0.4,
+                "constraint_error": 1e-06,
+                "constraint_max_iteration": 10,
+                "constraint_method": "energy",
+                "constraint_strength": 1.0,
+                "hubbard_subspace_method": "none",
                 "local": [
                     {
                         "J": 0.0,
@@ -58,6 +61,7 @@
                         "total_initial_occupancy": 6.0
                     }
                 ],
+                "local_constraint": [],
                 "nonlocal": [
                     {
                         "T": [
@@ -540,8 +544,6 @@
                         ]
                     }
                 ],
-                "normalize": false,
-                "orthogonalize": false,
                 "simplified": false
             },
             "iterative_solver": {
@@ -575,6 +577,7 @@
                 "T": 300.0,
                 "kappa": 0.3,
                 "maxiter": 300,
+                "processing_unit": "",
                 "restart": 10,
                 "tau": 0.1,
                 "tol": 1e-09
@@ -591,8 +594,8 @@
                 "gk_cutoff": 8.0,
                 "hubbard_correction": true,
                 "lmax_apw": -1,
-                "lmax_pot": 4,
-                "lmax_rho": 4,
+                "lmax_pot": -1,
+                "lmax_rho": -1,
                 "molecule": false,
                 "ngridk": [
                     4,
@@ -706,6 +709,16 @@
                     ]
                 ],
                 "lattice_vectors_scale": 1.0
+            },
+            "vcsqnm": {
+                "alpha0": 0.01,
+                "eps_subsp": 0.001,
+                "forces_tol": 0.0001,
+                "initial_step_size": -0.1,
+                "lattice_weight": 2.0,
+                "nhist_max": 10,
+                "num_steps": 300,
+                "stress_tol": 1e-05
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         },
         "fft_coarse_grid": [
@@ -721,52 +734,62 @@
         "omega": 244.65193599999998
     },
     "counters": {
-        "band_evp_work_count": 5453.145888459187,
-        "local_operator_num_applied": 41210
+        "band_evp_work_count": 6158.010482393651,
+        "local_operator_num_applied": 52573
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-    "git_hash": "e9f2d4bb3608d5c83dc05e3efb31a11ff7bf1c05",
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     "ground_state": {
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-            "vha": 245.4767965268977,
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         "forces": [
             [
@@ -780,41 +803,55 @@
                 0.0
             ],
             [
-                6.77625280764636e-21,
-                1.552895029097067e-20,
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+                2.876857854428433e-32,
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+                -9.68093569360508e-27
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-        "num_scf_iterations": 19,
+        "num_scf_iterations": 32,
+        "rho_min": 0.011482845699626917,
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+        "scf_time": 78.107713213
     },
     "task": 0,
-    "threads_per_rank": 16
+    "threads_per_rank": 4
 }
\ No newline at end of file
diff --git a/verification/test24/sirius.json b/verification/test24/sirius.json
index aae8a761b..588bcacb8 100644
--- a/verification/test24/sirius.json
+++ b/verification/test24/sirius.json
@@ -5,7 +5,6 @@
         "verbosity": 1
     },
     "hubbard": {
-        "full_orthogonalization": false,
         "local": [
             {
                 "atom_type": "Ni",
diff --git a/verification/test25/output_ref.json b/verification/test25/output_ref.json
index dd195b37b..5fefaa7f0 100644
--- a/verification/test25/output_ref.json
+++ b/verification/test25/output_ref.json
@@ -5,35 +5,38 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 32,
-                "fft_mode": "serial",
+                "fft_mode": "parallel",
                 "gen_evp_solver_name": "lapack",
-                "memory_usage": "high",
+                "gvec_chunk_size": 500000,
                 "mpi_grid_dims": [
                     1,
                     1
                 ],
                 "num_bands_to_print": 10,
                 "ortho_rf": false,
-                "print_checksum": false,
+                "output": "stdout:",
                 "print_forces": true,
-                "print_hash": false,
-                "print_memory_usage": false,
                 "print_neighbors": false,
-                "print_performance": false,
                 "print_stress": false,
-                "print_timers": true,
                 "processing_unit": "cpu",
                 "reduce_gvec": true,
                 "rmt_max": 2.2,
-                "spglib_tolerance": 0.0001,
+                "spglib_tolerance": 1e-06,
                 "std_evp_solver_name": "lapack",
                 "use_second_variation": true,
                 "verbosity": 2,
                 "verification": 0
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             "hubbard": {
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+                "constrained_calculation": false,
+                "constraint_beta_mixing": 0.4,
+                "constraint_error": 1e-06,
+                "constraint_max_iteration": 10,
+                "constraint_method": "energy",
+                "constraint_strength": 1.0,
+                "hubbard_subspace_method": "full_orthogonalization",
                 "local": [
                     {
                         "J": 0.0,
@@ -47,9 +50,8 @@
                         "total_initial_occupancy": 8.0
                     }
                 ],
+                "local_constraint": [],
                 "nonlocal": [],
-                "normalize": false,
-                "orthogonalize": false,
                 "simplified": false
             },
             "iterative_solver": {
@@ -71,7 +73,7 @@
             },
             "locked": true,
             "mixer": {
-                "beta": 0.7,
+                "beta": 0.5,
                 "beta0": 0.15,
                 "beta_scaling_factor": 1.0,
                 "linear_mix_rms_tol": 1000000.0,
@@ -83,6 +85,7 @@
                 "T": 300.0,
                 "kappa": 0.3,
                 "maxiter": 300,
+                "processing_unit": "",
                 "restart": 10,
                 "tau": 0.1,
                 "tol": 1e-09
@@ -99,8 +102,8 @@
                 "gk_cutoff": 8.0,
                 "hubbard_correction": true,
                 "lmax_apw": -1,
-                "lmax_pot": 4,
-                "lmax_rho": 4,
+                "lmax_pot": -1,
+                "lmax_rho": -1,
                 "molecule": false,
                 "ngridk": [
                     4,
@@ -214,6 +217,16 @@
                     ]
                 ],
                 "lattice_vectors_scale": 1.0
+            },
+            "vcsqnm": {
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+                "nhist_max": 10,
+                "num_steps": 300,
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         "fft_coarse_grid": [
@@ -229,54 +242,66 @@
         "omega": 244.65193599999998
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     "counters": {
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-        "local_operator_num_applied": 44814
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+            -375.403505084502,
+            -375.4035051163303,
+            -375.4035050844166,
+            -375.4035050542828,
+            -375.4035050072227,
+            -375.40350502166757,
+            -375.403505114621,
+            -375.40350508756666,
+            -375.4035050783742,
+            -375.40350507656706,
+            -375.4035050756796,
+            -375.40350507090795,
+            -375.40350507376155,
+            -375.4035050739261
         ],
         "forces": [
             [
@@ -290,43 +315,59 @@
                 0.0
             ],
             [
-                -0.003147380200048457,
-                -0.003147380200048471,
-                -0.003147380200048471
+                -0.0031472582171360656,
+                -0.0031472582171361073,
+                -0.0031472582171360795
             ],
             [
-                0.0031473802000484847,
-                0.003147380200048471,
-                0.003147380200048471
+                0.0031472582171360795,
+                0.0031472582171360795,
+                0.0031472582171360934
             ]
         ],
-        "num_scf_iterations": 21,
+        "num_scf_iterations": 36,
+        "rho_min": 0.011475481668429172,
         "rms_history": [
-            0.2608353227548882,
-            0.40858053508916237,
-            0.14421172485360406,
-            0.041156411707732835,
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-            0.008346834084517194,
-            0.006787574390022183,
-            0.003059261310011073,
-            0.0017782021845775772,
-            0.00036227811437645476,
-            0.00015023509806226333,
-            4.8187868205314456e-05,
-            2.622905749106282e-05,
-            2.2417964105640664e-05,
-            1.5211917520931938e-05,
-            7.513976811385638e-06,
-            2.418616766186595e-06,
-            1.4374599664458488e-06,
-            6.507210784613721e-07,
-            1.8600699115531217e-07
+            0.26083542472792376,
+            0.2957980492491547,
+            0.08752557935095763,
+            0.04860013029519488,
+            0.0440468309977496,
+            0.042179371739919154,
+            0.013616341571010718,
+            0.0049305478463861786,
+            0.004068627173199184,
+            0.0016711848358539495,
+            0.0007486507956986471,
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+            5.7420419825483055e-05,
+            2.904546933463338e-05,
+            1.9950335757937397e-05,
+            1.3346691842352391e-05,
+            5.905733262715128e-06,
+            4.1115962797466895e-06,
+            1.003734746140182e-06,
+            5.579930430637191e-07,
+            2.472257996237909e-07,
+            8.509055224221016e-08,
+            5.0891242948599986e-08,
+            3.515914890796067e-08,
+            4.492496161720844e-08,
+            3.006155291758761e-08,
+            3.2032644460567474e-08,
+            1.8071026715077872e-08,
+            1.3006767527641743e-08,
+            8.174931961367517e-09,
+            5.847816933936446e-09,
+            4.827506276379923e-09,
+            4.305504611000628e-09,
+            3.2185057222469003e-09,
+            2.2807992840266675e-08,
+            3.422334332627641e-09,
+            3.81031714969496e-09
         ],
-        "scf_time": 136.89833212
+        "scf_time": 83.969306889
     },
     "task": 0,
-    "threads_per_rank": 16
+    "threads_per_rank": 4
 }
\ No newline at end of file
diff --git a/verification/test25/sirius.json b/verification/test25/sirius.json
index 458d5fd12..8be0feb4d 100644
--- a/verification/test25/sirius.json
+++ b/verification/test25/sirius.json
@@ -1,13 +1,12 @@
 {
     "control": {
         "gen_evp_solver_name": "lapack",
-        "print_checksum": false,
         "print_forces": true,
         "processing_unit": "cpu",
         "verbosity": 2
     },
     "hubbard": {
-        "full_orthogonalization": true,
+        "hubbard_subspace_method": "full_orthogonalization",
         "local": [
             {
                 "atom_type": "Ni",
diff --git a/verification/test26/output_ref.json b/verification/test26/output_ref.json
index 3c93eb3fe..64fe9a5aa 100644
--- a/verification/test26/output_ref.json
+++ b/verification/test26/output_ref.json
@@ -5,35 +5,38 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 32,
-                "fft_mode": "serial",
+                "fft_mode": "parallel",
                 "gen_evp_solver_name": "lapack",
-                "memory_usage": "high",
+                "gvec_chunk_size": 500000,
                 "mpi_grid_dims": [
                     1,
                     1
                 ],
                 "num_bands_to_print": 10,
                 "ortho_rf": false,
-                "print_checksum": false,
+                "output": "stdout:",
                 "print_forces": true,
-                "print_hash": false,
-                "print_memory_usage": false,
                 "print_neighbors": false,
-                "print_performance": false,
                 "print_stress": true,
-                "print_timers": true,
                 "processing_unit": "cpu",
                 "reduce_gvec": true,
                 "rmt_max": 2.2,
-                "spglib_tolerance": 0.0001,
+                "spglib_tolerance": 1e-06,
                 "std_evp_solver_name": "lapack",
                 "use_second_variation": true,
                 "verbosity": 2,
                 "verification": 0
             },
             "hubbard": {
-                "full_orthogonalization": true,
+                "constrained_calculation": false,
+                "constraint_beta_mixing": 0.4,
+                "constraint_error": 1e-06,
+                "constraint_max_iteration": 10,
+                "constraint_method": "energy",
+                "constraint_strength": 1.0,
+                "hubbard_subspace_method": "full_orthogonalization",
                 "local": [
                     {
                         "J": 0.0,
@@ -45,9 +48,8 @@
                         "total_initial_occupancy": 8
                     }
                 ],
+                "local_constraint": [],
                 "nonlocal": [],
-                "normalize": false,
-                "orthogonalize": false,
                 "simplified": false
             },
             "iterative_solver": {
@@ -81,6 +83,7 @@
                 "T": 300.0,
                 "kappa": 0.3,
                 "maxiter": 300,
+                "processing_unit": "",
                 "restart": 10,
                 "tau": 0.1,
                 "tol": 1e-09
@@ -97,8 +100,8 @@
                 "gk_cutoff": 6.325,
                 "hubbard_correction": true,
                 "lmax_apw": -1,
-                "lmax_pot": 4,
-                "lmax_rho": 4,
+                "lmax_pot": -1,
+                "lmax_rho": -1,
                 "molecule": false,
                 "ngridk": [
                     4,
@@ -212,6 +215,16 @@
                     ]
                 ],
                 "lattice_vectors_scale": 1.0
+            },
+            "vcsqnm": {
+                "alpha0": 0.01,
+                "eps_subsp": 0.001,
+                "forces_tol": 0.0001,
+                "initial_step_size": -0.1,
+                "lattice_weight": 2.0,
+                "nhist_max": 10,
+                "num_steps": 300,
+                "stress_tol": 1e-05
             }
         },
         "fft_coarse_grid": [
@@ -224,61 +237,69 @@
             1
         ],
         "num_atoms": 4,
-        "omega": 249.33862849999997
+        "omega": 249.3386285
     },
     "counters": {
-        "band_evp_work_count": 6238.23570120089,
-        "local_operator_num_applied": 48595
+        "band_evp_work_count": 6688.102076124586,
+        "local_operator_num_applied": 58607
     },
-    "git_hash": "fc0597cef459d4d40fc311c62ff91198b238460a",
+    "git_hash": "bd14a5684ad99f193820ddeaa5247058e7cc21f4",
     "ground_state": {
-        "band_gap": 0.11290281496797305,
+        "band_gap": 0.11290281924384205,
         "converged": true,
-        "core_leakage": 0.0,
-        "efermi": 0.524603195877114,
+        "efermi": 0.5246031969631006,
         "energy": {
-            "bxc": -0.21860314932509944,
-            "core_eval_sum": 0.0,
-            "entropy_sum": -2.01531863354457e-16,
-            "enuc": 0.0,
-            "eval_sum": -27.43459627125252,
-            "ewald": -237.8173020943241,
-            "exc": -42.94622991112447,
-            "kin": 115.0079742325329,
-            "scf_correction": -1.6308047179336427e-07,
-            "total": -375.40235130515407,
-            "veff": -142.2239673544603,
-            "vha": 246.81645701452487,
-            "vloc": -335.38603447083693,
-            "vxc": -53.65438989814585
+            "bxc": -0.21860314224858918,
+            "entropy_sum": -2.015320078459703e-16,
+            "eval_sum": -27.43459641965039,
+            "ewald": -237.81730213845265,
+            "exc": -42.94622990705068,
+            "kin": 115.00797407028195,
+            "scf_correction": 3.447553353908006e-10,
+            "total": -375.4023513291656,
+            "veff": -142.22396734768375,
+            "vha": 246.81645700234358,
+            "vloc": -335.3860344486933,
+            "vxc": -53.65438990132177
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         "etot_history": [
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+            -375.4023513225519,
+            -375.40235132839825,
+            -375.40235132976545,
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+            -375.4023513290324,
+            -375.4023513291886,
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+            -375.4023513291813,
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+            -375.40235132919213,
+            -375.4023513291424,
+            -375.4023513291519,
+            -375.4023513291656
         ],
         "forces": [
             [
@@ -292,64 +313,76 @@
                 0.0
             ],
             [
-                -0.0030170646753711994,
-                -0.0030170646753712132,
-                -0.0030170646753711994
+                -0.0030171290616558795,
+                -0.003017129061655935,
+                -0.003017129061655935
             ],
             [
-                0.003017064675371227,
-                0.0030170646753712132,
-                0.0030170646753711994
+                0.0030171290616559073,
+                0.003017129061655935,
+                0.003017129061655921
             ]
         ],
-        "num_scf_iterations": 25,
+        "num_scf_iterations": 36,
+        "rho_min": 0.010971688340902341,
         "rms_history": [
-            0.2596323555656473,
-            0.42859956970267526,
-            0.15280128548289743,
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+            1.2613273373095966e-05,
+            6.025079405305266e-06,
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+            4.2694413600937465e-07,
+            8.002399724684633e-08,
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+            1.1904845779773785e-08,
+            7.699665802767538e-09,
+            5.794307245634845e-09,
+            2.9605929129422524e-09,
+            1.291136514214949e-09,
+            2.0662142732013067e-10,
+            1.0034045099485089e-10,
+            7.752706983962928e-11,
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+            6.683115843733248e-11,
+            5.3416643795689526e-11,
+            3.840764712243318e-11,
+            1.931539096430012e-11,
+            1.1920474807826677e-11
         ],
-        "scf_time": 130.905326636,
+        "scf_time": 67.42900069,
         "stress": [
             [
-                -0.00026776264852931483,
-                6.6095924659749335e-06,
-                6.609592465974934e-06
+                -0.000267761870508431,
+                6.609976010479542e-06,
+                6.6099760104795556e-06
             ],
             [
-                6.6095924659749335e-06,
-                -0.00026776264852932524,
-                6.609592465974954e-06
+                6.609976010479542e-06,
+                -0.0002677618705084466,
+                6.609976010479549e-06
             ],
             [
-                6.609592465974934e-06,
-                6.609592465974954e-06,
-                -0.00026776264852931483
+                6.6099760104795556e-06,
+                6.609976010479549e-06,
+                -0.00026776187050842927
             ]
         ]
     },
     "task": 0,
-    "threads_per_rank": 16
+    "threads_per_rank": 4
 }
\ No newline at end of file
diff --git a/verification/test26/sirius.json b/verification/test26/sirius.json
index 843439b18..db5308c32 100644
--- a/verification/test26/sirius.json
+++ b/verification/test26/sirius.json
@@ -66,7 +66,7 @@
                   }
     },
     "hubbard" : {
-        "full_orthogonalization": true,
+        "hubbard_subspace_method" :"full_orthogonalization",
         "local" : [
             {
                 "atom_type" : "Ni",
diff --git a/verification/test27/output_ref.json b/verification/test27/output_ref.json
index 23d1e6c83..6851bf086 100644
--- a/verification/test27/output_ref.json
+++ b/verification/test27/output_ref.json
@@ -5,43 +5,48 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 16,
                 "fft_mode": "parallel",
                 "gen_evp_solver_name": "lapack",
+                "gvec_chunk_size": 500000,
                 "mpi_grid_dims": [
                     1,
                     1
                 ],
                 "num_bands_to_print": 10,
                 "ortho_rf": false,
-                "print_checksum": false,
+                "output": "stdout:",
                 "print_forces": false,
-                "print_hash": false,
-                "print_memory_usage": false,
                 "print_neighbors": false,
-                "print_performance": false,
                 "print_stress": false,
-                "print_timers": true,
                 "processing_unit": "cpu",
                 "reduce_gvec": true,
                 "rmt_max": 2.2,
-                "spglib_tolerance": 9.999999747378752e-05,
+                "spglib_tolerance": 1e-06,
                 "std_evp_solver_name": "lapack",
                 "use_second_variation": true,
                 "verbosity": 1,
                 "verification": 0
             },
             "hubbard": {
-                "full_orthogonalization": true,
+                "constrained_calculation": false,
+                "constraint_beta_mixing": 0.4,
+                "constraint_error": 1e-06,
+                "constraint_max_iteration": 10,
+                "constraint_method": "energy",
+                "constraint_strength": 1.0,
+                "hubbard_subspace_method": "full_orthogonalization",
                 "local": [
                     {
-                        "U": 3.0,
+                        "U": 3,
                         "atom_type": "Co",
                         "l": 2,
                         "n": 3,
                         "total_initial_occupancy": 7
                     }
                 ],
+                "local_constraint": [],
                 "nonlocal": [
                     {
                         "T": [
@@ -49,7 +54,7 @@
                             0,
                             0
                         ],
-                        "V": 3.0,
+                        "V": 3,
                         "atom_pair": [
                             0,
                             1
@@ -69,7 +74,7 @@
                             -1,
                             -1
                         ],
-                        "V": 3.0,
+                        "V": 3,
                         "atom_pair": [
                             0,
                             2
@@ -89,7 +94,7 @@
                             0,
                             0
                         ],
-                        "V": 3.0,
+                        "V": 3,
                         "atom_pair": [
                             1,
                             0
@@ -109,7 +114,7 @@
                             1,
                             1
                         ],
-                        "V": 3.0,
+                        "V": 3,
                         "atom_pair": [
                             2,
                             0
@@ -124,8 +129,6 @@
                         ]
                     }
                 ],
-                "normalize": false,
-                "orthogonalize": false,
                 "simplified": false
             },
             "iterative_solver": {
@@ -159,6 +162,7 @@
                 "T": 300.0,
                 "kappa": 0.3,
                 "maxiter": 300,
+                "processing_unit": "",
                 "restart": 10,
                 "tau": 0.1,
                 "tol": 1e-09
@@ -175,8 +179,8 @@
                 "gk_cutoff": 7.0710678118654755,
                 "hubbard_correction": true,
                 "lmax_apw": -1,
-                "lmax_pot": 4,
-                "lmax_rho": 4,
+                "lmax_pot": -1,
+                "lmax_rho": -1,
                 "molecule": false,
                 "ngridk": [
                     2,
@@ -184,7 +188,7 @@
                     2
                 ],
                 "nn_radius": -1,
-                "num_bands": 16,
+                "num_bands": 26,
                 "num_dft_iter": 100,
                 "num_fv_states": -1,
                 "num_mag_dims": 0,
@@ -199,7 +203,7 @@
                     0
                 ],
                 "smearing": "gaussian",
-                "smearing_width": 0.0,
+                "smearing_width": 0.001,
                 "so_correction": false,
                 "use_ibz": true,
                 "use_scf_correction": true,
@@ -225,7 +229,7 @@
                 "itsol_tol_ratio": 0,
                 "itsol_tol_scale": [
                     0.1,
-                    0.95
+                    0.5
                 ],
                 "min_occupancy": 1e-14,
                 "mixer_rms_min": 1e-16,
@@ -294,6 +298,16 @@
                     ]
                 ],
                 "lattice_vectors_scale": 1.0
+            },
+            "vcsqnm": {
+                "alpha0": 0.01,
+                "eps_subsp": 0.001,
+                "forces_tol": 0.0001,
+                "initial_step_size": -0.1,
+                "lattice_weight": 2.0,
+                "nhist_max": 10,
+                "num_steps": 300,
+                "stress_tol": 1e-05
             }
         },
         "fft_coarse_grid": [
@@ -309,67 +323,59 @@
         "omega": 217.1091205794796
     },
     "counters": {
-        "band_evp_work_count": 1254.09814453125,
-        "local_operator_num_applied": 3397
+        "band_evp_work_count": 971.2717910787438,
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diff --git a/verification/test27/sirius.json b/verification/test27/sirius.json
index 0df5d85b4..eea47dab1 100644
--- a/verification/test27/sirius.json
+++ b/verification/test27/sirius.json
@@ -4,7 +4,7 @@
     "verbosity": 1
   },
   "hubbard": {
-    "full_orthogonalization": true,
+    "hubbard_subspace_method" : "full_orthogonalization",
     "local": [
       {
         "atom_type": "Co",
@@ -96,8 +96,6 @@
         ]
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-    "normalize": false,
-    "orthogonalize": false,
     "simplified": false
   },
   "iterative_solver": {
diff --git a/verification/test28/output_ref.json b/verification/test28/output_ref.json
index b927f3911..ca5de3578 100644
--- a/verification/test28/output_ref.json
+++ b/verification/test28/output_ref.json
@@ -5,43 +5,48 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 16,
                 "fft_mode": "parallel",
                 "gen_evp_solver_name": "lapack",
+                "gvec_chunk_size": 500000,
                 "mpi_grid_dims": [
                     1,
                     1
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                 "num_bands_to_print": 10,
                 "ortho_rf": false,
-                "print_checksum": false,
+                "output": "stdout:",
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-                "print_hash": false,
-                "print_memory_usage": false,
                 "print_neighbors": false,
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                 "processing_unit": "cpu",
                 "reduce_gvec": true,
                 "rmt_max": 2.2,
-                "spglib_tolerance": 9.999999747378752e-05,
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                 "use_second_variation": true,
                 "verbosity": 1,
                 "verification": 0
             },
             "hubbard": {
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+                "constrained_calculation": false,
+                "constraint_beta_mixing": 0.4,
+                "constraint_error": 1e-06,
+                "constraint_max_iteration": 10,
+                "constraint_method": "energy",
+                "constraint_strength": 1.0,
+                "hubbard_subspace_method": "full_orthogonalization",
                 "local": [
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-                        "U": 3.0,
+                        "U": 3,
                         "atom_type": "Co",
                         "l": 2,
                         "n": 3,
                         "total_initial_occupancy": 7
                     }
                 ],
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                 "nonlocal": [
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                         "T": [
@@ -49,7 +54,7 @@
                             0,
                             0
                         ],
-                        "V": 3.0,
+                        "V": 3,
                         "atom_pair": [
                             0,
                             1
@@ -69,7 +74,7 @@
                             -1,
                             -1
                         ],
-                        "V": 3.0,
+                        "V": 3,
                         "atom_pair": [
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                             2
@@ -89,7 +94,7 @@
                             0,
                             0
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-                        "V": 3.0,
+                        "V": 3,
                         "atom_pair": [
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                             0
@@ -109,7 +114,7 @@
                             1,
                             1
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+                        "V": 3,
                         "atom_pair": [
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                             0
@@ -124,8 +129,6 @@
                         ]
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@@ -149,8 +152,8 @@
             "mixer": {
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                 "beta0": 0.15,
-                "beta_scaling_factor": 1.0,
-                "linear_mix_rms_tol": 1000000.0,
+                "beta_scaling_factor": 1,
+                "linear_mix_rms_tol": 1000000,
                 "max_history": 8,
                 "type": "anderson",
                 "use_hartree": true
@@ -159,13 +162,14 @@
                 "T": 300.0,
                 "kappa": 0.3,
                 "maxiter": 300,
+                "processing_unit": "",
                 "restart": 10,
                 "tau": 0.1,
                 "tol": 1e-09
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             "parameters": {
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+                "aw_cutoff": 0,
                 "core_relativity": "dirac",
                 "density_tol": 1e-06,
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@@ -175,8 +179,8 @@
                 "gk_cutoff": 7.0710678118654755,
                 "hubbard_correction": true,
                 "lmax_apw": -1,
-                "lmax_pot": 4,
-                "lmax_rho": 4,
+                "lmax_pot": -1,
+                "lmax_rho": -1,
                 "molecule": false,
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@@ -199,7 +203,7 @@
                     0
                 ],
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-                "smearing_width": 0.0,
+                "smearing_width": 0.02,
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@@ -225,7 +229,7 @@
                 "itsol_tol_ratio": 0,
                 "itsol_tol_scale": [
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-                    0.95
+                    0.5
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                 "mixer_rms_min": 1e-16,
@@ -294,6 +298,16 @@
                     ]
                 ],
                 "lattice_vectors_scale": 1.0
+            },
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+                "eps_subsp": 0.001,
+                "forces_tol": 0.0001,
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+                "lattice_weight": 2.0,
+                "nhist_max": 10,
+                "num_steps": 300,
+                "stress_tol": 1e-05
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         "fft_coarse_grid": [
@@ -309,67 +323,73 @@
         "omega": 217.1091205794796
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diff --git a/verification/test28/sirius.json b/verification/test28/sirius.json
index ca2b1a16d..9698c5e24 100644
--- a/verification/test28/sirius.json
+++ b/verification/test28/sirius.json
@@ -4,7 +4,7 @@
     "verbosity": 1
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-    "full_orthogonalization": true,
+    "hubbard_subspace_method" : "full_orthogonalization",
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@@ -96,8 +96,6 @@
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     "simplified": true
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diff --git a/verification/test29/output_ref.json b/verification/test29/output_ref.json
index 4ed1204b6..029d8bc48 100644
--- a/verification/test29/output_ref.json
+++ b/verification/test29/output_ref.json
@@ -5,6 +5,7 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 16,
                 "fft_mode": "parallel",
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@@ -16,14 +17,9 @@
                 "num_bands_to_print": 10,
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@@ -34,7 +30,13 @@
                 "verification": 0
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@@ -59,6 +61,7 @@
                         "total_initial_occupancy": 4
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@@ -541,8 +544,6 @@
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@@ -576,7 +577,7 @@
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@@ -733,78 +734,110 @@
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-            1.2377609044597995e-05,
-            3.790634592163714e-06,
-            1.8554365156682989e-06,
-            6.015357081172674e-07,
-            1.8701361479789777e-07,
-            7.748960424952386e-08
+            0.8878513341252612,
+            1.6854043316871283,
+            0.463727545139178,
+            0.36269439189638075,
+            0.25899714599009904,
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+            0.09462725898941218,
+            0.026511061613232207,
+            0.029976981914179652,
+            0.0056148038297765355,
+            0.0019577987214029146,
+            0.002688843842542426,
+            0.0004121492535916677,
+            0.0006881771911103997,
+            0.00010520139275278407,
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+            4.7217844024385744e-07,
+            2.5217229149245803e-07,
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+            2.753111165308474e-08,
+            1.962716415510771e-08,
+            1.360415139799002e-08,
+            7.960803480673156e-09,
+            3.9393209755884405e-09,
+            1.8035447475066665e-09,
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+            1.1082329081729166e-09,
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+            1.7744616544733363e-09,
+            1.9677400605524027e-09,
+            2.1393162856281476e-09
         ],
-        "scf_time": 51.888197398
+        "scf_time": 64.497130815
     },
     "task": 0,
-    "threads_per_rank": 16
+    "threads_per_rank": 4
 }
\ No newline at end of file
diff --git a/verification/test29/sirius.json b/verification/test29/sirius.json
index 5fd61765e..9ae852b1d 100644
--- a/verification/test29/sirius.json
+++ b/verification/test29/sirius.json
@@ -1,10 +1,10 @@
 {
   "control": {
     "verbosity": 1,
-    "print_neighbors" : false
+    "print_neighbors": false
   },
   "hubbard": {
-    "orthogonalize": true,
+    "hubbard_subspace_method": "orthogonalize",
     "local": [
       {
         "J": 0,
@@ -31,182 +31,489 @@
     ],
     "nonlocal": [
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+          -1,
+          0
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         "V": 0.3653,
-        "atom_pair": [ 0, 2 ],
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-        "n": [ 3, 2 ]
+        "atom_pair": [
+          0,
+          2
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+        "l": [
+          2,
+          1
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+        "n": [
+          3,
+          2
+        ]
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+          -1
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         "V": 0.3653,
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-        "n": [ 3, 2 ]
+        "atom_pair": [
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+          2
+        ],
+        "l": [
+          2,
+          1
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+        "n": [
+          3,
+          2
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+          -1
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+        "n": [
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+          2
+        ]
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-        "atom_pair": [ 3, 0 ],
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-        "n": [ 2, 3 ]
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+          0
+        ],
+        "l": [
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+          2
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+          2,
+          3
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       },
       {
-        "T": [ 0, 1, 0 ],
+        "T": [
+          0,
+          1,
+          0
+        ],
         "V": 0.3653,
-        "atom_pair": [ 3, 0 ],
-        "l": [ 1, 2 ],
-        "n": [ 2, 3 ]
+        "atom_pair": [
+          3,
+          0
+        ],
+        "l": [
+          1,
+          2
+        ],
+        "n": [
+          2,
+          3
+        ]
       },
       {
-        "T": [ 1, 0, 0 ],
+        "T": [
+          1,
+          0,
+          0
+        ],
         "V": 0.3653,
-        "atom_pair": [ 3, 0 ],
-        "l": [ 1, 2 ],
-        "n": [ 2, 3 ]
+        "atom_pair": [
+          3,
+          0
+        ],
+        "l": [
+          1,
+          2
+        ],
+        "n": [
+          2,
+          3
+        ]
       }
-    ],
-    "normalize": false,
-    "simplified": false
+    ]
   },
   "iterative_solver": {
-    "empty_states_tolerance": 1e-05,
+    "empty_states_tolerance": 0.00001,
     "energy_tolerance": 0.01,
     "num_steps": 20,
     "type": "davidson"
@@ -218,14 +525,18 @@
     "use_hartree": false
   },
   "parameters": {
-    "density_tol": 1e-06,
+    "density_tol": 0.000001,
     "electronic_structure_method": "pseudopotential",
-    "energy_tol": 1e-06,
+    "energy_tol": 0.000001,
     "extra_charge": 0,
     "gamma_point": false,
     "gk_cutoff": 8.94427190999916,
     "hubbard_correction": true,
-    "ngridk": [ 2, 2, 2 ],
+    "ngridk": [
+      2,
+      2,
+      2
+    ],
     "num_bands": 29,
     "num_dft_iter": 100,
     "num_mag_dims": 1,
@@ -234,7 +545,7 @@
     "smearing_width": 0.0005,
     "use_scf_correction": true,
     "use_symmetry": true,
-    "use_ibz" : true,
+    "use_ibz": true,
     "xc_functionals": [
       "XC_GGA_X_PBE_SOL",
       "XC_GGA_C_PBE_SOL"
@@ -253,20 +564,32 @@
     "atoms": {
       "Ni": [
         [
-          0, 0, 0,
-          0, 0, 2
+          0,
+          0,
+          0,
+          0,
+          0,
+          2
         ],
         [
-          0.5, 0.5, 0.5,
-          0, 0, -2
+          0.5,
+          0.5,
+          0.5,
+          0,
+          0,
+          -2
         ]
       ],
       "O": [
         [
-          0.75, 0.75, 0.75
+          0.75,
+          0.75,
+          0.75
         ],
         [
-          0.25, 0.25, 0.25
+          0.25,
+          0.25,
+          0.25
         ]
       ]
     },
diff --git a/verification/test30/output_ref.json b/verification/test30/output_ref.json
index edb6f6fcd..c0f67e5c7 100644
--- a/verification/test30/output_ref.json
+++ b/verification/test30/output_ref.json
@@ -5,6 +5,7 @@
         "config": {
             "control": {
                 "beta_chunk_size": 256,
+                "beta_on_device": false,
                 "cyclic_block_size": 16,
                 "fft_mode": "parallel",
                 "gen_evp_solver_name": "lapack",
@@ -35,7 +36,7 @@
                 "constraint_max_iteration": 100,
                 "constraint_method": "energy",
                 "constraint_strength": 1.0,
-                "full_orthogonalization": true,
+                "hubbard_subspace_method": "full_orthogonalization",
                 "local": [
                     {
                         "U": 6.0,
@@ -136,8 +137,6 @@
                     }
                 ],
                 "nonlocal": [],
-                "normalize": false,
-                "orthogonalize": true,
                 "simplified": true
             },
             "iterative_solver": {
@@ -318,97 +317,97 @@
         "omega": 122.9505312592426
     },
     "counters": {
-        "band_evp_work_count": 1986.430908203125,
-        "local_operator_num_applied": 6950
+        "band_evp_work_count": 1986.6552734375,
+        "local_operator_num_applied": 6951
     },
-    "git_hash": "a65000f94e2393e2de179d7f1e4eb6bce9a0ff35",
+    "git_hash": "bd14a5684ad99f193820ddeaa5247058e7cc21f4",
     "ground_state": {
-        "band_gap": 0.11203006295945506,
+        "band_gap": 0.11203006296078155,
         "converged": true,
-        "efermi": 0.5549791568495448,
+        "efermi": 0.5549791567856392,
         "energy": {
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-            "entropy_sum": -9.844834615155195e-21,
-            "eval_sum": -13.86374657260652,
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-            "kin": 57.35621374832839,
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-            "vha": 121.7311113560253,
-            "vloc": -166.1834101987942,
-            "vxc": -26.643184422439194
+            "bxc": -0.12447705574231376,
+            "entropy_sum": -9.844834879902791e-21,
+            "eval_sum": -13.863746575595504,
+            "ewald": -119.4628074119577,
+            "exc": -21.233380879713025,
+            "kin": 57.3562137461151,
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+            "veff": -71.0954832659683,
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         "num_scf_iterations": 30,
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-            0.6781177991834277,
-            0.6969266502182917,
-            0.2745446837096553,
-            0.32576927252568894,
-            0.577701486475463,
-            0.6217206749921902,
-            0.07181658239389685,
-            0.03207138682899551,
-            0.029337060856090526,
-            0.005652204371439874,
-            0.001587375105217872,
-            0.0007398503523044155,
-            0.00024274114056605734,
-            0.00012872964994351503,
-            2.2172919006590185e-05,
-            1.0230747503741877e-05,
-            6.196902749245677e-06,
-            1.5249100898375833e-06,
-            4.0991005405545914e-07,
-            1.2389845821912608e-07
+            5.3807427761036015,
+            4.725138427072016,
+            1.2599789569125142,
+            0.2744546206261272,
+            0.8838445008341115,
+            0.9536910148232228,
+            0.6510362580936788,
+            0.34878666856046014,
+            0.44790626935044525,
+            0.48155373521775374,
+            0.43543401102108586,
+            0.6781177993937733,
+            0.6969266500816029,
+            0.2745446838080662,
+            0.3257692720609406,
+            0.5777014869906554,
+            0.6217206825973615,
+            0.07181658308957811,
+            0.03207138726835158,
+            0.02933706181643675,
+            0.005652204648551259,
+            0.0015873750384169391,
+            0.0007398503468742045,
+            0.00024274114273227268,
+            0.0001287296525682561,
+            2.2172916520888254e-05,
+            1.0230745730060152e-05,
+            6.196901285249176e-06,
+            1.5250930129294447e-06,
+            4.0993058809414875e-07,
+            1.2380236606581567e-07
         ],
-        "scf_time": 5.926917684
+        "scf_time": 6.094843018
     },
     "task": 0,
     "threads_per_rank": 4
diff --git a/verification/test30/sirius.json b/verification/test30/sirius.json
index 7de7b1e9e..47162de34 100644
--- a/verification/test30/sirius.json
+++ b/verification/test30/sirius.json
@@ -31,7 +31,7 @@
         "constraint_max_iteration": 100,
         "constraint_method": "energy",
         "constraint_strength": 1.0,
-        "full_orthogonalization": true,
+        "hubbard_subspace_method" : "full_orthogonalization",
         "local": [
             {
                 "atom_type": "Ni",
@@ -132,8 +132,6 @@
             }
         ],
         "nonlocal": [],
-        "normalize": false,
-        "orthogonalize": true,
         "simplified": true
     },
     "iterative_solver": {