mo_basis

Molecular orbitals are expressed as

\[\phi_k({\bf r}) = \sum_i C_{ik} \chi_k({\bf r})\]

where \(\chi_k\) are normalized atomic basis functions.

The current set of MOs has a label mo_label. When the orbitals are modified, the label should also be updated to keep everything consistent.

When saving the MOs, the mo_basis directory of the EZFIO database is copied in the save directory, named by the current mo_label. All this is done with the script named save_current_mos.sh in the $QP_ROOT/scripts directory.

EZFIO parameters

mo_num

Total number of MOs

mo_coef

Coefficient of the i-th AO on the j-th MO

mo_label

Label characterizing the MOS (Local, Canonical, Natural, etc)

mo_occ

MO occupation numbers

mo_class

[ Core | Inactive | Active | Virtual | Deleted ], as defined by qp_set_mo_class

ao_md5

MD5 checksum characterizing the AO basis set.

Providers

mo_class

File : mo_basis/mo_class.irp.f

character*(32), allocatable     :: mo_class     (mo_num)

[ Core | Inactive | Active | Virtual | Deleted ], as defined by qp_set_mo_class

Needs:

ezfio_filename mo_num

mpi_master

output_wall_time_0

Needed by:

full_ijkl_bitmask list_act list_all_but_del_orb list_core list_del

list_inact list_virt mo_two_e_integrals_in_map n_act_orb n_all_but_del_orb

n_core_orb n_del_orb n_inact_orb n_virt_orb

mo_coef

File : mo_basis/mos.irp.f

double precision, allocatable   :: mo_coef      (ao_num,mo_num)

Molecular orbital coefficients on AO basis set

mo_coef(i,j) = coefficient of the i-th AO on the jth MO

mo_label : Label characterizing the MOs (local, canonical, natural, etc)

Needs:

ao_num ao_ortho_canonical_coef

ezfio_filename mo_num

mpi_master

Needed by:

mo_coef_in_ao_ortho_basis mo_coef_novirt mo_coef_transp mo_dipole_x mo_integrals_n_e mo_integrals_n_e_per_atom mo_kinetic_integrals

mo_overlap mo_pseudo_integrals mo_spread_x mo_two_e_integral_jj_from_ao mo_two_e_integrals_in_map mo_two_e_integrals_vv_from_ao one_e_dm_alpha_ao_for_dft

one_e_dm_alpha_ao_for_dft_no_core one_e_dm_ao_alpha one_e_dm_mo_alpha_for_dft one_e_dm_mo_beta_for_dft one_e_spin_density_ao psi_det s_mo_coef

mo_coef_imag

File : mo_basis/mos.irp.f

double precision, allocatable   :: mo_coef_imag (ao_num,mo_num)

Molecular orbital coefficients on AO basis set

mo_coef_imag(i,j) = coefficient of the i-th AO on the jth MO

mo_label : Label characterizing the MOs (local, canonical, natural, etc)

Needs:

ao_num ezfio_filename

mo_num

mpi_master

mo_coef_in_ao_ortho_basis

File : mo_basis/mos.irp.f

double precision, allocatable   :: mo_coef_in_ao_ortho_basis    (ao_num,mo_num)

MO coefficients in orthogonalized AO basis

\(C^{-1}.C_{mo}\)

Needs:

ao_num ao_ortho_canonical_coef_inv

mo_coef

mo_num

mo_coef_transp

File : mo_basis/mos.irp.f

double precision, allocatable   :: mo_coef_transp       (mo_num,ao_num)

MO coefficients on AO basis set

Needs:

ao_num

mo_coef

mo_num

Needed by:

mo_two_e_integral_jj_from_ao

mo_two_e_integrals_in_map

mo_two_e_integrals_vv_from_ao

mo_label

File : mo_basis/mos.irp.f

character*(64)  :: mo_label

MO coefficients on AO basis set

mo_coef(i,j) = coefficient of the i-th AO on the j-th MO

mo_label : Label characterizing the MOs (local, canonical, natural, etc)

Needs:

ezfio_filename

mpi_master

Needed by:

n_det

psi_coef

psi_det

mo_num

File : mo_basis/mos.irp.f

integer :: mo_num

Number of MOs

Needs:

ao_ortho_canonical_coef

ezfio_filename

mpi_master

Needed by:

banned_excitation big_array_coulomb_integrals core_fock_operator data_one_e_dm_alpha_mo data_one_e_dm_beta_mo fock_operator_closed_shell_ref_bitmask fock_wee_closed_shell full_ijkl_bitmask list_act list_all_but_del_orb list_core list_core_inact list_core_inact_act list_del list_inact list_inact_act list_virt mo_class mo_coef mo_coef_begin_iteration mo_coef_imag mo_coef_in_ao_ortho_basis mo_coef_transp

mo_dipole_x mo_integrals_cache_min mo_integrals_map mo_integrals_n_e mo_integrals_n_e_per_atom mo_kinetic_integrals mo_occ mo_one_e_integrals mo_overlap mo_pseudo_integrals mo_spread_x mo_two_e_integral_jj_from_ao mo_two_e_integrals_in_map mo_two_e_integrals_jj mo_two_e_integrals_vv_from_ao n_act_orb n_all_but_del_orb n_core_orb n_del_orb n_inact_orb n_int n_virt_orb one_body_dm_mo_alpha_one_det

one_e_dm_alpha_ao_for_dft one_e_dm_alpha_ao_for_dft_no_core one_e_dm_ao_alpha one_e_dm_average_alpha_mo_for_dft one_e_dm_average_beta_mo_for_dft one_e_dm_average_mo_for_dft one_e_dm_dagger_mo_spin_index one_e_dm_mo one_e_dm_mo_alpha one_e_dm_mo_alpha_average one_e_dm_mo_alpha_for_dft one_e_dm_mo_alpha_for_dft_no_core one_e_dm_mo_beta_for_dft one_e_dm_mo_beta_for_dft_no_core one_e_dm_mo_diff one_e_dm_mo_for_dft one_e_dm_mo_spin_index one_e_spin_density_ao one_e_spin_density_mo psi_energy_h_core s_mo_coef singles_alpha_csc_idx singles_beta_csc_idx

mo_occ

File : mo_basis/mos.irp.f

double precision, allocatable   :: mo_occ       (mo_num)

MO occupation numbers

Needs:

elec_alpha_num elec_beta_num

ezfio_filename mo_num

mpi_master

Subroutines / functions

ao_ortho_cano_to_ao:

File : mo_basis/mos.irp.f

subroutine ao_ortho_cano_to_ao(A_ao,LDA_ao,A,LDA)

Transform A from the AO basis to the orthogonal AO basis

$C^{-1}.A_{ao}.C^{dagger-1}$

Needs:

ao_num

ao_ortho_canonical_coef_inv

Calls:

dgemm()

ao_to_mo:

File : mo_basis/mos.irp.f

subroutine ao_to_mo(A_ao,LDA_ao,A_mo,LDA_mo)

Transform A from the AO basis to the MO basis

$C^dagger.A_{ao}.C$

Needs:

ao_num

mo_coef

mo_num

Called by:

four_idx_novvvv() mo_dipole_x mo_integrals_n_e

mo_integrals_n_e_per_atom mo_kinetic_integrals mo_pseudo_integrals

mo_spread_x one_e_dm_mo_alpha_for_dft one_e_dm_mo_beta_for_dft

Calls:

dgemm()

restore_symmetry()

give_all_mos_and_grad_and_lapl_at_r:

File : mo_basis/mos_in_r.irp.f

subroutine give_all_mos_and_grad_and_lapl_at_r(r,mos_array,mos_grad_array,mos_lapl_array)

Needs:

ao_num

mo_coef

mo_num

Calls:

give_all_aos_and_grad_and_lapl_at_r()

give_all_mos_and_grad_at_r:

File : mo_basis/mos_in_r.irp.f

subroutine give_all_mos_and_grad_at_r(r,mos_array,mos_grad_array)

Needs:

ao_num

mo_coef

mo_num

Calls:

give_all_aos_and_grad_at_r()

give_all_mos_at_r:

File : mo_basis/mos_in_r.irp.f

subroutine give_all_mos_at_r(r,mos_array)

Needs:

ao_num

mo_coef_transp

mo_num

Calls:

dgemv()

give_all_aos_at_r()

mix_mo_jk:

File : mo_basis/mos.irp.f

subroutine mix_mo_jk(j,k)

Rotates the j-th MO with the k-th MO to give two new MOs that are

• $+ = frac{1}{sqrt{2}} ( | jrangle + | krangle)$

• $- = frac{1}{sqrt{2}} ( | jrangle - | krangle)$

by convention, the ‘+’ MO is in the lowest index (min(j,k)) by convention, the ‘-’ MO is in the highest index (max(j,k))

Needs:

ao_num

mo_coef

mo_as_eigvectors_of_mo_matrix:

File : mo_basis/utils.irp.f

subroutine mo_as_eigvectors_of_mo_matrix(matrix,n,m,label,sign,output)

Needs:

ao_num mo_coef

mo_label

mo_num

Calls:

dgemm()

lapack_diag()

write_time()

mo_as_svd_vectors_of_mo_matrix:

File : mo_basis/utils.irp.f

subroutine mo_as_svd_vectors_of_mo_matrix(matrix,lda,m,n,label)

Needs:

ao_num mo_coef

mo_label

mo_num

Calls:

dgemm()

svd()

write_time()

mo_as_svd_vectors_of_mo_matrix_eig:

File : mo_basis/utils.irp.f

subroutine mo_as_svd_vectors_of_mo_matrix_eig(matrix,lda,m,n,eig,label)

Needs:

ao_num mo_coef

mo_label

mo_num

Called by:

set_natural_mos()

Calls:

dgemm()

svd()

write_time()

mo_coef_new_as_svd_vectors_of_mo_matrix_eig:

File : mo_basis/utils.irp.f

subroutine mo_coef_new_as_svd_vectors_of_mo_matrix_eig(matrix,lda,m,n,mo_coef_before,eig,mo_coef_new)

You enter with matrix in the MO basis defined with the mo_coef_before.

You SVD the matrix and set the eigenvectors as mo_coef_new ordered by increasing singular values

Needs:

ao_num

mo_num

Calls:

dgemm()

svd()

write_time()

save_mos:

File : mo_basis/utils.irp.f

subroutine save_mos

Needs:

ao_md5 ao_num ezfio_filename

mo_class mo_coef mo_label

mo_num mo_occ

Called by:

save_natural_mos()

Calls:

ezfio_set_mo_basis_ao_md5() ezfio_set_mo_basis_mo_class() ezfio_set_mo_basis_mo_coef()

ezfio_set_mo_basis_mo_label() ezfio_set_mo_basis_mo_num()

ezfio_set_mo_basis_mo_occ() system()

save_mos_no_occ:

File : mo_basis/utils.irp.f

subroutine save_mos_no_occ

Needs:

ao_num ezfio_filename

mo_coef

mo_num

Calls:

ezfio_set_mo_basis_mo_coef()

system()

save_mos_truncated:

File : mo_basis/utils.irp.f

subroutine save_mos_truncated(n)

Needs:

ao_md5 ao_num ezfio_filename

mo_class mo_coef

mo_label mo_occ

Calls:

ezfio_set_mo_basis_ao_md5() ezfio_set_mo_basis_mo_class() ezfio_set_mo_basis_mo_coef()

ezfio_set_mo_basis_mo_label() ezfio_set_mo_basis_mo_num()

ezfio_set_mo_basis_mo_occ() system()