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|
!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright (C) 2000 - 2018 CP2K developers group !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Calculate MAO's and analyze wavefunctions
!> \par History
!> 03.2016 created [JGH]
!> 12.2016 split into four modules [JGH]
!> \author JGH
! **************************************************************************************************
MODULE mao_wfn_analysis
USE atomic_kind_types, ONLY: get_atomic_kind
USE basis_set_types, ONLY: gto_basis_set_p_type
USE bibliography, ONLY: Ehrhardt1985,&
Heinzmann1976,&
cite_reference
USE cp_blacs_env, ONLY: cp_blacs_env_type
USE cp_control_types, ONLY: dft_control_type
USE cp_dbcsr_cholesky, ONLY: cp_dbcsr_cholesky_decompose,&
cp_dbcsr_cholesky_restore
USE cp_dbcsr_cp2k_link, ONLY: cp_dbcsr_alloc_block_from_nbl
USE cp_para_types, ONLY: cp_para_env_type
USE dbcsr_api, ONLY: &
dbcsr_allocate_matrix_set, dbcsr_copy, dbcsr_create, dbcsr_deallocate_matrix_set, &
dbcsr_desymmetrize, dbcsr_distribution_type, dbcsr_get_block_diag, dbcsr_get_block_p, &
dbcsr_get_info, dbcsr_iterator_blocks_left, dbcsr_iterator_next_block, &
dbcsr_iterator_start, dbcsr_iterator_stop, dbcsr_iterator_type, dbcsr_multiply, &
dbcsr_p_type, dbcsr_release, dbcsr_replicate_all, dbcsr_reserve_diag_blocks, dbcsr_trace, &
dbcsr_type, dbcsr_type_no_symmetry, dbcsr_type_symmetric
USE input_section_types, ONLY: section_vals_get,&
section_vals_type,&
section_vals_val_get
USE iterate_matrix, ONLY: invert_Hotelling
USE kinds, ONLY: dp
USE kpoint_types, ONLY: kpoint_type
USE mao_methods, ONLY: mao_basis_analysis,&
mao_build_q,&
mao_reference_basis
USE mao_optimizer, ONLY: mao_optimize
USE mathlib, ONLY: invmat_symm
USE message_passing, ONLY: mp_sum
USE particle_methods, ONLY: get_particle_set
USE particle_types, ONLY: particle_type
USE qs_environment_types, ONLY: get_qs_env,&
qs_environment_type
USE qs_kind_types, ONLY: get_qs_kind,&
qs_kind_type
USE qs_ks_types, ONLY: get_ks_env,&
qs_ks_env_type
USE qs_neighbor_list_types, ONLY: deallocate_neighbor_list_set,&
get_iterator_info,&
neighbor_list_iterate,&
neighbor_list_iterator_create,&
neighbor_list_iterator_p_type,&
neighbor_list_iterator_release,&
neighbor_list_set_p_type
USE qs_neighbor_lists, ONLY: setup_neighbor_list
USE qs_overlap, ONLY: build_overlap_matrix_simple
USE qs_rho_types, ONLY: qs_rho_get,&
qs_rho_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
TYPE block_type
REAL(KIND=dp), DIMENSION(:, :), ALLOCATABLE :: mat
END TYPE block_type
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'mao_wfn_analysis'
PUBLIC :: mao_analysis
! **************************************************************************************************
CONTAINS
! **************************************************************************************************
!> \brief ...
!> \param qs_env ...
!> \param input_section ...
!> \param unit_nr ...
! **************************************************************************************************
SUBROUTINE mao_analysis(qs_env, input_section, unit_nr)
TYPE(qs_environment_type), POINTER :: qs_env
TYPE(section_vals_type), POINTER :: input_section
INTEGER, INTENT(IN) :: unit_nr
CHARACTER(len=*), PARAMETER :: routineN = 'mao_analysis', routineP = moduleN//':'//routineN
CHARACTER(len=2) :: element_symbol, esa, esb, esc
INTEGER :: fall, handle, ia, iab, iabc, iatom, ib, ic, icol, ikind, irow, ispin, jatom, &
mao_basis, max_iter, me, na, nab, nabc, natom, nb, nc, nimages, nspin, ssize
INTEGER, DIMENSION(:), POINTER :: col_blk_sizes, mao_blk, mao_blk_sizes, &
orb_blk, row_blk_sizes
LOGICAL :: analyze_ua, explicit, fo, for, fos, &
found, neglect_abc, print_basis
REAL(KIND=dp) :: deltaq, electra(2), eps_ab, eps_abc, eps_filter, eps_fun, eps_grad, epsx, &
senabc, senmax, threshold, total_charge, total_spin, ua_charge(2), zeff
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :) :: occnumA, occnumABC, qab, qmatab, qmatac, &
qmatbc, raq, sab, selnABC, sinv, &
smatab, smatac, smatbc, uaq
REAL(KIND=dp), ALLOCATABLE, DIMENSION(:, :, :) :: occnumAB, selnAB
REAL(KIND=dp), DIMENSION(:, :), POINTER :: block, cmao, diag, qblka, qblkb, qblkc, &
rblkl, rblku, sblk, sblka, sblkb, sblkc
TYPE(block_type), ALLOCATABLE, DIMENSION(:) :: rowblock
TYPE(cp_blacs_env_type), POINTER :: blacs_env
TYPE(cp_para_env_type), POINTER :: para_env
TYPE(dbcsr_distribution_type), POINTER :: dbcsr_dist
TYPE(dbcsr_iterator_type) :: dbcsr_iter
TYPE(dbcsr_p_type), DIMENSION(:), POINTER :: mao_coef, mao_dmat, mao_qmat, mao_smat, &
matrix_q, matrix_smm, matrix_smo
TYPE(dbcsr_p_type), DIMENSION(:, :), POINTER :: matrix_ks, matrix_p, matrix_s
TYPE(dbcsr_type) :: amat, axmat, cgmat, cholmat, crumat, &
qmat, qmat_diag, rumat, smat_diag, &
sumat, tmat
TYPE(dft_control_type), POINTER :: dft_control
TYPE(gto_basis_set_p_type), DIMENSION(:), POINTER :: mao_basis_set_list, orb_basis_set_list
TYPE(kpoint_type), POINTER :: kpoints
TYPE(neighbor_list_iterator_p_type), &
DIMENSION(:), POINTER :: nl_iterator
TYPE(neighbor_list_set_p_type), DIMENSION(:), &
POINTER :: sab_all, sab_orb, smm_list, smo_list
TYPE(particle_type), DIMENSION(:), POINTER :: particle_set
TYPE(qs_kind_type), DIMENSION(:), POINTER :: qs_kind_set
TYPE(qs_ks_env_type), POINTER :: ks_env
TYPE(qs_rho_type), POINTER :: rho
! only do MAO analysis if explicitely requested
CALL section_vals_get(input_section, explicit=explicit)
IF (.NOT. explicit) RETURN
CALL timeset(routineN, handle)
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(/,T2,A)') '!-----------------------------------------------------------------------------!'
WRITE (UNIT=unit_nr, FMT="(T36,A)") "MAO ANALYSIS"
WRITE (UNIT=unit_nr, FMT="(T12,A)") "Claus Ehrhardt and Reinhart Ahlrichs, TCA 68:231-245 (1985)"
WRITE (unit_nr, '(T2,A)') '!-----------------------------------------------------------------------------!'
END IF
CALL cite_reference(Heinzmann1976)
CALL cite_reference(Ehrhardt1985)
! input options
CALL section_vals_val_get(input_section, "REFERENCE_BASIS", i_val=mao_basis)
CALL section_vals_val_get(input_section, "EPS_FILTER", r_val=eps_filter)
CALL section_vals_val_get(input_section, "EPS_FUNCTION", r_val=eps_fun)
CALL section_vals_val_get(input_section, "EPS_GRAD", r_val=eps_grad)
CALL section_vals_val_get(input_section, "MAX_ITER", i_val=max_iter)
CALL section_vals_val_get(input_section, "PRINT_BASIS", l_val=print_basis)
CALL section_vals_val_get(input_section, "NEGLECT_ABC", l_val=neglect_abc)
CALL section_vals_val_get(input_section, "AB_THRESHOLD", r_val=eps_ab)
CALL section_vals_val_get(input_section, "ABC_THRESHOLD", r_val=eps_abc)
CALL section_vals_val_get(input_section, "ANALYZE_UNASSIGNED_CHARGE", l_val=analyze_ua)
! k-points?
CALL get_qs_env(qs_env, dft_control=dft_control)
nimages = dft_control%nimages
IF (nimages > 1) THEN
IF (unit_nr > 0) THEN
WRITE (UNIT=unit_nr, FMT="(T2,A)") &
"K-Points: MAO's determined and analyzed using Gamma-Point only."
END IF
END IF
! Reference basis set
NULLIFY (mao_basis_set_list, orb_basis_set_list)
CALL mao_reference_basis(qs_env, mao_basis, mao_basis_set_list, orb_basis_set_list, &
unit_nr, print_basis)
! neighbor lists
NULLIFY (smm_list, smo_list)
CALL setup_neighbor_list(smm_list, mao_basis_set_list, qs_env=qs_env)
CALL setup_neighbor_list(smo_list, mao_basis_set_list, orb_basis_set_list, qs_env=qs_env)
! overlap matrices
NULLIFY (matrix_smm, matrix_smo)
CALL get_qs_env(qs_env, ks_env=ks_env)
CALL build_overlap_matrix_simple(ks_env, matrix_smm, &
mao_basis_set_list, mao_basis_set_list, smm_list)
CALL build_overlap_matrix_simple(ks_env, matrix_smo, &
mao_basis_set_list, orb_basis_set_list, smo_list)
! get reference density matrix and overlap matrix
CALL get_qs_env(qs_env, rho=rho, matrix_s_kp=matrix_s)
CALL qs_rho_get(rho, rho_ao_kp=matrix_p)
nspin = SIZE(matrix_p, 1)
!
! Q matrix
IF (nimages == 1) THEN
CALL mao_build_q(matrix_q, matrix_p, matrix_s, matrix_smm, matrix_smo, smm_list, electra, eps_filter)
ELSE
CALL get_qs_env(qs_env, matrix_ks_kp=matrix_ks, kpoints=kpoints)
CALL mao_build_q(matrix_q, matrix_p, matrix_s, matrix_smm, matrix_smo, smm_list, electra, eps_filter, &
nimages=nimages, kpoints=kpoints, matrix_ks=matrix_ks, sab_orb=sab_orb)
END IF
! check for extended basis sets
fall = 0
CALL neighbor_list_iterator_create(nl_iterator, smm_list)
DO WHILE (neighbor_list_iterate(nl_iterator) == 0)
CALL get_iterator_info(nl_iterator, iatom=iatom, jatom=jatom)
IF (iatom <= jatom) THEN
irow = iatom
icol = jatom
ELSE
irow = jatom
icol = iatom
END IF
CALL dbcsr_get_block_p(matrix=matrix_p(1, 1)%matrix, &
row=irow, col=icol, block=block, found=found)
IF (.NOT. found) fall = fall+1
END DO
CALL neighbor_list_iterator_release(nl_iterator)
CALL get_qs_env(qs_env=qs_env, para_env=para_env)
CALL mp_sum(fall, para_env%group)
IF (unit_nr > 0 .AND. fall > 0) THEN
WRITE (UNIT=unit_nr, FMT="(/,T2,A,/,T2,A,/)") &
"Warning: Extended MAO basis used with original basis filtered density matrix", &
"Warning: Possible errors can be controled with EPS_PGF_ORB"
END IF
! MAO matrices
CALL get_qs_env(qs_env=qs_env, qs_kind_set=qs_kind_set, natom=natom)
CALL get_ks_env(ks_env=ks_env, particle_set=particle_set, dbcsr_dist=dbcsr_dist)
NULLIFY (mao_coef)
CALL dbcsr_allocate_matrix_set(mao_coef, nspin)
ALLOCATE (row_blk_sizes(natom), col_blk_sizes(natom))
CALL get_particle_set(particle_set, qs_kind_set, nsgf=row_blk_sizes, &
basis=mao_basis_set_list)
CALL get_particle_set(particle_set, qs_kind_set, nmao=col_blk_sizes)
! check if MAOs have been specified
DO iab = 1, natom
IF (col_blk_sizes(iab) < 0) &
CPABORT("Number of MAOs has to be specified in KIND section for all elements")
END DO
DO ispin = 1, nspin
! coeficients
ALLOCATE (mao_coef(ispin)%matrix)
CALL dbcsr_create(matrix=mao_coef(ispin)%matrix, &
name="MAO_COEF", dist=dbcsr_dist, matrix_type=dbcsr_type_no_symmetry, &
row_blk_size=row_blk_sizes, col_blk_size=col_blk_sizes, nze=0)
CALL dbcsr_reserve_diag_blocks(matrix=mao_coef(ispin)%matrix)
END DO
DEALLOCATE (row_blk_sizes, col_blk_sizes)
! optimze MAOs
epsx = 1000.0_dp
CALL mao_optimize(mao_coef, matrix_q, matrix_smm, electra, max_iter, eps_grad, epsx, unit_nr)
! Analyze the MAO basis
CALL mao_basis_analysis(mao_coef, matrix_smm, mao_basis_set_list, particle_set, &
qs_kind_set, unit_nr, para_env)
! Calculate the overlap and density matrix in the new MAO basis
NULLIFY (mao_dmat, mao_smat, mao_qmat)
CALL dbcsr_allocate_matrix_set(mao_qmat, nspin)
CALL dbcsr_allocate_matrix_set(mao_dmat, nspin)
CALL dbcsr_allocate_matrix_set(mao_smat, nspin)
CALL dbcsr_get_info(mao_coef(1)%matrix, col_blk_size=col_blk_sizes, distribution=dbcsr_dist)
DO ispin = 1, nspin
ALLOCATE (mao_dmat(ispin)%matrix)
CALL dbcsr_create(mao_dmat(ispin)%matrix, name="MAO density", dist=dbcsr_dist, &
matrix_type=dbcsr_type_symmetric, row_blk_size=col_blk_sizes, &
col_blk_size=col_blk_sizes, nze=0)
ALLOCATE (mao_smat(ispin)%matrix)
CALL dbcsr_create(mao_smat(ispin)%matrix, name="MAO overlap", dist=dbcsr_dist, &
matrix_type=dbcsr_type_symmetric, row_blk_size=col_blk_sizes, &
col_blk_size=col_blk_sizes, nze=0)
ALLOCATE (mao_qmat(ispin)%matrix)
CALL dbcsr_create(mao_qmat(ispin)%matrix, name="MAO covar density", dist=dbcsr_dist, &
matrix_type=dbcsr_type_symmetric, row_blk_size=col_blk_sizes, &
col_blk_size=col_blk_sizes, nze=0)
END DO
CALL dbcsr_create(amat, name="MAO overlap", template=mao_dmat(1)%matrix)
CALL dbcsr_create(tmat, name="MAO Overlap Inverse", template=amat)
CALL dbcsr_create(qmat, name="MAO covar density", template=amat)
CALL dbcsr_create(cgmat, name="TEMP matrix", template=mao_coef(1)%matrix)
CALL dbcsr_create(axmat, name="TEMP", template=amat, matrix_type=dbcsr_type_no_symmetry)
DO ispin = 1, nspin
! calculate MAO overlap matrix
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_smm(1)%matrix, mao_coef(ispin)%matrix, &
0.0_dp, cgmat)
CALL dbcsr_multiply("T", "N", 1.0_dp, mao_coef(ispin)%matrix, cgmat, 0.0_dp, amat)
! calculate inverse of MAO overlap
threshold = 1.e-8_dp
CALL invert_Hotelling(tmat, amat, threshold, norm_convergence=1.e-4_dp, silent=.TRUE.)
CALL dbcsr_copy(mao_smat(ispin)%matrix, amat)
! calculate q-matrix q = C*Q*C
CALL dbcsr_multiply("N", "N", 1.0_dp, matrix_q(ispin)%matrix, mao_coef(ispin)%matrix, &
0.0_dp, cgmat, filter_eps=eps_filter)
CALL dbcsr_multiply("T", "N", 1.0_dp, mao_coef(ispin)%matrix, cgmat, &
0.0_dp, qmat, filter_eps=eps_filter)
CALL dbcsr_copy(mao_qmat(ispin)%matrix, qmat)
! calculate density matrix
CALL dbcsr_multiply("N", "N", 1.0_dp, qmat, tmat, 0.0_dp, axmat, filter_eps=eps_filter)
CALL dbcsr_multiply("N", "N", 1.0_dp, tmat, axmat, 0.0_dp, mao_dmat(ispin)%matrix, &
filter_eps=eps_filter)
END DO
CALL dbcsr_release(amat)
CALL dbcsr_release(tmat)
CALL dbcsr_release(qmat)
CALL dbcsr_release(cgmat)
CALL dbcsr_release(axmat)
! calculate unassigned charge : n - Tr PS
DO ispin = 1, nspin
CALL dbcsr_trace(mao_dmat(ispin)%matrix, mao_smat(ispin)%matrix, ua_charge(ispin))
ua_charge(ispin) = electra(ispin)-ua_charge(ispin)
END DO
IF (unit_nr > 0) THEN
WRITE (unit_nr, *)
DO ispin = 1, nspin
WRITE (UNIT=unit_nr, FMT="(T2,A,T32,A,i2,T55,A,F12.8)") &
"Unassigned charge", "Spin ", ispin, "delta charge =", ua_charge(ispin)
END DO
END IF
! occupation numbers: single atoms
! We use S_A = 1
! At the gamma point we use an effective MIC
CALL get_qs_env(qs_env, natom=natom)
ALLOCATE (occnumA(natom, nspin))
occnumA = 0.0_dp
DO ispin = 1, nspin
DO iatom = 1, natom
CALL dbcsr_get_block_p(matrix=mao_qmat(ispin)%matrix, &
row=iatom, col=iatom, block=block, found=found)
IF (found) THEN
DO iab = 1, SIZE(block, 1)
occnumA(iatom, ispin) = occnumA(iatom, ispin)+block(iab, iab)
END DO
END IF
END DO
END DO
CALL mp_sum(occnumA, para_env%group)
! occupation numbers: atom pairs
ALLOCATE (occnumAB(natom, natom, nspin))
occnumAB = 0.0_dp
DO ispin = 1, nspin
CALL dbcsr_create(qmat_diag, name="MAO diagonal density", template=mao_dmat(1)%matrix)
CALL dbcsr_create(smat_diag, name="MAO diagonal overlap", template=mao_dmat(1)%matrix)
! replicate the diagonal blocks of the density and overlap matrices
CALL dbcsr_get_block_diag(mao_qmat(ispin)%matrix, qmat_diag)
CALL dbcsr_replicate_all(qmat_diag)
CALL dbcsr_get_block_diag(mao_smat(ispin)%matrix, smat_diag)
CALL dbcsr_replicate_all(smat_diag)
DO ia = 1, natom
DO ib = ia+1, natom
iab = 0
CALL dbcsr_get_block_p(matrix=mao_qmat(ispin)%matrix, &
row=ia, col=ib, block=block, found=found)
IF (found) iab = 1
CALL mp_sum(iab, para_env%group)
CPASSERT(iab <= 1)
IF (iab == 0 .AND. para_env%ionode) THEN
! AB block is not available N_AB = N_A + N_B
! Do this only on the "source" processor
occnumAB(ia, ib, ispin) = occnumA(ia, ispin)+occnumA(ib, ispin)
occnumAB(ib, ia, ispin) = occnumA(ia, ispin)+occnumA(ib, ispin)
ELSE IF (found) THEN
! owner of AB block performs calculation
na = SIZE(block, 1)
nb = SIZE(block, 2)
nab = na+nb
ALLOCATE (sab(nab, nab), qab(nab, nab), sinv(nab, nab))
! qmat
qab(1:na, na+1:nab) = block(1:na, 1:nb)
qab(na+1:nab, 1:na) = TRANSPOSE(block(1:na, 1:nb))
CALL dbcsr_get_block_p(matrix=qmat_diag, row=ia, col=ia, block=diag, found=fo)
CPASSERT(fo)
qab(1:na, 1:na) = diag(1:na, 1:na)
CALL dbcsr_get_block_p(matrix=qmat_diag, row=ib, col=ib, block=diag, found=fo)
CPASSERT(fo)
qab(na+1:nab, na+1:nab) = diag(1:nb, 1:nb)
! smat
CALL dbcsr_get_block_p(matrix=mao_smat(ispin)%matrix, &
row=ia, col=ib, block=block, found=fo)
CPASSERT(fo)
sab(1:na, na+1:nab) = block(1:na, 1:nb)
sab(na+1:nab, 1:na) = TRANSPOSE(block(1:na, 1:nb))
CALL dbcsr_get_block_p(matrix=smat_diag, row=ia, col=ia, block=diag, found=fo)
CPASSERT(fo)
sab(1:na, 1:na) = diag(1:na, 1:na)
CALL dbcsr_get_block_p(matrix=smat_diag, row=ib, col=ib, block=diag, found=fo)
CPASSERT(fo)
sab(na+1:nab, na+1:nab) = diag(1:nb, 1:nb)
! inv smat
sinv(1:nab, 1:nab) = sab(1:nab, 1:nab)
CALL invmat_symm(sinv)
! Tr(Q*Sinv)
occnumAB(ia, ib, ispin) = SUM(qab*sinv)
occnumAB(ib, ia, ispin) = occnumAB(ia, ib, ispin)
!
DEALLOCATE (sab, qab, sinv)
END IF
END DO
END DO
CALL dbcsr_release(qmat_diag)
CALL dbcsr_release(smat_diag)
END DO
CALL mp_sum(occnumAB, para_env%group)
! calculate shared electron numbers (AB)
ALLOCATE (selnAB(natom, natom, nspin))
selnAB = 0.0_dp
DO ispin = 1, nspin
DO ia = 1, natom
DO ib = ia+1, natom
selnAB(ia, ib, ispin) = occnumA(ia, ispin)+occnumA(ib, ispin)-occnumAB(ia, ib, ispin)
selnAB(ib, ia, ispin) = selnAB(ia, ib, ispin)
END DO
END DO
END DO
IF (.NOT. neglect_abc) THEN
! calculate N_ABC
nabc = (natom*(natom-1)*(natom-2))/6
ALLOCATE (occnumABC(nabc, nspin))
occnumABC = -1.0_dp
DO ispin = 1, nspin
CALL dbcsr_create(qmat_diag, name="MAO diagonal density", template=mao_dmat(1)%matrix)
CALL dbcsr_create(smat_diag, name="MAO diagonal overlap", template=mao_dmat(1)%matrix)
! replicate the diagonal blocks of the density and overlap matrices
CALL dbcsr_get_block_diag(mao_qmat(ispin)%matrix, qmat_diag)
CALL dbcsr_replicate_all(qmat_diag)
CALL dbcsr_get_block_diag(mao_smat(ispin)%matrix, smat_diag)
CALL dbcsr_replicate_all(smat_diag)
iabc = 0
DO ia = 1, natom
CALL dbcsr_get_block_p(matrix=qmat_diag, row=ia, col=ia, block=qblka, found=fo)
CPASSERT(fo)
CALL dbcsr_get_block_p(matrix=smat_diag, row=ia, col=ia, block=sblka, found=fo)
CPASSERT(fo)
na = SIZE(qblka, 1)
DO ib = ia+1, natom
! screen with SEN(AB)
IF (selnAB(ia, ib, ispin) < eps_abc) THEN
iabc = iabc+(natom-ib)
CYCLE
END IF
CALL dbcsr_get_block_p(matrix=qmat_diag, row=ib, col=ib, block=qblkb, found=fo)
CPASSERT(fo)
CALL dbcsr_get_block_p(matrix=smat_diag, row=ib, col=ib, block=sblkb, found=fo)
CPASSERT(fo)
nb = SIZE(qblkb, 1)
nab = na+nb
ALLOCATE (qmatab(na, nb), smatab(na, nb))
CALL dbcsr_get_block_p(matrix=mao_qmat(ispin)%matrix, row=ia, col=ib, &
block=block, found=found)
qmatab = 0.0_dp
IF (found) qmatab(1:na, 1:nb) = block(1:na, 1:nb)
CALL mp_sum(qmatab, para_env%group)
CALL dbcsr_get_block_p(matrix=mao_smat(ispin)%matrix, row=ia, col=ib, &
block=block, found=found)
smatab = 0.0_dp
IF (found) smatab(1:na, 1:nb) = block(1:na, 1:nb)
CALL mp_sum(smatab, para_env%group)
DO ic = ib+1, natom
! screen with SEN(AB)
IF ((selnAB(ia, ic, ispin) < eps_abc) .OR. (selnAB(ib, ic, ispin) < eps_abc)) THEN
iabc = iabc+1
CYCLE
END IF
CALL dbcsr_get_block_p(matrix=qmat_diag, row=ic, col=ic, block=qblkc, found=fo)
CPASSERT(fo)
CALL dbcsr_get_block_p(matrix=smat_diag, row=ic, col=ic, block=sblkc, found=fo)
CPASSERT(fo)
nc = SIZE(qblkc, 1)
ALLOCATE (qmatac(na, nc), smatac(na, nc))
CALL dbcsr_get_block_p(matrix=mao_qmat(ispin)%matrix, row=ia, col=ic, &
block=block, found=found)
qmatac = 0.0_dp
IF (found) qmatac(1:na, 1:nc) = block(1:na, 1:nc)
CALL mp_sum(qmatac, para_env%group)
CALL dbcsr_get_block_p(matrix=mao_smat(ispin)%matrix, row=ia, col=ic, &
block=block, found=found)
smatac = 0.0_dp
IF (found) smatac(1:na, 1:nc) = block(1:na, 1:nc)
CALL mp_sum(smatac, para_env%group)
ALLOCATE (qmatbc(nb, nc), smatbc(nb, nc))
CALL dbcsr_get_block_p(matrix=mao_qmat(ispin)%matrix, row=ib, col=ic, &
block=block, found=found)
qmatbc = 0.0_dp
IF (found) qmatbc(1:nb, 1:nc) = block(1:nb, 1:nc)
CALL mp_sum(qmatbc, para_env%group)
CALL dbcsr_get_block_p(matrix=mao_smat(ispin)%matrix, row=ib, col=ic, &
block=block, found=found)
smatbc = 0.0_dp
IF (found) smatbc(1:nb, 1:nc) = block(1:nb, 1:nc)
CALL mp_sum(smatbc, para_env%group)
!
nabc = na+nb+nc
ALLOCATE (sab(nabc, nabc), sinv(nabc, nabc), qab(nabc, nabc))
!
qab(1:na, 1:na) = qblka(1:na, 1:na)
qab(na+1:nab, na+1:nab) = qblkb(1:nb, 1:nb)
qab(nab+1:nabc, nab+1:nabc) = qblkc(1:nc, 1:nc)
qab(1:na, na+1:nab) = qmatab(1:na, 1:nb)
qab(na+1:nab, 1:na) = TRANSPOSE(qmatab(1:na, 1:nb))
qab(1:na, nab+1:nabc) = qmatac(1:na, 1:nc)
qab(nab+1:nabc, 1:na) = TRANSPOSE(qmatac(1:na, 1:nc))
qab(na+1:nab, nab+1:nabc) = qmatbc(1:nb, 1:nc)
qab(nab+1:nabc, na+1:nab) = TRANSPOSE(qmatbc(1:nb, 1:nc))
!
sab(1:na, 1:na) = sblka(1:na, 1:na)
sab(na+1:nab, na+1:nab) = sblkb(1:nb, 1:nb)
sab(nab+1:nabc, nab+1:nabc) = sblkc(1:nc, 1:nc)
sab(1:na, na+1:nab) = smatab(1:na, 1:nb)
sab(na+1:nab, 1:na) = TRANSPOSE(smatab(1:na, 1:nb))
sab(1:na, nab+1:nabc) = smatac(1:na, 1:nc)
sab(nab+1:nabc, 1:na) = TRANSPOSE(smatac(1:na, 1:nc))
sab(na+1:nab, nab+1:nabc) = smatbc(1:nb, 1:nc)
sab(nab+1:nabc, na+1:nab) = TRANSPOSE(smatbc(1:nb, 1:nc))
! inv smat
sinv(1:nabc, 1:nabc) = sab(1:nabc, 1:nabc)
CALL invmat_symm(sinv)
! Tr(Q*Sinv)
iabc = iabc+1
me = MOD(iabc, para_env%num_pe)
IF (me == para_env%mepos) THEN
occnumABC(iabc, ispin) = SUM(qab*sinv)
ELSE
occnumABC(iabc, ispin) = 0.0_dp
END IF
!
DEALLOCATE (sab, sinv, qab)
DEALLOCATE (qmatac, smatac)
DEALLOCATE (qmatbc, smatbc)
END DO
DEALLOCATE (qmatab, smatab)
END DO
END DO
CALL dbcsr_release(qmat_diag)
CALL dbcsr_release(smat_diag)
END DO
CALL mp_sum(occnumABC, para_env%group)
END IF
IF (.NOT. neglect_abc) THEN
! calculate shared electron numbers (ABC)
nabc = (natom*(natom-1)*(natom-2))/6
ALLOCATE (selnABC(nabc, nspin))
selnABC = 0.0_dp
DO ispin = 1, nspin
iabc = 0
DO ia = 1, natom
DO ib = ia+1, natom
DO ic = ib+1, natom
iabc = iabc+1
IF (occnumABC(iabc, ispin) >= 0.0_dp) THEN
selnABC(iabc, ispin) = occnumA(ia, ispin)+occnumA(ib, ispin)+occnumA(ic, ispin)- &
occnumAB(ia, ib, ispin)-occnumAB(ia, ic, ispin)-occnumAB(ib, ic, ispin)+ &
occnumABC(iabc, ispin)
END IF
END DO
END DO
END DO
END DO
END IF
! calculate atomic charge
ALLOCATE (raq(natom, nspin))
raq = 0.0_dp
DO ispin = 1, nspin
DO ia = 1, natom
raq(ia, ispin) = occnumA(ia, ispin)
DO ib = 1, natom
raq(ia, ispin) = raq(ia, ispin)-0.5_dp*selnAB(ia, ib, ispin)
END DO
END DO
IF (.NOT. neglect_abc) THEN
iabc = 0
DO ia = 1, natom
DO ib = ia+1, natom
DO ic = ib+1, natom
iabc = iabc+1
raq(ia, ispin) = raq(ia, ispin)+selnABC(iabc, ispin)/3._dp
raq(ib, ispin) = raq(ib, ispin)+selnABC(iabc, ispin)/3._dp
raq(ic, ispin) = raq(ic, ispin)+selnABC(iabc, ispin)/3._dp
END DO
END DO
END DO
END IF
END DO
! calculate unassigned charge (from sum over atomic charges)
DO ispin = 1, nspin
deltaq = (electra(ispin)-SUM(raq(1:natom, ispin)))-ua_charge(ispin)
IF (unit_nr > 0) THEN
WRITE (UNIT=unit_nr, FMT="(T2,A,T32,A,i2,T55,A,F12.8)") &
"Cutoff error on charge", "Spin ", ispin, "error charge =", deltaq
END IF
END DO
! analyze unassigned charge
ALLOCATE (uaq(natom, nspin))
uaq = 0.0_dp
IF (analyze_ua) THEN
CALL get_qs_env(qs_env=qs_env, para_env=para_env, blacs_env=blacs_env)
CALL get_qs_env(qs_env=qs_env, sab_orb=sab_orb, sab_all=sab_all)
CALL dbcsr_get_info(mao_coef(1)%matrix, row_blk_size=mao_blk_sizes, &
col_blk_size=col_blk_sizes, distribution=dbcsr_dist)
CALL dbcsr_get_info(matrix_s(1, 1)%matrix, row_blk_size=row_blk_sizes)
CALL dbcsr_create(amat, name="temp", template=matrix_s(1, 1)%matrix)
CALL dbcsr_create(tmat, name="temp", template=mao_coef(1)%matrix)
! replicate diagonal of smm matrix
CALL dbcsr_get_block_diag(matrix_smm(1)%matrix, smat_diag)
CALL dbcsr_replicate_all(smat_diag)
ALLOCATE (orb_blk(natom), mao_blk(natom))
DO ia = 1, natom
orb_blk = row_blk_sizes
mao_blk = row_blk_sizes
mao_blk(ia) = col_blk_sizes(ia)
CALL dbcsr_create(sumat, name="Smat", dist=dbcsr_dist, matrix_type=dbcsr_type_symmetric, &
row_blk_size=mao_blk, col_blk_size=mao_blk, nze=0)
CALL cp_dbcsr_alloc_block_from_nbl(sumat, sab_orb)
CALL dbcsr_create(cholmat, name="Cholesky matrix", dist=dbcsr_dist, &
matrix_type=dbcsr_type_no_symmetry, row_blk_size=mao_blk, col_blk_size=mao_blk, nze=0)
CALL dbcsr_create(rumat, name="Rmat", dist=dbcsr_dist, matrix_type=dbcsr_type_no_symmetry, &
row_blk_size=orb_blk, col_blk_size=mao_blk, nze=0)
CALL cp_dbcsr_alloc_block_from_nbl(rumat, sab_orb, .TRUE.)
CALL dbcsr_create(crumat, name="Rmat*Umat", dist=dbcsr_dist, matrix_type=dbcsr_type_no_symmetry, &
row_blk_size=orb_blk, col_blk_size=mao_blk, nze=0)
! replicate row and col of smo matrix
ALLOCATE (rowblock(natom))
DO ib = 1, natom
na = mao_blk_sizes(ia)
nb = row_blk_sizes(ib)
ALLOCATE (rowblock(ib)%mat(na, nb))
rowblock(ib)%mat = 0.0_dp
CALL dbcsr_get_block_p(matrix=matrix_smo(1)%matrix, row=ia, col=ib, &
block=block, found=found)
IF (found) rowblock(ib)%mat(1:na, 1:nb) = block(1:na, 1:nb)
CALL mp_sum(rowblock(ib)%mat, para_env%group)
END DO
!
DO ispin = 1, nspin
CALL dbcsr_copy(tmat, mao_coef(ispin)%matrix)
CALL dbcsr_replicate_all(tmat)
CALL dbcsr_iterator_start(dbcsr_iter, matrix_s(1, 1)%matrix)
DO WHILE (dbcsr_iterator_blocks_left(dbcsr_iter))
CALL dbcsr_iterator_next_block(dbcsr_iter, iatom, jatom, block)
CALL dbcsr_get_block_p(matrix=sumat, row=iatom, col=jatom, block=sblk, found=fos)
CPASSERT(fos)
CALL dbcsr_get_block_p(matrix=rumat, row=iatom, col=jatom, block=rblku, found=for)
CPASSERT(for)
CALL dbcsr_get_block_p(matrix=rumat, row=jatom, col=iatom, block=rblkl, found=for)
CPASSERT(for)
CALL dbcsr_get_block_p(matrix=tmat, row=ia, col=ia, block=cmao, found=found)
CPASSERT(found)
IF (iatom /= ia .AND. jatom /= ia) THEN
! copy original overlap matrix
sblk = block
rblku = block
rblkl = TRANSPOSE(block)
ELSE IF (iatom /= ia) THEN
rblkl = TRANSPOSE(block)
sblk = MATMUL(TRANSPOSE(rowblock(iatom)%mat), cmao)
rblku = sblk
ELSE IF (jatom /= ia) THEN
rblku = block
sblk = MATMUL(TRANSPOSE(cmao), rowblock(jatom)%mat)
rblkl = TRANSPOSE(sblk)
ELSE
CALL dbcsr_get_block_p(matrix=smat_diag, row=ia, col=ia, block=block, found=found)
CPASSERT(found)
sblk = MATMUL(TRANSPOSE(cmao), MATMUL(block, cmao))
rblku = MATMUL(TRANSPOSE(rowblock(ia)%mat), cmao)
END IF
END DO
CALL dbcsr_iterator_stop(dbcsr_iter)
! Cholesky decomposition of SUMAT = U'U
CALL dbcsr_desymmetrize(sumat, cholmat)
CALL cp_dbcsr_cholesky_decompose(cholmat, para_env=para_env, blacs_env=blacs_env)
! T = R*inv(U)
ssize = SUM(mao_blk)
CALL cp_dbcsr_cholesky_restore(rumat, ssize, cholmat, crumat, op="SOLVE", pos="RIGHT", &
transa="N", para_env=para_env, blacs_env=blacs_env)
! A = T*transpose(T)
CALL dbcsr_multiply("N", "T", 1.0_dp, crumat, crumat, 0.0_dp, amat, &
filter_eps=eps_filter)
! Tr(P*A)
CALL dbcsr_trace(matrix_p(ispin, 1)%matrix, amat, uaq(ia, ispin))
uaq(ia, ispin) = uaq(ia, ispin)-electra(ispin)
END DO
!
CALL dbcsr_release(sumat)
CALL dbcsr_release(cholmat)
CALL dbcsr_release(rumat)
CALL dbcsr_release(crumat)
!
DO ib = 1, natom
DEALLOCATE (rowblock(ib)%mat)
END DO
DEALLOCATE (rowblock)
END DO
CALL dbcsr_release(smat_diag)
CALL dbcsr_release(amat)
CALL dbcsr_release(tmat)
DEALLOCATE (orb_blk, mao_blk)
END IF
!
raq(1:natom, 1:nspin) = raq(1:natom, 1:nspin)-uaq(1:natom, 1:nspin)
DO ispin = 1, nspin
deltaq = electra(ispin)-SUM(raq(1:natom, ispin))
IF (unit_nr > 0) THEN
WRITE (UNIT=unit_nr, FMT="(T2,A,T32,A,i2,T55,A,F12.8)") &
"Charge/Atom redistributed", "Spin ", ispin, "delta charge =", &
(deltaq+ua_charge(ispin))/REAL(natom, KIND=dp)
END IF
END DO
! output charges
IF (unit_nr > 0) THEN
IF (nspin == 1) THEN
WRITE (unit_nr, "(/,T2,A,T40,A,T75,A)") "MAO atomic charges ", "Atom", "Charge"
ELSE
WRITE (unit_nr, "(/,T2,A,T40,A,T55,A,T70,A)") "MAO atomic charges ", "Atom", "Charge", "Spin Charge"
END IF
DO ispin = 1, nspin
deltaq = electra(ispin)-SUM(raq(1:natom, ispin))
raq(:, ispin) = raq(:, ispin)+deltaq/REAL(natom, KIND=dp)
END DO
total_charge = 0.0_dp
total_spin = 0.0_dp
DO iatom = 1, natom
CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, &
element_symbol=element_symbol, kind_number=ikind)
CALL get_qs_kind(qs_kind_set(ikind), zeff=zeff)
IF (nspin == 1) THEN
WRITE (unit_nr, "(T30,I6,T42,A2,T69,F12.6)") iatom, element_symbol, zeff-raq(iatom, 1)
total_charge = total_charge+(zeff-raq(iatom, 1))
ELSE
WRITE (unit_nr, "(T30,I6,T42,A2,T48,F12.6,T69,F12.6)") iatom, element_symbol, &
zeff-raq(iatom, 1)-raq(iatom, 2), raq(iatom, 1)-raq(iatom, 2)
total_charge = total_charge+(zeff-raq(iatom, 1)-raq(iatom, 2))
total_spin = total_spin+(raq(iatom, 1)-raq(iatom, 2))
END IF
END DO
IF (nspin == 1) THEN
WRITE (unit_nr, "(T2,A,T69,F12.6)") "Total Charge", total_charge
ELSE
WRITE (unit_nr, "(T2,A,T49,F12.6,T69,F12.6)") "Total Charge", total_charge, total_spin
END IF
END IF
IF (analyze_ua) THEN
! output unassigned charges
IF (unit_nr > 0) THEN
IF (nspin == 1) THEN
WRITE (unit_nr, "(/,T2,A,T40,A,T75,A)") "MAO hypervalent charges ", "Atom", "Charge"
ELSE
WRITE (unit_nr, "(/,T2,A,T40,A,T55,A,T70,A)") "MAO hypervalent charges ", "Atom", &
"Charge", "Spin Charge"
END IF
total_charge = 0.0_dp
total_spin = 0.0_dp
DO iatom = 1, natom
CALL get_atomic_kind(atomic_kind=particle_set(iatom)%atomic_kind, &
element_symbol=element_symbol)
IF (nspin == 1) THEN
WRITE (unit_nr, "(T30,I6,T42,A2,T69,F12.6)") iatom, element_symbol, uaq(iatom, 1)
total_charge = total_charge+uaq(iatom, 1)
ELSE
WRITE (unit_nr, "(T30,I6,T42,A2,T48,F12.6,T69,F12.6)") iatom, element_symbol, &
uaq(iatom, 1)+uaq(iatom, 2), uaq(iatom, 1)-uaq(iatom, 2)
total_charge = total_charge+uaq(iatom, 1)+uaq(iatom, 2)
total_spin = total_spin+uaq(iatom, 1)-uaq(iatom, 2)
END IF
END DO
IF (nspin == 1) THEN
WRITE (unit_nr, "(T2,A,T69,F12.6)") "Total Charge", total_charge
ELSE
WRITE (unit_nr, "(T2,A,T49,F12.6,T69,F12.6)") "Total Charge", total_charge, total_spin
END IF
END IF
END IF
! output shared electron numbers AB
IF (unit_nr > 0) THEN
IF (nspin == 1) THEN
WRITE (unit_nr, "(/,T2,A,T31,A,T40,A,T78,A)") "Shared electron numbers ", "Atom", "Atom", "SEN"
ELSE
WRITE (unit_nr, "(/,T2,A,T31,A,T40,A,T51,A,T63,A,T71,A)") "Shared electron numbers ", "Atom", "Atom", &
"SEN(1)", "SEN(2)", "SEN(total)"
END IF
DO ia = 1, natom
DO ib = ia+1, natom
CALL get_atomic_kind(atomic_kind=particle_set(ia)%atomic_kind, element_symbol=esa)
CALL get_atomic_kind(atomic_kind=particle_set(ib)%atomic_kind, element_symbol=esb)
IF (nspin == 1) THEN
IF (selnAB(ia, ib, 1) > eps_ab) THEN
WRITE (unit_nr, "(T26,I6,' ',A2,T35,I6,' ',A2,T69,F12.6)") ia, esa, ib, esb, selnAB(ia, ib, 1)
END IF
ELSE
IF ((selnAB(ia, ib, 1)+selnAB(ia, ib, 2)) > eps_ab) THEN
WRITE (unit_nr, "(T26,I6,' ',A2,T35,I6,' ',A2,T45,3F12.6)") ia, esa, ib, esb, &
selnAB(ia, ib, 1), selnAB(ia, ib, 2), (selnAB(ia, ib, 1)+selnAB(ia, ib, 2))
END IF
END IF
END DO
END DO
END IF
IF (.NOT. neglect_abc) THEN
! output shared electron numbers ABC
IF (unit_nr > 0) THEN
WRITE (unit_nr, "(/,T2,A,T40,A,T49,A,T58,A,T78,A)") "Shared electron numbers ABC", &
"Atom", "Atom", "Atom", "SEN"
senmax = 0.0_dp
iabc = 0
DO ia = 1, natom
DO ib = ia+1, natom
DO ic = ib+1, natom
iabc = iabc+1
senabc = SUM(selnABC(iabc, :))
senmax = MAX(senmax, senabc)
IF (senabc > eps_abc) THEN
CALL get_atomic_kind(atomic_kind=particle_set(ia)%atomic_kind, element_symbol=esa)
CALL get_atomic_kind(atomic_kind=particle_set(ib)%atomic_kind, element_symbol=esb)
CALL get_atomic_kind(atomic_kind=particle_set(ic)%atomic_kind, element_symbol=esc)
WRITE (unit_nr, "(T35,I6,' ',A2,T44,I6,' ',A2,T53,I6,' ',A2,T69,F12.6)") &
ia, esa, ib, esb, ic, esc, senabc
END IF
END DO
END DO
END DO
WRITE (unit_nr, "(T2,A,T69,F12.6)") "Maximum SEN value calculated", senmax
END IF
END IF
IF (unit_nr > 0) THEN
WRITE (unit_nr, '(/,T2,A)') &
'!---------------------------END OF MAO ANALYSIS-------------------------------!'
END IF
! Deallocate temporary arrays
DEALLOCATE (occnumA, occnumAB, selnAB, raq, uaq)
IF (.NOT. neglect_abc) THEN
DEALLOCATE (occnumABC, selnABC)
END IF
! Deallocate the neighbor list structure
IF (ASSOCIATED(smm_list)) THEN
DO iab = 1, SIZE(smm_list)
CALL deallocate_neighbor_list_set(smm_list(iab)%neighbor_list_set)
END DO
DEALLOCATE (smm_list)
END IF
IF (ASSOCIATED(smo_list)) THEN
DO iab = 1, SIZE(smo_list)
CALL deallocate_neighbor_list_set(smo_list(iab)%neighbor_list_set)
END DO
DEALLOCATE (smo_list)
END IF
DEALLOCATE (mao_basis_set_list, orb_basis_set_list)
IF (ASSOCIATED(matrix_smm)) CALL dbcsr_deallocate_matrix_set(matrix_smm)
IF (ASSOCIATED(matrix_smo)) CALL dbcsr_deallocate_matrix_set(matrix_smo)
IF (ASSOCIATED(matrix_q)) CALL dbcsr_deallocate_matrix_set(matrix_q)
IF (ASSOCIATED(mao_coef)) CALL dbcsr_deallocate_matrix_set(mao_coef)
IF (ASSOCIATED(mao_dmat)) CALL dbcsr_deallocate_matrix_set(mao_dmat)
IF (ASSOCIATED(mao_smat)) CALL dbcsr_deallocate_matrix_set(mao_smat)
IF (ASSOCIATED(mao_qmat)) CALL dbcsr_deallocate_matrix_set(mao_qmat)
CALL timestop(handle)
END SUBROUTINE mao_analysis
END MODULE mao_wfn_analysis
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