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semi_empirical_mpole_methods.F
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semi_empirical_mpole_methods.F
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!--------------------------------------------------------------------------------------------------!
! CP2K: A general program to perform molecular dynamics simulations !
! Copyright 2000-2024 CP2K developers group <https://cp2k.org> !
! !
! SPDX-License-Identifier: GPL-2.0-or-later !
!--------------------------------------------------------------------------------------------------!
! **************************************************************************************************
!> \brief Setup and Methods for semi-empirical multipole types
!> \author Teodoro Laino [tlaino] - 08.2008 Zurich University
! **************************************************************************************************
MODULE semi_empirical_mpole_methods
USE input_constants, ONLY: do_method_pnnl
USE kinds, ONLY: dp
USE semi_empirical_int_arrays, ONLY: alm,&
indexa,&
indexb,&
se_map_alm
USE semi_empirical_mpole_types, ONLY: nddo_mpole_create,&
nddo_mpole_release,&
nddo_mpole_type,&
semi_empirical_mpole_p_create,&
semi_empirical_mpole_p_type,&
semi_empirical_mpole_type
USE semi_empirical_par_utils, ONLY: amn_l
USE semi_empirical_types, ONLY: semi_empirical_type
#include "./base/base_uses.f90"
IMPLICIT NONE
PRIVATE
! *** Global parameters ***
LOGICAL, PARAMETER, PRIVATE :: debug_this_module = .FALSE.
CHARACTER(len=*), PARAMETER, PRIVATE :: moduleN = 'semi_empirical_mpole_methods'
PUBLIC :: semi_empirical_mpole_p_setup, &
nddo_mpole_setup, &
quadrupole_sph_to_cart
CONTAINS
! **************************************************************************************************
!> \brief Setup semi-empirical mpole type
!> This function setup for each semi-empirical type a structure containing
!> the multipolar expansion for all possible combination on-site of atomic
!> orbitals ( \mu \nu |
!> \param mpoles ...
!> \param se_parameter ...
!> \param method ...
!> \date 09.2008
!> \author Teodoro Laino [tlaino] - University of Zurich
! **************************************************************************************************
SUBROUTINE semi_empirical_mpole_p_setup(mpoles, se_parameter, method)
TYPE(semi_empirical_mpole_p_type), DIMENSION(:), &
POINTER :: mpoles
TYPE(semi_empirical_type), POINTER :: se_parameter
INTEGER, INTENT(IN) :: method
CHARACTER(LEN=3), DIMENSION(9), PARAMETER :: &
label_print_orb = (/" s", " px", " py", " pz", "dx2", "dzx", "dz2", "dzy", "dxy"/)
INTEGER, DIMENSION(9), PARAMETER :: loc_index = (/1, 2, 2, 2, 3, 3, 3, 3, 3/)
INTEGER :: a, b, i, ind1, ind2, j, k, k1, k2, mu, &
natorb, ndim, nr
REAL(KIND=dp) :: dlm, tmp, wp, ws, zb, ZP, ZS, zt
REAL(KIND=dp), DIMENSION(3, 3, 45) :: M2
REAL(KIND=dp), DIMENSION(3, 45) :: M1
REAL(KIND=dp), DIMENSION(45) :: M0
REAL(KIND=dp), DIMENSION(6, 0:2) :: amn
TYPE(semi_empirical_mpole_type), POINTER :: mpole
CPASSERT(.NOT. ASSOCIATED(mpoles))
! If there are atomic orbitals proceed with the expansion in multipoles
natorb = se_parameter%natorb
IF (natorb /= 0) THEN
ndim = natorb*(natorb + 1)/2
CALL semi_empirical_mpole_p_create(mpoles, ndim)
! Select method for multipolar expansion
! Fill in information on multipole expansion due to atomic orbitals charge
! distribution
NULLIFY (mpole)
CALL amn_l(se_parameter, amn)
DO i = 1, natorb
DO j = 1, i
ind1 = indexa(se_map_alm(i), se_map_alm(j))
ind2 = indexb(i, j)
! the order in the mpoles structure is like the standard one for the
! integrals: s px py pz dx2-y2 dzx dz2 dzy dxy (lower triangular)
! which differs from the order of the Hamiltonian in CP2K. But I
! preferred to keep this order for consistency with the integrals
mpole => mpoles(ind2)%mpole
mpole%indi = i
mpole%indj = j
a = loc_index(i)
b = loc_index(j)
mpole%c = HUGE(0.0_dp)
mpole%d = HUGE(0.0_dp)
mpole%qs = HUGE(0.0_dp)
mpole%qc = HUGE(0.0_dp)
! Charge
IF (alm(ind1, 0, 0) /= 0.0_dp) THEN
dlm = 1.0_dp/SQRT(REAL((2*0 + 1), KIND=dp))
tmp = -dlm*amn(indexb(a, b), 0)
mpole%c = tmp*alm(ind1, 0, 0)
mpole%task(1) = .TRUE.
END IF
! Dipole
IF (ANY(alm(ind1, 1, -1:1) /= 0.0_dp)) THEN
dlm = 1.0_dp/SQRT(REAL((2*1 + 1), KIND=dp))
tmp = -dlm*amn(indexb(a, b), 1)
mpole%d(1) = tmp*alm(ind1, 1, 1)
mpole%d(2) = tmp*alm(ind1, 1, -1)
mpole%d(3) = tmp*alm(ind1, 1, 0)
mpole%task(2) = .TRUE.
END IF
! Quadrupole
IF (ANY(alm(ind1, 2, -2:2) /= 0.0_dp)) THEN
dlm = 1.0_dp/SQRT(REAL((2*2 + 1), KIND=dp))
tmp = -dlm*amn(indexb(a, b), 2)
! Spherical components
mpole%qs(1) = tmp*alm(ind1, 2, 0) ! d3z2-r2
mpole%qs(2) = tmp*alm(ind1, 2, 1) ! dzx
mpole%qs(3) = tmp*alm(ind1, 2, -1) ! dzy
mpole%qs(4) = tmp*alm(ind1, 2, 2) ! dx2-y2
mpole%qs(5) = tmp*alm(ind1, 2, -2) ! dxy
! Convert into cartesian components
CALL quadrupole_sph_to_cart(mpole%qc, mpole%qs)
mpole%task(3) = .TRUE.
END IF
IF (debug_this_module) THEN
WRITE (*, '(A,2I6,A)') "Orbitals ", i, j, &
" ("//label_print_orb(i)//","//label_print_orb(j)//")"
IF (mpole%task(1)) WRITE (*, '(9F12.6)') mpole%c
IF (mpole%task(2)) WRITE (*, '(9F12.6)') mpole%d
IF (mpole%task(3)) WRITE (*, '(9F12.6)') mpole%qc
WRITE (*, *)
END IF
END DO
END DO
IF (method == do_method_pnnl) THEN
! No d-function for Schenter type integrals
CPASSERT(natorb <= 4)
M0 = 0.0_dp
M1 = 0.0_dp
M2 = 0.0_dp
DO mu = 1, se_parameter%natorb
M0(indexb(mu, mu)) = 1.0_dp
END DO
ZS = se_parameter%sto_exponents(0)
ZP = se_parameter%sto_exponents(1)
nr = se_parameter%nr
ws = REAL((2*nr + 2)*(2*nr + 1), dp)/(24.0_dp*ZS**2)
DO k = 1, 3
M2(k, k, indexb(1, 1)) = ws
END DO
IF (ZP > 0._dp) THEN
zt = SQRT(ZS*ZP)
zb = 0.5_dp*(ZS + ZP)
DO k = 1, 3
M1(k, indexb(1, 1 + k)) = (zt/zb)**(2*nr + 1)*REAL(2*nr + 1, dp)/(2.0*zb*SQRT(3.0_dp))
END DO
wp = REAL((2*nr + 2)*(2*nr + 1), dp)/(40.0_dp*ZP**2)
DO k1 = 1, 3
DO k2 = 1, 3
IF (k1 == k2) THEN
M2(k2, k2, indexb(1 + k1, 1 + k1)) = 3.0_dp*wp
ELSE
M2(k2, k2, indexb(1 + k1, 1 + k1)) = wp
END IF
END DO
END DO
M2(1, 2, indexb(1 + 1, 1 + 2)) = wp
M2(2, 1, indexb(1 + 1, 1 + 2)) = wp
M2(2, 3, indexb(1 + 2, 1 + 3)) = wp
M2(3, 2, indexb(1 + 2, 1 + 3)) = wp
M2(3, 1, indexb(1 + 3, 1 + 1)) = wp
M2(1, 3, indexb(1 + 3, 1 + 1)) = wp
END IF
DO i = 1, natorb
DO j = 1, i
ind1 = indexa(se_map_alm(i), se_map_alm(j))
ind2 = indexb(i, j)
mpole => mpoles(ind2)%mpole
mpole%indi = i
mpole%indj = j
! Charge
mpole%cs = -M0(indexb(i, j))
! Dipole
mpole%ds = -M1(1:3, indexb(i, j))
! Quadrupole
mpole%qq = -3._dp*M2(1:3, 1:3, indexb(i, j))
IF (debug_this_module) THEN
WRITE (*, '(A,2I6,A)') "Orbitals ", i, j, &
" ("//label_print_orb(i)//","//label_print_orb(j)//")"
WRITE (*, '(9F12.6)') mpole%cs
WRITE (*, '(9F12.6)') mpole%ds
WRITE (*, '(9F12.6)') mpole%qq
WRITE (*, *)
END IF
END DO
END DO
ELSE
mpole%cs = mpole%c
mpole%ds = mpole%d
mpole%qq = mpole%qc
END IF
END IF
END SUBROUTINE semi_empirical_mpole_p_setup
! **************************************************************************************************
!> \brief Transforms the quadrupole components from sphericals to cartesians
!> \param qcart ...
!> \param qsph ...
!> \date 09.2008
!> \author Teodoro Laino [tlaino] - University of Zurich
! **************************************************************************************************
SUBROUTINE quadrupole_sph_to_cart(qcart, qsph)
REAL(KIND=dp), DIMENSION(3, 3), INTENT(OUT) :: qcart
REAL(KIND=dp), DIMENSION(5), INTENT(IN) :: qsph
! Notation
! qs(1) - d3z2-r2
! qs(2) - dzx
! qs(3) - dzy
! qs(4) - dx2-y2
! qs(5) - dxy
! Cartesian components
qcart(1, 1) = (qsph(4) - qsph(1)/SQRT(3.0_dp))*SQRT(3.0_dp)/2.0_dp
qcart(2, 1) = qsph(5)*SQRT(3.0_dp)/2.0_dp
qcart(3, 1) = qsph(2)*SQRT(3.0_dp)/2.0_dp
qcart(2, 2) = -(qsph(4) + qsph(1)/SQRT(3.0_dp))*SQRT(3.0_dp)/2.0_dp
qcart(3, 2) = qsph(3)*SQRT(3.0_dp)/2.0_dp
qcart(3, 3) = qsph(1)
! Symmetrize tensor
qcart(1, 2) = qcart(2, 1)
qcart(1, 3) = qcart(3, 1)
qcart(2, 3) = qcart(3, 2)
END SUBROUTINE quadrupole_sph_to_cart
! **************************************************************************************************
!> \brief Setup NDDO multipole type
!> \param nddo_mpole ...
!> \param natom ...
!> \date 09.2008
!> \author Teodoro Laino [tlaino] - University of Zurich
! **************************************************************************************************
SUBROUTINE nddo_mpole_setup(nddo_mpole, natom)
TYPE(nddo_mpole_type), POINTER :: nddo_mpole
INTEGER, INTENT(IN) :: natom
CHARACTER(len=*), PARAMETER :: routineN = 'nddo_mpole_setup'
INTEGER :: handle
CALL timeset(routineN, handle)
IF (ASSOCIATED(nddo_mpole)) THEN
CALL nddo_mpole_release(nddo_mpole)
END IF
CALL nddo_mpole_create(nddo_mpole)
! Allocate Global Arrays
ALLOCATE (nddo_mpole%charge(natom))
ALLOCATE (nddo_mpole%dipole(3, natom))
ALLOCATE (nddo_mpole%quadrupole(3, 3, natom))
ALLOCATE (nddo_mpole%efield0(natom))
ALLOCATE (nddo_mpole%efield1(3, natom))
ALLOCATE (nddo_mpole%efield2(9, natom))
CALL timestop(handle)
END SUBROUTINE nddo_mpole_setup
END MODULE semi_empirical_mpole_methods