Calculates the moment integrals <a|r^m|b> and <a|r x d/dr|b>. More...

Functions/Subroutines
subroutine, public	build_local_moment_matrix (qs_env, moments, nmoments, ref_point, ref_points, basis_type, all_images, minimum_image, neighbor_image, first_component)
	...
subroutine, public	get_multipoles_ao (qs_env, n_moments, matrix_multipole, rpoint)
	The AO multipoles M^k_µν = <φ_µ\|(r - r_0)^k\|φ_ν> of every order up to n_moments, on the block pattern of the overlap, about r_0, the centre of atomic charges; k = x, y, z for order 1, then xx, xy, xz, yy, yz, zz for order 2.
subroutine, public	build_local_moments_der_matrix (qs_env, moments_der, nmoments_der, nmoments, ref_point, moments, basis_type, minimum_image, ordered, lambda, deltar, neighbor_image)
	Calculate right-hand sided derivatives of multipole moments, e. g. < a \| xy d/dz \| b > Optionally stores the multipole moments themselves for free. Note that the multipole moments are symmetric while their derivatives are anti-symmetric Only first derivatives are performed, e. g. x d/dy.
subroutine, public	build_local_magmom_matrix (qs_env, magmom, nmoments, ref_point, ref_points, basis_type)
	...
subroutine, public	build_berry_moment_matrix (qs_env, cosmat, sinmat, kvec, sab_orb_external, basis_type)
	...
subroutine, public	build_berry_kpoint_matrix (qs_env, cosmat, sinmat, kvec, basis_type, ordered, ordered_kpoints)
	...
subroutine, public	qs_moment_berry_phase (qs_env, magnetic, nmoments, reference, ref_point, unit_number, unit_str)
	...
subroutine, public	op_orbbas (cosmat, sinmat, mos, op_fm_set, opvec)
	...
subroutine, public	op_orbbas_rtp (cosmat, sinmat, mos, op_fm_set, mos_new)
	...
subroutine, public	qs_moment_locop (qs_env, magnetic, nmoments, reference, ref_point, unit_number, vel_reprs, com_nl, unit_str)
	...
subroutine, public	set_label (label, ix, iy, iz)
	...
subroutine, public	print_moments (unit_number, nmom, rmom, rlab, rcc, cell, periodic, mmom, rmom_vel, unit_str)
	...
subroutine, public	print_moments_nl (unit_number, nmom, rlab, mmom, rmom_vel)
	...
subroutine, public	calculate_commutator_nl_terms (qs_env, nlcom_rv, nlcom_rxrv, nlcom_rrv, nlcom_rvr, nlcom_rrv_vrr, ref_point)
	Calculate the expectation value of operators related to non-local potential: [r, Vnl], noted rv r x [r,Vnl], noted rxrv [rr,Vnl], noted rrv r x Vnl x r, noted rvr r x r x Vnl + Vnl x r x r, noted rrv_vrr Note that the 3 first operator are commutator while the 2 last are not. For reading clarity the same notation is used for all 5 operators.
subroutine, public	build_local_moment_matrix_rs_img (qs_env, moments_rs_img, rcc)
	Calculate local moment matrix for a periodic system for all image cells.
subroutine, public	qs_moment_kpoints_deep (qs_env, xkp, dipole, rcc, berry_c, momentum, energy, do_parallel)
	Calculate interband k-point dipole moments d_nm(k) = i<u_n\|∇_k\|u_m>, Berry curvature, momentum and band energies for a periodic system for k-points.
subroutine, public	qs_moment_kpoints_deep_soc (qs_env, xkp, dipole, rcc, berry_c, momentum, energy, do_parallel)
	Calculate interband k-point dipole moments d_nm(k) = i<u_n\|∇_k\|u_m>, Berry curvature, momentum and band energies for a periodic system for k-points with spin-orbit coupling (SOC) in the 2nao spinor basis, via the length-gauge sum rule. SOC enters both the Hamiltonian and the velocity operator (the k-derivative of V^SOC is included). Mirrors qs_moment_kpoints_deep but promoted to spinor space; the two spin channels are merged into 2nao spinor bands (returned with spin dimension 1).
subroutine, public	qs_moment_kpoints_scf_mos (qs_env, dipole, rcc, nmo_spin_out)
	Calculates interband k-point dipoles in the existing SCF MO basis.
subroutine, public	qs_moment_kpoints (qs_env, nmoments, reference, ref_point, max_nmo, unit_number, do_soc, unit_str, dip_file, bc_file)
	Calculate and print dipole moment elements d_nm(k) = i<u_n\|∇_k\|u_m> for k-point calculations.

Detailed Description

Calculates the moment integrals <a|r^m|b> and <a|r x d/dr|b>.

History: added angular moments (JGH 11.2012)

Author: JGH (20.07.2006)

Function/Subroutine Documentation

◆ build_local_moment_matrix()

subroutine, public qs_moments::build_local_moment_matrix	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_p_type), dimension(:), pointer	moments,
		integer, intent(in)	nmoments,
		real(kind=dp), dimension(:), intent(in), optional	ref_point,
		real(kind=dp), dimension(:, :), intent(in), optional	ref_points,
		character(len=*), optional	basis_type,
		logical, optional	all_images,
		logical, optional	minimum_image,
		logical, optional	neighbor_image,
		integer, optional	first_component )

...

Parameters

qs_env	...
moments	...
nmoments	...
ref_point	...
ref_points	...
basis_type	...
all_images	accumulate all neighbor images belonging to one atom pair
minimum_image	apply the half-cell image filter
neighbor_image	preserve the neighbor-list image geometry
first_component	first Cartesian moment component to write

Definition at line 176 of file qs_moments.F.

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◆ get_multipoles_ao()

subroutine, public qs_moments::get_multipoles_ao	(	type(qs_environment_type), pointer	qs_env,
		integer, intent(in)	n_moments,
		type(dbcsr_p_type), dimension(:), pointer	matrix_multipole,
		real(kind=dp), dimension(3), intent(out)	rpoint )

The AO multipoles M^k_µν = <φ_µ|(r - r_0)^k|φ_ν> of every order up to n_moments, on the block pattern of the overlap, about r_0, the centre of atomic charges; k = x, y, z for order 1, then xx, xy, xz, yy, yz, zz for order 2.

Parameters

qs_env	source of the basis, the geometry and the overlap's block pattern
n_moments	highest order, 1 for dipoles, 2 adds quadrupoles
matrix_multipole	M^k_µν, one entry per component k, allocated here; the caller releases it
rpoint	r_0

Definition at line 441 of file qs_moments.F.

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◆ build_local_moments_der_matrix()

subroutine, public qs_moments::build_local_moments_der_matrix	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_p_type), dimension(:, :), intent(inout), pointer	moments_der,
		integer, intent(in)	nmoments_der,
		integer, intent(in)	nmoments,
		real(kind=dp), dimension(:), intent(in), optional	ref_point,
		type(dbcsr_p_type), dimension(:), intent(inout), optional, pointer	moments,
		character(len=*), optional	basis_type,
		logical, optional	minimum_image,
		logical, optional	ordered,
		integer, optional	lambda,
		real(kind=dp), dimension(:, :), optional, pointer	deltar,
		logical, optional	neighbor_image )

Calculate right-hand sided derivatives of multipole moments, e. g. < a | xy d/dz | b > Optionally stores the multipole moments themselves for free. Note that the multipole moments are symmetric while their derivatives are anti-symmetric Only first derivatives are performed, e. g. x d/dy.

Parameters

qs_env	...
moments_der	will contain the derivatives of the multipole moments
nmoments_der	order of the moments with derivatives
nmoments	order of the multipole moments (no derivatives, same output as build_local_moment_matrix, needs moments as arguments to store results)
ref_point	...
moments	contains the multipole moments, optionally for free, up to order nmoments
basis_type	basis set used for the integral evaluation
minimum_image	apply the half-cell image filter
ordered	use ordered neighbor blocks and, for ordinary derivatives, the full neighbor list
lambda	optional atom selector for the right-hand derivative
deltaR	optional weights for left and right nuclear-coordinate derivatives
neighbor_image	use the neighbor-list image for coordinate construction

Definition at line 499 of file qs_moments.F.

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◆ build_local_magmom_matrix()

subroutine, public qs_moments::build_local_magmom_matrix	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_p_type), dimension(:), pointer	magmom,
		integer, intent(in)	nmoments,
		real(kind=dp), dimension(:), intent(in), optional	ref_point,
		real(kind=dp), dimension(:, :), intent(in), optional	ref_points,
		character(len=*), optional	basis_type )

...

Parameters

qs_env	...
magmom	...
nmoments	...
ref_point	...
ref_points	...
basis_type	...

Definition at line 907 of file qs_moments.F.

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◆ build_berry_moment_matrix()

subroutine, public qs_moments::build_berry_moment_matrix	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_type), pointer	cosmat,
		type(dbcsr_type), pointer	sinmat,
		real(kind=dp), dimension(3), intent(in)	kvec,
		type(neighbor_list_set_p_type), dimension(:), optional, pointer	sab_orb_external,
		character(len=*), optional	basis_type )

...

Parameters

qs_env	...
cosmat	...
sinmat	...
kvec	...
sab_orb_external	...
basis_type	...

Definition at line 1113 of file qs_moments.F.

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◆ build_berry_kpoint_matrix()

subroutine, public qs_moments::build_berry_kpoint_matrix	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_p_type), dimension(:, :), pointer	cosmat,
		type(dbcsr_p_type), dimension(:, :), pointer	sinmat,
		real(kind=dp), dimension(3), intent(in)	kvec,
		character(len=*), optional	basis_type,
		logical, intent(in), optional	ordered,
		type(kpoint_type), optional, pointer	ordered_kpoints )

...

Parameters

qs_env	...
cosmat	...
sinmat	...
kvec	...
basis_type	...
ordered	use all ordered atom pairs for a non-Hermitian cross-k overlap
ordered_kpoints	image-cell mapping for the ordered neighbour list

Definition at line 1151 of file qs_moments.F.

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◆ qs_moment_berry_phase()

subroutine, public qs_moments::qs_moment_berry_phase	(	type(qs_environment_type), pointer	qs_env,
		logical, intent(in)	magnetic,
		integer, intent(in)	nmoments,
		integer, intent(in)	reference,
		real(dp), dimension(:), pointer	ref_point,
		integer, intent(in)	unit_number,
		character(len=*), intent(in), optional	unit_str )

...

Parameters

qs_env	...
magnetic	...
nmoments	...
reference	...
ref_point	...
unit_number	...
unit_str	unit of the printed moments (dipole unit of cp_units), default debye

Definition at line 1380 of file qs_moments.F.

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◆ op_orbbas()

subroutine, public qs_moments::op_orbbas	(	type(dbcsr_type), pointer	cosmat,
		type(dbcsr_type), pointer	sinmat,
		type(mo_set_type), dimension(:), intent(in)	mos,
		type(cp_fm_type), dimension(:, :), intent(in)	op_fm_set,
		type(cp_fm_type), dimension(:), intent(inout)	opvec )

...

Parameters

cosmat	...
sinmat	...
mos	...
op_fm_set	...
opvec	...

Definition at line 1835 of file qs_moments.F.

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◆ op_orbbas_rtp()

subroutine, public qs_moments::op_orbbas_rtp	(	type(dbcsr_type), pointer	cosmat,
		type(dbcsr_type), pointer	sinmat,
		type(mo_set_type), dimension(:), intent(in)	mos,
		type(cp_fm_type), dimension(:, :), intent(in)	op_fm_set,
		type(cp_fm_type), dimension(:), pointer	mos_new )

...

Parameters

cosmat	...
sinmat	...
mos	...
op_fm_set	...
mos_new	...

Definition at line 1865 of file qs_moments.F.

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◆ qs_moment_locop()

subroutine, public qs_moments::qs_moment_locop	(	type(qs_environment_type), pointer	qs_env,
		logical, intent(in)	magnetic,
		integer, intent(in)	nmoments,
		integer, intent(in)	reference,
		real(dp), dimension(:), intent(in), pointer	ref_point,
		integer, intent(in)	unit_number,
		logical, intent(in), optional	vel_reprs,
		logical, intent(in), optional	com_nl,
		character(len=*), intent(in), optional	unit_str )

...

Parameters

qs_env	...
magnetic	...
nmoments	...
reference	...
ref_point	...
unit_number	...
vel_reprs	...
com_nl	...
unit_str	unit of the printed moments (dipole unit of cp_units), default debye

Definition at line 1958 of file qs_moments.F.

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◆ set_label()

subroutine, public qs_moments::set_label	(	character(len=*), intent(out)	label,
		integer, intent(in)	ix,
		integer, intent(in)	iy,
		integer, intent(in)	iz )

...

Parameters

label	...
ix	...
iy	...
iz	...

Definition at line 2372 of file qs_moments.F.

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◆ print_moments()

subroutine, public qs_moments::print_moments	(	integer, intent(in)	unit_number,
		integer, intent(in)	nmom,
		real(dp), dimension(:, :), intent(in)	rmom,
		character(len=8), dimension(:)	rlab,
		real(dp), dimension(3), intent(in)	rcc,
		type(cell_type), pointer	cell,
		logical	periodic,
		real(dp), dimension(:), intent(in), optional	mmom,
		real(dp), dimension(:), intent(in), optional	rmom_vel,
		character(len=*), intent(in), optional	unit_str )

...

Parameters

unit_number	...
nmom	...
rmom	...
rlab	...
rcc	...
cell	...
periodic	...
mmom	...
rmom_vel	...
unit_str	unit of the printed electric moments (a dipole unit of cp_units), default debye

Definition at line 2404 of file qs_moments.F.

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◆ print_moments_nl()

subroutine, public qs_moments::print_moments_nl	(	integer, intent(in)	unit_number,
		integer, intent(in)	nmom,
		character(len=8), dimension(:)	rlab,
		real(dp), dimension(:), intent(in), optional	mmom,
		real(dp), dimension(:), intent(in), optional	rmom_vel )

...

Parameters

unit_number	...
nmom	...
rlab	...
mmom	...
rmom_vel	...

Definition at line 2585 of file qs_moments.F.

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◆ calculate_commutator_nl_terms()

subroutine, public qs_moments::calculate_commutator_nl_terms	(	type(qs_environment_type), pointer	qs_env,
		real(dp), dimension(:), optional, allocatable	nlcom_rv,
		real(dp), dimension(:), optional, allocatable	nlcom_rxrv,
		real(dp), dimension(:), optional, allocatable	nlcom_rrv,
		real(dp), dimension(:), optional, allocatable	nlcom_rvr,
		real(dp), dimension(:), optional, allocatable	nlcom_rrv_vrr,
		real(dp), dimension(3)	ref_point )

Calculate the expectation value of operators related to non-local potential: [r, Vnl], noted rv r x [r,Vnl], noted rxrv [rr,Vnl], noted rrv r x Vnl x r, noted rvr r x r x Vnl + Vnl x r x r, noted rrv_vrr Note that the 3 first operator are commutator while the 2 last are not. For reading clarity the same notation is used for all 5 operators.

Parameters

qs_env	...
nlcom_rv	...
nlcom_rxrv	...
nlcom_rrv	...
nlcom_rvr	...
nlcom_rrv_vrr	...
ref_point	...

Definition at line 2652 of file qs_moments.F.

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◆ build_local_moment_matrix_rs_img()

subroutine, public qs_moments::build_local_moment_matrix_rs_img	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_p_type), dimension(:, :), pointer	moments_rs_img,
		real(kind=dp), dimension(3), optional	rcc )

Calculate local moment matrix for a periodic system for all image cells.

Parameters

qs_env	...
moments_rs_img	...
rcc	...

Author: Shridhar Shanbhag

Definition at line 3029 of file qs_moments.F.

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◆ qs_moment_kpoints_deep()

subroutine, public qs_moments::qs_moment_kpoints_deep	(	type(qs_environment_type), pointer	qs_env,
		real(kind=dp), dimension(:, :), allocatable	xkp,
		complex(kind=dp), dimension(:, :, :, :, :), optional, allocatable	dipole,
		real(kind=dp), dimension(3), optional	rcc,
		real(kind=dp), dimension(:, :, :, :), optional, allocatable	berry_c,
		complex(kind=dp), dimension(:, :, :, :, :), optional, allocatable	momentum,
		real(kind=dp), dimension(:, :, :), optional, allocatable	energy,
		logical, optional	do_parallel )

Calculate interband k-point dipole moments d_nm(k) = i<u_n|∇_k|u_m>, Berry curvature, momentum and band energies for a periodic system for k-points.

Parameters

qs_env	...
xkp	list of kpoints
dipole	...
rcc	coordinates about which to calculate the dipole
berry_c	berry curvature calculated using Ω^γ_n = -Σ_{m≠n} 2*Im[d^α_nm d^β_mn]
momentum	...
energy	...
do_parallel	option to distribute the result in dipole across different MPI ranks

Author: Shridhar Shanbhag

Definition at line 3271 of file qs_moments.F.

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◆ qs_moment_kpoints_deep_soc()

subroutine, public qs_moments::qs_moment_kpoints_deep_soc	(	type(qs_environment_type), pointer	qs_env,
		real(kind=dp), dimension(:, :), allocatable	xkp,
		complex(kind=dp), dimension(:, :, :, :, :), optional, allocatable	dipole,
		real(kind=dp), dimension(3), optional	rcc,
		real(kind=dp), dimension(:, :, :, :), optional, allocatable	berry_c,
		complex(kind=dp), dimension(:, :, :, :, :), optional, allocatable	momentum,
		real(kind=dp), dimension(:, :, :), optional, allocatable	energy,
		logical, optional	do_parallel )

Calculate interband k-point dipole moments d_nm(k) = i<u_n|∇_k|u_m>, Berry curvature, momentum and band energies for a periodic system for k-points with spin-orbit coupling (SOC) in the 2*nao spinor basis, via the length-gauge sum rule. SOC enters both the Hamiltonian and the velocity operator (the k-derivative of V^SOC is included). Mirrors qs_moment_kpoints_deep but promoted to spinor space; the two spin channels are merged into 2*nao spinor bands (returned with spin dimension 1).

Parameters

qs_env	...
xkp	k-points at which the dipoles are evaluated
dipole	optional output dipoles, dim (1, k copy, 3, 2nao, 2nao)
rcc	reference point for the local dipole operator (interband dipoles are origin-independent)
berry_c	optional SOC Berry curvature, dim (1, k copy, 3, 2*nao)
momentum	optional SOC momentum matrix elements p_nm, dim (1, k copy, 3, 2nao, 2nao)
energy	optional spinor band energies, dim (1, k copy, 2*nao)
do_parallel	distribute k-points over MPI ranks

Author: Shridhar Shanbhag

Definition at line 3572 of file qs_moments.F.

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◆ qs_moment_kpoints_scf_mos()

subroutine, public qs_moments::qs_moment_kpoints_scf_mos	(	type(qs_environment_type), pointer	qs_env,
		complex(kind=dp), dimension(:, :, :, :, :), allocatable	dipole,
		real(kind=dp), dimension(3), optional	rcc,
		integer, dimension(:), intent(out), optional, allocatable	nmo_spin_out )

Calculates interband k-point dipoles in the existing SCF MO basis.

Parameters

qs_env	...
dipole	...
rcc	retained for interface compatibility; interband dipoles are origin independent
nmo_spin_out	number of SCF MOs available for each spin

Definition at line 3846 of file qs_moments.F.

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◆ qs_moment_kpoints()

subroutine, public qs_moments::qs_moment_kpoints	(	type(qs_environment_type), pointer	qs_env,
		integer, intent(in)	nmoments,
		integer, intent(in)	reference,
		real(dp), dimension(:), intent(in), pointer	ref_point,
		integer, intent(in)	max_nmo,
		integer, intent(in)	unit_number,
		logical, intent(in)	do_soc,
		character(len=*), intent(in), optional	unit_str,
		character(len=*), intent(in), optional	dip_file,
		character(len=*), intent(in), optional	bc_file )

Calculate and print dipole moment elements d_nm(k) = i<u_n|∇_k|u_m> for k-point calculations.

Parameters

qs_env	...
nmoments	...
reference	...
ref_point	...
max_nmo	...
unit_number	...
do_soc	include spin-orbit coupling (spinor sum-rule; requires an explicit KPOINT set)
unit_str	unit of the printed dipoles (dipole unit of cp_units), default debye; the Berry curvature is printed in the paired length unit squared
dip_file	if present and non-empty, the dipole matrix elements are written to this file instead of being printed to unit_number
bc_file	if present and non-empty, the Berry curvature is written to this file instead of being printed to unit_number

Author: Shridhar Shanbhag

Definition at line 4080 of file qs_moments.F.

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ build_local_moment_matrix()

◆ get_multipoles_ao()

◆ build_local_moments_der_matrix()

◆ build_local_magmom_matrix()

◆ build_berry_moment_matrix()

◆ build_berry_kpoint_matrix()

◆ qs_moment_berry_phase()

◆ op_orbbas()

◆ op_orbbas_rtp()

◆ qs_moment_locop()

◆ set_label()

◆ print_moments()

◆ print_moments_nl()

◆ calculate_commutator_nl_terms()

◆ build_local_moment_matrix_rs_img()

◆ qs_moment_kpoints_deep()

◆ qs_moment_kpoints_deep_soc()

◆ qs_moment_kpoints_scf_mos()

◆ qs_moment_kpoints()