qs_operators_ao Module Reference

Functions/Subroutines
subroutine, public	build_lin_mom_matrix (qs_env, matrix)
	Calculation of the linear momentum matrix <mu|∂|nu> over Cartesian Gaussian functions.
subroutine, public	build_ang_mom_matrix (qs_env, matrix, rc)
	Calculation of the angular momentum matrix over Cartesian Gaussian functions.
subroutine, public	p_xyz_ao (op, qs_env, minimum_image)
	Calculation of the components of the dipole operator in the velocity form The elements of the sparse matrices are the integrals in the basis functions.
subroutine, public	rrc_xyz_ao (op, qs_env, rc, order, minimum_image, soft)
	Calculation of the components of the dipole operator in the length form by taking the relative position operator r-Rc, with respect a reference point Rc Probably it does not work for PBC, or maybe yes if the wfn are sufficiently localized The elements of the sparse matrices are the integrals in the basis functions.
subroutine, public	rrc_xyz_der_ao (op, op_der, qs_env, rc, order, minimum_image, soft)
	Calculation of the multipole operators integrals and of its derivatives of the type [\mu | op | d(\nu)/dR(\nu)]-[d(\mu)/dR(\mu)| op | \nu] by taking the relative position operator r-Rc, with respect a reference point Rc The derivative are with respect to the primitive position, The multipole operator is symmetric and if it does not depend on R(\mu) or R(\nu) therefore [\mu | op | d(\nu)/dR(\nu)] = -[d(\mu)/dR(\mu)| op | \nu] [\mu|op|d(\nu)/dR]-[d(\mu)/dR|op|\nu]=2[\mu|op|d(\nu)/dR] When it is not the case a correction term is needed.

Detailed Description

History

created 07.2005

Author

MI (07.2005)

Function/Subroutine Documentation

build_lin_mom_matrix()

subroutine, public qs_operators_ao::build_lin_mom_matrix	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_p_type), dimension(:), pointer	matrix
	)

Calculation of the linear momentum matrix <mu|∂|nu> over Cartesian Gaussian functions.

Parameters

qs_env	...
matrix	...

Date

27.02.2009

Author

VW

Version

1.0

Definition at line 73 of file qs_operators_ao.F.

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build_ang_mom_matrix()

subroutine, public qs_operators_ao::build_ang_mom_matrix	(	type(qs_environment_type), pointer	qs_env,
		type(dbcsr_p_type), dimension(:), pointer	matrix,
		real(dp), dimension(:), intent(in)	rc
	)

Calculation of the angular momentum matrix over Cartesian Gaussian functions.

Parameters

qs_env	...
matrix	...
rc	...

Date

27.02.2009

Author

VW

Version

1.0

Definition at line 443 of file qs_operators_ao.F.

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p_xyz_ao()

subroutine, public qs_operators_ao::p_xyz_ao	(	type(dbcsr_p_type), dimension(:), pointer	op,
		type(qs_environment_type), pointer	qs_env,
		logical, intent(in), optional	minimum_image
	)

Calculation of the components of the dipole operator in the velocity form The elements of the sparse matrices are the integrals in the basis functions.

Parameters

op	matrix representation of the p operator calculated in terms of the contracted basis functions
qs_env	environment for the lists and the basis sets
minimum_image	take into account only the first neighbors in the lists

History

06.2005 created [MI]

Author

MI

Definition at line 817 of file qs_operators_ao.F.

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rrc_xyz_ao()

subroutine, public qs_operators_ao::rrc_xyz_ao	(	type(dbcsr_p_type), dimension(:), pointer	op,
		type(qs_environment_type), pointer	qs_env,
		real(dp), dimension(3)	rc,
		integer, intent(in)	order,
		logical, intent(in), optional	minimum_image,
		logical, intent(in), optional	soft
	)

Calculation of the components of the dipole operator in the length form by taking the relative position operator r-Rc, with respect a reference point Rc Probably it does not work for PBC, or maybe yes if the wfn are sufficiently localized The elements of the sparse matrices are the integrals in the basis functions.

Parameters

op	matrix representation of the p operator calculated in terms of the contracted basis functions
qs_env	environment for the lists and the basis sets
rc	reference vector position
order	maximum order of the momentum, for the dipole order = 1, order = -2 for quad only
minimum_image	take into account only the first neighbors in the lists
soft	...

History

03.2006 created [MI] 06.2019 added quarupole only option (A.Bussy)

Author

MI

Definition at line 1083 of file qs_operators_ao.F.

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rrc_xyz_der_ao()

subroutine, public qs_operators_ao::rrc_xyz_der_ao	(	type(dbcsr_p_type), dimension(:), pointer	op,
		type(dbcsr_p_type), dimension(:, :), pointer	op_der,
		type(qs_environment_type), pointer	qs_env,
		real(dp), dimension(3)	rc,
		integer, intent(in)	order,
		logical, intent(in), optional	minimum_image,
		logical, intent(in), optional	soft
	)

Calculation of the multipole operators integrals and of its derivatives of the type [\mu | op | d(\nu)/dR(\nu)]-[d(\mu)/dR(\mu)| op | \nu] by taking the relative position operator r-Rc, with respect a reference point Rc The derivative are with respect to the primitive position, The multipole operator is symmetric and if it does not depend on R(\mu) or R(\nu) therefore [\mu | op | d(\nu)/dR(\nu)] = -[d(\mu)/dR(\mu)| op | \nu] [\mu|op|d(\nu)/dR]-[d(\mu)/dR|op|\nu]=2[\mu|op|d(\nu)/dR] When it is not the case a correction term is needed.

The momentum operator [\mu|M|\nu] is symmetric, the number of components is determined by the order: 3 for order 1 (x,y,x), 9 for order 2(xx,xy,xz,yy,yz,zz) The derivative of the type [\mu | op | d(\nu)/dR_i(\nu)], where i indicates the cartesian direction, is antisymmetric only when the no component M =(r_i) or (r_i r_j) is in the same cartesian direction of the derivative, indeed d([\mu|M|\nu])/dr_i = [d(\mu)/dr_i|M|\nu] + [\mu|M|d(\nu)/dr_i] + [\mu |d(M)/dr_i|\nu] d([\mu|M|\nu])/dr_i = -[d(\mu)/dR_i(\mu)|M|\nu] -[\mu|M|d(\nu)/dR_i(\nu)] + [\mu |d(M)/dr_i|\nu] Therefore we cannot use an antisymmetric matrix

The same holds for the derivative with respect to the electronic position r taking into account that [\mu|op|d(\nu)/dR] = -[\mu|op|d(\nu)/dr]

Parameters

op	matrix representation of the p operator calculated in terms of the contracted basis functions
op_der	...
qs_env	environment for the lists and the basis sets
rc	reference vector position
order	maximum order of the momentum, for the dipole order = 1
minimum_image	take into account only the first neighbors in the lists
soft	...

History

03.2006 created [MI]

Author

MI

Note

Probably it does not work for PBC, or maybe yes if the wfn are sufficiently localized The elements of the sparse matrices are the integrals in the basis functions

Definition at line 1349 of file qs_operators_ao.F.

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