Module to compute the density matrix response and related quantities. More...

Data Types
type	respdata_type

Functions/Subroutines
subroutine, public	prg_parse_response (RespData, filename)
	The parser for the calculation of the DM response. More...

subroutine, public	prg_compute_dipole (charges, coordinate, dipoleMoment, factor, verbose)
	To compute the dipole moment of the system. The units of the dipole moment are determined by the units of the coordinates and charges that are given. More...

subroutine, public	prg_write_dipole_tcl (dipoleMoment, file, factor, verbose)
	To visualize a dipole moment using VMD. This will prg_generate a .tcl script that could be run using VMD To visualize with VMD: $ vmd -e dipole.tcl. More...

subroutine, public	prg_compute_polarizability (rsp_bml, prt_bml, polarizability, factor, verbose)
	To compute the polarizability of the system. The units of the directional polarizability are determined by the units of the perturbation and Hamiltonian. This equation can be found in [5] equation 4a. Note that in equation 4a of the reference there is a 2 that account for the double occupancy which is not present in this case cause the density matrix construction is done by taking the occupancy into account. More...

subroutine, public	prg_pert_from_file (prt_bml, norb)
	Read perturbation from file. More...

subroutine, public	prg_compute_response_rs (ham_bml, prt_bml, rsp_bml, lambda, bndfil, threshold, verbose)
	Computes the first order response density matrix using Rayleigh Schrodinger Perturbation theory The transformation hereby performed are: More...

subroutine, public	prg_compute_response_fd (ham_bml, prt_bml, rsp_bml, prg_delta, bndfil, threshold, verbose)
	Computes the first order response density matrix using finite differences. The transformation hereby performed are: More...

subroutine, public	prg_pert_constant_field (field, intensity, coordinate, lambda, prt_bml, threshold, spindex, norbi, verbose, over_bml)
	Apply a constant field perturbation through the dipole moment operator ( $ \hat{\mu} = e \hat{\textbf{r}} $). In the matrix representation, this is: $ H^{(1)} = \lambda \frac{1}{2}(\,S \, e \textbf{r} \cdot \textbf{E} + \, e \textbf{r} \cdot \textbf{E}S) $. The symmetrization is done in order to preserve the Hermiticity of H. In this case the whole system will be affected by the field. In a latter version we will add the possibility of applying this field to a region of the system. In this implementation $ e= 1 $ and units can be transformed by using the parameter $ \lambda $. More...

subroutine, public	prg_pert_sin_pot (direction, lx, coordinate, lambda, prt_bml, threshold, spindex, norbi, verbose, over_bml)
	Apply a sinusoidal length dependent potential ( $ \sin(\tilde{\textbf{r}}_x) $) where $ \textbf{r}_x $ is the x coordinate. The Hamiltonian gets modified as follows: $ H^{(1)} = \frac{1}{2}\lambda (S \sin(\tilde{\textbf{r}}_x) + \sin(\tilde{\textbf{r}}_x) S) $. $ \tilde{\textbf{r}}_x = 2\pi(\textbf{r}/l_x) - \pi $. The symmetrization is done in order to preserve the Hermiticity of H. Units can be transformed by using the parameter $ \lambda $. More...

subroutine, public	prg_pert_cos_pot (direction, lx, coordinate, lambda, prt_bml, threshold, spindex, norbi, verbose, over_bml)
	Apply a cosine length dependent potential ( $ \cos(\tilde{\textbf{r}}_x) $) where $ \textbf{r}_x $ is the x coordinate. The Hamiltonian gets modified as follows: $ H^{(1)} = \frac{1}{2}\lambda (S \sin(\tilde{\textbf{r}}_x) + \sin(\tilde{\textbf{r}}_x) S) $. $ \tilde{\textbf{r}}_x = 2\pi(\textbf{r}/l_x) - \pi $. The symmetrization is done in order to preserve the Hermiticity of H. Units can be transformed by using the parameter $ \lambda $. More...

subroutine, public	prg_compute_response_sp2 (ham_bml, prt_bml, rsp_bml, rho_bml, lambda, bndfil, minsp2iter, maxsp2iter, sp2conv, idemtol, threshold, verbose)
	Finds the first order response matrix from a Hamiltonian matrix. More...

subroutine, public	prg_project_response (rsp_bml, over_bml, spindex, norbi, coordinates, rspfunc, verbose)
	Project the response onto atomic positions. First order response to the perturbation ( $ \rho^{(1)} $) projected onto the atomic position. Basically: $ rsp(i) = \sum_{\alpha \in i}\rho^{(1)}_{\alpha \alpha} $, where orbital $ \alpha $ belong to atom $ i $. More...

subroutine, public	prg_canon_response_vector (P1_bml, H1_bml, Nocc, beta, evals, mu0, m, thresh, HDIM)
	First-order Canonical Density Matrix Perturbation Theory. More...

subroutine, public	prg_canon_response (P1_bml, H1_bml, Nocc, beta, evals, mu0, m, HDIM)
	First-order Canonical Density Matrix Perturbation Theory. More...

subroutine, public	prg_canon_response_orig (P1_bml, H1_bml, Nocc, beta, evals, mu0, m, thresh, HDIM)
	First-order Canonical Density Matrix Perturbation Theory. More...

subroutine, public	prg_canon_response_p1_dpdmu (P1_bml, dPdMu, H1_bml, Norbs, beta, Q_bml, evals, mu0, m, HDIM)
	First-order Canonical Density Matrix Perturbation Theory. More...

Variables
integer, parameter	dp = kind(1.0d0)

real(dp), parameter	pi = 3.14159265358979323846264338327950_dp

Detailed Description

Module to compute the density matrix response and related quantities.

Todo:

Add the response scf

Change name response_SP2 to dm_prt_response

Change name response_rs to rs_prt_response

More information about the theory can be found at [3] and Niklasson2015

Function/Subroutine Documentation

◆ prg_canon_response()

subroutine, public prg_response_mod::prg_canon_response	(	type(bml_matrix_t), intent(inout)	P1_bml,
		type(bml_matrix_t), intent(inout)	H1_bml,
		real(dp), intent(in)	Nocc,
		real(dp), intent(in)	beta,
		real(dp), dimension(hdim), intent(in)	evals,
		real(dp), intent(in)	mu0,
		integer, intent(in)	m,
		integer, intent(in)	HDIM
	)

First-order Canonical Density Matrix Perturbation Theory.

Assuming known mu0 and representation in H0's eigenbasis Q, where H0 and P0 become diagonal. (mu0, eigenvalues e and eigenvectors Q of H0 are assumed known) Based on PRL 92, 193001 (2004) and PRE 92, 063301 (2015).

Parameters

P1_bml	First-order canonical response output.
H1_bml	Perturbative hamiltonian input.
Nocc	Number of ocupied orbitals.
beta	Inverse electronic temperature.
evals	Eigenvalues of the system.
mu0	Chemical potential.
m	Number of recursive steps.
HDIM	Number of orbitals - Hamiltonina zise.

Definition at line 947 of file prg_response_mod.F90.

◆ prg_canon_response_orig()

subroutine, public prg_response_mod::prg_canon_response_orig	(	type(bml_matrix_t), intent(inout)	P1_bml,
		type(bml_matrix_t), intent(inout)	H1_bml,
		real(dp), intent(in)	Nocc,
		real(dp), intent(in)	beta,
		real(dp), dimension(hdim), intent(in)	evals,
		real(dp), intent(in)	mu0,
		integer, intent(in)	m,
		real(dp), intent(in)	thresh,
		integer, intent(in)	HDIM
	)

First-order Canonical Density Matrix Perturbation Theory.

Assuming known mu0 and representation in H0's eigenbasis Q, where H0 and P0 become diagonal. Original routine. (mu0, eigenvalues e and eigenvectors Q of H0 are assumed known) Based on PRL 92, 193001 (2004) and PRE 92, 063301 (2015).

Parameters

P1_bml	First-order canonical response output.
H1_bml	Perturbative hamiltonian input.
Nocc	Number of ocupied orbitals.
beta	Inverse electronic temperature.
evals	Eigenvalues of the system.
mu0	Chemical potential.
m	Number of recursive steps.
HDIM	Number of orbitals - Hamiltonina zise.

Definition at line 1038 of file prg_response_mod.F90.

◆ prg_canon_response_p1_dpdmu()

subroutine, public prg_response_mod::prg_canon_response_p1_dpdmu	(	type(bml_matrix_t), intent(inout)	P1_bml,
		real(dp), dimension(hdim), intent(inout)	dPdMu,
		type(bml_matrix_t), intent(inout)	H1_bml,
		integer, intent(in)	Norbs,
		real(dp), intent(in)	beta,
		type(bml_matrix_t)	Q_bml,
		real(dp), dimension(hdim), intent(in)	evals,
		real(dp), intent(in)	mu0,
		integer, intent(in)	m,
		integer, intent(in)	HDIM
	)

First-order Canonical Density Matrix Perturbation Theory.

Assuming known mu0 and representation in H0's eigenbasis Q, where H0 and P0 become diagonal. (mu0, eigenvalues e and eigenvectors Q of H0 are assumed known) Based on PRL 92, 193001 (2004) and PRE 92, 063301 (2015)

Definition at line 1112 of file prg_response_mod.F90.

◆ prg_canon_response_vector()

subroutine, public prg_response_mod::prg_canon_response_vector	(	type(bml_matrix_t), intent(inout)	P1_bml,
		type(bml_matrix_t), intent(inout)	H1_bml,
		real(dp), intent(in)	Nocc,
		real(dp), intent(in)	beta,
		real(dp), dimension(hdim), intent(in)	evals,
		real(dp), intent(in)	mu0,
		integer, intent(in)	m,
		real(dp), intent(in)	thresh,
		integer, intent(in)	HDIM
	)

First-order Canonical Density Matrix Perturbation Theory.

Assuming known mu0 and representation in H0's eigenbasis Q, where H0 and P0 become diagonal. (mu0, eigenvalues e and eigenvectors Q of H0 are assumed known) Based on PRL 92, 193001 (2004) and PRE 92, 063301 (2015).

Parameters

P1_bml	First-order canonical response output.
H1_bml	Perturbative hamiltonian input.
Nocc	Number of ocupied orbitals.
beta	Inverse electronic temperature.
evals	Eigenvalues of the system.
mu0	Chemical potential.
m	Number of recursive steps.
HDIM	Number of orbitals - Hamiltonina zise.

Definition at line 849 of file prg_response_mod.F90.

◆ prg_compute_dipole()

subroutine, public prg_response_mod::prg_compute_dipole	(	real(dp), dimension(:), intent(in)	charges,
		real(dp), dimension(:,:), intent(in)	coordinate,
		real(dp), dimension(3), intent(inout)	dipoleMoment,
		real(dp), intent(in)	factor,
		integer	verbose
	)

To compute the dipole moment of the system. The units of the dipole moment are determined by the units of the coordinates and charges that are given.

Parameters

charges	Charges on each atomic position.
coordinate	Coordinates of the atoms.
nats	Number of atoms.
dipoleMoment	Dipole moment vector.
factor	Unit conversion factor (use 1.0 is no conversion is required).
verbose	To give different verbosity levels. If coordinates are in $ \AA $ and charges are in fractions of electron, then transformation ea2debye form LATTE lib can be used to change units to Debye.

Definition at line 122 of file prg_response_mod.F90.

◆ prg_compute_polarizability()

subroutine, public prg_response_mod::prg_compute_polarizability	(	type(bml_matrix_t), intent(in)	rsp_bml,
		type(bml_matrix_t), intent(in)	prt_bml,
		real(dp), intent(inout)	polarizability,
		real(dp), intent(in)	factor,
		integer	verbose
	)

To compute the polarizability of the system. The units of the directional polarizability are determined by the units of the perturbation and Hamiltonian. This equation can be found in [5] equation 4a. Note that in equation 4a of the reference there is a 2 that account for the double occupancy which is not present in this case cause the density matrix construction is done by taking the occupancy into account.

Parameters

charges	Charges on each atomic position.
coordinate	Coordinates of the atoms.
nats	Number of atoms.
dipoleMoment	Dipole moment vector.
factor	Unit conversion factor (use 1.0 is no conversion is required).
verbose	To give different verbosity levels. If coordinates are in $ \AA $ and charges are in fractions of electron, then transformation ea2debye form LATTE lib can be used to change units to Debye.

Definition at line 200 of file prg_response_mod.F90.

◆ prg_compute_response_fd()

subroutine, public prg_response_mod::prg_compute_response_fd	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(in)	prt_bml,
		type(bml_matrix_t), intent(inout)	rsp_bml,
		real(dp)	prg_delta,
		real(dp), intent(in)	bndfil,
		real(dp), intent(in)	threshold,
		integer	verbose
	)

Computes the first order response density matrix using finite differences. The transformation hereby performed are:

$ H^+ = H^{(0)} + \delta H^{(1)} $
$ H^- = H^{(0)} - \delta H^{(1)} $
$ \rho^+ = f(H^+) $
$ \rho^- = f(H^-) $

$ \rho^{(1)} = (\rho^+ - \rho^-)/(2\delta) $. Where f denotes the Fermi function (construction of the density matrix)

Parameters

ham_bml	Hamiltonian in bml format ( $ H^{(0)} $).
prt_bml	Perturbation in bml format ( $ H^{(1)} $).
rsp_bml	First order response to the perturbation ( $ \rho^{(1)} $).
bndfil	Filing factor.
threshold	Threshold value for matrix elements.
verbose	Different levels of verbosity.

Warning: This works only for the prg_orthogonalized form of ham_bml.; The response must be in the prg_orthogonalized form.

Definition at line 380 of file prg_response_mod.F90.

◆ prg_compute_response_rs()

subroutine, public prg_response_mod::prg_compute_response_rs	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(in)	prt_bml,
		type(bml_matrix_t), intent(inout)	rsp_bml,
		real(dp)	lambda,
		real(dp), intent(in)	bndfil,
		real(dp), intent(in)	threshold,
		integer	verbose
	)

Computes the first order response density matrix using Rayleigh Schrodinger Perturbation theory The transformation hereby performed are:

$ V = C^{\dagger} H^{(1)} C $
$ \tilde{V}_{ij} = \frac{V_{ij}}{\epsilon_j - \epsilon_i} $, with $ \tilde{V}_{ii} = 0 \, \forall i $.
$ C^{(1)} = C \tilde{V} $

And finally: $ \rho^{(1)} = Cf(C^{(1)})^{\dagger} + C^{(1)}fC^{\dagger}$

Parameters

ham_bml	Hamiltonian in bml format ( $ H^{(0)} $).
prt_bml	Perturbation in bml format ( $ H^{(1)} $).
rsp_bml	First order response to the perturbation ( $ \rho^{(1)} $).
bndfil	Filing factor.
threshold	Threshold value for matrix elements.
verbose	Different levels of verbosity.

Warning: This works only for the prg_orthogonalized form of ham_bml.; The response must be in the prg_orthogonalized form.

Definition at line 250 of file prg_response_mod.F90.

◆ prg_compute_response_sp2()

subroutine, public prg_response_mod::prg_compute_response_sp2	(	type(bml_matrix_t), intent(in)	ham_bml,
		type(bml_matrix_t), intent(in)	prt_bml,
		type(bml_matrix_t), intent(inout)	rsp_bml,
		type(bml_matrix_t), intent(inout)	rho_bml,
		real(dp)	lambda,
		real(dp), intent(in)	bndfil,
		integer, intent(in)	minsp2iter,
		integer, intent(in)	maxsp2iter,
		character(len=*), intent(in)	sp2conv,
		real(dp), intent(in)	idemtol,
		real(dp), intent(in)	threshold,
		integer	verbose
	)

Finds the first order response matrix from a Hamiltonian matrix.

Definition at line 653 of file prg_response_mod.F90.

◆ prg_parse_response()

subroutine, public prg_response_mod::prg_parse_response	(	type(respdata_type)	RespData,
		character(len=*)	filename
	)

The parser for the calculation of the DM response.

Parameters

RespData	Response data type.
filename	Name of the file to parse.

Definition at line 45 of file prg_response_mod.F90.

◆ prg_pert_constant_field()

subroutine, public prg_response_mod::prg_pert_constant_field	(	real(dp), dimension(3), intent(in)	field,
		real(dp)	intensity,
		real(dp), dimension(:,:), intent(in)	coordinate,
		real(dp)	lambda,
		type(bml_matrix_t), intent(inout)	prt_bml,
		real(dp)	threshold,
		integer, dimension(:), intent(in)	spindex,
		integer, dimension(:), intent(in)	norbi,
		integer, intent(in)	verbose,
		type(bml_matrix_t), intent(in), optional	over_bml
	)

Apply a constant field perturbation through the dipole moment operator ( $ \hat{\mu} = e \hat{\textbf{r}} $). In the matrix representation, this is: $ H^{(1)} = \lambda \frac{1}{2}(\,S \, e \textbf{r} \cdot \textbf{E} + \, e \textbf{r} \cdot \textbf{E}S) $. The symmetrization is done in order to preserve the Hermiticity of H. In this case the whole system will be affected by the field. In a latter version we will add the possibility of applying this field to a region of the system. In this implementation $ e= 1 $ and units can be transformed by using the parameter $ \lambda $.

Note: If the Hamiltonian is already in the prg_orthogonalized form, then parameter over_bml can be omitted.

Parameters

field	Direction of the applied field ( $ \hat{\textbf{E}} $).
intensity	Intensity of the field ( $ \|\|\textbf{E}\|\| $)..
coordinate	Coordinates of the system ( $ \textbf{r}$).
lambda	Constant to premultiply the perturbation ( $ \lambda$).
prt_bml	Perturbation in bml format ( $ H^{(1)} $).
threshold	Threshold value for bml format matrices.
spindex	Species index. It gives the species index of a particular atom.
norbi	Number of orbitals for each atomic site.
verbose	Different levels of verbosity.
over_bml	It has to be present for a nonorthogonal representation ( $ S $).

Definition at line 447 of file prg_response_mod.F90.

◆ prg_pert_cos_pot()

subroutine, public prg_response_mod::prg_pert_cos_pot	(	character	direction,
		real(dp)	lx,
		real(dp), dimension(:,:), intent(in)	coordinate,
		real(dp)	lambda,
		type(bml_matrix_t), intent(inout)	prt_bml,
		real(dp)	threshold,
		integer, dimension(:), intent(in)	spindex,
		integer, dimension(:), intent(in)	norbi,
		integer, intent(in)	verbose,
		type(bml_matrix_t), intent(in), optional	over_bml
	)

Apply a cosine length dependent potential ( $ \cos(\tilde{\textbf{r}}_x) $) where $ \textbf{r}_x $ is the x coordinate. The Hamiltonian gets modified as follows: $ H^{(1)} = \frac{1}{2}\lambda (S \sin(\tilde{\textbf{r}}_x) + \sin(\tilde{\textbf{r}}_x) S) $. $ \tilde{\textbf{r}}_x = 2\pi(\textbf{r}/l_x) - \pi $. The symmetrization is done in order to preserve the Hermiticity of H. Units can be transformed by using the parameter $ \lambda $.

Note: If the Hamiltonian is already in the prg_orthogonalized form, then parameter over_bml can be omitted.

Parameters

direction	Direction of the potential gradient (x,y or z).
lx	Lenght of the box in x direction.
coordinate	Coordinates of the system ( $ \textbf{r}$).
lambda	Constant to premultiply the perturbation ( $ \lambda$).
prt_bml	Perturbation in bml format ( $ H^{(1)} $).
threshold	Threshold value for bml format matrices.
norbi	Number of orbitals for each atomic site.
verbose	Different levels of verbosity.
over_bml	It has to be present for a nonorthogonal representation ( $ S $).

Definition at line 592 of file prg_response_mod.F90.

◆ prg_pert_from_file()

subroutine, public prg_response_mod::prg_pert_from_file	(	type(bml_matrix_t), intent(inout)	prt_bml,
		integer	norb
	)

Read perturbation from file.

Todo:: Add read perturbation from file

Definition at line 225 of file prg_response_mod.F90.

◆ prg_pert_sin_pot()

subroutine, public prg_response_mod::prg_pert_sin_pot	(	character	direction,
		real(dp)	lx,
		real(dp), dimension(:,:), intent(in)	coordinate,
		real(dp)	lambda,
		type(bml_matrix_t), intent(inout)	prt_bml,
		real(dp)	threshold,
		integer, dimension(:), intent(in)	spindex,
		integer, dimension(:), intent(in)	norbi,
		integer, intent(in)	verbose,
		type(bml_matrix_t), intent(in), optional	over_bml
	)

Apply a sinusoidal length dependent potential ( $ \sin(\tilde{\textbf{r}}_x) $) where $ \textbf{r}_x $ is the x coordinate. The Hamiltonian gets modified as follows: $ H^{(1)} = \frac{1}{2}\lambda (S \sin(\tilde{\textbf{r}}_x) + \sin(\tilde{\textbf{r}}_x) S) $. $ \tilde{\textbf{r}}_x = 2\pi(\textbf{r}/l_x) - \pi $. The symmetrization is done in order to preserve the Hermiticity of H. Units can be transformed by using the parameter $ \lambda $.

Note: If the Hamiltonian is already in the prg_orthogonalized form, then parameter over_bml can be omitted.

Parameters

direction	Direction of the potential gradient (x,y or z).
lx	Length of the box in x direction.
coordinate	Coordinates of the system ( $ \textbf{r}$).
lambda	Constant to premultiply the perturbation ( $ \lambda$).
prt_bml	Perturbation in bml format ( $ H^{(1)} $).
threshold	Threshold value for bml format matrices.
norbi	Number of orbitals for each atomic site.
verbose	Different levels of verbosity.
over_bml	It has to be present for a nonorthogonal representation ( $ S $).

Definition at line 524 of file prg_response_mod.F90.

◆ prg_project_response()

subroutine, public prg_response_mod::prg_project_response	(	type(bml_matrix_t), intent(inout)	rsp_bml,
		type(bml_matrix_t), intent(in)	over_bml,
		integer, dimension(:), intent(in)	spindex,
		integer, dimension(:), intent(in)	norbi,
		real(dp), dimension(:,:), intent(in)	coordinates,
		real(dp), dimension(:), intent(inout), allocatable	rspfunc,
		integer, intent(in)	verbose
	)

Project the response onto atomic positions. First order response to the perturbation ( $ \rho^{(1)} $) projected onto the atomic position. Basically: $ rsp(i) = \sum_{\alpha \in i}\rho^{(1)}_{\alpha \alpha} $, where orbital $ \alpha $ belong to atom $ i $.

Parameters

rsp_bml	First order response density matrix.
spindex	It gives the species index of a particular atom.
norbi	Number of orbitals of species i.
coordinates	Atomic coordinates.
rspfunc	Response function at atomic positions.
verbose	Different levels of verbosity.

Definition at line 797 of file prg_response_mod.F90.

◆ prg_write_dipole_tcl()

subroutine, public prg_response_mod::prg_write_dipole_tcl	(	real(dp), dimension(3), intent(in)	dipoleMoment,
		character(*), intent(in)	file,
		real(dp), intent(in)	factor,
		integer	verbose
	)

To visualize a dipole moment using VMD. This will prg_generate a .tcl script that could be run using VMD To visualize with VMD: $ vmd -e dipole.tcl.

Parameters

dipoleMoment	Dipole moment vector.
file	PDB/XYZ file to load for visualization.
factor	Arbitrary scale for visualization.
verbose	To give different verbosity levels.

Definition at line 160 of file prg_response_mod.F90.

Variable Documentation

◆ dp

integer, parameter prg_response_mod::dp = kind(1.0d0)

private

Definition at line 18 of file prg_response_mod.F90.

◆ pi

real(dp), parameter prg_response_mod::pi = 3.14159265358979323846264338327950_dp

private

Definition at line 19 of file prg_response_mod.F90.

ham_bml	Hamiltonian in bml format ( \( H^{(0)} \)).
prt_bml	Perturbation in bml format ( \( H^{(1)} \)).
rsp_bml	First order response to the perturbation ( \( \rho^{(1)} \)).
bndfil	Filing factor.
threshold	Threshold value for matrix elements.
verbose	Different levels of verbosity.

field	Direction of the applied field ( \( \hat{\textbf{E}} \)).
intensity	Intensity of the field ( \( \|\|\textbf{E}\|\| \))..
coordinate	Coordinates of the system ( \( \textbf{r}\)).
lambda	Constant to premultiply the perturbation ( \( \lambda\)).
prt_bml	Perturbation in bml format ( \( H^{(1)} \)).
threshold	Threshold value for bml format matrices.
spindex	Species index. It gives the species index of a particular atom.
norbi	Number of orbitals for each atomic site.
verbose	Different levels of verbosity.
over_bml	It has to be present for a nonorthogonal representation ( \( S \)).

Data Types

Functions/Subroutines

Variables

Detailed Description

Function/Subroutine Documentation

◆ prg_canon_response()

◆ prg_canon_response_orig()

◆ prg_canon_response_p1_dpdmu()

◆ prg_canon_response_vector()

◆ prg_compute_dipole()

◆ prg_compute_polarizability()

◆ prg_compute_response_fd()

◆ prg_compute_response_rs()

◆ prg_compute_response_sp2()

◆ prg_parse_response()

◆ prg_pert_constant_field()

◆ prg_pert_cos_pot()

◆ prg_pert_from_file()

◆ prg_pert_sin_pot()

◆ prg_project_response()

◆ prg_write_dipole_tcl()

Variable Documentation

◆ dp

◆ pi