casida_oct_m Module Reference

This module implements the Casida equations for excited states. More...

Detailed Description

This module implements the Casida equations for excited states.

The linear-response (Casida) formalism casts the excitation energies as the eigenvalues of a coupled (A, B) matrix problem. For a pedagogic derivation of this polarization-propagator / RPA formulation see J. Oddershede, P. Joergensen, and D. L. Yeager, "Polarization propagator methods in atomic and molecular calculations", Comput. Phys. Rep. 2, 33 (1984); https://doi.org/10.1016/0167-7977(84)90003-0 and M. E. Casida, "Time-Dependent Density Functional Response Theory for Molecules", in Recent Advances in Density Functional Methods, ed. D. P. Chong (World Scientific, 1995), p. 155; https://doi.org/10.1142/9789812830586_0005 .

The only difference between TDDFT (Casida) and TDHF (the RPA of Hartree-Fock) is the coupling kernel entering A and B: TDDFT uses the (semilocal) xc kernel f_xc, whereas TDHF uses the non-local Fock exchange. This is made explicit in Eqns. 12 and 13 (the A and B matrices) of W. Liang, S. A. Fischer, M. J. Frisch, and X. Li, J. Chem. Theory Comput. 7, 3540 (2011); https://doi.org/10.1021/ct200485x . The reduction of the full (A, B) problem to the Hermitian half-size problem solved here follows R. E. Stratmann, G. E. Scuseria, and M. J. Frisch, J. Chem. Phys. 109, 8218 (1998); https://doi.org/10.1063/1.477483 .

Data Types
type	casida_save_pot_t
type	casida_t
	This class contains all parameters, needed for Casida calculations. More...

Functions/Subroutines
subroutine, public	casida_run (system, from_scratch)
subroutine	casida_run_legacy (sys, fromScratch)
subroutine	casida_count_pairs (st, namespace, n_pairs, n_occ, n_unocc, is_included, is_frac_occ)
	number of occupied-unoccupied pairs for Casida More...
subroutine	casida_type_init (cas, sys)
	allocates stuff, and constructs the arrays pair_i and pair_j More...
subroutine	casida_type_end (cas)
subroutine	casida_work (sys, cas)
	this subroutine calculates electronic excitation energies using the matrix formulation of M. Petersilka, or of M. Casida More...
real(real64) function	casida_matrix_factor (cas, sys)
subroutine	qcasida_write (cas, namespace)
character(len=80) pure function	theory_name (cas)
logical function	isnt_degenerate (cas, st, ia, jb)
integer function	get_global_row (cas, jb_local)
integer function	get_global_col (cas, ia_local)
subroutine	local_indices (cas, ia, jb, on_this_processor, ia_local, jb_local)
subroutine	doscillator_strengths (cas, mesh, st, hm)
real(real64) function, dimension(cas%n_pairs)	dks_matrix_elements (cas, st, mesh, dv)
real(real64) function	dtransition_matrix_element (cas, ia, xx)
	calculate transition matrix elements More...
subroutine	dtransition_density (cas, st, mesh, ia, n0I)
subroutine	dget_transition_densities (cas, sys)
subroutine	dcasida_get_rho (st, mesh, ii, ia, kk, rho)
subroutine	dcasida_calc_lr_hmat1 (sys, pert, hvar, lr_hmat1, is_saved, st_start, st_end, ik)
	calculate one-particle matrix elements of perturbation More...
subroutine	dcasida_lr_hmat2 (cas, st, lr_hmat1, ik)
	calculate two-particle matrix elements of perturbation More...
subroutine	dcasida_get_matrix (cas, namespace, hm, st, ks, gr, matrix, fxc, fxc_grad, fxc_grad_spin, restart_file, is_forces, matrixB)
subroutine	dwrite_k_term (cas, mat_val, iunit, ia, jb)
	write matrix element to casida_restart file More...
subroutine	dcasida_forces (cas, sys, gr, st)
subroutine	dcasida_get_lr_hmat1 (cas, sys, iatom, idir, dl_rho, lr_hmat1)
subroutine	dcasida_solve (cas, sys)
subroutine	dcasida_write (cas, sys)
subroutine	dwrite_implied_occupations (cas, iunit, ind)
subroutine	dwrite_distributed_matrix (cas, matrix, filename)
real(real64) function	dallreduce_sum (cas, variable)
subroutine	zoscillator_strengths (cas, mesh, st, hm)
complex(real64) function, dimension(cas%n_pairs)	zks_matrix_elements (cas, st, mesh, dv)
complex(real64) function	ztransition_matrix_element (cas, ia, xx)
	calculate transition matrix elements More...
subroutine	ztransition_density (cas, st, mesh, ia, n0I)
subroutine	zget_transition_densities (cas, sys)
subroutine	zcasida_get_rho (st, mesh, ii, ia, kk, rho)
subroutine	zcasida_calc_lr_hmat1 (sys, pert, hvar, lr_hmat1, is_saved, st_start, st_end, ik)
	calculate one-particle matrix elements of perturbation More...
subroutine	zcasida_lr_hmat2 (cas, st, lr_hmat1, ik)
	calculate two-particle matrix elements of perturbation More...
subroutine	zcasida_get_matrix (cas, namespace, hm, st, ks, gr, matrix, fxc, fxc_grad, fxc_grad_spin, restart_file, is_forces, matrixB)
subroutine	zwrite_k_term (cas, mat_val, iunit, ia, jb)
	write matrix element to casida_restart file More...
subroutine	zcasida_forces (cas, sys, gr, st)
subroutine	zcasida_get_lr_hmat1 (cas, sys, iatom, idir, dl_rho, lr_hmat1)
subroutine	zcasida_solve (cas, sys)
subroutine	zcasida_write (cas, sys)
subroutine	zwrite_implied_occupations (cas, iunit, ind)
subroutine	zwrite_distributed_matrix (cas, matrix, filename)
complex(real64) function	zallreduce_sum (cas, variable)

Variables
integer, parameter	casida_eps_diff = 1
integer, parameter	casida_petersilka = 2
integer, parameter	casida_tamm_dancoff = 4
integer, parameter	casida_variational = 8
integer, parameter	casida_casida = 16
integer, parameter	solver_elpa = 1
integer, parameter	solver_scalapack = 2

Function/Subroutine Documentation

casida_run()

subroutine, public casida_oct_m::casida_run	(	class(*), intent(inout)	system,
		logical, intent(in)	from_scratch
	)

Definition at line 295 of file casida.F90.

casida_run_legacy()

subroutine casida_oct_m::casida_run_legacy ( type(electrons_t), intent(inout)  sys, logical, intent(in)  fromScratch  )

private

Definition at line 313 of file casida.F90.

casida_count_pairs()

subroutine casida_oct_m::casida_count_pairs ( type(states_elec_t), intent(in)  st, type(namespace_t), intent(in)  namespace, integer, intent(out)  n_pairs, integer, dimension(:), intent(out), contiguous  n_occ, integer, dimension(:), intent(out), contiguous  n_unocc, logical, dimension(:,:,:), intent(out), allocatable  is_included, logical, intent(out)  is_frac_occ  )

private

number of occupied-unoccupied pairs for Casida

Parameters

[out]	n_pairs	result: number of pairs
[out]	n_occ	result: number of occ. states per k-point; dimension (1:nik)
[out]	n_unocc	result: number of unocc. states per k-point;dimension (1:nik)
[out]	is_included	result: mask whether a state is included; dimension (st%d%nst, st%d%nst, st%d%nik)
[out]	is_frac_occ	result: are there fractional occupations?

Definition at line 816 of file casida.F90.

casida_type_init()

subroutine casida_oct_m::casida_type_init ( type(casida_t), intent(inout)  cas, type(electrons_t), intent(in)  sys  )

private

allocates stuff, and constructs the arrays pair_i and pair_j

Definition at line 951 of file casida.F90.

casida_type_end()

subroutine casida_oct_m::casida_type_end ( type(casida_t), intent(inout)  cas )

private

Definition at line 1078 of file casida.F90.

casida_work()

subroutine casida_oct_m::casida_work ( type(electrons_t), intent(inout), target  sys, type(casida_t), intent(inout)  cas  )

private

this subroutine calculates electronic excitation energies using the matrix formulation of M. Petersilka, or of M. Casida

Definition at line 1135 of file casida.F90.

casida_matrix_factor()

real(real64) function casida_oct_m::casida_matrix_factor ( type(casida_t), intent(in)  cas, type(electrons_t), intent(in)  sys  )

private

Definition at line 1347 of file casida.F90.

qcasida_write()

subroutine casida_oct_m::qcasida_write ( type(casida_t), intent(in)  cas, type(namespace_t), intent(in)  namespace  )

private

Definition at line 1368 of file casida.F90.

theory_name()

character(len=80) pure function casida_oct_m::theory_name ( type(casida_t), intent(in)  cas )

private

Definition at line 1406 of file casida.F90.

isnt_degenerate()

logical function casida_oct_m::isnt_degenerate ( type(casida_t), intent(in)  cas, type(states_elec_t), intent(in)  st, integer, intent(in)  ia, integer, intent(in)  jb  )

private

Definition at line 1426 of file casida.F90.

get_global_row()

integer function casida_oct_m::get_global_row ( type(casida_t), intent(inout)  cas, integer, intent(in)  jb_local  )

private

Definition at line 1440 of file casida.F90.

get_global_col()

integer function casida_oct_m::get_global_col ( type(casida_t), intent(inout)  cas, integer, intent(in)  ia_local  )

private

Definition at line 1454 of file casida.F90.

local_indices()

subroutine casida_oct_m::local_indices ( type(casida_t), intent(in)  cas, integer, intent(in)  ia, integer, intent(in)  jb, logical, intent(out)  on_this_processor, integer, intent(out)  ia_local, integer, intent(out)  jb_local  )

private

Definition at line 1468 of file casida.F90.

doscillator_strengths()

subroutine casida_oct_m::doscillator_strengths ( type(casida_t), intent(inout)  cas, class(mesh_t), intent(in)  mesh, type(states_elec_t), intent(in)  st, type(hamiltonian_elec_t), intent(in)  hm  )

private

Definition at line 1556 of file casida.F90.

dks_matrix_elements()

real(real64) function, dimension(cas%n_pairs) casida_oct_m::dks_matrix_elements ( type(casida_t), intent(in)  cas, type(states_elec_t), intent(in)  st, class(mesh_t), intent(in)  mesh, real(real64), dimension(:), intent(in), contiguous  dv  )

private

Definition at line 1755 of file casida.F90.

dtransition_matrix_element()

real(real64) function casida_oct_m::dtransition_matrix_element ( type(casida_t), intent(in)  cas, integer, intent(in)  ia, real(real64), dimension(:), intent(in), contiguous  xx  )

private

calculate transition matrix elements

Casida: \( \vec{d}_k = \sum_{cv} \vec{d}_{cv} x_{cv} \sqrt{\frac{\epsilon_c - \epsilon_v}{\omega_k}} \) others: \( \vec{d}_k = \sum_{cv} \vec{d}_{cv} x_{cv} \)

Parameters

[in]

xx

these are KS matrix elements

Definition at line 1799 of file casida.F90.

dtransition_density()

subroutine casida_oct_m::dtransition_density ( type(casida_t), intent(in)  cas, type(states_elec_t), intent(in)  st, class(mesh_t), intent(in)  mesh, integer, intent(in)  ia, real(real64), dimension(:), intent(out), contiguous  n0I  )

private

Definition at line 1843 of file casida.F90.

dget_transition_densities()

subroutine casida_oct_m::dget_transition_densities ( type(casida_t), intent(in)  cas, type(electrons_t), intent(in)  sys  )

private

Definition at line 1887 of file casida.F90.

dcasida_get_rho()

subroutine casida_oct_m::dcasida_get_rho ( type(states_elec_t), intent(in)  st, class(mesh_t), intent(in)  mesh, integer, intent(in)  ii, integer, intent(in)  ia, integer, intent(in)  kk, real(real64), dimension(:), intent(out), contiguous  rho  )

private

Definition at line 1920 of file casida.F90.

dcasida_calc_lr_hmat1()

subroutine casida_oct_m::dcasida_calc_lr_hmat1 ( type(electrons_t), intent(inout)  sys, class(perturbation_t), intent(in)  pert, real(real64), dimension(:,:,:), intent(in), contiguous  hvar, real(real64), dimension(:,:,:), intent(out), contiguous  lr_hmat1, logical, dimension(:,:,:), intent(in), contiguous  is_saved, integer, intent(in)  st_start, integer, intent(in)  st_end, integer, intent(in)  ik  )

private

calculate one-particle matrix elements of perturbation

Definition at line 1958 of file casida.F90.

dcasida_lr_hmat2()

subroutine casida_oct_m::dcasida_lr_hmat2 ( type(casida_t), intent(inout)  cas, type(states_elec_t), intent(in)  st, real(real64), dimension(:,:,:), intent(in), contiguous  lr_hmat1, integer, intent(in)  ik  )

private

calculate two-particle matrix elements of perturbation

Definition at line 2009 of file casida.F90.

dcasida_get_matrix()

subroutine casida_oct_m::dcasida_get_matrix ( type(casida_t), intent(inout)  cas, type(namespace_t), intent(in)  namespace, type(hamiltonian_elec_t), intent(in)  hm, type(states_elec_t), intent(in)  st, type(v_ks_t), intent(in)  ks, type(grid_t), intent(in)  gr, real(real64), dimension(:,:), intent(out), contiguous  matrix, real(real64), dimension(:,:,:), intent(in), contiguous  fxc, real(real64), dimension(:,:,:,:,:), intent(in), contiguous  fxc_grad, real(real64), dimension(:,:,:,:), intent(in), contiguous  fxc_grad_spin, character(len=*), intent(in)  restart_file, logical, intent(in), optional  is_forces, real(real64), dimension(:,:), intent(out), optional, contiguous  matrixB  )

private

Parameters

[out]

matrixb

Off-diagonal B coupling matrix for the full TDHF (RPA) problem.

Definition at line 2045 of file casida.F90.

dwrite_k_term()

subroutine casida_oct_m::dwrite_k_term ( type(casida_t), intent(in)  cas, real(real64), intent(in)  mat_val, integer, intent(in)  iunit, integer, intent(in)  ia, integer, intent(in)  jb  )

private

write matrix element to casida_restart file

Definition at line 2934 of file casida.F90.

dcasida_forces()

subroutine casida_oct_m::dcasida_forces ( type(casida_t), intent(inout)  cas, type(electrons_t), intent(inout)  sys, type(grid_t), intent(in)  gr, type(states_elec_t), intent(inout)  st  )

private

Definition at line 2950 of file casida.F90.

dcasida_get_lr_hmat1()

subroutine casida_oct_m::dcasida_get_lr_hmat1 ( type(casida_t), intent(in)  cas, type(electrons_t), intent(inout)  sys, integer, intent(in)  iatom, integer, intent(in)  idir, real(real64), dimension(:,:), intent(in), contiguous  dl_rho, real(real64), dimension(:,:,:), intent(out), contiguous  lr_hmat1  )

private

Definition at line 3099 of file casida.F90.

dcasida_solve()

subroutine casida_oct_m::dcasida_solve ( type(casida_t), intent(inout)  cas, type(electrons_t), intent(in)  sys  )

private

Definition at line 3213 of file casida.F90.

dcasida_write()

subroutine casida_oct_m::dcasida_write ( type(casida_t), intent(inout)  cas, type(electrons_t), intent(in)  sys  )

private

Definition at line 3439 of file casida.F90.

dwrite_implied_occupations()

subroutine casida_oct_m::dwrite_implied_occupations ( type(casida_t), intent(in)  cas, integer, intent(in)  iunit, integer, intent(in)  ind  )

private

Definition at line 3600 of file casida.F90.

dwrite_distributed_matrix()

subroutine casida_oct_m::dwrite_distributed_matrix ( type(casida_t), intent(inout)  cas, real(real64), dimension(:,:), intent(in), contiguous  matrix, character(len=*), intent(in)  filename  )

private

Definition at line 3639 of file casida.F90.

dallreduce_sum()

real(real64) function casida_oct_m::dallreduce_sum ( type(casida_t), intent(in)  cas, real(real64), intent(in)  variable  )

private

Definition at line 3662 of file casida.F90.

zoscillator_strengths()

subroutine casida_oct_m::zoscillator_strengths ( type(casida_t), intent(inout)  cas, class(mesh_t), intent(in)  mesh, type(states_elec_t), intent(in)  st, type(hamiltonian_elec_t), intent(in)  hm  )

private

Definition at line 3755 of file casida.F90.

zks_matrix_elements()

complex(real64) function, dimension(cas%n_pairs) casida_oct_m::zks_matrix_elements ( type(casida_t), intent(in)  cas, type(states_elec_t), intent(in)  st, class(mesh_t), intent(in)  mesh, real(real64), dimension(:), intent(in), contiguous  dv  )

private

Definition at line 3954 of file casida.F90.

ztransition_matrix_element()

complex(real64) function casida_oct_m::ztransition_matrix_element ( type(casida_t), intent(in)  cas, integer, intent(in)  ia, complex(real64), dimension(:), intent(in), contiguous  xx  )

private

calculate transition matrix elements

Casida: \( \vec{d}_k = \sum_{cv} \vec{d}_{cv} x_{cv} \sqrt{\frac{\epsilon_c - \epsilon_v}{\omega_k}} \) others: \( \vec{d}_k = \sum_{cv} \vec{d}_{cv} x_{cv} \)

Parameters

[in]

xx

these are KS matrix elements

Definition at line 3998 of file casida.F90.

ztransition_density()

subroutine casida_oct_m::ztransition_density ( type(casida_t), intent(in)  cas, type(states_elec_t), intent(in)  st, class(mesh_t), intent(in)  mesh, integer, intent(in)  ia, complex(real64), dimension(:), intent(out), contiguous  n0I  )

private

Definition at line 4042 of file casida.F90.

zget_transition_densities()

subroutine casida_oct_m::zget_transition_densities ( type(casida_t), intent(in)  cas, type(electrons_t), intent(in)  sys  )

private

Definition at line 4086 of file casida.F90.

zcasida_get_rho()

subroutine casida_oct_m::zcasida_get_rho ( type(states_elec_t), intent(in)  st, class(mesh_t), intent(in)  mesh, integer, intent(in)  ii, integer, intent(in)  ia, integer, intent(in)  kk, complex(real64), dimension(:), intent(out), contiguous  rho  )

private

Definition at line 4119 of file casida.F90.

zcasida_calc_lr_hmat1()

subroutine casida_oct_m::zcasida_calc_lr_hmat1 ( type(electrons_t), intent(inout)  sys, class(perturbation_t), intent(in)  pert, real(real64), dimension(:,:,:), intent(in), contiguous  hvar, complex(real64), dimension(:,:,:), intent(out), contiguous  lr_hmat1, logical, dimension(:,:,:), intent(in), contiguous  is_saved, integer, intent(in)  st_start, integer, intent(in)  st_end, integer, intent(in)  ik  )

private

calculate one-particle matrix elements of perturbation

Definition at line 4157 of file casida.F90.

zcasida_lr_hmat2()

subroutine casida_oct_m::zcasida_lr_hmat2 ( type(casida_t), intent(inout)  cas, type(states_elec_t), intent(in)  st, complex(real64), dimension(:,:,:), intent(in), contiguous  lr_hmat1, integer, intent(in)  ik  )

private

calculate two-particle matrix elements of perturbation

Definition at line 4208 of file casida.F90.

zcasida_get_matrix()

subroutine casida_oct_m::zcasida_get_matrix ( type(casida_t), intent(inout)  cas, type(namespace_t), intent(in)  namespace, type(hamiltonian_elec_t), intent(in)  hm, type(states_elec_t), intent(in)  st, type(v_ks_t), intent(in)  ks, type(grid_t), intent(in)  gr, complex(real64), dimension(:,:), intent(out), contiguous  matrix, real(real64), dimension(:,:,:), intent(in), contiguous  fxc, real(real64), dimension(:,:,:,:,:), intent(in), contiguous  fxc_grad, real(real64), dimension(:,:,:,:), intent(in), contiguous  fxc_grad_spin, character(len=*), intent(in)  restart_file, logical, intent(in), optional  is_forces, complex(real64), dimension(:,:), intent(out), optional, contiguous  matrixB  )

private

Parameters

[out]

matrixb

Off-diagonal B coupling matrix for the full TDHF (RPA) problem.

Definition at line 4244 of file casida.F90.

zwrite_k_term()

subroutine casida_oct_m::zwrite_k_term ( type(casida_t), intent(in)  cas, complex(real64), intent(in)  mat_val, integer, intent(in)  iunit, integer, intent(in)  ia, integer, intent(in)  jb  )

private

write matrix element to casida_restart file

Definition at line 5133 of file casida.F90.

zcasida_forces()

subroutine casida_oct_m::zcasida_forces ( type(casida_t), intent(inout)  cas, type(electrons_t), intent(inout)  sys, type(grid_t), intent(in)  gr, type(states_elec_t), intent(inout)  st  )

private

Definition at line 5149 of file casida.F90.

zcasida_get_lr_hmat1()

subroutine casida_oct_m::zcasida_get_lr_hmat1 ( type(casida_t), intent(in)  cas, type(electrons_t), intent(inout)  sys, integer, intent(in)  iatom, integer, intent(in)  idir, real(real64), dimension(:,:), intent(in), contiguous  dl_rho, complex(real64), dimension(:,:,:), intent(out), contiguous  lr_hmat1  )

private

Definition at line 5298 of file casida.F90.

zcasida_solve()

subroutine casida_oct_m::zcasida_solve ( type(casida_t), intent(inout)  cas, type(electrons_t), intent(in)  sys  )

private

Definition at line 5412 of file casida.F90.

zcasida_write()

subroutine casida_oct_m::zcasida_write ( type(casida_t), intent(inout)  cas, type(electrons_t), intent(in)  sys  )

private

Definition at line 5638 of file casida.F90.

zwrite_implied_occupations()

subroutine casida_oct_m::zwrite_implied_occupations ( type(casida_t), intent(in)  cas, integer, intent(in)  iunit, integer, intent(in)  ind  )

private

Definition at line 5799 of file casida.F90.

zwrite_distributed_matrix()

subroutine casida_oct_m::zwrite_distributed_matrix ( type(casida_t), intent(inout)  cas, complex(real64), dimension(:,:), intent(in), contiguous  matrix, character(len=*), intent(in)  filename  )

private

Definition at line 5838 of file casida.F90.

zallreduce_sum()

complex(real64) function casida_oct_m::zallreduce_sum ( type(casida_t), intent(in)  cas, complex(real64), intent(in)  variable  )

private

Definition at line 5861 of file casida.F90.

Variable Documentation

casida_eps_diff

integer, parameter casida_oct_m::casida_eps_diff = 1

private

Definition at line 189 of file casida.F90.

casida_petersilka

integer, parameter casida_oct_m::casida_petersilka = 2

private

Definition at line 189 of file casida.F90.

casida_tamm_dancoff

integer, parameter casida_oct_m::casida_tamm_dancoff = 4

private

Definition at line 189 of file casida.F90.

casida_variational

integer, parameter casida_oct_m::casida_variational = 8

private

Definition at line 189 of file casida.F90.

casida_casida

integer, parameter casida_oct_m::casida_casida = 16

private

Definition at line 189 of file casida.F90.

solver_elpa

integer, parameter casida_oct_m::solver_elpa = 1

private

Definition at line 196 of file casida.F90.

solver_scalapack

integer, parameter casida_oct_m::solver_scalapack = 2

private

Definition at line 196 of file casida.F90.