qs_tddfpt2_eigensolver Module Reference

Functions/Subroutines
subroutine, public	tddfpt_orthogonalize_psi1_psi0 (evects, S_C0_C0T)
	Make TDDFPT trial vectors orthogonal to all occupied molecular orbitals. More...
subroutine, public	tddfpt_orthonormalize_psi1_psi1 (evects, nvects_new, S_evects, matrix_s)
	Make new TDDFPT trial vectors orthonormal to all previous trial vectors. More...
real(kind=dp) function, public	tddfpt_davidson_solver (evects, evals, S_evects, gs_mos, tddfpt_control, matrix_ks, qs_env, kernel_env, sub_env, logger, iter_unit, energy_unit, tddfpt_print_section, work_matrices)
	Perform Davidson iterations. More...

Function/Subroutine Documentation

tddfpt_orthogonalize_psi1_psi0()

subroutine, public qs_tddfpt2_eigensolver::tddfpt_orthogonalize_psi1_psi0	(	type(cp_fm_type), dimension(:, :), intent(in)	evects,
		type(cp_fm_type), dimension(:), intent(in)	S_C0_C0T
	)

Make TDDFPT trial vectors orthogonal to all occupied molecular orbitals.

Parameters

evects	trial vectors distributed across all processors (modified on exit)
S_C0_C0T	matrix product S * C_0 * C_0^T, where C_0 is the ground state wave function for each spin expressed in atomic basis set, and S is the corresponding overlap matrix

History

• 05.2016 created [Sergey Chulkov]
• 05.2019 use a temporary work matrix [JHU]

Note

Based on the subroutine p_preortho() which was created by Thomas Chassaing on 09.2002. Should be useless when ground state MOs are computed with extremely high accuracy, as all virtual orbitals are already orthogonal to the occupied ones by design. However, when the norm of residual vectors is relatively small (e.g. less then SCF_EPS), new Krylov's vectors seem to be random and should be orthogonalised even with respect to the occupied MOs.

Definition at line 94 of file qs_tddfpt2_eigensolver.F.

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tddfpt_orthonormalize_psi1_psi1()

subroutine, public qs_tddfpt2_eigensolver::tddfpt_orthonormalize_psi1_psi1	(	type(cp_fm_type), dimension(:, :), intent(in)	evects,
		integer, intent(in)	nvects_new,
		type(cp_fm_type), dimension(:, :), intent(in)	S_evects,
		type(dbcsr_type), pointer	matrix_s
	)

Make new TDDFPT trial vectors orthonormal to all previous trial vectors.

Parameters

evects	trial vectors (modified on exit)
nvects_new	number of new trial vectors to orthogonalise
S_evects	set of matrices to store matrix product S * evects (modified on exit)
matrix_s	overlap matrix

History

• 05.2016 created [Sergey Chulkov]
• 02.2017 caching the matrix product S * evects [Sergey Chulkov]

Note

Based on the subroutines reorthogonalize() and normalize() which were originally created by Thomas Chassaing on 03.2003.

In order to orthogonalise a trial vector C3 = evects(:,3) with respect to previously orthogonalised vectors C1 = evects(:,1) and C2 = evects(:,2) we need to compute the quantity C3'' using the following formulae: C3' = C3 - Tr(C3^T * S * C1) * C1, C3'' = C3' - Tr(C3'^T * S * C2) * C2, which can be expanded as: C3'' = C3 - Tr(C3^T * S * C1) * C1 - Tr(C3^T * S * C2) * C2 + Tr(C3^T * S * C1) * Tr(C2^T * S * C1) * C2 . In case of unlimited float-point precision, the last term in above expression is exactly 0, due to orthogonality condition between C1 and C2. In this case the expression could be simplified as (taking into account the identity: Tr(A * S * B) = Tr(B * S * A)): C3'' = C3 - Tr(C1^T * S * C3) * C1 - Tr(C2^T * S * C3) * C2 , which means we do not need the variable S_evects to keep the matrix products S * Ci .

In reality, however, we deal with limited float-point precision arithmetic meaning that the trace Tr(C2^T * S * C1) is close to 0 but does not equal to 0 exactly. The term Tr(C3^T * S * C1) * Tr(C2^T * S * C1) * C2 can not be ignored anymore. Ignorance of this term will lead to numerical instability when the trace Tr(C3^T * S * C1) is large enough.

Definition at line 224 of file qs_tddfpt2_eigensolver.F.

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tddfpt_davidson_solver()

real(kind=dp) function, public qs_tddfpt2_eigensolver::tddfpt_davidson_solver	(	type(cp_fm_type), dimension(:, :), intent(inout)	evects,
		real(kind=dp), dimension(:), intent(inout)	evals,
		type(cp_fm_type), dimension(:, :), intent(inout)	S_evects,
		type(tddfpt_ground_state_mos), dimension(:), intent(in)	gs_mos,
		type(tddfpt2_control_type), pointer	tddfpt_control,
		type(dbcsr_p_type), dimension(:), pointer	matrix_ks,
		type(qs_environment_type), pointer	qs_env,
		type(kernel_env_type), intent(in)	kernel_env,
		type(tddfpt_subgroup_env_type), intent(in)	sub_env,
		type(cp_logger_type), pointer	logger,
		integer, intent(in)	iter_unit,
		integer, intent(in)	energy_unit,
		type(section_vals_type), pointer	tddfpt_print_section,
		type(tddfpt_work_matrices), intent(inout)	work_matrices
	)

Perform Davidson iterations.

Parameters

evects	TDDFPT trial vectors (modified on exit)
evals	TDDFPT eigenvalues (modified on exit)
S_evects	cached matrix product S * evects (modified on exit)
gs_mos	molecular orbitals optimised for the ground state
tddfpt_control	TDDFPT control parameters
matrix_ks	Kohn-Sham matrix
qs_env	Quickstep environment
kernel_env	kernel environment
sub_env	parallel (sub)group environment
logger	CP2K logger
iter_unit	I/O unit to write basic iteration information
energy_unit	I/O unit to write detailed energy information
tddfpt_print_section	TDDFPT print input section (need to write TDDFPT restart files)
work_matrices	collection of work matrices (modified on exit)

Returns

energy convergence achieved (in Hartree)

History

• 03.2017 code related to Davidson eigensolver has been moved here from the main subroutine tddfpt() [Sergey Chulkov]

Note

Based on the subroutines apply_op() and iterative_solver() originally created by Thomas Chassaing in 2002.

Definition at line 720 of file qs_tddfpt2_eigensolver.F.

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