propagator_etrs_oct_m Module Reference

Functions/Subroutines
subroutine, public	td_etrs (ks, namespace, space, hm, ext_partners, gr, st, tr, time, dt, ions_dyn, ions, mc)
	Propagator with enforced time-reversal symmetry, ETRS. More...
subroutine	td_etrs_independent_particles (namespace, space, hm, ext_partners, gr, st, tr, time, dt, ions_dyn, ions, mc)
	Propagator with enforced time-reversal symmetry for independent particles. More...
subroutine	td_etrs_predictor (ks, namespace, space, hm, ext_partners, gr, st, tr, time, dt, ions_dyn, ions, mc)
	ETRS predictor step. More...
subroutine, public	td_etrs_sc (ks, namespace, space, hm, ext_partners, gr, st, tr, time, dt, ions_dyn, ions, mc, sctol, scsteps)
	Propagator with enforced time-reversal symmetry and self-consistency. More...
subroutine, public	td_aetrs (namespace, space, hm, gr, st, tr, time, dt, ions_dyn, ions, ext_partners, mc)
	Propagator with approximate enforced time-reversal symmetry. More...
subroutine, public	td_aetrs_sc (ks, namespace, space, hm, ext_partners, gr, st, tr, time, dt, ions_dyn, ions, mc, sctol, scsteps)
	Propagator with approximate enforced time-reversal symmetry and self-consistency. More...
subroutine, public	td_caetrs (ks, namespace, space, hm, ext_partners, gr, st, tr, time, dt, ions_dyn, ions, mc)
	Propagator with approximate enforced time-reversal symmetry. More...

Function/Subroutine Documentation

td_etrs()

subroutine, public propagator_etrs_oct_m::td_etrs	(	type(v_ks_t), intent(inout)	ks,
		type(namespace_t), intent(in)	namespace,
		type(electron_space_t), intent(in)	space,
		type(hamiltonian_elec_t), intent(inout)	hm,
		type(partner_list_t), intent(in)	ext_partners,
		type(grid_t), intent(inout)	gr,
		type(states_elec_t), intent(inout)	st,
		type(propagator_base_t), intent(inout)	tr,
		real(real64), intent(in)	time,
		real(real64), intent(in)	dt,
		type(ion_dynamics_t), intent(inout)	ions_dyn,
		type(ions_t), intent(inout)	ions,
		type(multicomm_t), intent(inout)	mc
	)

Propagator with enforced time-reversal symmetry, ETRS.

Due to time-reversal symmetry, propagating backwards by \(\Delta t/2\) starting from \(\psi_{j,n+1}\) should lead to the same result as propagating forwards by \(\Delta t/2\) starting from \(\psi_{j,n}\). Using the simplest approximation to the evolution operator, the propagated states are defined as:

\[ \psi_{j,n+1} = e^{-i(\Delta t/2)\tilde{H}_{n+1}} e^{-i(\Delta t/2)H_n} \psi_{j,n}, \]

which can be expressed in terms of the half-step orbitals \(\psi_{j,n+1/2}\) from td_etrs_predictor:

\[ \psi_{j,n+1} = e^{-i(\Delta t/2)\tilde{H}_{n+1}} \psi_{j,n+1/2}, \]

where \(n\) labels discrete time steps, and \(\tilde{H}_{n+1}\) is the approximate Hamiltonian at time \(t_{n+1} = t_n + \Delta t\). This is constructed from the predictor density and (when appropriate) orbitals.

Parameters

[in,out]

mc

index and domain communicators

Definition at line 182 of file propagator_etrs.F90.

td_etrs_independent_particles()

subroutine propagator_etrs_oct_m::td_etrs_independent_particles ( type(namespace_t), intent(in)  namespace, type(electron_space_t), intent(in)  space, type(hamiltonian_elec_t), intent(inout)  hm, type(partner_list_t), intent(in)  ext_partners, type(grid_t), intent(inout)  gr, type(states_elec_t), intent(inout)  st, type(propagator_base_t), intent(inout)  tr, real(real64), intent(in)  time, real(real64), intent(in)  dt, type(ion_dynamics_t), intent(inout)  ions_dyn, type(ions_t), intent(inout)  ions, type(multicomm_t), intent(inout)  mc  )

private

Propagator with enforced time-reversal symmetry for independent particles.

Parameters

[in,out]

mc

index and domain communicators

Definition at line 215 of file propagator_etrs.F90.

td_etrs_predictor()

subroutine propagator_etrs_oct_m::td_etrs_predictor ( type(v_ks_t), intent(inout)  ks, type(namespace_t), intent(in)  namespace, type(electron_space_t), intent(in)  space, type(hamiltonian_elec_t), intent(inout)  hm, type(partner_list_t), intent(in)  ext_partners, type(grid_t), intent(inout)  gr, type(states_elec_t), intent(inout)  st, type(propagator_base_t), intent(inout)  tr, real(real64), intent(in)  time, real(real64), intent(in)  dt, type(ion_dynamics_t), intent(inout)  ions_dyn, type(ions_t), intent(inout)  ions, type(multicomm_t), intent(inout)  mc  )

private

ETRS predictor step.

Propagate the current KS orbitals twice. Once by a half step:

\[ \psi_{j,n+1/2} = e^{-i(\Delta t/2)H_n} \psi_{j,n}, \]

and once by a full step:

\[ \tilde{\psi}_{j,n+1} = e^{-i\Delta t H_n} \psi_{j,n}, \]

\( \tilde{\psi}_{j,n+1} \) estimate the end point orbitals, and are used to define the predictor density:

\[ \tilde{\rho}_{n+1}(\mathbf r) = \sum_j f_j |\tilde{\psi}_{j,n+1}(\mathbf r)|^2. \]

Todo:

KS inversion and orbital-dependent photon contributions require additional modifications, followed by testing. As it stands, they currently receive half-step orbitals.

Parameters

[in,out]

mc

index and domain communicators

Definition at line 275 of file propagator_etrs.F90.

td_etrs_sc()

subroutine, public propagator_etrs_oct_m::td_etrs_sc	(	type(v_ks_t), intent(inout)	ks,
		type(namespace_t), intent(in)	namespace,
		type(electron_space_t), intent(in)	space,
		type(hamiltonian_elec_t), intent(inout)	hm,
		type(partner_list_t), intent(in)	ext_partners,
		type(grid_t), intent(inout)	gr,
		type(states_elec_t), intent(inout)	st,
		type(propagator_base_t), intent(inout)	tr,
		real(real64), intent(in)	time,
		real(real64), intent(in)	dt,
		type(ion_dynamics_t), intent(inout)	ions_dyn,
		type(ions_t), intent(inout)	ions,
		type(multicomm_t), intent(inout)	mc,
		real(real64), intent(in)	sctol,
		integer, intent(out), optional	scsteps
	)

Propagator with enforced time-reversal symmetry and self-consistency.

Parameters

[in,out]

mc

index and domain communicators

Definition at line 345 of file propagator_etrs.F90.

td_aetrs()

subroutine, public propagator_etrs_oct_m::td_aetrs	(	type(namespace_t), intent(in)	namespace,
		type(electron_space_t), intent(in)	space,
		type(hamiltonian_elec_t), intent(inout)	hm,
		type(grid_t), intent(inout)	gr,
		type(states_elec_t), intent(inout)	st,
		type(propagator_base_t), intent(inout)	tr,
		real(real64), intent(in)	time,
		real(real64), intent(in)	dt,
		type(ion_dynamics_t), intent(inout)	ions_dyn,
		type(ions_t), intent(inout)	ions,
		type(partner_list_t), intent(in)	ext_partners,
		type(multicomm_t), intent(inout)	mc
	)

Propagator with approximate enforced time-reversal symmetry.

Parameters

[in,out]

mc

index and domain communicators

Definition at line 462 of file propagator_etrs.F90.

td_aetrs_sc()

subroutine, public propagator_etrs_oct_m::td_aetrs_sc	(	type(v_ks_t), intent(inout)	ks,
		type(namespace_t), intent(in)	namespace,
		type(electron_space_t), intent(in)	space,
		type(hamiltonian_elec_t), intent(inout)	hm,
		type(partner_list_t), intent(in)	ext_partners,
		type(grid_t), intent(inout)	gr,
		type(states_elec_t), intent(inout)	st,
		type(propagator_base_t), intent(inout)	tr,
		real(real64), intent(in)	time,
		real(real64), intent(in)	dt,
		type(ion_dynamics_t), intent(inout)	ions_dyn,
		type(ions_t), intent(inout)	ions,
		type(multicomm_t), intent(inout)	mc,
		real(real64), intent(in)	sctol,
		integer, intent(out), optional	scsteps
	)

Propagator with approximate enforced time-reversal symmetry and self-consistency.

Parameters

[in,out]

mc

index and domain communicators

Definition at line 507 of file propagator_etrs.F90.

td_caetrs()

subroutine, public propagator_etrs_oct_m::td_caetrs	(	type(v_ks_t), intent(inout)	ks,
		type(namespace_t), intent(in)	namespace,
		type(electron_space_t), intent(in)	space,
		type(hamiltonian_elec_t), intent(inout)	hm,
		type(partner_list_t), intent(in)	ext_partners,
		type(grid_t), intent(inout)	gr,
		type(states_elec_t), intent(inout)	st,
		type(propagator_base_t), intent(inout)	tr,
		real(real64), intent(in)	time,
		real(real64), intent(in)	dt,
		type(ion_dynamics_t), intent(inout)	ions_dyn,
		type(ions_t), intent(inout)	ions,
		type(multicomm_t), intent(inout)	mc
	)

Propagator with approximate enforced time-reversal symmetry.

Parameters

[in,out]

mc

index and domain communicators

Definition at line 601 of file propagator_etrs.F90.