exchange_operator_oct_m Module Reference

Data Types
type	ace_t
type	exchange_operator_t

Functions/Subroutines
subroutine	ace_init (this, namespace, st)
	Initialize an instance of ACE_t. More...
subroutine	ace_end (this)
	End an instance of ACE_t. More...
subroutine	ace_write_info (this, namespace)
subroutine, public	exchange_operator_init (this, namespace, space, st, der, mc, stencil, kpoints, cam)
subroutine, public	exchange_operator_reinit (this, cam, st)
subroutine, public	exchange_operator_end (this)
subroutine, public	exchange_operator_rdmft_occ_apply (this, mesh, hpsib)
subroutine	exchange_operator_write_info (this, namespace)
subroutine, public	dexchange_operator_single (this, namespace, space, mesh, st_d, kpoints, phase, ist, ik, psi, hpsi, rdmft, force_noace)
subroutine, public	dexchange_operator_apply (this, namespace, space, mesh, st_d, kpoints, phase, psib, hpsib, rdmft, force_noace)
subroutine	dexchange_operator_apply_standard (this, namespace, space, mesh, st_d, kpoints, phase, psib, hpsib, rdmft)
subroutine	dexchange_operator_apply_ace (this, mesh, st_d, psib, hpsib)
subroutine	dexchange_operator_apply_ace_gemm (this, mesh, chib, psib, hpsib)
	Apply the ACE operator \( |h\psi_j\rangle \mathrel{-}= \sum_i \langle\chi_i|\psi_j\rangle\,|\chi_i\rangle \) to a packed batch as GEMM operations on the device buffers. More...
subroutine, public	dexchange_operator_compute_potentials (this, namespace, space, gr, st, xst, kpoints, F_out)
subroutine	dexchange_accumulate (np, xket, ff, ff_bra_host, pot_host, bra_buffer, ld_bra, ist_bra, pot_buffer)
	Accumulate the exchange contribution \( |x_j\rangle \mathrel{-}= ff\,\psi_{sym}\,V_{ij} \) into the whole target block xket, on host or device. More...
subroutine	dexchange_operator_accumulate_return (gr, st, kpoints, ib2, ik2, exx_weight, pot, psi2, xpsi_ret, pot_buffer, xret_buffer, ff2_buffer, ff2_base, base_ret)
	Accumulates the exchange contribution of one batch of local states acting on a received state. More...
subroutine	dexchange_operator_add_returned (gr, st, xst, ib_send, ik_send, xpsi_rec, xret_buffer)
	Add the returned exchange potential into the local xst block (sending task). More...
real(real64) function, public	dexchange_operator_compute_ex (mesh, st, xst)
	Compute the exact exchange energy. More...
subroutine, public	dexchange_operator_ace (this, namespace, mesh, st, xst, phase)
	Construct the ACE vectors. More...
subroutine	dexchange_operator_ace_overlap (this, mesh, st, xst, xpsi, MM)
	Build the ACE overlap matrix for state-parallel wave functions. More...
subroutine	dexchange_operator_ace_overlap_batched (this, mesh, st, xst, MM)
	Build the ACE overlap matrix from non-state-parallel wave-function batches. More...
subroutine, public	dexchange_operator_commute_r (this, namespace, mesh, st_d, ik, psi, gpsi)
subroutine, public	dexchange_operator_hartree_apply (this, namespace, mesh, st_d, kpoints, exx_coef, psib, hpsib)
subroutine, public	zexchange_operator_single (this, namespace, space, mesh, st_d, kpoints, phase, ist, ik, psi, hpsi, rdmft, force_noace)
subroutine, public	zexchange_operator_apply (this, namespace, space, mesh, st_d, kpoints, phase, psib, hpsib, rdmft, force_noace)
subroutine	zexchange_operator_apply_standard (this, namespace, space, mesh, st_d, kpoints, phase, psib, hpsib, rdmft)
subroutine	zexchange_operator_apply_ace (this, mesh, st_d, psib, hpsib)
subroutine	zexchange_operator_apply_ace_gemm (this, mesh, chib, psib, hpsib)
	Apply the ACE operator \( |h\psi_j\rangle \mathrel{-}= \sum_i \langle\chi_i|\psi_j\rangle\,|\chi_i\rangle \) to a packed batch as GEMM operations on the device buffers. More...
subroutine, public	zexchange_operator_compute_potentials (this, namespace, space, gr, st, xst, kpoints, F_out)
subroutine	zexchange_accumulate (np, xket, ff, ff_bra_host, pot_host, bra_buffer, ld_bra, ist_bra, pot_buffer)
	Accumulate the exchange contribution \( |x_j\rangle \mathrel{-}= ff\,\psi_{sym}\,V_{ij} \) into the whole target block xket, on host or device. More...
subroutine	zexchange_operator_accumulate_return (gr, st, kpoints, ib2, ik2, exx_weight, pot, psi2, xpsi_ret, pot_buffer, xret_buffer, ff2_buffer, ff2_base, base_ret)
	Accumulates the exchange contribution of one batch of local states acting on a received state. More...
subroutine	zexchange_operator_add_returned (gr, st, xst, ib_send, ik_send, xpsi_rec, xret_buffer)
	Add the returned exchange potential into the local xst block (sending task). More...
real(real64) function, public	zexchange_operator_compute_ex (mesh, st, xst)
	Compute the exact exchange energy. More...
subroutine, public	zexchange_operator_ace (this, namespace, mesh, st, xst, phase)
	Construct the ACE vectors. More...
subroutine	zexchange_operator_ace_overlap (this, mesh, st, xst, xpsi, MM)
	Build the ACE overlap matrix for state-parallel wave functions. More...
subroutine	zexchange_operator_ace_overlap_batched (this, mesh, st, xst, MM)
	Build the ACE overlap matrix from non-state-parallel wave-function batches. More...
subroutine, public	zexchange_operator_commute_r (this, namespace, mesh, st_d, ik, psi, gpsi)
subroutine, public	zexchange_operator_hartree_apply (this, namespace, mesh, st_d, kpoints, exx_coef, psib, hpsib)

Variables
type(fourier_space_op_t)	coulb
	Operator in Fourier space. More...
real(real64), parameter, private	tol_exx_weight = 1.0e-3_real64
	Minimum weight below which EXX is not added. More...

Function/Subroutine Documentation

ace_init()

subroutine exchange_operator_oct_m::ace_init ( class(ace_t), intent(inout)  this, type(namespace_t), intent(in)  namespace, type(states_elec_t), intent(in)  st  )

private

Initialize an instance of ACE_t.

Definition at line 230 of file exchange_operator.F90.

ace_end()

subroutine exchange_operator_oct_m::ace_end ( class(ace_t), intent(inout)  this )

private

End an instance of ACE_t.

Definition at line 271 of file exchange_operator.F90.

ace_write_info()

subroutine exchange_operator_oct_m::ace_write_info ( class(ace_t), intent(in)  this, type(namespace_t), intent(in)  namespace  )

private

Definition at line 293 of file exchange_operator.F90.

exchange_operator_init()

subroutine, public exchange_operator_oct_m::exchange_operator_init	(	type(exchange_operator_t), intent(inout)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(states_elec_t), intent(in)	st,
		type(derivatives_t), intent(in)	der,
		type(multicomm_t), intent(in)	mc,
		type(stencil_t), intent(in)	stencil,
		type(kpoints_t), intent(in)	kpoints,
		type(xc_cam_t), intent(in)	cam
	)

Definition at line 306 of file exchange_operator.F90.

exchange_operator_reinit()

subroutine, public exchange_operator_oct_m::exchange_operator_reinit	(	type(exchange_operator_t), intent(inout)	this,
		type(xc_cam_t), intent(in)	cam,
		type(states_elec_t), intent(in), optional, target	st
	)

Definition at line 414 of file exchange_operator.F90.

exchange_operator_end()

subroutine, public exchange_operator_oct_m::exchange_operator_end

(

type(exchange_operator_t), intent(inout)

this

)

Definition at line 430 of file exchange_operator.F90.

exchange_operator_rdmft_occ_apply()

subroutine, public exchange_operator_oct_m::exchange_operator_rdmft_occ_apply	(	type(exchange_operator_t), intent(in)	this,
		type(mesh_t), intent(in)	mesh,
		class(wfs_elec_t), intent(inout)	hpsib
	)

Definition at line 451 of file exchange_operator.F90.

exchange_operator_write_info()

subroutine exchange_operator_oct_m::exchange_operator_write_info ( class(exchange_operator_t), intent(in)  this, type(namespace_t), intent(in)  namespace  )

private

Definition at line 465 of file exchange_operator.F90.

dexchange_operator_single()

subroutine, public exchange_operator_oct_m::dexchange_operator_single	(	type(exchange_operator_t), intent(inout)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		class(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		type(kpoints_t), intent(in)	kpoints,
		type(phase_t), intent(in)	phase,
		integer, intent(in)	ist,
		integer, intent(in)	ik,
		real(real64), dimension(:, :), intent(inout), contiguous	psi,
		real(real64), dimension(:, :), intent(inout), contiguous	hpsi,
		logical, intent(in)	rdmft,
		logical, intent(in), optional	force_noace
	)

Definition at line 554 of file exchange_operator.F90.

dexchange_operator_apply()

subroutine, public exchange_operator_oct_m::dexchange_operator_apply	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		type(kpoints_t), intent(in)	kpoints,
		type(phase_t), intent(in)	phase,
		class(wfs_elec_t), intent(inout)	psib,
		class(wfs_elec_t), intent(inout)	hpsib,
		logical, intent(in)	rdmft,
		logical, intent(in), optional	force_noace
	)

Definition at line 585 of file exchange_operator.F90.

dexchange_operator_apply_standard()

subroutine exchange_operator_oct_m::dexchange_operator_apply_standard ( type(exchange_operator_t), intent(in)  this, type(namespace_t), intent(in)  namespace, class(space_t), intent(in)  space, type(mesh_t), intent(in)  mesh, type(states_elec_dim_t), intent(in)  st_d, type(kpoints_t), intent(in)  kpoints, type(phase_t), intent(in)  phase, class(wfs_elec_t), intent(inout)  psib, class(wfs_elec_t), intent(inout)  hpsib, logical, intent(in)  rdmft  )

private

Definition at line 612 of file exchange_operator.F90.

dexchange_operator_apply_ace()

subroutine exchange_operator_oct_m::dexchange_operator_apply_ace ( type(exchange_operator_t), intent(in)  this, type(mesh_t), intent(in)  mesh, type(states_elec_dim_t), intent(in)  st_d, type(wfs_elec_t), intent(in)  psib, type(wfs_elec_t), intent(inout)  hpsib  )

private

Definition at line 774 of file exchange_operator.F90.

dexchange_operator_apply_ace_gemm()

subroutine exchange_operator_oct_m::dexchange_operator_apply_ace_gemm ( type(exchange_operator_t), intent(in)  this, type(mesh_t), intent(in)  mesh, type(wfs_elec_t), intent(in)  chib, type(wfs_elec_t), intent(in)  psib, type(wfs_elec_t), intent(inout)  hpsib  )

private

Apply the ACE operator \( |h\psi_j\rangle \mathrel{-}= \sum_i \langle\chi_i|\psi_j\rangle\,|\chi_i\rangle \) to a packed batch as GEMM operations on the device buffers.

GEMM operations run on the packed buffers (ist-1)*dim+idim. For spinors the spin diagonal of the coefficient matrix is summed and re-expanded so the same S(i,j) is applied to every spinor component.

Definition at line 858 of file exchange_operator.F90.

dexchange_operator_compute_potentials()

subroutine, public exchange_operator_oct_m::dexchange_operator_compute_potentials	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(grid_t), intent(in)	gr,
		type(states_elec_t), intent(inout), target	st,
		type(states_elec_t), intent(inout)	xst,
		type(kpoints_t), intent(in)	kpoints,
		real(real64), dimension(:,:,:,:,:), intent(out), optional	F_out
	)

Parameters

[in,out]	xst	Action of V_X on a set of KS states
[out]	f_out	For RDMFT

Definition at line 994 of file exchange_operator.F90.

dexchange_accumulate()

subroutine exchange_operator_oct_m::dexchange_accumulate ( integer, intent(in)  np, class(batch_t), intent(inout)  xket, real(real64), intent(in)  ff, real(real64), dimension(:,:), intent(in), optional  ff_bra_host, real(real64), dimension(:,:), intent(in), optional  pot_host, type(accel_mem_t), intent(in), optional  bra_buffer, integer, intent(in), optional  ld_bra, integer, intent(in), optional  ist_bra, type(accel_mem_t), intent(in), optional  pot_buffer  )

private

Accumulate the exchange contribution \( |x_j\rangle \mathrel{-}= ff\,\psi_{sym}\,V_{ij} \) into the whole target block xket, on host or device.

Parameters

[in]	ff	device: scaling factor; host: unused (folded in ff_bra_host)
[in]	ff_bra_host	host: ff*psi_sym (np,dim)
[in]	pot_host	host: pot(:,1:xketnst)

Definition at line 1612 of file exchange_operator.F90.

dexchange_operator_accumulate_return()

subroutine exchange_operator_oct_m::dexchange_operator_accumulate_return ( type(grid_t), intent(in)  gr, type(states_elec_t), intent(in)  st, type(kpoints_t), intent(in)  kpoints, integer, intent(in)  ib2, integer, intent(in)  ik2, real(real64), intent(in)  exx_weight, real(real64), dimension(:,:), intent(in), optional, contiguous  pot, real(real64), dimension(:,:), intent(inout), optional  psi2, real(real64), dimension(:,:), intent(inout), optional, contiguous  xpsi_ret, type(accel_mem_t), intent(in), optional  pot_buffer, type(accel_mem_t), intent(inout), optional  xret_buffer, type(accel_mem_t), intent(in), optional  ff2_buffer, integer, intent(in), optional  ff2_base, integer, intent(in), optional  base_ret  )

private

Accumulates the exchange contribution of one batch of local states acting on a received state.

Parameters

[in]	ib2	Block index of the local states
[in]	ik2	k-point index of the local states
[in]	exx_weight	Weight of the exchange operator
[in]	pot	host: potentials for the local states of the batch
[in,out]	psi2	host: workspace for accessing device batches
[in,out]	xpsi_ret	host: accumulated potential to be returned
[in]	pot_buffer	device: potentials (np, nst2)
[in,out]	xret_buffer	device: (np, dim, nst_received) return buffer
[in]	ff2_buffer	device: precomputed per-lane weights (real64)
[in]	ff2_base	device: offset of this block weights in ff2_buffer
[in]	base_ret	device: element offset of the current bra in xret_buffer

Definition at line 1702 of file exchange_operator.F90.

dexchange_operator_add_returned()

subroutine exchange_operator_oct_m::dexchange_operator_add_returned ( type(grid_t), intent(in)  gr, type(states_elec_t), intent(in)  st, type(states_elec_t), intent(inout), target  xst, integer, intent(in)  ib_send, integer, intent(in)  ik_send, real(real64), dimension(:,:,:), intent(in), optional, contiguous  xpsi_rec, type(accel_mem_t), intent(in), optional  xret_buffer  )

private

Add the returned exchange potential into the local xst block (sending task).

Parameters

[in]	ib_send	Block index of the states that were sent
[in]	ik_send	k-point index of the states that were sent
[in]	xpsi_rec	host: returned potential, (np, dim, nst)
[in]	xret_buffer	device: returned potential, (np, dim, nst)

Definition at line 1799 of file exchange_operator.F90.

dexchange_operator_compute_ex()

real(real64) function, public exchange_operator_oct_m::dexchange_operator_compute_ex	(	class(mesh_t), intent(in)	mesh,
		type(states_elec_t), intent(in)	st,
		type(states_elec_t), intent(in)	xst
	)

Compute the exact exchange energy.

\[ E_X = \frac{1}{2} \sum_{i, \sigma \mathbf{k}} w_\mathbf{k} f_{i\sigma\mathbf{k}} \int \psi^\ast_{i \sigma \mathbf{k}}(\mathbf{r}) W_{i \sigma \mathbf{k}}(\mathbf{r}) d\mathbf{r} \]

where

\[ W_{i\sigma\mathbf{k}}(\mathbf{r}) = - \sum_{j,\mathbf{k}^\prime} f_{j\sigma\mathbf{k}^\prime}\,\omega_{\mathbf{k}^\prime} V_{ij}^{\mathbf{k},\mathbf{k}^\prime,\sigma}(\mathbf{r}) \psi_{j\sigma\mathbf{k}^\prime}(\mathbf{r}) \]

is the action of the exchange operator on a set of Kohn-Sham states.

Note

The implementation ASSUMES that the appropriate range separation weight, exx_weight, and the electron occupation constant, stsmearel_per_state, have been absorbed in xst. This is what is done in the routine exchange_operator_compute_potentials.

Parameters

[in]	st	A set of KS states
[in]	xst	V_X operating on a set of KS states

Returns

Exact exchange energy

Definition at line 1917 of file exchange_operator.F90.

dexchange_operator_ace()

subroutine, public exchange_operator_oct_m::dexchange_operator_ace	(	type(exchange_operator_t), intent(inout)	this,
		type(namespace_t), intent(in)	namespace,
		class(mesh_t), intent(in)	mesh,
		type(states_elec_t), intent(inout)	st,
		type(states_elec_t), intent(inout)	xst,
		type(phase_t), intent(in), optional	phase
	)

Construct the ACE vectors.

This follows the procedure defined in Lin, J. Chem. Theory Comput. 2016, 12, 2242. It constructs the \( M \) matrix, defined as the projection of the exact exchange operator onto the occupied Kohn-Sham states:

\[ M_{ij} = \langle \psi_i | \hat{V}_X | \psi_j \rangle = \langle \psi_i | W_j \rangle, \]

where \( W_j(\mathbf{r}) = (\hat{V}_X \psi_j)(\mathbf{r}) \) is the exchange operator applied to state \( j \). \( M \) is then decomposed into \( L \), which is inverted and used to construct the ACE vectors:

\[ \xi_k(\mathbf{r}) = \sum_{j=1}^n W_j(\mathbf{r}) \left(L^{-H}\right)_{j k} \]

Parameters

[in,out]	this	ACE vectors, of size thisacenst
[in,out]	xst	Application of the exact exchange

Definition at line 1972 of file exchange_operator.F90.

dexchange_operator_ace_overlap()

subroutine exchange_operator_oct_m::dexchange_operator_ace_overlap ( type(exchange_operator_t), intent(in)  this, class(mesh_t), intent(in)  mesh, type(states_elec_t), intent(in)  st, type(states_elec_t), intent(inout)  xst, real(real64), dimension(:,:), intent(inout)  xpsi, real(real64), dimension(1:this%ace%nst, 1:this%ace%nst, st%d%kpt%start:st%d%kpt%end), intent(out)  MM  )

private

Build the ACE overlap matrix for state-parallel wave functions.

For each local spin/k-point, construct the lower triangle of the ACE overlap matrix:

\[ M_{ij}^{(k)} = -\left\langle \psi_i^{(k)} \middle| \hat{X} \middle| \psi_j^{(k)} \right\rangle, \qquad (i, j) \leq N_{\mathrm{ACE}}. \]

Here, st contains the Kohn–Sham states \(\psi_i\) and xst contains their images under the exact-exchange operator, \(\hat{X}\psi_j\).

Parameters

[in,out]

xpsi

Work array

Definition at line 2121 of file exchange_operator.F90.

dexchange_operator_ace_overlap_batched()

subroutine exchange_operator_oct_m::dexchange_operator_ace_overlap_batched ( type(exchange_operator_t), intent(in)  this, class(mesh_t), intent(in)  mesh, type(states_elec_t), intent(in)  st, type(states_elec_t), intent(in)  xst, real(real64), dimension(1:this%ace%nst, 1:this%ace%nst, st%d%kpt%start:st%d%kpt%end), intent(out)  MM  )

private

Build the ACE overlap matrix from non-state-parallel wave-function batches.

For each local spin/k-point, construct the lower triangle of the ACE overlap matrix:

\[ M_{ij}^{(k)} = -\left\langle \psi_i^{(k)} \middle| \hat{X} \middle| \psi_j^{(k)} \right\rangle, \qquad (i, j) \leq N_{\mathrm{ACE}}. \]

The unused upper triangle, and spin/k-points without electrons, are returned as zero.

Parameters

[out]

mm

Overlap

Definition at line 2186 of file exchange_operator.F90.

dexchange_operator_commute_r()

subroutine, public exchange_operator_oct_m::dexchange_operator_commute_r	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		class(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		integer, intent(in)	ik,
		real(real64), dimension(:, :), intent(in), contiguous	psi,
		real(real64), dimension(:, :, :), intent(inout), contiguous	gpsi
	)

Definition at line 2235 of file exchange_operator.F90.

dexchange_operator_hartree_apply()

subroutine, public exchange_operator_oct_m::dexchange_operator_hartree_apply	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		type(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		type(kpoints_t), intent(in)	kpoints,
		real(real64), intent(in)	exx_coef,
		class(wfs_elec_t), intent(inout)	psib,
		class(wfs_elec_t), intent(inout)	hpsib
	)

Definition at line 2306 of file exchange_operator.F90.

zexchange_operator_single()

subroutine, public exchange_operator_oct_m::zexchange_operator_single	(	type(exchange_operator_t), intent(inout)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		class(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		type(kpoints_t), intent(in)	kpoints,
		type(phase_t), intent(in)	phase,
		integer, intent(in)	ist,
		integer, intent(in)	ik,
		complex(real64), dimension(:, :), intent(inout), contiguous	psi,
		complex(real64), dimension(:, :), intent(inout), contiguous	hpsi,
		logical, intent(in)	rdmft,
		logical, intent(in), optional	force_noace
	)

Definition at line 2459 of file exchange_operator.F90.

zexchange_operator_apply()

subroutine, public exchange_operator_oct_m::zexchange_operator_apply	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		type(kpoints_t), intent(in)	kpoints,
		type(phase_t), intent(in)	phase,
		class(wfs_elec_t), intent(inout)	psib,
		class(wfs_elec_t), intent(inout)	hpsib,
		logical, intent(in)	rdmft,
		logical, intent(in), optional	force_noace
	)

Definition at line 2490 of file exchange_operator.F90.

zexchange_operator_apply_standard()

subroutine exchange_operator_oct_m::zexchange_operator_apply_standard ( type(exchange_operator_t), intent(in)  this, type(namespace_t), intent(in)  namespace, class(space_t), intent(in)  space, type(mesh_t), intent(in)  mesh, type(states_elec_dim_t), intent(in)  st_d, type(kpoints_t), intent(in)  kpoints, type(phase_t), intent(in)  phase, class(wfs_elec_t), intent(inout)  psib, class(wfs_elec_t), intent(inout)  hpsib, logical, intent(in)  rdmft  )

private

Definition at line 2517 of file exchange_operator.F90.

zexchange_operator_apply_ace()

subroutine exchange_operator_oct_m::zexchange_operator_apply_ace ( type(exchange_operator_t), intent(in)  this, type(mesh_t), intent(in)  mesh, type(states_elec_dim_t), intent(in)  st_d, type(wfs_elec_t), intent(in)  psib, type(wfs_elec_t), intent(inout)  hpsib  )

private

Definition at line 2679 of file exchange_operator.F90.

zexchange_operator_apply_ace_gemm()

subroutine exchange_operator_oct_m::zexchange_operator_apply_ace_gemm ( type(exchange_operator_t), intent(in)  this, type(mesh_t), intent(in)  mesh, type(wfs_elec_t), intent(in)  chib, type(wfs_elec_t), intent(in)  psib, type(wfs_elec_t), intent(inout)  hpsib  )

private

Apply the ACE operator \( |h\psi_j\rangle \mathrel{-}= \sum_i \langle\chi_i|\psi_j\rangle\,|\chi_i\rangle \) to a packed batch as GEMM operations on the device buffers.

GEMM operations run on the packed buffers (ist-1)*dim+idim. For spinors the spin diagonal of the coefficient matrix is summed and re-expanded so the same S(i,j) is applied to every spinor component.

Definition at line 2763 of file exchange_operator.F90.

zexchange_operator_compute_potentials()

subroutine, public exchange_operator_oct_m::zexchange_operator_compute_potentials	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		class(space_t), intent(in)	space,
		type(grid_t), intent(in)	gr,
		type(states_elec_t), intent(inout), target	st,
		type(states_elec_t), intent(inout)	xst,
		type(kpoints_t), intent(in)	kpoints,
		complex(real64), dimension(:,:,:,:,:), intent(out), optional	F_out
	)

Parameters

[in,out]	xst	Action of V_X on a set of KS states
[out]	f_out	For RDMFT

Definition at line 2899 of file exchange_operator.F90.

zexchange_accumulate()

subroutine exchange_operator_oct_m::zexchange_accumulate ( integer, intent(in)  np, class(batch_t), intent(inout)  xket, real(real64), intent(in)  ff, complex(real64), dimension(:,:), intent(in), optional  ff_bra_host, complex(real64), dimension(:,:), intent(in), optional  pot_host, type(accel_mem_t), intent(in), optional  bra_buffer, integer, intent(in), optional  ld_bra, integer, intent(in), optional  ist_bra, type(accel_mem_t), intent(in), optional  pot_buffer  )

private

Accumulate the exchange contribution \( |x_j\rangle \mathrel{-}= ff\,\psi_{sym}\,V_{ij} \) into the whole target block xket, on host or device.

Parameters

[in]	ff	device: scaling factor; host: unused (folded in ff_bra_host)
[in]	ff_bra_host	host: ff*psi_sym (np,dim)
[in]	pot_host	host: pot(:,1:xketnst)

Definition at line 3526 of file exchange_operator.F90.

zexchange_operator_accumulate_return()

subroutine exchange_operator_oct_m::zexchange_operator_accumulate_return ( type(grid_t), intent(in)  gr, type(states_elec_t), intent(in)  st, type(kpoints_t), intent(in)  kpoints, integer, intent(in)  ib2, integer, intent(in)  ik2, real(real64), intent(in)  exx_weight, complex(real64), dimension(:,:), intent(in), optional, contiguous  pot, complex(real64), dimension(:,:), intent(inout), optional  psi2, complex(real64), dimension(:,:), intent(inout), optional, contiguous  xpsi_ret, type(accel_mem_t), intent(in), optional  pot_buffer, type(accel_mem_t), intent(inout), optional  xret_buffer, type(accel_mem_t), intent(in), optional  ff2_buffer, integer, intent(in), optional  ff2_base, integer, intent(in), optional  base_ret  )

private

Accumulates the exchange contribution of one batch of local states acting on a received state.

Parameters

[in]	ib2	Block index of the local states
[in]	ik2	k-point index of the local states
[in]	exx_weight	Weight of the exchange operator
[in]	pot	host: potentials for the local states of the batch
[in,out]	psi2	host: workspace for accessing device batches
[in,out]	xpsi_ret	host: accumulated potential to be returned
[in]	pot_buffer	device: potentials (np, nst2)
[in,out]	xret_buffer	device: (np, dim, nst_received) return buffer
[in]	ff2_buffer	device: precomputed per-lane weights (real64)
[in]	ff2_base	device: offset of this block weights in ff2_buffer
[in]	base_ret	device: element offset of the current bra in xret_buffer

Definition at line 3616 of file exchange_operator.F90.

zexchange_operator_add_returned()

subroutine exchange_operator_oct_m::zexchange_operator_add_returned ( type(grid_t), intent(in)  gr, type(states_elec_t), intent(in)  st, type(states_elec_t), intent(inout), target  xst, integer, intent(in)  ib_send, integer, intent(in)  ik_send, complex(real64), dimension(:,:,:), intent(in), optional, contiguous  xpsi_rec, type(accel_mem_t), intent(in), optional  xret_buffer  )

private

Add the returned exchange potential into the local xst block (sending task).

Parameters

[in]	ib_send	Block index of the states that were sent
[in]	ik_send	k-point index of the states that were sent
[in]	xpsi_rec	host: returned potential, (np, dim, nst)
[in]	xret_buffer	device: returned potential, (np, dim, nst)

Definition at line 3713 of file exchange_operator.F90.

zexchange_operator_compute_ex()

real(real64) function, public exchange_operator_oct_m::zexchange_operator_compute_ex	(	class(mesh_t), intent(in)	mesh,
		type(states_elec_t), intent(in)	st,
		type(states_elec_t), intent(in)	xst
	)

Compute the exact exchange energy.

\[ E_X = \frac{1}{2} \sum_{i, \sigma \mathbf{k}} w_\mathbf{k} f_{i\sigma\mathbf{k}} \int \psi^\ast_{i \sigma \mathbf{k}}(\mathbf{r}) W_{i \sigma \mathbf{k}}(\mathbf{r}) d\mathbf{r} \]

where

\[ W_{i\sigma\mathbf{k}}(\mathbf{r}) = - \sum_{j,\mathbf{k}^\prime} f_{j\sigma\mathbf{k}^\prime}\,\omega_{\mathbf{k}^\prime} V_{ij}^{\mathbf{k},\mathbf{k}^\prime,\sigma}(\mathbf{r}) \psi_{j\sigma\mathbf{k}^\prime}(\mathbf{r}) \]

is the action of the exchange operator on a set of Kohn-Sham states.

Note

The implementation ASSUMES that the appropriate range separation weight, exx_weight, and the electron occupation constant, stsmearel_per_state, have been absorbed in xst. This is what is done in the routine exchange_operator_compute_potentials.

Parameters

[in]	st	A set of KS states
[in]	xst	V_X operating on a set of KS states

Returns

Exact exchange energy

Definition at line 3831 of file exchange_operator.F90.

zexchange_operator_ace()

subroutine, public exchange_operator_oct_m::zexchange_operator_ace	(	type(exchange_operator_t), intent(inout)	this,
		type(namespace_t), intent(in)	namespace,
		class(mesh_t), intent(in)	mesh,
		type(states_elec_t), intent(inout)	st,
		type(states_elec_t), intent(inout)	xst,
		type(phase_t), intent(in), optional	phase
	)

Construct the ACE vectors.

This follows the procedure defined in Lin, J. Chem. Theory Comput. 2016, 12, 2242. It constructs the \( M \) matrix, defined as the projection of the exact exchange operator onto the occupied Kohn-Sham states:

\[ M_{ij} = \langle \psi_i | \hat{V}_X | \psi_j \rangle = \langle \psi_i | W_j \rangle, \]

where \( W_j(\mathbf{r}) = (\hat{V}_X \psi_j)(\mathbf{r}) \) is the exchange operator applied to state \( j \). \( M \) is then decomposed into \( L \), which is inverted and used to construct the ACE vectors:

\[ \xi_k(\mathbf{r}) = \sum_{j=1}^n W_j(\mathbf{r}) \left(L^{-H}\right)_{j k} \]

Parameters

[in,out]	this	ACE vectors, of size thisacenst
[in,out]	xst	Application of the exact exchange

Definition at line 3886 of file exchange_operator.F90.

zexchange_operator_ace_overlap()

subroutine exchange_operator_oct_m::zexchange_operator_ace_overlap ( type(exchange_operator_t), intent(in)  this, class(mesh_t), intent(in)  mesh, type(states_elec_t), intent(in)  st, type(states_elec_t), intent(inout)  xst, complex(real64), dimension(:,:), intent(inout)  xpsi, complex(real64), dimension(1:this%ace%nst, 1:this%ace%nst, st%d%kpt%start:st%d%kpt%end), intent(out)  MM  )

private

Build the ACE overlap matrix for state-parallel wave functions.

For each local spin/k-point, construct the lower triangle of the ACE overlap matrix:

\[ M_{ij}^{(k)} = -\left\langle \psi_i^{(k)} \middle| \hat{X} \middle| \psi_j^{(k)} \right\rangle, \qquad (i, j) \leq N_{\mathrm{ACE}}. \]

Here, st contains the Kohn–Sham states \(\psi_i\) and xst contains their images under the exact-exchange operator, \(\hat{X}\psi_j\).

Parameters

[in,out]

xpsi

Work array

Definition at line 4035 of file exchange_operator.F90.

zexchange_operator_ace_overlap_batched()

subroutine exchange_operator_oct_m::zexchange_operator_ace_overlap_batched ( type(exchange_operator_t), intent(in)  this, class(mesh_t), intent(in)  mesh, type(states_elec_t), intent(in)  st, type(states_elec_t), intent(in)  xst, complex(real64), dimension(1:this%ace%nst, 1:this%ace%nst, st%d%kpt%start:st%d%kpt%end), intent(out)  MM  )

private

Build the ACE overlap matrix from non-state-parallel wave-function batches.

For each local spin/k-point, construct the lower triangle of the ACE overlap matrix:

\[ M_{ij}^{(k)} = -\left\langle \psi_i^{(k)} \middle| \hat{X} \middle| \psi_j^{(k)} \right\rangle, \qquad (i, j) \leq N_{\mathrm{ACE}}. \]

The unused upper triangle, and spin/k-points without electrons, are returned as zero.

Parameters

[out]

mm

Overlap

Definition at line 4100 of file exchange_operator.F90.

zexchange_operator_commute_r()

subroutine, public exchange_operator_oct_m::zexchange_operator_commute_r	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		class(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		integer, intent(in)	ik,
		complex(real64), dimension(:, :), intent(in), contiguous	psi,
		complex(real64), dimension(:, :, :), intent(inout), contiguous	gpsi
	)

Definition at line 4149 of file exchange_operator.F90.

zexchange_operator_hartree_apply()

subroutine, public exchange_operator_oct_m::zexchange_operator_hartree_apply	(	type(exchange_operator_t), intent(in)	this,
		type(namespace_t), intent(in)	namespace,
		type(mesh_t), intent(in)	mesh,
		type(states_elec_dim_t), intent(in)	st_d,
		type(kpoints_t), intent(in)	kpoints,
		real(real64), intent(in)	exx_coef,
		class(wfs_elec_t), intent(inout)	psib,
		class(wfs_elec_t), intent(inout)	hpsib
	)

Definition at line 4220 of file exchange_operator.F90.

Variable Documentation

coulb

type(fourier_space_op_t) exchange_operator_oct_m::coulb

private

Operator in Fourier space.

Definition at line 221 of file exchange_operator.F90.

tol_exx_weight

real(real64), parameter, private exchange_operator_oct_m::tol_exx_weight = 1.0e-3_real64

private

Minimum weight below which EXX is not added.

Definition at line 225 of file exchange_operator.F90.