librpa_compute.h File Reference

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librpa_compute.h File Reference

Computing data APIs for LibRPA. More...

#include "librpa_handler.h"
#include "librpa_options.h"

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Functions
void	librpa_get_imaginary_frequency_grids (LibrpaHandler *h, const LibrpaOptions *p_opts, double *omegas, double *weights)
	Construct and return frequency grids for numerical integration.
double	librpa_get_rpa_correlation_energy (LibrpaHandler *h, const LibrpaOptions *p_opts, int n_ibz_kpoints, double *rpa_corr_ibzk_contrib_re, double *rpa_corr_ibzk_contrib_im)
	Compute RPA correlation energy.
void	librpa_build_exx (LibrpaHandler *h, const LibrpaOptions *p_opts)
	Build exact-exchange matrix.
void	librpa_get_exx_pot_kgrid (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_this, const int *iks_this, int i_state_low, int i_state_high, double *vexx)
	Obtain exact-exchange potential for selected states.
void	librpa_get_exx_pot_band_k (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_band_this, const int *iks_band_this, int i_state_low, int i_state_high, double *vexx_band)
	Obtain exact-exchange potential for selected states at band k-points.
void	librpa_build_g0w0_sigma (LibrpaHandler *h, const LibrpaOptions *p_opts)
	Build self-energy matrix of G0W0, including the correlation and exchange contributions.
void	librpa_get_g0w0_sigc_kgrid (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_this, const int *iks_this, int i_state_low, int i_state_high, const double *vxc, const double *vexx, double *sigc_re, double *sigc_im)
	Obtain correlation self-energies for selected states.
void	librpa_get_g0w0_qpe_kgrid (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_this, const int *iks_this, int i_state_low, int i_state_high, const double *vxc, const double *vexx, double *sigc_re, double *sigc_im, double *eqp)
	Obtain correlation self-energies and QP energies for selected states.
void	librpa_get_g0w0_spectral_function_kgrid (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_this, const int *iks_this, int i_state_low, int i_state_high, const int n_omegas, const double *omegas, const double *vxc, const double *vexx, double *spectral_function, double *sigc)
	Obtain spectral functions for selected k-grid states.
void	librpa_get_g0w0_sigc_band_k (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_band_this, const int *iks_band_this, int i_state_low, int i_state_high, const double *vxc_band, const double *vexx_band, double *sigc_band_re, double *sigc_band_im)
	Obtain correlation self-energies for selected states at band k-points.
void	librpa_get_g0w0_qpe_band_k (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_band_this, const int *iks_band_this, int i_state_low, int i_state_high, const double *vxc_band, const double *vexx_band, double *sigc_band_re, double *sigc_band_im, double *eqp_band)
	Obtain correlation self-energies and QP energies for selected band-k states.
void	librpa_get_g0w0_spectral_function_band_k (LibrpaHandler *h, const LibrpaOptions *p_opts, const int n_spins, const int n_kpts_band_this, const int *iks_band_this, int i_state_low, int i_state_high, const int n_omegas, const double *omegas, const double *vxc_band, const double *vexx_band, double *spectral_function_band, double *sigc_band)
	Obtain spectral functions for selected band-k states.

Detailed Description

Computing data APIs for LibRPA.

Function Documentation

◆ librpa_build_exx()

void librpa_build_exx	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts )

Build exact-exchange matrix.

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.

◆ librpa_build_g0w0_sigma()

void librpa_build_g0w0_sigma	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts )

Build self-energy matrix of G0W0, including the correlation and exchange contributions.

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.

◆ librpa_get_exx_pot_band_k()

void librpa_get_exx_pot_band_k	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_band_this,
		const int *	iks_band_this,
		int	i_state_low,
		int	i_state_high,
		double *	vexx_band )

Obtain exact-exchange potential for selected states at band k-points.

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_band_this	Number of k-points to compute on this process.
[in]	iks_band_this	(Global) index of k-points that this process compute. Each process can have different indices. Must be a subset of band k-points at which the eigenvetors are parsed.
[in]	i_state_low	Index of the first state to compute the potential (inclusive)
[in]	i_state_high	Index of the last state to compute the potential (exclusive)
[out]	vexx_band	Exact-exchange potential for selected states at band k-points. It should be at least as long as n_spins * n_kpts_band_this * (i_state_high - i_state_low).

◆ librpa_get_exx_pot_kgrid()

void librpa_get_exx_pot_kgrid	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_this,
		const int *	iks_this,
		int	i_state_low,
		int	i_state_high,
		double *	vexx )

Obtain exact-exchange potential for selected states.

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_this	Number of k-points to compute on this process.
[in]	iks_this	(Global) index of k-points that this process compute. Each process can have different indices. Must be a subset of k-points at which the eigenvetors are parsed.
[in]	i_state_low	Index of the first state to compute the potential (inclusive)
[in]	i_state_high	Index of the last state to compute the potential (exclusive)
[out]	vexx	Exact-exchange potential for selected states. It should be at least as long as n_spins * n_kpts_local * (i_state_high - i_state_low).

◆ librpa_get_g0w0_qpe_band_k()

void librpa_get_g0w0_qpe_band_k	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_band_this,
		const int *	iks_band_this,
		int	i_state_low,
		int	i_state_high,
		const double *	vxc_band,
		const double *	vexx_band,
		double *	sigc_band_re,
		double *	sigc_band_im,
		double *	eqp_band )

Obtain correlation self-energies and QP energies for selected band-k states.

Same inputs and SigC outputs as librpa_get_g0w0_sigc_band_k. If p_opts->use_hedin_shift is enabled, the QP solver evaluates

\[\Sigma_c(E - E_F - \Delta). \]

If p_opts->istate_ref_hedin_shift is negative, Delta is computed separately for each selected band state. Otherwise, that absolute zero-based reference state at each band k-point and spin provides Delta for all states in the same channel.

Parameters

[in]	h	LibRPA handler.
[in]	p_opts	Runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_band_this	Number of band k-points computed on this process.
[in]	iks_band_this	Global indices of those band k-points.
[in]	i_state_low	First state index (inclusive).
[in]	i_state_high	Last state index (exclusive).
[in]	vxc_band	XC potential for the selected band states.
[in]	vexx_band	Exact-exchange potential for the selected band states.
[out]	sigc_band_re	Real part of the correlation self-energy.
[out]	sigc_band_im	Imaginary part of the correlation self-energy.
[out]	eqp_band	Quasi-particle energy solved by the selected QPE solver. It should be at least as long as sigc_band_re/sigc_band_im.

◆ librpa_get_g0w0_qpe_kgrid()

void librpa_get_g0w0_qpe_kgrid	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_this,
		const int *	iks_this,
		int	i_state_low,
		int	i_state_high,
		const double *	vxc,
		const double *	vexx,
		double *	sigc_re,
		double *	sigc_im,
		double *	eqp )

Obtain correlation self-energies and QP energies for selected states.

Same inputs and SigC outputs as librpa_get_g0w0_sigc_kgrid. If p_opts->use_hedin_shift is enabled, the QP solver evaluates

\[\Sigma_c(E - E_F - \Delta). \]

If p_opts->istate_ref_hedin_shift is negative, Delta is computed separately for each selected state. Otherwise, that absolute zero-based reference state at each k-point and spin provides Delta for all states in the same channel.

Parameters

[in]	h	LibRPA handler.
[in]	p_opts	Runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_this	Number of k-points computed on this process.
[in]	iks_this	Global indices of those k-points.
[in]	i_state_low	First state index (inclusive).
[in]	i_state_high	Last state index (exclusive).
[in]	vxc	XC potential for the selected states.
[in]	vexx	Exact-exchange potential for the selected states.
[out]	sigc_re	Real part of the correlation self-energy.
[out]	sigc_im	Imaginary part of the correlation self-energy.
[out]	eqp	Quasi-particle energy solved by the selected QPE solver. It should be at least as long as sigc_re/sigc_im.

◆ librpa_get_g0w0_sigc_band_k()

void librpa_get_g0w0_sigc_band_k	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_band_this,
		const int *	iks_band_this,
		int	i_state_low,
		int	i_state_high,
		const double *	vxc_band,
		const double *	vexx_band,
		double *	sigc_band_re,
		double *	sigc_band_im )

Obtain correlation self-energies for selected states at band k-points.

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_band_this	Number of k-points to compute on this process.
[in]	iks_band_this	(Global) index of k-points that this process compute. Each process can have different indices. Must be a subset of k-points at which the eigenvetors are parsed.
[in]	i_state_low	Index of the first state to compute the potential (inclusive)
[in]	i_state_high	Index of the last state to compute the potential (exclusive)
[in]	vxc_band	exchange-correlation potential of the selected states at band k-points.
[in]	vexx_band	Exact-exchange potential for the selected states at band k-points. It should be at least as long as n_spins * n_kpts_band_this * (i_state_high - i_state_low). It can be obtained using librpa_get_exx_pot_kgrid.
[out]	sigc_band_re	Real-part of the correlation self-energy for the selected states. For option_qpe_solver=2, this is the perturbative effective real contribution that reconstructs the perturbative QP energy. It should be at least as long as n_spins * n_kpts_band_this * (i_state_high - i_state_low).
[out]	sigc_band_im	Same as sigc_band_re, but for the imaginary part.

◆ librpa_get_g0w0_sigc_kgrid()

void librpa_get_g0w0_sigc_kgrid	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_this,
		const int *	iks_this,
		int	i_state_low,
		int	i_state_high,
		const double *	vxc,
		const double *	vexx,
		double *	sigc_re,
		double *	sigc_im )

Obtain correlation self-energies for selected states.

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_this	Number of k-points to compute on this process.
[in]	iks_this	(Global) index of k-points that this process compute. Each process can have different indices. Must be a subset of k-points at which the eigenvetors are parsed.
[in]	i_state_low	Index of the first state to compute the potential (inclusive)
[in]	i_state_high	Index of the last state to compute the potential (exclusive)
[in]	vxc	exchange-correlation potential of the selected states.
[in]	vexx	Exact-exchange potential for the selected states. It should be at least as long as n_spins * n_kpoints_local * (i_state_high - i_state_low). It can be obtained using librpa_get_exx_pot_kgrid.
[out]	sigc_re	Real-part of the correlation self-energy for the selected states. For option_qpe_solver=2, this is the perturbative effective real contribution that reconstructs the perturbative QP energy. It should be at least as long as n_spins * n_kpoints_local * (i_state_high - i_state_low).
[out]	sigc_im	Same as sigc_re, but for the imaginary part.

◆ librpa_get_g0w0_spectral_function_band_k()

void librpa_get_g0w0_spectral_function_band_k	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_band_this,
		const int *	iks_band_this,
		int	i_state_low,
		int	i_state_high,
		const int	n_omegas,
		const double *	omegas,
		const double *	vxc_band,
		const double *	vexx_band,
		double *	spectral_function_band,
		double *	sigc_band )

Obtain spectral functions for selected band-k states.

Same convention as librpa_get_g0w0_spectral_function_kgrid, but evaluates states at band k-points.

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_band_this	Number of band k-points to compute on this process.
[in]	iks_band_this	Global band-k indices computed on this process.
[in]	i_state_low	First state index (inclusive).
[in]	i_state_high	Last state index (exclusive).
[in]	n_omegas	Number of real-frequency points.
[in]	omegas	Real-frequency points, in Hartree.
[in]	vxc_band	XC potential for selected band states.
[in]	vexx_band	Exact-exchange potential for selected band states.
[out]	spectral_function_band	Spectral functions. This output array should be at least as long as n_spins * n_kpts_band_this * (i_state_high - i_state_low) * n_omegas. The order is [spin][band k-point][state][omega].
[out]	sigc_band	Optional continued correlation self-energy. Pass nullptr if this output is not needed. If present, this is a packed complex<double> buffer with the same [spin][band k-point][state][omega] order as spectral_function_band.

◆ librpa_get_g0w0_spectral_function_kgrid()

void librpa_get_g0w0_spectral_function_kgrid	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		const int	n_spins,
		const int	n_kpts_this,
		const int *	iks_this,
		int	i_state_low,
		int	i_state_high,
		const int	n_omegas,
		const double *	omegas,
		const double *	vxc,
		const double *	vexx,
		double *	spectral_function,
		double *	sigc )

Obtain spectral functions for selected k-grid states.

Computes spectral functions under the diagonal approximation of the Green's function: \(A_{n\mathbf{k}}(\omega) = -\pi^{-1}\mathrm{Im}\,G_{n\mathbf{k}}(\omega)\).

Parameters

[in]	h	Pointer to LibRPA handler.
[in]	p_opts	Pointer to runtime options.
[in]	n_spins	Number of spin channels.
[in]	n_kpts_this	Number of k-points to compute on this process.
[in]	iks_this	Global k-point indices computed on this process.
[in]	i_state_low	First state index (inclusive).
[in]	i_state_high	Last state index (exclusive).
[in]	n_omegas	Number of real-frequency points.
[in]	omegas	Real-frequency points, in Hartree.
[in]	vxc	XC potential for selected states.
[in]	vexx	Exact-exchange potential for selected states.
[out]	spectral_function	Spectral functions. This output array should be at least as long as n_spins * n_kpts_this * (i_state_high - i_state_low) * n_omegas. The order is [spin][k-point][state][omega].
[out]	sigc	Optional continued correlation self-energy. Pass nullptr if this output is not needed. If present, this is a packed complex<double> buffer with the same [spin][k-point][state][omega] order as spectral_function.

◆ librpa_get_imaginary_frequency_grids()

void librpa_get_imaginary_frequency_grids	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		double *	omegas,
		double *	weights )

Construct and return frequency grids for numerical integration.

Generates the frequency points and quadrature weights based on the grid type specified in the options (e.g., Gauss-Legendre, Minimax, etc.).

Parameters

[in]	h	Handler.
[in]	p_opts	Runtime options.
[out]	omegas	Array of frequency points (size: opts->nfreq).
[out]	weights	Array of quadrature weights (size: opts->nfreq).

◆ librpa_get_rpa_correlation_energy()

double librpa_get_rpa_correlation_energy	(	LibrpaHandler *	h,
		const LibrpaOptions *	p_opts,
		int	n_ibz_kpoints,
		double *	rpa_corr_ibzk_contrib_re,
		double *	rpa_corr_ibzk_contrib_im )

Compute RPA correlation energy.

Calculates the RPA correlation energy using the input data (wavefunctions, Coulomb matrices, etc.) that has been set via the input parsing functions.

Parameters

[in]	h	Handler.
[in]	p_opts	Runtime options.
[in]	n_ibz_kpoints	Number of irreducible k-points.
[out]	rpa_corr_ibzk_contrib_re	Real part of correlation energy per IBZ k-point.
[out]	rpa_corr_ibzk_contrib_im	Imaginary part of correlation energy per IBZ k-point.

Returns

Total RPA correlation energy (real part).

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