votca::xtp::RPA_UKS::rpa_eigensolution Struct Reference

Solution of the two-particle Hamiltonian in the unrestricted basis. More...

#include <rpa_uks.h>

Public Attributes
Eigen::VectorXd	omega
Eigen::MatrixXd	XpY
double	ERPA_correlation

Detailed Description

Solution of the two-particle Hamiltonian in the unrestricted basis.

Transition-index ordering for unrestricted RPA (UKS)

The particle-hole basis is constructed as a concatenation:

[ all alpha excitations | all beta excitations ]

where each excitation corresponds to a same-spin transition

v_sigma -> c_sigma

within the selected RPA window [rpamin_, rpamax_].

Definitions:

n_occ_alpha = (homo_alpha_ + 1) - rpamin_ n_unocc_alpha = rpamax_ - (homo_alpha_ + 1) + 1

n_occ_beta = (homo_beta_ + 1) - rpamin_ n_unocc_beta = rpamax_ - (homo_beta_ + 1) + 1

Row indices are assigned as:

I_alpha(v,c) = v * n_unocc_alpha + c

I_beta(v,c) = n_occ_alpha * n_unocc_alpha

• v * n_unocc_beta + c

with: v = 0..n_occ_alpha-1, c = 0..n_unocc_alpha-1 (alpha) v = 0..n_occ_beta -1, c = 0..n_unocc_beta -1 (beta)

Orbital indexing inside energies_alpha_/energies_beta_:

occupied: index = v virtual: index = n_occ_spin + c

The matrix XpY is ordered according to this indexing:

XpY(I_alpha(v,c), s) -> amplitude of (v_alpha -> c_alpha) XpY(I_beta(v,c), s) -> amplitude of (v_beta -> c_beta)

Each column s corresponds to one RPA screening mode with energy omega(s).

NOTE: The RPA modes represent charge-density fluctuations and therefore mix alpha and beta transitions. Downstream GW self-energy evaluators must:

• sum over both alpha and beta rows of XpY (screening)
• but use spin-diagonal one-particle states (Green's function)

The particle-hole basis is ordered as

[ all alpha excitations | all beta excitations ]

with alpha excitations enumerated first and beta excitations appended afterwards. This ordering is used consistently in Calculate_H2p_AmB() and Calculate_H2p_ApB().

Definition at line 242 of file rpa_uks.h.

Member Data Documentation

ERPA_correlation

double votca::xtp::RPA_UKS::rpa_eigensolution::ERPA_correlation

Definition at line 245 of file rpa_uks.h.

omega

Eigen::VectorXd votca::xtp::RPA_UKS::rpa_eigensolution::omega

Definition at line 243 of file rpa_uks.h.

XpY

Eigen::MatrixXd votca::xtp::RPA_UKS::rpa_eigensolution::XpY

Definition at line 244 of file rpa_uks.h.

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The documentation for this struct was generated from the following file:

• xtp/include/votca/xtp/rpa_uks.h