Generalized adiabatic connection in ensemble density-functional theory for excited states: example of the H2 molecule

TL;DR

This paper introduces a generalized adiabatic connection for ensembles (GACE) in density-functional theory, allowing variation of ensemble weights and interaction strength, and demonstrates its application to the H2 molecule for excited state calculations.

Contribution

The paper develops a GACE formalism that extends traditional methods by varying ensemble weights and interaction strength simultaneously, enabling new insights into excited state DFT.

Findings

Derived an exact expression for ensemble exchange-correlation energy.

Applied GACE to H2 molecule, showing promising results for excited states.

Proposed a pathway for state-average multi-determinant DFT development.

Abstract

A generalized adiabatic connection for ensembles (GACE) is presented. In contrast to the traditional adiabatic connection formulation, both ensemble weights and interaction strength can vary along a GACE path while the ensemble density is held fixed. The theory is presented for non-degenerate two-state ensembles but it can in principle be extended to any ensemble of fractionally occupied excited states. Within such a formalism an exact expression for the ensemble exchange-correlation density-functional energy, in terms of the conventional ground-state exchange-correlation energy, is obtained by integration over the ensemble weight. Stringent constraints on the functional are thus obtained when expanding the ensemble exchange-correlation energy through second order in the ensemble weight. For illustration purposes, the analytical derivation of the GACE is presented for the H2 model system in a minimal basis, leading thus to a simple density-functional approximation to the ensemble exchange-correlation energy. Encouraging results were obtained with this approximation for the description in a large basis of the first ^1\Sigma^+_g excitation in H2 upon bond stretching. Finally, a range-dependent GACE has been derived, providing thus a pathway to the development of a rigorous state-average multi-determinant density-functional theory.