Long-range correlation energies and off-diagonal interactions for the $\pi$ electronic systems

TL;DR

This paper derives a comprehensive formula for the correlation energy in $b5$ electron systems, incorporating long-range and off-diagonal interactions, revealing their contrasting effects and dependence on screening.

Contribution

It introduces a general correlation energy formula that includes off-diagonal interactions beyond nearest neighbors in $b5$ systems, highlighting their differing impacts.

Findings

Off-diagonal interactions $W$ and $X$ have opposite effects on correlation energy.

The influence of $X$ on correlation energy is stronger than that of $W$.

Correlation energies decrease with increased screening.

Abstract

The long-range correlation energies and the off-diagonal interactions are studied and a general formula for correlation energy $E_c$ of the $\pi$ electron systems is given, which is beyond the nearest-neighbor electron-electron interactions and includes the off-diagonal interactions. It is found that the effects of the off-diagonal interactions $W$ and $X$ on the correlation energies are opposite, but the influence of $X$ on the correlation energies is much stronger than that of $W$ on the correlation energies, and the correlation energies decrease with increasing the screening effect.