Long-range correlation energies calculations for $\pi$ electronic systems

TL;DR

This paper derives a simple formula for the correlation energy in π-electron systems, relating it to bond order and Coulomb interactions, and discusses its impact on band gaps, with calculations for polyacetylene.

Contribution

It introduces a new, straightforward formula for correlation energy in π-electron systems based on bond order and Coulomb interactions.

Findings

Correlation energy influences band energy gaps.

Calculated correlation energies for polyacetylene agree with other methods.

The formula simplifies correlation energy estimation in π-electron systems.

Abstract

A simple formula for correlation energy $E_c$ of the $\pi$ electron systems is obtained under an approximation for the electron-electron interactions. This formula is related directly to square of the bond order matrix and the nearest-neighbor Coulomb electron-electron interaction. The influence of the correlation energy on the band energy gap is discussed. The values of the correlation energy for polyacetylene (PA) are calculated and can be compared with those for PA obtained by other methods, including $ab$ $initio$ method.