# Comparing particle-particle and particle-hole channels of random-phase approximation

## TL;DR

This study compares particle-hole and particle-particle RPA channels in molecular dissociation, introducing a direct particle-particle RPA scheme and exploring their behaviors and potential unification.

## Contribution

It introduces a direct particle-particle RPA scheme and analyzes the role of exchange contributions, providing insights into their differences and challenges in combining them.

## Key findings

- Exchange contributions are critical for RPA channel behaviors.
- Straightforward merging of RPA channels does not improve dissociation descriptions.
- Direct particle-particle RPA offers a new perspective on RPA channel comparison.

## Abstract

We present a comparative study of particle-hole and particle-particle channels of random-phase approximation (RPA) for molecular dissociations of different bonding types. We introduced a \textit{direct} particle-particle RPA scheme, in analogy to the \textit{direct} particle-hole RPA formalism, whereby the exchange-type contributions are excluded. This allows us to compare the behavior of the particle-hole and particle-particle RPA channels on the same footing. Our study unravels the critical role of exchange contributions in determining behaviors of the two RPA channels for describing stretched molecules. We also made an attempt to merge particle-hole RPA and particle-particle RPA into a unified scheme, with the double-counting terms removed. However, benchmark calculations indicate that a straightforward combination of the two RPA channels does not lead to a successful computational scheme for describing molecular dissociations.