# An optimized twist angle to find the twist-averaged correlation energy applied to the uniform electron gas

## TL;DR

This paper proposes a single, optimized twist angle for coupled cluster doubles calculations that approximates twist averaging, significantly reducing computational cost while maintaining accuracy in the thermodynamic limit for the uniform electron gas.

## Contribution

It introduces the concept of connectivity to identify a special twist angle that mimics full twist averaging in CCD calculations, improving efficiency.

## Key findings

- The special twist angle yields results comparable to full twist averaging.
- The method reduces computational cost from multiple CCD calculations to one CCD plus several MP2 calculations.
- It enhances the accuracy of finite electron number calculations in representing the thermodynamic limit.

## Abstract

We explore an alternative to twist averaging in order to obtain more cost-effective and accurate extrapolations to the thermodynamic limit (TDL) for coupled cluster doubles (CCD) calculations. We seek a single twist angle to perform calculations at, instead of integrating over many random points or a grid. We introduce the concept of connectivity, a quantity derived from the non-zero four-index integrals in an MP2 calculation. This allows us to find a special twist angle that provides appropriate connectivity in the energy equation, and which yields results comparable to full twist averaging. This special twist angle effectively makes the finite electron number CCD calculation represent the TDL more accurately, reducing the cost of twist-averaged CCD over $N_\mathrm{s}$ twist angles from $N_s$ CCD calculations to $N_s$ MP2 calculations plus one CCD calculation.