# Diagrammatic Simplification of Linearized Coupled Cluster Theory

## TL;DR

This paper introduces a simplified and more accurate method for calculating energies in chemically complex systems using a modified version of coupled cluster theory.

## Contribution

The novel contribution is the development of a size-consistent LinLCCD method that avoids divergences by retaining only linear ladder diagrams.

## Key findings

- LinLCCD is robust in statically correlated systems and achieves O(nocc4nvir2) scaling with a hole–hole approximation.
- LinLCCD outperforms full CCD and CCSD for noncovalent interactions in small-to-medium molecules.
- The method provides accurate energy differences and can be adapted to include more dynamical correlation.

## Abstract

Linearized Coupled Cluster Doubles (LinCCD) often provides
near-singular
energies in small-gap systems that exhibit static correlation. This
has been attributed to the lack of quadratic T̂
2
2 terms that
typically balance out small energy denominators in the CCD amplitude
equations. Herein, I show that exchange contributions to ring and
crossed-ring contractions (not small denominators per se) cause the divergent behavior of LinCC­(S)­D approaches. Rather than
omitting exchange terms, I recommend a regular and size-consistent
method that retains only linear ladder diagrams. As LinCCD and configuration
interaction doubles (CID) equations are isomorphic, this also implies
that simplification (rather than quadratic extensions) of CID amplitude
equations can lead to a size-consistent theory. Linearized ladder
CCD (LinLCCD) is robust in statically correlated systems and can be
made
O(nocc4nvir2)
with a hole–hole approximation.
The results presented here show that LinLCCD and its hole–hole
approximation can accurately capture energy differences, even outperforming
full CCD and CCSD for noncovalent interactions in small-to-medium
sized molecules, setting the stage for further adaptations of these
approaches that incorporate more dynamical correlation.