# Frozen Natural Orbitals‐Based Coupled‐Cluster Singles, Doubles, and (full) Triples ‐ A Computational Study

## TL;DR

This paper introduces a cost-effective computational method using frozen natural orbitals in coupled cluster theory to speed up calculations with minimal error.

## Contribution

The novel contribution is extending frozen natural orbitals to CCSDT and introducing XFNO-CCSDT for enhanced accuracy.

## Key findings

- FNO-CCSDT provides significant computational speed-up with minimal error (standard deviation ∼0.9 millihartrees).
- XFNO-CCSDT improves accuracy with a standard deviation of ∼0.6 millihartrees.
- The method is effective for spectroscopic parameters like force constants and vibrational frequencies.

## Abstract

Frozen (F) natural orbitals (NO) approach in coupled cluster (CC) singles and doubles (SD) and equation‐of‐motion (EOM) CCSD methods is well‐known for provide cost‐effective yet accurate alternative for energy computation. In this article, we extend the FNO approach to CCSDT (CC with singles, doubles, and triples) implemented within Q‐CHEM. This can be employed within both the (conventional) double precision (DP) as well as the single precision (SP) algorithms. Errors due to employing SP algorithm instead of DP are insignificant and therefore are not discussed. However, for computational timings, we present the performance of FNO‐CCSDT versus conventional CCSDT methods with both SP and DP algorithms using water molecule as a test system. FNO‐CCSDT results at different thresholds can be extrapolated to give the XFNO‐CCSDT approach, which provides an enhanced accuracy. To illustrate this, we present total energies of a few molecules, adiabatic triplet–singlet gaps of a few chromophores and bond‐stretching trends in total energies and vertical triplet–singlet gaps of hydrogen fluoride molecule. We also examine these methods for numerical estimation of spectroscopic parameters – force constants and vibrational frequencies of some diatomic molecules.

The frozen natural orbitals (FNO)‐based CCSDT is a cost‐effective approach and provides significant computational speed‐up with rather insignificant errors (standard deviation ∼0.9 millihartrees) – smaller than the CCSDT accuracy limit of ∼1.5 millihartrees. Extrapolation of FNO‐CCSDT energies computed using different occupation thresholds results in the XFNO‐CCSDT method, which has more balanced accuracy with a standard deviation of ∼0.6 millihartrees.