Analytic Gradients of Approximate Coupled Cluster Methods with Quadruple Excitations

TL;DR

This paper develops and implements analytic gradient methods for approximate coupled-cluster theories with quadruple excitations, enabling efficient geometry and vibrational frequency calculations with some limitations.

Contribution

It introduces analytic gradient formulations for CCSDT(Q) and related methods, extending coupled-cluster theory capabilities for larger systems.

Findings

Methods approximate full CCSDTQ well for simple systems

CCSDT(Q) shows limitations with complex molecules

Implementation in CFOUR facilitates practical applications

Abstract

The analytic gradient theory for both iterative and non-iterative coupled-cluster approximations that include connected quadruple excitations is presented. These methods include, in particular, CCSDT(Q), which is an analog of the well-known CCSD(T) method which starts from the full CCSDT method rather than CCSD. The resulting methods are implemented in the CFOUR program suite, and pilot applications are presented for the equilibrium geometries and harmonic vibrational frequencies of the simplest Criegee intermediate, CH$_2$OO, as well as to the isomerization pathway between dimethylcarbene and propene. While all methods are seen to approximate the full CCSDTQ results well for "well-behaved" systems, the more difficult case of the Criegee intermediate shows that CCSDT(Q), as well as certain iterative approximations, display problematic behavior.