On the Regularity and Interpolation of Coupled Cluster Amplitudes in Canonical Orbital Basis

TL;DR

This paper investigates the regularity of coupled cluster amplitudes with respect to nuclear displacements, aiming to enable interpolation methods for efficient energy calculations across different geometries.

Contribution

It demonstrates that coupled cluster amplitudes are theoretically real analytic under certain conditions and analyzes practical artifacts affecting their regularity.

Findings

Amplitudes behave real analytically under non-degeneracy assumptions.

Artifacts in canonical orbitals hinder regularity and are analyzed.

Interpolated amplitudes closely match exact values in numerical tests.

Abstract

Arguably the most widely used approaches for obtaining highly accurate molecular ground-state energies are coupled cluster methods. Despite introducing two layers of approximation, a linear and a nonlinear one, coupled cluster methods remain computationally intensive, with the complexity scaling as $O(poly(N))$, where $N$ is the number of electrons. Moreover, this method must be applied over a large set of different nuclear coordinates in order to study certain chemical phenomena. Therefore, in this work, we investigate the regularity of single-reference coupled cluster amplitudes with respect to nuclear coordinate displacements, with the aim of enabling interpolation or extrapolation approaches that rely on only a limited number of reference geometries. We show that, in theory, under certain non-degeneracy assumptions on the Hartree-Fock level of theory, and the coupled cluster level of theory the amplitudes behave real analytic. Furthermore, we analyze the artifacts that arise in practical calculations that use canonical orbitals, which hinder this high degree of regularity, and suggest strategies to mitigate these issues. Finally, we validate our findings through numerical experiments by interpolating the amplitudes and comparing the performance of the interpolants with that of the exact amplitudes.