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

Fuente: arXiv
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Main Authors: Beck, Jonas, Stamm, Benjamin
Format: Preprint
Published: 2026
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_version_ 1866911704846172160
author Beck, Jonas
Stamm, Benjamin
author_facet Beck, Jonas
Stamm, Benjamin
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2605_22584
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the Regularity and Interpolation of Coupled Cluster Amplitudes in Canonical Orbital Basis
Beck, Jonas
Stamm, Benjamin
Numerical Analysis
Chemical Physics
Primary 81V55, 41A05, Secondary 65D05, 81-08
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.
title On the Regularity and Interpolation of Coupled Cluster Amplitudes in Canonical Orbital Basis
topic Numerical Analysis
Chemical Physics
Primary 81V55, 41A05, Secondary 65D05, 81-08
url https://arxiv.org/abs/2605.22584