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This study investigates the mathematical regularity of coupled cluster amplitudes as a function of nuclear coordinate displacements, a key step toward enabling efficient interpolation and extrapolation of molecular ground-state energies across different molecular geometries. The authors demonstrate theoretically that, under certain non-degeneracy conditions at both the Hartree-Fock and coupled cluster levels of theory, the amplitudes are real analytic functions of the nuclear coordinates. They also identify practical artifacts introduced by the use of canonical orbitals that disrupt this regularity and propose mitigation strategies, which are validated through numerical interpolation experiments.
Why it matters
Coupled cluster methods are computationally expensive and must be applied across many molecular geometries to study chemical processes, so establishing a rigorous basis for interpolating amplitudes could significantly reduce computational cost in quantum chemistry applications such as reaction pathway analysis and molecular dynamics simulations.
arXiv:2605.22584v1 Announce Type: cross
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.
Source: On the Regularity and Interpolation of Coupled Cluster Amplitudes in Canonical Orbital Basis