Investigating the basis set convergence of diagrammatically decomposed coupled-cluster correlation energy contributions for the uniform electron gas
arxiv(2024)
摘要
We investigate the convergence of coupled-cluster correlation energies and
related quantities with respect to the employed basis set size for the uniform
electron gas to gain a better understanding of the basis set incompleteness
error. To this end, coupled-cluster doubles (CCD) theory is applied to the
three dimensional uniform electron gas for a range of densities, basis set
sizes and electron numbers. We present a detailed analysis of individual,
diagrammatically decomposed contributions to the amplitudes at the level of CCD
theory. In particular, we show that only two terms from the amplitude equations
contribute to the asymptotic large-momentum behavior of the transition
structure factor, corresponding to the cusp region at short interelectronic
distances. However, due to the coupling present in the amplitude equations, all
decomposed correlation energy contributions show the same asymptotic
convergence behavior to the complete basis set limit. These findings provide an
additional rationale for the success of a recently proposed correction to the
basis set incompleteness error (BSIE) of coupled-cluster theory. Lastly, we
examine the BSIE in the coupled-cluster doubles plus perturbative triples
[CCD(T)] method, as well as in the newly proposed coupled-cluster doubles plus
complete perturbative triples [CCD(cT)] method.
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