Quadrupling and pairing in the shell model

Susi Lehtola, John Parkhill, Martin Head‐Gordon

We describe the implementation of orbital optimisation for the models in the perfect pairing hierarchy. Orbital optimisation, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the π space. While local minima and σ-π symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the π subspace, as well as in the full σπ valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimised orbitals are used. PH is found to yield good agreement with previously published density matrix renormalisation group data in the π space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger basis sets or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.

Huiyao Chen, T. Song, DAVID J. ROWE

Susi Lehtola, John Parkhill, Martin Head-Gordon

We describe the implementation of orbital optimisation for the models in the perfect pairing hierarchy. Orbital optimisation, which is generally necessary to obtain reliable results, is pursued at perfect pairing (PP) and perfect quadruples (PQ) levels of theory for applications on linear polyacenes, which are believed to exhibit strong correlation in the π space. While local minima and σ-π symmetry breaking solutions were found for PP orbitals, no such problems were encountered for PQ orbitals. The PQ orbitals are used for single-point calculations at PP, PQ and perfect hextuples (PH) levels of theory, both only in the π subspace, as well as in the full σπ valence space. It is numerically demonstrated that the inclusion of single excitations is necessary also when optimised orbitals are used. PH is found to yield good agreement with previously published density matrix renormalisation group data in the π space, capturing over 95% of the correlation energy. Full-valence calculations made possible by our novel, efficient code reveal that strong correlations are weaker when larger basis sets or active spaces are employed than in previous calculations. The largest full-valence PH calculations presented correspond to a (192e,192o) problem.

J. Bang, Joachim Krumlinde

Hsi-Tseng Chen, D.H. Feng, Cheng-Li Wu

An unusual optimum pair basis exists in the nuclear shell-model wave function for an even system of like particles. This prompts the proposal of a generalized pair mean-field method, in which the desired goal of avoiding the dimensional difficulty in the traditional shell-model approaches may be possible.