Comparing Perturbative and Commutator-Rank-Based Truncation Schemes in Unitary Coupled-Cluster Theory
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arXiv
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| Format: | Preprint |
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2025
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| author | Phillips, Justin T. Koulias, Lauren N. Yuwono, Stephen H. DePrince III, A. Eugene |
| author_facet | Phillips, Justin T. Koulias, Lauren N. Yuwono, Stephen H. DePrince III, A. Eugene |
| contents | Unitary coupled cluster (UCC) theory offers a promising Hermitian alternative to conventional coupled cluster (CC) theory, but its practical implementation is hindered by the non-truncating nature of the Baker-Campbell-Hausdorff (BCH) expansion of the similarity-transformed Hamiltonian ($\bar{H}$). To address this challenge, various truncation strategies have been developed to approximate $\bar{H}$ in a compact and reliable manner. In this work, we compare the numerical performance of approximate UCC with single and double excitations (UCCSD) methods that employ many-body perturbation theory (MBPT) and commutator rank based truncation schemes. Our results indicate low-order MBPT-based schemes, such as UCC(2) and UCC(3), yield reasonable results near equilibrium, but they become unreliable at stretched geometries. Higher-order MBPT-based schemes do not necessarily improve performance, as the UCCSD(4) and UCCSD(5) amplitude equations sometimes lack solutions. In contrast, commutator-rank-based truncations exhibit greater numerical stability, with the Bernoulli representation of the BCH expansion enabling more rapid convergence to the UCCSD limit compared to the standard BCH formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00617 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Comparing Perturbative and Commutator-Rank-Based Truncation Schemes in Unitary Coupled-Cluster Theory Phillips, Justin T. Koulias, Lauren N. Yuwono, Stephen H. DePrince III, A. Eugene Chemical Physics Unitary coupled cluster (UCC) theory offers a promising Hermitian alternative to conventional coupled cluster (CC) theory, but its practical implementation is hindered by the non-truncating nature of the Baker-Campbell-Hausdorff (BCH) expansion of the similarity-transformed Hamiltonian ($\bar{H}$). To address this challenge, various truncation strategies have been developed to approximate $\bar{H}$ in a compact and reliable manner. In this work, we compare the numerical performance of approximate UCC with single and double excitations (UCCSD) methods that employ many-body perturbation theory (MBPT) and commutator rank based truncation schemes. Our results indicate low-order MBPT-based schemes, such as UCC(2) and UCC(3), yield reasonable results near equilibrium, but they become unreliable at stretched geometries. Higher-order MBPT-based schemes do not necessarily improve performance, as the UCCSD(4) and UCCSD(5) amplitude equations sometimes lack solutions. In contrast, commutator-rank-based truncations exhibit greater numerical stability, with the Bernoulli representation of the BCH expansion enabling more rapid convergence to the UCCSD limit compared to the standard BCH formulation. |
| title | Comparing Perturbative and Commutator-Rank-Based Truncation Schemes in Unitary Coupled-Cluster Theory |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2503.00617 |