标题： 比较微扰和对易子秩的截断方案在单元耦合簇理论中的应用 显示英文标题

标题： Comparing Perturbative and Commutator-Rank-Based Truncation Schemes in Unitary Coupled-Cluster Theory

摘要： 单位耦合簇（UCC）理论为传统耦合簇（CC）理论提供了一种有前途的厄米特替代方法，但其实际实现受到相似变换哈密顿量（$\bar{H}$）的巴克-坎贝尔-豪斯多夫（BCH）展开非截断性质的阻碍。 为解决这一挑战，已经开发了各种截断策略，以简洁可靠的方式近似$\bar{H}$。 在本工作中，我们比较了采用多体微扰理论（MBPT）和对易子秩截断方案的近似UCC与单重和双重激发方法（UCCSD）的数值性能。 我们的结果表明，低阶基于MBPT的方案，如UCC(2)和UCC(3)，在平衡几何附近产生合理的结果，但在拉伸几何下变得不可靠。 高阶基于MBPT的方案不一定能提高性能，因为UCCSD(4)和UCCSD(5)振幅方程有时缺乏解。 相比之下，基于对易子秩的截断表现出更大的数值稳定性，其中BCH展开的伯努利表示相比于标准BCH公式能够更快地收敛到UCCSD极限。 显示英文摘要

摘要： 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.