通过活性空间划分降低单元耦合簇的成本
Reducing the Cost of Unitary Coupled Cluster via Active Space Partitioning
AI总结：
本文提出了一种活性空间UCCSD(4)/MP2方法，通过截断多体微扰理论和处理外部激发，有效降低计算成本并提高强相关系统的计算精度。
摘要：
单元耦合簇（UCC）理论是一种有前途的变分方法，用于电子结构计算，尤其适用于强相关系统和量子计算机。然而，其实际应用受到其非终止的贝克-坎贝尔-豪斯多尔夫展开的陡峭扩展限制。我们介绍了一种活性空间UCCSD(4)/MP2方法，该方法在选定的活性空间内利用UCCSD的四阶多体微扰理论截断，同时在外部激发处处理为MP2水平。我们探索了两种变种：一种是将内部和外部贡献分别求和的复合方法，另一种是耦合振幅以提高精度的方法。我们在GW100数据集、磷酸氢酯水解反应和乙烯强相关扭转上测试了我们的方法。我们的结果表明，使用标准轨道的交互方法对弱相关和中等相关的系统是稳健的，并且仅使用其活性空间中15-25%的虚拟轨道就能准确重现完整的UCCSD(4)势能曲线。相比之下，复合方法对轨道基组和活性空间大小更敏感，导致在基准集中系统行为不一致。对于受强静态相关主导的乙烯扭转系统，使用标准轨道的复合和交互方法紧密跟踪完整的UCCSD(4)参考，但并未缓解来自底层单参考UCCSD(4)描述继承的非物理特征。这种活性空间框架为在经典计算机上建模相关分子和反应提供了一种可行的方法，并为资源受限的量子硬件扩展UCC计算提供了一条可行路径。
英文摘要：
Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, especially for strongly correlated systems and quantum computers. However, its practical application is limited by the steep scaling of its non-terminating Baker-Campbell-Hausdorff expansion. We introduce an active space UCCSD(4)/MP2 approach that leverages a fourth-order many-body perturbation theory truncation of UCCSD within a selected active space, while treating external excitations at the MP2 level. We explore two variants: a composite method that sums separate internal and external contributions and an interacting method that couples the amplitudes for greater accuracy. We test our approach on the GW100 dataset, a metaphosphate hydrolysis reaction, and the strongly correlated torsion of ethylene. Our results suggest that the interacting method with canonical orbitals is robust for weakly and moderately correlated systems and accurately reproduces the full UCCSD(4) potential energy curves using only 15-25% of the virtual orbitals in its active space. In comparison, the composite formulation exhibits greater sensitivity to the orbital basis and active space size, leading to less systematic behavior across the benchmark set. For ethylene torsion, a system dominated by strong static correlation, both composite and interacting formulations employing canonical orbitals closely track the full UCCSD(4) reference but do not alleviate the unphysical features inherited from the underlying single-reference UCCSD(4) description. This active space framework offers a tractable approach for modeling correlated molecules and reactions on classical computers and provides a viable path for scaling UCC calculations for resource-constrained quantum hardware.
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