Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating systems has been observed to satisfy the inverse volume scaling, even in the absence of any correction schemes. This is surprising, as simpler theories that utilize only a subset of the coupled cluster diagrams exhibit much slower decay of the finite-size error, which scales inversely with the length of the system. In this study, we review the current understanding of finite-size error in quantum chemistry methods for periodic systems. We introduce new tools that elucidate the mechanisms behind this phenomenon in the context of coupled cluster doubles calculations. This reconciles some seemingly paradoxical statements related to finite-size scaling. Our findings also show that singularity subtraction can be a powerful method to effectively reduce finite-size errors in practical quantum chemistry calculations for periodic systems.

中文翻译：

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周期性耦合簇理论中有限尺寸误差的反体积标度

耦合簇理论是从头开始分子量子化学中最流行的后 Hartree-Fock 方法之一。即使在没有任何校正方案的情况下，三维绝缘系统的周期性耦合簇计算中的相关能量的有限尺寸误差也已被观察到满足逆体积缩放。这是令人惊讶的，因为仅利用耦合簇图的子集的更简单的理论表现出有限尺寸误差的衰减要慢得多，该误差与系统的长度成反比。在这项研究中，我们回顾了当前对周期系统量子化学方法中有限尺寸误差的理解。我们引入了新工具，在耦合簇双打计算的背景下阐明了这种现象背后的机制。这协调了一些与有限尺寸缩放相关的看似矛盾的陈述。我们的研究结果还表明，奇点减法可以成为有效减少周期系统实际量子化学计算中有限尺寸误差的有效方法。