Coupled cluster theory is considered to be the ``gold standard'' ansatz of 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 present a rigorous numerical analysis that explains the underlying mechanisms behind this phenomenon in the context of coupled cluster doubles (CCD) calculations, and reconciles a few seemingly paradoxical statements with respect to the finite-size scaling. Our findings also have implications on how to effectively address finite-size errors in practical quantum chemistry calculations for periodic systems.

翻译：耦合簇理论被认为是分子量子化学的“金标准”方法。对于三维绝缘体系，周期性耦合簇计算中相关能的有限尺寸误差被观察到满足逆体积标度，即使在没有任何校正方案的情况下也是如此。这一现象令人惊讶，因为仅使用耦合簇图子集的简化理论所展现出的有限尺寸误差衰减要慢得多，且其标度与系统长度成反比。在本研究中，我们基于耦合簇双激发（CCD）计算，通过严格的数值分析揭示了这一现象背后的机制，并调和了关于有限尺寸标度的若干看似矛盾的陈述。我们的发现对于如何有效处理周期体系在实际量子化学计算中的有限尺寸误差也具有启示意义。