Approaching chemical accuracy in the electronic structure theory of solids: Linearly-scaling periodic local coupled cluster method in combination with explicitly correlated Møller-Plesset perturbation theory

量子化学的电子结构层次方法允许系统地提高计算的精度。这是DFT所缺乏的，这使得波函数方法对于第一原理预测非常有效。特别是，CCSD(T)方法被认为是量子化学的黄金标准，因为在基组极限下，已知在大范围闭合壳层体系的化学精度范围内与实验一致。不幸的是，精确的量子化学模型比标准的DFT要昂贵得多，而且计算成本与系统大小的比例高得令人不快。这对于周期系统尤其重要，因为周期系统是本项目的目标系统。克服令人望而却步的标度墙的一种方法是局部相关方案。该项目旨在继续开展工作，在地方相关框架内发展一系列基于周期性波函数的方法。在这个项目的第一阶段，主要的重点是通过实施局部周期MP2-F12方法来纠正基集的不完备性和区域误差。它允许基于Triple-Zeta的计算中的一个人获得接近MP2基本设置限制的结果。有了这个方法，我们现在可以集中讨论LMP2方法错误。计划实施后MP2模型的层次结构：从环-LCCD和LMP3通过LCCSD到目标方法LCCSD(T)。最终能量将被表示为两个分量的和：LMP2-F12能量和MP2后能量校正，即LCCSD(T)和LMP2之间的能量差。该方法将能够在接近CCSD(T)基集极限的水平上处理周期系统，同时在不是很高的预因子的情况下呈现计算代价的线性标度。本提案中所述的发展情况将列入可供公众查阅的CRYSCOR代码。在这样的水平上处理周期系统的可能性将对社区在实验和理论研究中都非常有用。与目前可用于周期体系CCSD(T)计算的其他技术相比，该方法还具有几个重要的优点。例如，与基于片段的方法相比，它将没有由于有限簇表示而产生的错误，并且使用起来直接。与VASP的平面波CCSD(T)实现相比，局部直接空间方法将基于多层局部近似，从而获得高效率和计算代价的线性缩放。该方法的另一个优点是对表面、聚合物或分子的直接适用性。此外，直接空间实施将使基于单个耦合星系团贡献的直接拟合的自动力场生成器的后续发展非常有希望。

Quantum chemical hierarchy of electronic structure methods allows for systematic improvement of the accuracy of the calculations. This feature, which is lacking in DFT, makes the wave-function approach very powerful for first-principle predictions. In particular, the CCSD(T) method is considered a gold standard of quantum chemistry, as at the basis set limit it is known to agree with experiment within the chemical accuracy for a broad range of closed shell systems. Unfortunately, accurate quantum chemical models are considerably more expensive that standard DFT and possess unfavorably high scaling of the computational cost with system size. This becomes especially critical for periodic systems, which are the target systems of this project.One way to defeat the prohibitive scaling wall is the local correlation scheme. The project aims at a continuation of work on development a hierarchy of periodic wave-function-based methods within the local correlation framework. In the first phase of this project the main focus was on correcting the basis set incompleteness and domain errors by implementing local periodic MP2-F12 method. It allows one in a triple-zeta-based calculation to get the result close to the MP2 basis set limit. Having this method at hand, we can now concentrate on the LMP2 method error. It is planned to implement the hierarchy of the post MP2 models: starting from ring-LCCD and LMP3 via LCCSD to the target method LCCSD(T). The final energy will be represented as a sum of two components: the LMP2-F12 energy and the post-MP2 energy correction i.e. the energy difference between LCCSD(T) and LMP2. The method will be able to treat periodic systems at the level, close to the CCSD(T) at the basis set limit, at the same time exhibiting linear scaling of the computational cost with not a very high prefactor. The developments, described in the present proposal, will be included in the publicly available CRYSCOR code. The possibility to treat periodic systems at such a level will be very useful for the community in both experimental and theoretical investigations. The method will also possess several important advantages over other techniques that can presently be used for CCSD(T) calculations on periodic systems. For example, in contrast to fragment-based methods, it will be free of the errors due the finite-cluster representation and straightforward to use. Compared to the plane-wave CCSD(T) implementation of VASP, the local direct-space approach will be based on a multilevel local approximation and thus attain high efficiency and linear scaling of the computational cost. Another strong side of the method will be the straightforward applicability to surfaces, polymers or molecules. Additionally, the direct-space implementation will allow for a very promising follow-up development of automatic force-field generator, based on direct fitting of individual coupled cluster contributions.