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

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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.