Periodic and fragment models based on the local correlation approach

A rigorous treatment of dynamical electron correlation in crystalline solids is one of the main challenges in today's materials quantum chemistry and theoretical solid state physics. In this study, we address this problem by using the local correlation approach and exploring a variety of methods, ranging from the full periodic treatment through embedded fragments to finite clusters. Apart from the computational advantages, the direct-space local representation for the occupied space allows one to partition the system into fragments and thus forms a natural basis for a hierarchy of embedding models. Furthermore, a subset of localized orbitals in a cluster or a fragment can be chosen to mimic the unit cell of the reference periodic system. Introduction of such subsets allows one to define a formal quantity “the correlation energy per unit cell”, which is directly related to the correlation energy per unit cell in the crystal. The orbital pairs, where neither of the two localized orbital indices belongs to the “unit cell” do not explicitly contribute to the “energy per cell”: Their role is to provide correlated embedding via the couplings in the amplitude equations. The periodic, fragment and finite-cluster approaches can be combined in a form of high precision computational protocols, where progressively higher-level corrections are evaluated using lower-level embedding models. We apply these techniques to investigate the importance of Coulomb screening in dispersively interacting systems on the examples of the phosphorene bilayer and the adsorption of water on 2D silica.