Fragment-Based Direct-Local-Ring-Coupled-Cluster Doubles Treatment Embedded in the Periodic Hartree-Fock Solution

We present a periodic/finite-cluster interface for fragment-based direct local ring-coupled-cluster doubles (d-LrCCD) calculations embedded in the periodic mean field. The fragment is defined by a set of Wannier functions (WFs), obtained from a periodic Hartree–Fock calculation. The pair-specific virtual space is spanned by projected atomic orbitals (PAOs) truncated to pair domains. The computational procedure is initiated by a periodic local Møller–Plesset (LMP2) calculation. A subset of the WF pairs is then subsequently subjected to a finite-cluster d-LrCCD treatment using the local coupled cluster program of Molpro; this subset is specified by an interorbital cutoff distance. The orbital, pair, and domain lists, as well as other essential quantities needed for d-LrCCD such as the Fock and overlap matrices, and the electron repulsion integrals (ERIs) in the basis of WFs and PAOs are evaluated in the periodic framework and passed to Molpro via an interface. These periodic quantities provide the correct periodic mean-field embedding for the fragment d-LrCCD. Moreover, no expensive orbital transformations involving orbital coefficients related to large supporting clusters are necessary. ERIs appearing in the d-LrCCD diagrams are factorized via density fitting, which enables an efficient processing of the corresponding terms via three-index intermediates. The corresponding 3-index and the metric 2-index ERIs involving auxiliary functions are also computed and transformed to the WF-PAO basis (the 3-index ERI) on the periodic side. Although the direct ring-CCD method itself is not generally more accurate than MP2, it is more stable in the case of small band gap systems, as it sums up the ring diagrams to infinite order. Furthermore, this interface is a first step toward a high-level fragment-based quantum chemical treatment such as local CCSD(T) within a periodic embedding that is treated at a lower level. As two test examples we study the physisorption of H2 and argon on graphane.