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A computational technique for solving the MP2 equations for periodic systems using a local-correlation approach and implemented in the CRYSCOR code is presented. The Hartree-Fock solution provided by the CRYSTAL program is used as a reference. The motivations for the implementation of the new code are discussed, and the techniques adopted are briefly recalled. With respect to the original formulation (Pisani et al., J Chem Phys 2005, 122, 094113), many new features have been introduced in CRYSCOR to improve its efficiency and robustness. In particular, an adaptation of the density fitting scheme to translationally periodic systems is described, based on Fourier transformation techniques. Three examples of application are provided, concerning the CO(2) crystal, proton transfer in ice XI, and the adsorption of methane on MgO (001). The results obtained with the periodic LMP2 method for these systems appear more reliable than the ones obtained using density functional theory.

CRYSCOR is a periodic post-Hartree-Fock program based on local functions in direct space, i.e., Wannier functions and projected atomic orbitals. It uses atom centered Gaussians as basis functions. The Hartree-Fock reference, as well as symmetry information, is provided by the CRYSTAL program. CRYSCOR presently features an efficient and parallel implementation of periodic local second order Møller-Plesset perturbation theory (MP2), which allows us to study 1D-, 2D-and 3D-periodic systems beyond 1000 basis functions per unit cell. Apart from the correlation energy also the MP2 density matrix, and from that the Compton profile, are available. Very recently, a new module for calculating excitonic band gaps at the uncorrelated Configuration-Interaction-Singles (CIS) level has been added. Other advancements include new extrapolation techniques for calculating surface adsorption on semiinfinite solids. In this paper the diverse features and recent advances of the present CRYSCOR version are illustrated by exemplary applications to various systems: the adsorption of an argon monolayer on the MgO (100) surface, the rolling energy of a boron nitride nanoscroll, the relative stability of different aluminosilicates, the inclusion energy of methane in methane-ice-clathrates, and the effect of electron correlation on charge and momentum density of a-quartz. Furthermore, we present some first tentative CIS results for excitonic band gaps of simple 3D-crystals, and their dependence on the diffuseness of the basis set.

Rigorous methods for the post-HF (HF-Hartree-Fock) determination of correlation corrections for crystalline solids are currently being developed following different strategies. The CRYSTAL program developed in Torino and Daresbury provides accurate HF solutions for periodic systems in a basis set of Gaussian type functions; for insulators, the occupied HF manifold can be represented as an antisymmetrized product of well localized Wannier functions. This makes possible the extension to nonconducting crystals of local correlation linear scaling On techniques as successfully and efficiently implemented in Stuttgart's MOLPRO program. These methods exploit the fact that dynamic electron correlation effects between remote parts of a molecule (manifesting as dispersive interactions in intermolecular perturbation theory) decay as an inverse sixth power of the distance R between these fragments, that is, much more quickly than the Coulomb interactions that are treated already at the HF level. Translational symmetry then permits the crystalline problem to be reduced to one concerning a cluster around the reference zero cell. A periodic local correlation program (CRYSCOR) has been prepared along these lines, limited for the moment to the solution of second-order Moller-Plesset equations. Exploitation of point group symmetry is shown to be more important and useful than in the molecular case. The computational strategy adopted and preliminary results concerning five semiconductors with tetrahedral structure (C, Si, SiC, BN, and BeS) are presented and discussed.

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The oxygen vacancy in bulk MgO and at its ͑001͒ surface have been studied by means of the EMBED program which adopts an embedded-cluster approach in the frame of the Hartree-Fock ͑HF͒ approximation ͓Comp. Phys. Comm. 82, 139 ͑1994͒; 96, 152 ͑1996͔͒: A spin restricted ͑RHF͒ or unrestricted ͑UHF͒ method has been used according to whether the vacancy contains an even number ͑F and F 2ϩ centers͒ or an odd number ͑F ϩ center͒ of electrons. The semi-infinite crystal has been simulated with a three-layer slab. Particular attention has been given to the optimization of the basis functions which serve to describe the trapped electron͑s͒ in the vacancy. The correlation energy was estimated using second order Mo "ller-Plesset theory. The three electronic configurations have been studied by allowing for relaxation of all neighboring ions. For the paramagnetic center, spin density data are provided and discussed with reference to results from EPR experiments and molecular cluster calculations.

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A quantum-mechanical ab initio study is presented concerning the physisorption of HCl and HF on ice surfaces, modeled with periodic, proton-ordered thin films. Three methods are adopted: (1) Periodic two-dimensional calculations concerning ice surfaces, both clean and covered with ordered overlayers; (2) embedded cluster calculations, concerning two-dimensional ordered structures interacting with a single molecule; (3) molecular cluster calculations, simulating a portion of the surface. The combined and interactive use of these techniques has permitted us to recognize some deficiencies of molecular cluster models of ice and to correct for them. The energy of physisorption of HCl on a perfect basal surface of ice is estimated to be about 8 kcal/mol, on prismatic faces about 11 kcal/mol. Adsorption energies of HF are larger by 4 to 5 kcal/mol.