Local-MP2 electron correlation method for nonconducting crystals

Abstract

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.

Silica Surface Features and Their Role in the Adsorption of Biomolecules: Computational Modeling and Experiments

“…Local correlation methods, [375][376][377][378][379][380][381][382][383] allow exploiting the fundamental local character of dynamical electron correlation, leading to methods that may scale linearly with the size of the system and thus largely reducing the computational costs of post-Hartree-Fock methods. As already anticipated in section 4.1, it is worth mentioning that local-MP2 has been implemented for extended systems by exploiting the translational and point symmetry poperties of crystalline structures 384 with the periodic boundary conditions as implemented in the CRYSCOR program, 328 and in the VASP program 330 through the random phase approximation associated to exact exchange. 329 These methods are, in general, very expensive when applied to extended systems but the development of codes apt to exploit the power of the high performance computing architectures 332 will soon make this kind of calculations available to the scientific community.…”

A prioriWannier functions from modified Hartree-Fock and Kohn-Sham equations

“…, K and expansion coefficients ( C ̺ ) g µ ≡ C g µ 0 ̺ for all K N 0 indices g µ. In expression (18), the coupling of the Wannier orbitals in the origin cell to the Wannier orbitals in neighboring unit cells reappears by means of the basis-set representation (16) which could be avoided by omitting the Lagrangian multipliers in Eq. (8).…”

“…Consequently, the dimension of the matrices in Eq. (18) The solution of the Wannier-Roothaan-Hall equations (18) has been implemented in the wannier program 24,25 and its accuracy was tested in a series of studies. Systematic comparisons were made of groundstate properties and band structures of crystals 25,27 and infinite chains.…”

“…9,10 Moreover, as soon as electron correlations in the ground state and in excited states are regarded, a local representation offers big advantages. 5,8,11,12,13,14,15,16,17,18 Conventionally, Wannier functions are determined a posteriori from Bloch functions utilizing the Wannier transformation. 1,2,3,4,6,7 It is unique up to a unitary matrix, which can be chosen freely to obtain a certain set of Wannier functions, e.g., those which are maximally localized with respect to a given criterion.…”

Response Properties of Periodic Materials Subjected to External Electric and Magnetic Fields

“…Another longer-term perspective is the development of optical properties calculations for solids at the post-Hartree-Fock level. This could be done in connection with the local-correlation CRYSCOR code, [47,48,49] which presently features a very efficient implementation of the local MP2 approach for periodic systems. This implementation makes use of advanced techniques such as density fitting [38] and orbital-specific virtuals [62], as well as efficient parallel implementation.…”