Improved embedded molecular cluster model

Abstract

ABSTRACT:We demonstrate that boundary effects (i.e., displacements of the cluster boundary atoms from their lattice sites and the difference between effective charges of the perfect crystal atoms and those of the cluster atoms in the case of a cluster with no point defect in it) in an embedded molecular cluster (EMC) model can be radically reduced. A new embedding scheme is proposed. It includes search for the structural elements (SE) of which perfect crystal is composed, use of corresponding to these SE expression for the total energy, and application of the degree of localization of equations consistent with the wave functions of the cluster. To get equations for the cluster wave functions, the problem of varied subsystem in the field of the frozen remaining part of the whole electron system" is investigated in the framework of a oneelectron approximation. The consideration is general for every task of this type. Homogeneous equations resulting directly from variation of the total energy expression are obtained and transformed to the eigenvalue problem equations. Orthogonality constraints are not imposed during variation. A particular case of the equations describing mutually orthogonal one-electron wave functions of the cluster staying nonorthogonal to those of the remaining crystal is found. A proposed embedding scheme is realized in the CLUSTER code based on the calculation scheme of the semiempirical INDO method. Boundary effects both in the standard (cluster in the field of the infinite lattice of nonpoint spherical charges) and new embedding scheme are investigated, calculating the clusters of LiF, MgO, NaCl, KCl, and AgCl crystals. Significant reduction of the boundary effects in the new embedding scheme is achieved. Reasons for the boundary effects are discussed.

Hybrid QM/MM embedding approach for the treatment of localized surface states in ionic materials

“…A number of alternative approaches have been developed and implemented in computer codes to treat point defects in ionic solids, with ICECAP 7, GUESS 8, and AIMP 9 being of particular relevance to us, but also of note are the closely related yet differing methods reported in the literature 10–29. In the context of embedding, rather than hybrid quantum mechanical (QM) molecular mechanical (MM) approaches in general, the important distinctions between these methods primarily concern: The boundary conditions on the cluster (compare the perturbed cluster approach by Pisani et al 13 with the embedded and cyclic cluster approaches by Bredow et al 15) and the localization procedure (compare the derivation procedures of Barandiaran and Seijo 9, who employ the strong orthogonality approximation with the recent, more general approach by Shidlovskaya 14). The cluster termination, employed in the field of semicovalent materials (compare the popular hydrogen termination with the semiempirical link atom approaches developed independently by Antes et al 27, Sushko et al 8, and Nasluzov et al 23.…”

“…The boundary conditions on the cluster (compare the perturbed cluster approach by Pisani et al 13 with the embedded and cyclic cluster approaches by Bredow et al 15) and the localization procedure (compare the derivation procedures of Barandiaran and Seijo 9, who employ the strong orthogonality approximation with the recent, more general approach by Shidlovskaya 14).…”

Comparison of localization procedures for applications in crystal embedding

“…[38] as the specific localization method. This technique was implemented in [28] for the embedded molecular cluster calculations. The LMOs resulting from a single AG calculation are orthogonal as solutions of a single secular problem.…”

“…A rather general method based on overlapping (not strongly orthogonal) group functions [26,27] is presently being developed in our laboratory. Our method which is similar in spirit to some one-electron methods [28,29,30] is based on construction of strongly localized orbitals which are designed to represent the true electronic density of the entire system via a combination of elementary densities associated in simple cases with atoms, ions and/or bonds. Our initial effort in this project is focused on the development of an embedding scheme based on the HF approximation and applied to point defects in the bulk or at surfaces of periodic crystals.…”

Treating periodic systems using embedding: Adams-Gilbert approach

“…We have shown previously 20,21,25 that by lifting the orthogonality condition, highly localized molecular orbitals ͑LMOs͒ may be obtained that can span the whole occupied Fock space, and thus are capable of representing correctly the system total electron density. 25 Our method, which is similar in spirit to some existing one-electron methods, [26][27][28] is based on the partitioning of the entire periodic system into overlapping electronic groups ͑EGs͒ corresponding to atoms, ions, bonds, or molecules comprising the entire system. The LMOs are obtained selfconsistently by solving Adams-Gilbert equations 29-32 separately for each group within the primitive unit cell.…”