Development of the cyclic cluster approach for ionic systems

Abstract

ABSTRACT:The cyclic cluster approach has been implemented in the semiempirical SCF MO method MSINDO for calculations of two-and three-dimensional periodic systems. Several new features are introduced. Special emphasis was given to the description of ionic compounds including long-range Coulomb interactions. At variance with previous implementations all interaction integrals are calculated in real space. This allows for a direct comparison of results from the cyclic cluster approach and from free and embedded cluster calculations with the original MSINDO method. A scheme based on diatomic contributions was used to calculate analytical gradients for the optimization of lattice parameters. A comparison with extrapolated cluster results for bulk and surface properties of MgO and NiO reveals that relatively small cyclic clusters are sufficient to reach the infinite limit.

Implementation of the Cyclic Cluster Model in Hartree-Fock LCAO Calculations of Crystalline Systems

“…DM P(k) and overlap matrix S(k) are M Â M matrices. As mentioned in Section 2, the idempotency of DM is connected with the balance between the choice of k vectors in (21) and direct lattice summation in (22).…”

“…The method has been designed for the quantum chemical treatment of molecular systems, but has recently been extended to calculations of cyclic clusters [21].…”

“…This has been realized by an averaging of two-center integrals (overlap, nuclear attraction, electron repulsion) between the central atom of the interaction region and atoms at the boundaries [21]. In this approach, the cyclicity and summation regions are the same and not dependent on integral thresholds as for periodic methods.…”

“…The method MSINDO [27] has been chosen since it has been successfully applied to calculations of solid state properties [28,29] and it has been shown that the recent implementation of the CCM in MSINDO is able to reproduce the symmetry of electronic states of crystalline compounds [21]. The problems arising in the non-local DFT calculations of cyclic clusters are briefly discussed.…”

Fotocolheita em interface híbrida de molécula orgânica e óxido de titânio

“…Iniciando ainda pelas aproximações para o cálculo de Hartree-Fock, de forma a melhorar a factibilidade de cálculo são adotadas parametrizações semi-empíricas para as integrais do termo de Fock [87,88], e também o uso do caroço congelado para reduzir o número de elétrons para o mínimo (no caso do Titânio, por exemplo, apenas os orbitais ocupados 3d e 4s são calculados explicitamente) O Modelo de Aglomerado Cíclico, ou Cyclic Cluster Model [89,90,91,92] é a proposta presente no código MSINDO para tratar sistemas periódicos. É inicialmente criado um "super aglomerado (cluster)" através de repetição da célula unitária original, de forma a manter uma boa descrição das interações de longo alcance, já que não serão incluídos pontos k no cálculo.…”