Self-consistent and environment-dependent Hamiltonian for quantum-mechanics materials simulations.

Abstract

A reliable semi-empirical Hamiltonian for materials simulations must allow electron screening and charge redistribution effects. Using the framework of linear combination of atomic orbitals (LCAO), a self-consistent and environment-dependent (SCED)Hamiltonian has been constructed for quantum mechanics based simulations of materials. This Hamiltonian contains environment-dependent multi-center interaction terms and electron-electron correlation terms that allow electron screening and charge-redistribution effects. As a case study, we have developed the SCED/LCAO Hamiltonian for silicon. The robustness of this Hamiltonian is demonstrated by scrutinizing a variety of different structures of silicon. In particular, we have studied the following: (i) the bulk phase diagrams of silicon, (ii) the structure of an intermediate-size Si 71 cluster, (iii) the reconstruction of Si(100) surface, and (iv) the energy landscape for a silicon monomer adsorbed on the reconstructed Si(111)-7x7 surface. The success of the silicon SCED/LCAO Hamiltonian in the above applications, where silicon exists in a variety of different co-ordinations, is a testament to the predictive power of the scheme.

Towards a Coherent Treatment of the Self-Consistency and the Environment-Dependency in a Semi-Empirical Hamiltonian for Materials Simulation

“…We have recently developed a scheme for the construction of semi-empirical Hamiltonians for materials within the framework of linear combination of atomic orbitals (LCAO) that allows a coherent treatment of the SC determination of the charge redistribution and the environment-dependent (ED) multi-center interactions in a transparent manner [5]. In this scheme, we set up the framework of the semi-empirical Hamiltonian in accordance with the Hamiltonian of the many-atom aggregate.…”

“…We have tested the SCED/LCAO Hamiltonian by investigating a variety of different structures of silicon (Si), including the bulk phase diagrams of Si, the equilibrium structure of an intermediate-size Si 71 cluster, the reconstruction of the Si(100) surface, and the energy landscape for a Si monomer adsorbed on the reconstructed Si(111)-7×7 surface [5]. In all the cases studied, the results have demonstrated the robustness of the SCED/LCAO Hamiltonian.…”

A semi-empirical Hamiltonian for boron, phosphorus and compounds containing boron, phosphorus and silicon.

“…The onsite electron and offsite ion interaction energy, plus, onsite electron and offsite electron interaction energy is a complex formulation detailed in two previous works 1,15 . I refer the reader to these works.…”

“…Even though our initial guess for the boron parameters were carefully thought out, many of the processors failed to produce a fairly low residual, and many instances the code halted completely. But, out of the 30 plus processors that were running, at least 6 produced a residual 15 lower than 130 (a residual of 50 scale in the mid-30s is the goal). Of these 6 sets of fitting parameters several characteristics of the overlap were inspected.…”

“…Details of the order N method and philosophy of the SCED-LCAO method with selected applications to silicon are explained in previous works by the CMT group at the University of Louisville 1,15,16 . This dissertation will explore the alteration of the Hamiltonian to improve the accuracy of the boron Hamiltonian along with the heterogeneous case of mixing multiple different elements together.…”