A self-consistent and environment-dependent Hamiltonian for large-scale simulations of complex nanostructures

This review is devoted to the development of a robust semi-empirical Hamiltonian for quantum-mechanics-based simulations. The Hamiltonian referred as self-consistent (SC) and environment-dependent (ED) Hamiltonian is developed in the framework of linear combination of atomic orbitals (LCAO) and includes multi-center electron–ion and electron–electron interactions. Furthermore, the framework allows for a self-consistent treatment of charge-redistributions. The parameterized Hamiltonian matrix elements and overlap functions are obtained by fitting them to accurate first-principles database of properties corresponding to clusters and bulk phases of materials. The total energy includes the band structure energy, the correction term from the double-counting of electrons, and ion–ion repulsions, where the band structure energy is obtained by solving a generalized eigenvalue equation. Linear scaling algorithms for large-scale simulations of materials have also been incorporated. The present approach goes beyond the traditional two-center tight-binding Hamiltonians in terms of its accuracy and transferability and allows the study of system sizes that are beyond the scope of ab-initio simulations. We have studied a wide-variety of complex materials and complex phenomena using the SCED-LCAO MD that include: (i) the structure and stability of bucky-diamond carbon clusters and their phase transformations upon annealing, (ii) the initial stage of growth of single-wall carbon nanotubes (SWCNTs), and (iii) structural and electronic properties of bucky-diamond SiC clusters and SiC nanowires (NWs). The successful outcome of these case studies is a testament to the transferability of the Hamiltonian to different types of atomic environments (i.e., co-ordinations and bonding configurations).