New Electron Correlation Methods And Their Applications And Use Of Atomic Orbitals With Exponential Asymptotes PDF Download

ABSTRACT: This dissertation is focused on the development of highly accurate electron-correlation methods for one- and two-dimensional periodic systems. For one-dimensional systems, atomic-orbital based many-body perturbation theory and coupled cluster theory are developed and applied to polyacetylene and lithium-hydride model chain. Use of atomic orbitals instead of conventional crystalline (molecular) orbitals enables us to control runtime and accuracy of the calculation. The gain in the atomic-orbital based coupled cluster method originates from the locality and sparsity of matrices needed in the framework of the theory. Provided, efficient sparse matrix-matrix multiplication routines, we obtain good estimates of the correlation energy much faster than the conventional method for large systems. 90 percent of the correlation energy can be recovered very quickly, and 2 to 3 digit accuracy can be obtained for polymers with relatively simple unit cells such as polyacetylene. The formalism behind the atomic-orbital based coupled cluster theory is applicable for both large molecular systems and periodic systems. Formal aspects of the atomic-orbital based coupled cluster theory are discussed and correspondence between the atomic-orbital based framework and crystalline (molecular) orbital based framework are shown. Two-dimensional code development is based on Hartree-Fock and density functional theories due to the fact that coupled-cluster theory is too costly. Efficient inclusion of the Coulomb effects by the fast multipole method and analytical gradient techniques are the core elements that contribute robustness and computational efficiency for two-dimensional systems. The fast multipole method is an algorithm to include the long-range Coulomb effects for uniform systems with linear-scaling costs for molecular systems and with logarithmic scaling for infinite periodic systems. The analytical gradient technique is a powerful tool when optimized geometries or vibrational frequencies are computed. If optimum geometries or vibrational frequencies are required, then analytical gradients are for all practical purposes, a necessity.