Local and canonical approximations in Moller-Plesset perturbation theory with applications to dispersion interactions

The central theme of this thesis is the synergy between theoretical method development, efficient computational implementation, and relevant chemical application of second-order Moller-Plesset perturbation (MP2) theory. The central approximation utilized throughout this work involves the resolution-of-the-identity (RI) linear expansion of atomic orbital (AO) products in terms of an atom-centered auxiliary basis, thereby offering significant reductions in the computational effort necessary during AO integral evaluation and subsequent transformation into the molecular orbital (MO) basis. The primary chemical applications in this work center around dispersion interactions the ubiquitous, non-bonded intra- and inter-molecular interactions that play a key role in the stability and formation of protein secondary structure, base-pair stacking in the DNA double helix, dimer formation among rare gases, and other long-range correlation effects.;By incorporating the RI-approximation into the theoretical framework of the local triatomics-in-molecules (TRIM) model, we were able to simultaneously reduce the computational prefactor, via the RI-approximation for integral transformations from the AO to MO basis, and the inherent scaling of canonical MP2 theory, via the TRIM ansatz for local electron correlation, in which only double excitations that involve up to three atomic centers are retained. The resulting methodology, RI-TRIM MP2, emerged as a robust fourth-order method with the ability to extend the regime of practical MP2 calculations and to allow for treatment of electron correlation in molecular systems containing hundreds of atoms on a single processor.;An efficient serial implementation of the RI-MP2 analytical gradient utilizing a semi-direct t-amplitude batching approach was also presented and thoroughly assessed in terms of computational performance and chemical accuracy. As an application of this analytical RI-MP2 nuclear gradient algorithm, the structures and energetics characterizing the extended and globular conformations of alanine tetrapeptide were investigated with a focus on the role of dispersion interactions in the stability of folded conformational isomers of small polypeptide sequences.;Further exploration of analytical MP2 gradient theory was pursued in the development of the analytical gradient of RI-MP2 theory within the dual-basis (DB) approximation (DB-RI-MP2). By achieving self-consistent field (SCF) convergence in a small basis, projecting the small basis density into a target basis, and then approximating a single Roothaan step in the target basis via diagonalization of the Fock matrix built from the projected density, the DB formalism captures the linear energetic response to changes in the density matrix. In doing so, the DB model provides a fast and accurate route to obtaining the reference Hartree-Fock (HF) wavefunction, upon which MP2 corrections can be applied to account for dynamical electron correlation. A detailed analysis of the computational efficiency and chemical accuracy of the DB-RI-MP2 analytical gradient was presented herein and the significant changes to both the theory and computation of the coupled-perturbed self-consistent field equations (CPSCF) were explored. It was found that the simultaneous use of the DB- and RI-approximations not only provided highly-accurate MP2 analytical forces, but also directly targeted the computationally intensive underlying SCF-related steps necessary during analytical force determinations at the RI-MP2 level of theory, thereby allowing routine exploration of medium-sized molecular systems with large AO basis sets at the MP2 level of theory.;On the chemical application front, the spin-component scaled MP2 model (SCSMP2), in which the same and opposite spin contributions of the MP2 correlation energy are differentially scaled, was specialized to deal with Molecular Interactions by reoptimizing both spin-component scaling parameters on a diverse set of non-bonded complexes. The resultant model, SCS(MI)-MP2, emerged as a highly accurate methodology for obtaining intermolecular binding energies among both hydrogen-bonded and dispersion complexes with no additional cost over the underlying MP2 computation. An in-depth chemical application at the RI-MP2 level of theory followed that focused on the gas-phase benzene dimer, a primarily dispersion-bound molecular complex that serves as the prototype for pi-pi stacking in double-stranded DNA. A comparative analysis of the structure and energetics of the benzene dimer revealed the existence of two distorted dimeric binding motifs---configurations that represent the lowest energy T-shaped benzene dimer structures reported to date. (Abstract shortened by UMI.)...