Linear-scaling methodology in large-scale ab initio electronic structure calculations and applications in biological studies

The ability to perform ab initio electronic structure calculations with times that scale linearly with the system size is one of the central aims in theoretical chemistry. In this dissertation, the implementation of the divide-and-conquer (DC) algorithm, an algorithm with the potential to aid in linear scaling capability in Hartree-Fock (HF) and second-order Moller-Plesset perturbation (MP2) calculations, is discussed. Standard HF calculations solve the Roothaan-Hall equations for the whole system; in the DC-HF approach, the diagonalization of the Fock matrix is carried out on smaller subsystems. For DC-MP2 calculations, after localized molecular orbitals of each subsystem are obtained from the DC-HF calculations, the correlation energy of the whole system can be derived by taking the sum of the local electron correlation of each subsystem. Preliminary DC-MP2 results on extended polyglycine systems show the linear-scaling behavior.;We have also proposed an automated fragmentation quantum mechanics/molecular mechanics approach (AF-QM/MM) to routinely calculate ab initio protein NMR chemical shielding constants. The AF-QM/MM method is linear-scaling and trivially parallel. A general fragmentation scheme is employed to generate each residue-centric region which is treated by quantum mechanics, and the environmental electrostatic field is described with molecular mechanics. The AF-QM/MM method shows good agreement with standard self-consistent field calculations of the NMR chemical shieldings for the mini-protein Trp-cage.;This dissertation also deals with an application of these faster implementations of ab initio methods to examine future uses of our code. Our linear-scaling approach is still in the development stages, we therefore chose to use the fastest currently available method for carrying out ab initio electronic structure calculations, the fragment-molecular-orbital (FMO) approach. By utilizing the available software GAMESS-US, we employed both FMO-HF and FMO-MP2 calculations in conjunction with the Polarizable Continuum Model on the native structures of two proteins and their corresponding computer-generated decoy sets. We show the sum of the HF energy and force field (LJ6) derived dispersion energy (HF + LJ6) is well correlated with the energies obtained using second-order MP2 theory. In one of the two examples studied the correlation energy as well as the empirical dispersive energy term was able to discriminate between native and decoy structures. On the other hand, for the second protein we studied, neither the correlation energy nor dispersion energy showed discriminative capabilities; however, the ab initio MP2 energy and the HF+LJ6 both ranked the native structure correctly.