Direct ab initio molecular orbital methods for the study of large molecules

Direct methods, in which the two electron integrals are recalculated whenever they are needed instead of being stored, are a promising way of extending the range of applicability of ab initio molecular orbital theory to larger molecules. In this work, several developments designed to improve the viability of direct methods are presented and applied.

Firstly, a new method for gaussian two electron integral evaluation is described. It is shown to be superior to existing approaches, particularly for basis sets containing d functions, by floating point operation counts and comparative computer timings.

Secondly, a new approach to geometry optimization in the Hartree-Fock method is explored, in which the wavefunction and geometric variables are optimized simultaneously. A simultaneous optimization scheme based on first derivatives, and a quadratically convergent scheme based on first and second derivatives are formulated and implemented. The latter in particular appears to have considerable merit.

Thirdly, a direct formulation of second order Moller-Plesset theory (MP2) is presented. Direct MP2 calculations of the correlation energy of large molecules can usually be performed very cheaply relative to Hartree-Fock geometry optimizations using direct methods, and should hence find wide application.

Finally a study of the barriers to internal rotation in substituted benzenes and ethylenes is reported, utilizing direct methods. Obtaining reliable barriers for these conjugated molecules is shown to generally require extended basis sets and beyond Hartree-Fock methods, such as MP2. Theoretically determined barriers are thought to be more reliable than current experimental values for nitrobenzene, benzaldehyde and benzoyl fluoride.