The development of second-quantization theory for the calculation of response functions with perturbation-dependent basis functions; its implementation and application to geometrical and magnetic molecular properties. The calculation of NMR parameters, including the calculation of indirect spin-spin coupling constants in molecules containing several hundred atoms by linear-scaling density-functional techniques. The unconstrained parameterization of the atomic-orbital density matrix in self-consistent field theories, with applications to energy optimization and property evaluation.

The introduction of the variational Lagrangian method for the calculation of molecular properties for nonvariational wave functions in the same manner as for variational wave functions (a generalization of the Handy-Schaefer technique, applicable to dynamic as well as static perturbations), with the wave-function parameters obeying the 2n+1 rule and their multipliers the 2n+2 rule.

The development of the integral-direct coupled-cluster method, making possible calculations in very large basis sets. Its application to the study of the basis-set convergence of orbital-based correlated methods; the establishment of the principal orbital expansion and the two-point extrapolation technique, typically reducing basis-set errors by an order of magnitude, thereby making standard, orbital-based calculations competitive with explicitly correlated ones. The accurate and systematic benchmarking of quantum chemistry, including the rigorous calculation of atomization energies and spectroscopic constants to within the errors imposed by the Schrödinger equation.

The introduction of ab initio direct dynamics for integrating the classical Born-Oppenheimer trajectories on the fly, without constructing the potential energy surface in advance, with several applications using multiconfigurational self-consistent field theory.