This project is being sponsored jointly by the Divisions of Chemistry and Advanced Scientific Computing. Professor Friesner intends to develop new and rapid means for carrying out quantum-mechanical calculations on molecules too large to be treated by conventional means. The methods would be of significant value to experimental chemists, allowing detailed quantum-mechanical treatments of systems now accessible only to semi-empirical approximate methods. The work involves a novel algorithm for solving self-consistent electronic structure equations that leads to a reduction of computation time by a factor of 1.6N, where N is the basis set size, while maintaining accuracy comparable to existing methods. The method involves a synthesis of the usual quantum-chemical LCAO approach with the pseudospectral method, a numerical technique used in hydrodynamic simulations of turbulence. The efficiency of the calculations is achieved by eliminating the vast majority of two-electron integrals and by altering the computational scaling from a proportionality to N^4 to one of only N^3. Accuracy in relative energies is retained by removing aliasing errors, rendering the results nearly equivalent to those obtained from the Roothaan procedure. The algorithm will be tested and optimized for a series of small molecules and will be generalized to excited state, density functional, and generalized valence-bond calculations.
