Rates of Convergence, Error Estimation Formulas, and Improved Basis Sets for Variational Methods in Atomic and Molecular Physics

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The principal goal of this work is the development of techniques for the efficient, reliable calculation of atomic and molecular properties, taking full account of electron correlation effects. The techniques will be tested via high accuracy bound state calculations on small atomic systems. The principal tool used will be the principal investigator's extension of the work of Charles Schwartz and of Klahn and Morgan on rates of convergence for the Rayleigh Ritz variational method. The recently developed formulas for the analytic evaluation of three electron matrix element integrals, which are based on earlier work of Bonham, and which have now been programmed in FORTRAN, will also be used. Significant improvements in accuracy and reliability with a reduced expenditure of computer time are expected. The initial stages of the work would be of interest to applied mathematicians and to atomic theorists concerned with high accuracy bound state calculations on small systems. Subsequent extensions to larger systems should be of interest to other atomic and molecular theorists and to quantum chemists.