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Improved Accuracy and Convergence of Electron Densities Derived from the Hiller-Sucher-Feinberg Identity
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| Ph.D. dissertation, Florida State University, Tallahassee, FL |
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The Hiller-Sucher-Feinberg (HSF) identity for matrix elements of Dirac's delta-function is used to obtain an alternative equation for the electron density. Asymptotics of the HSF electron density are derived; the HSF density obeys a relationship analogous to Kato's cusp condition, and decays to a constant if the sum of Hellmann-Feynman forces is finite. The HSF molecular integrals, L, U and V, involving s-type Gaussian basis functions are derived. Formulae that yield optimal quadrature parameters for the numerical integration of the U and V integrals are developed. An analytic component, corresponding to Rosser's rocket flight function is extracted from the V integral, and novel methods for its computation are presented. Mathematica programs that calculate accurate and efficient approximates of special functions are listed, including rational approximates with expanding interpolation grids. These developments are implemented in RHODOS, which runs at sustained rates of 120 MFLOPS on a single, Cray Y-MP CPU. Results obtained with RHODOS demonstrate that the HSF density is an order of magnitude more accurate than the conventional density at the nuclei of heavy atoms, but is less accurate at hydrogen nuclei bound to heavy atoms due to its improper decay. The constrained-variational method is developed to eliminate Hellmann-Feynman forces/ application of this method increases the accuracy of the HSF density at hydrogen nuclei dramatically. In the case of the di-lithium molecule, the electron density and its topological properties converge more rapidly when derived from the HSF identity.
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