A formalism is developed for obtaining ab initio effective core potentials from numerical Hartree–Fock wavefunctions and such potentials are presented for C, N, O, F, Cl, Fe, Br, and I. The effective core potentials enable one to eliminate the core electrons and the associated orthogonality constraints from electronic structure calculations on atoms and molecules. The effective core potentials are angular momentum dependent, basis set independent, and stable against variational collapse of their eigenfunctions to core functions. They are derived from neutral atom wavefunctions using a pseudo-orbital transformation which is motivated by considerations of the expected accuracy of their use and of basis set economy in molecular calculations. Then the accuracy is demonstrated by multiconfiguration Hartree–Fock calculations of potential energy curves for HF, HCl, HBr, HI, F2, Cl2, Br2, and I2 and one-electron properties for HF and HBr. The differences between valence-electron calculations employing the present effective core potentials and all-electron calculations are smaller than differences due to basis set choices, even though the basis sets are extended ones. Thus the effective core potentials are quite successful. In addition larger configuration mixing calculations are performed for HBr and Br2 (1637 and 3396 configurations, respectively) and again the effective core potentials are judged to perform well.
This paper presents a survey and comparative evaluation of methods which have been developed for the determination of uncertainties in accident consequences and probabilities, for use in probabilistic risk assessment. The methods considered are: analytic techniques, Monte Carlo simulation, response surface approaches, differential sensitivity techniques, and evaluation of classical statistical confidence bounds. It is concluded that only the response surface and differential sensitivity approaches are sufficiently general and flexible for use as overall methods of uncertainty analysis in probabilistic risk assessment. The other methods considered, however, are very useful in particular problems.KEY WORDS: uncertainty analysis; probabilistic risk assessment; response surfaces; differential sensitivity methods.
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