A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.

General atomic and molecular electronic structure system

Ab initio effective core potentials (ECP’s) have been generated to replace the Coulomb, exchange, and core‐orthogonality effects of the chemically inert core electron in the transition metal atoms Sc to Hg. For the second and third transition series relative ECP’s have been generated which also incorporate the mass–velocity and Darwin relativistic effects into the potential. The ab initio ECP’s should facilitate valence electron calculations on molecules containing transition‐metal atoms with accuracies approaching all‐electron calculations at a fraction of the computational cost. Analytic fits to the potentials are presented for use in multicenter integral evaluation. Gaussian orbital valence basis sets are developed for the (3d,4s,4p), (4d,5s,5p), and (5d,6s,6p) orbitals of the first, second, and third transition series atoms, respectively. All‐electron and valence‐electron atomic excitation energies are also compared for the low‐lying states of Sc–Hg, and the valence‐electron calculations are found to reproduce the all‐electron excitation energies (typically within a few tenths of an eV).

Ab initio effective core potentials for molecular calculations. Potentials for the transition metal atoms Sc to Hg

A consistent set of ab initio effective core potentials (ECP) has been generated for the main group elements from Na to Bi using the procedure originally developed by Kahn. The ECP’s are derived from all‐electron numerical Hartree–Fock atomic wave functions and fit to analytical representations for use in molecular calculations. For Rb to Bi the ECP’s are generated from the relativistic Hartree–Fock atomic wave functions of Cowan which incorporate the Darwin and mass–velocity terms. Energy‐optimized valence basis sets of (3s3p) primitive Gaussians are presented for use with the ECP’s. Comparisons between all‐electron and valence‐electron ECP calculations are presented for NaF, NaCl, Cl2, Cl2−, Br2, Br2−, and Xe2+. The results show that the average errors introduced by the ECP’s are generally only a few percent.

Ab initio effective core potentials for molecular calculations. Potentials for main group elements Na to Bi

A method is presented for developing probability density functions for parameters of soil moisture relationships of capillary head [h(θ)] and hydraulic conductivity [K(θ)]. These soil moisture parameters are required for the assessment of water flow and solute transport in unsaturated media. The method employs a statistical multiple regression equation proposed in the literature for estimating [h(θ)] or [K(θ)] relationships using the soil saturated water content and the percentages of sand and clay. In the absence of known statistical distributions for either [h(θ)] or [K(θ)] relationships, the method facilitates modeling by providing variability estimates that can be used to examine the uncertainty associated with water flow or solute transport in unsaturated media.

Developing joint probability distributions of soil water retention characteristics

Compact effective potentials, which replace the atomic core electrons in molecular calculations, are presented for atoms in the first and second rows of the periodic table. The angular‐dependent components of these potentials are represented by compact one‐ and two‐term Gaussian expansions obtained directly from the appropriate eigenvalue equation. Energy‐optimized Gaussian basis set expansions of the atomic pseudo‐orbitals, which have a common set of exponents (shared exponents) for the s and p orbitals, are also presented. The potentials and basis sets have been used to calculate the equilibrium structures and spectroscopic properties of several molecules. The results compare extremely favorably with corresponding all‐electron calculations.

Compact effective potentials and efficient shared‐exponent basis sets for the first‐ and second‐row atoms

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...

Ab initio effective core potentials: Reduction of all-electron molecular structure calculations to calculations involving only valence electrons

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.

Methods for Uncertainty Analysis: A Comparative Survey

Approaches to the regulation of risk from technological systems, such as nuclear power plants or chemical process plants, in which potential accidents may result in a broad range of adverse consequences must take into account several different aspects of risk. These include overall or average risk, accidents posing high relative risks, the rate at which accident probability decreases with increasing accident consequences, and the impact of high frequency, low consequence accidents. A hypothetical complementary cumulative distribution function (CCDF), with appropriately chosen parametric form, meets all these requirements. The Farmer limit line, by contrast, places limits on the risks due to individual accident sequences, and cannot adequately account for overall risk. This reduces its usefulness as a regulatory tool. In practice, the CCDF is used in the Canadian nuclear licensing process, while the Farmer limit line approach, supplemented by separate qualitative limits on overall risk, is employed in the United Kingdom.

Limit lines for risk

Ab initio quantum mechanical calculations have been carried out to predict the H+Br2→HBr+Br potential energy surface. We used ab initio effective core potentials and an extended valence basis set including polarization functions on each center and carried out open‐shell self‐consistent‐field calculations in the generalized valence bond–perfect‐pairing (GVB–PP) approximation. The orbitals of this calculation were used as a starting point for eight‐configuration–configuration‐interaction (GVB–CI) calculations. The CI calculations not only bring in electron correlation effects but also make up to a large extent the inability of the GVB–PP calculation to adequately treat the recoupling of orbitals which occurs near the transition state. The classical barrier height is predicted to be about 12 kcal mole−1 by the GVB–PP calculations and about 3.0 kcal mole−1 by the GVB–CI calculations. The latter value is in reasonable agreement with the experimental Arrhenius activation energy. The saddle point is predicted fr...

Paul Baybutt

Papers

Ab initio effective core potentials: Reduction of all-electron molecular structure calculations to calculations involving only valence electrons

Methods for Uncertainty Analysis: A Comparative Survey

Limit lines for risk

Generalized valence‐bond investigation of the reaction H+Br2 →HBr+Br

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