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

The symmetry‐adapted‐cluster (SAC) expansion of an exact wavefunction is given. It is constructed from the generators of the symmetry‐adapted excited configurations having the symmetry under consideration, and includes their higher‐order effect and self‐consistency effect. It is different from the conventional cluster expansions in several important points, and is suitable for applications to open‐shell systems as well as closed‐shell systems. The variational equation for the SAC wavefunction has a form similar to the generalized Brillouin theorem in accordance with the inclusion of the higher‐order effect and the self‐consistency effect. We have expressed some existing open‐shell orbital theories equivalently in the conventional cluster expansion formulas, and on this basis, we have given the pseudo‐orbital theory which is an extension of open‐shell orbital theory in the SAC expansion formula.

Cluster expansion of the wavefunction. Symmetry-adapted-cluster expansion, its variational determination, and extension of open-shell orbital theory

The Dirac Hamiltonian is transformed by extracting the operator (sigma x p)/2mc from the small component of the wave function and applying it to the operators of the original Hamiltonian. The resultant operators contain products of Paull matrices that can be rearranged to give spin-free and spin-dependent operators. These operators are the ones encountered in the Breit-Pauli Hamiltonian, as well as some of higher order in alpha(sup 2). However, since the transformation of the original Dirac Hamiltonian is exact, the new Hamiltonian can be used in variational calculations, with or without the spin-dependent terms. The new small component functions have the same symmetry properties as the large component. Use of only the spin-free terms of the new Hamiltonian permits the same factorization over spin variables as in nonrelativistic theory, and therefore all the post-Self-Consistent Field (SCF) machinery of nonrelativistic calculations can be applied. However, the single-particle functions are two-component orbitals having a large and small component, and the SCF methods must be modified accordingly. Numerical examples are presented, and comparisons are made with the spin-free second-order Douglas-Kroll transformed Hamiltonian of Hess.

An exact separation of the spin‐free and spin‐dependent terms of the Dirac–Coulomb–Breit Hamiltonian

Recent publications have suggested that the satisfaction of a principle we call kinetic balance can provide variational safety in Dirac calculations. The theoretical foundation for this proposal is examined, first in simple one‐electron problems, and then (less rigorously) in SCF calculations. The conclusion is that finite basis calculations using kinetic balance are safe from catastrophic variational collapse, but that the ‘‘bounds’’ provided by these calculations can be in error by an amount of order 1/c4. The bounds are applicable to total SCF energies, but not to SCF orbital energies. The theory is illustrated by a series of one‐electron calculations.

Kinetic balance: A partial solution to the problem of variational safety in Dirac calculations

The direct observation of the “transition state" for
chemical reaction clearly merits a place in this series
devoted to the “Holy Grails” of chemistry. The transition
state is neither one thing, namely, chemical reagents, nor the other, reaction products. Instead it illustrates the mystical event of trans-substantiation.

Direct Observation of the Transition State

Dirac-Fock discrete-basis calculations on the beryllium atom

We have measured the far wing absorption profiles of the MgH2 collision system leading to both the nonreactive formation of Mg* and into two distinct final rotational states of the reaction product MgH (v‘=0, J‘=6, 23). We have observed qualitatively expected behavior including a pronounced red wing in the reactive absorption profile indicating strong reaction probability on the excited attractive potential surfaces. We have also observed novel aspects of the excited state dynamics including reactive vs nonreactive channel competition effects and a strong far blue wing reactive absorption suggesting significant reaction probability even for trajectories on the repulsive surfaces. We have developed a simple theoretical model to semiquantitatively explain our experimental results. This model uses standard quasistatic theory to estimate the absorption probability as a function of detuning between levels of MgH2 and with assumed nonreactive vs reactive branching ratios, accounts for the subsequent evolution on the excited potential surfaces. This theory correctly predicts the overall shapes of the profiles and in general gives reasonable predictions for the relative magnitudes of the wing intensities.

Reactive collision dynamics by far wing laser scattering: Mg+H2

We have used a ‘‘half‐collision’’ pump–probe technique to measure the far wing absorption profiles of the NaH2 collision complex leading to the nonreactive formation of Na* and to four distinct final rotational states of the reaction product NaH(v‘=1, J‘=3, 4, 11, and 13). We have observed reaction on both the attractive potential energy surfaces and over a barrier on the repulsive surface. We have observed the effect of the Na* reagent electronic orbital alignment on the NaH final product rotational state distribution. Specifically, absorption to the repulsive surface leads preferentially to low‐rotational product states, while absorption to the attractive surfaces leads preferentially to high‐rotational product states of NaH. Isotopic substitution experiments give evidence of a kinematic isotope effect on the product rotational state distribution for reactive trajectories on the repulsive surface. We have developed a simple model using a quantum mechanical line shape calculation to estimate the NaH2 absorption probability as a function of wavelength. We then make simple phenomenological dynamical arguments to predict final state branching. There is an overall qualitative agreement between the experimental results and theoretical model predictions.

Reactive collision dynamics of Na*(4 2P)+H2 and HD: Experiment and theory

We report on preliminary studies of the far-wing absorption of laser light into the MgH/sub 2/ reactive collision complex. We have measured the far-wing absorption profile leading both to the nonreactive channel (Mg( formation) and into a specific vibrational-rotational level of the reactive channel (MgH (v'' = 0, J'' = 23) formation).

Far-wing absorption profiles of a reactive collision: Mg+H2

A comparison is presented of the energies associated with different SCF types: spin restricted, unrestricted, projected unrestricted, and extended. A method of obtaining spin‐extended SCF functions is discussed. Sample calculations are done for simple hydrocarbon pi‐electron radicals in the Pariser—Parr approximation, and both energies and spin densities are reported.

K. M. Sando

Papers

Dirac-Fock discrete-basis calculations on the beryllium atom

Reactive collision dynamics by far wing laser scattering: Mg+H2

Reactive collision dynamics of Na*(4 2P)+H2 and HD: Experiment and theory

Far-wing absorption profiles of a reactive collision: Mg+H2

Spin‐Projected and Extended SCF Calculations