The reaction path on the potential energy surface of a polyatomic molecule is the steepest descent path (if mass‐weighted Cartesian coordinates are used) connecting saddle points and minima. For an N‐atom system in 3d space it is shown how the 3N‐6 internal coordinates can be chosen to be the reaction coordinate s, the arc length along the reaction path, plus (3N‐7) normal coordinates that describe vibrations orthogonal to the reaction path. The classical (and quantum) Hamiltonian is derived in terms of these coordinates and their conjugate momenta for the general case of an N atom system with a given nonzero value of the total angular momentum. One of the important facts that makes this analysis feasible (and therefore interesting) is that all the quantities necessary to construct this Hamiltonian, and thus permit dynamical studies, are obtainable from a relatively modest number of ab initio quantum chemistry calculations of the potential energy surface. As a simple example, it is shown how the effects o...

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Reaction path Hamiltonian for polyatomic molecules

In recent years our research group has made a systematic effort to study the validity of transition state theory (TST). We have found that the conventional theory is sometimes remarkably accurate, but in many other cases it leads to large errors. Fortunately we have found that a much more reliable theory that has many of the advantages of conventional TST can also be formulated, and it can be applied to practical problems with an effort that is much closer to that required for conventional transition state theory than to that required for quantal dynamics calculations. The two most important features in the improved approach to transition state theory state theory are the variational determination of the transition state and the incorporation of tunneling contributions by multidimensional semiclassical approximations. 13 refs.

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Variational Transition State Theory

A quasiclassical procedure for the examination of the collision dynamics of atom—diatomic‐molecule reactions with activation energy is introduced. By means of Monte Carlo averages over a large number of appropriately chosen three‐dimensional classical trajectories, the total reaction cross section (Sr) and other reaction attributes can be determined as a function of the initial relative velocity (Vr) and the initial molecular rotation‐vibration state (J, ν).The method is applied to the exchange reaction resulting from a hydrogen atom and a hydrogen molecule moving on a simple barrier potential of the London—Eyring—Polanyi—Sato type. It is found that Sr is a monotonically increasing function of relative velocity that rises smoothly from a threshold at ∼0.9×106 cm/sec to its asymptotic value of ∼4.5a02 at ∼1.8×106 cm/sec. The zero‐point vibrational energy of the molecule contributes to the energy required for reaction, but the rotational energy does not. The reaction probability, which depends on VR, ν, and...

Exchange Reactions with Activation Energy. I. Simple Barrier Potential for (H, H2)

Concepts in reaction dynamics

An accurate three‐dimensional potential energy surface for H3 has been obtained by the configuration interaction (CI) method. The calculated energies, for 156 nuclear configurations, with the energy of the saddle point taken to be zero, are believed to lie within 0.1 kcal/mole of the exact clamped‐nuclei limit. The CI calculations used an extended one‐particle basis set of 4 s‐type, 3 p‐type, and 1 d‐type contracted Gaussian functions, and a nearly complete n‐particle basis set. In order to solve the large secular problem, the direct CI method was adapted to the problem of complete CI for three valence electrons. The properties of the accurate H3 potential surface were used to evaluate ab initio and semiempirical methods for potential surface calculations, with emphasis on their applications to other exchange reactions.

An accurate three‐dimensional potential energy surface for H3

An analytic semiempirical expression is developed for the ground‐state potential‐energy surface of the H3 system. Use is made of the valence‐bond formulation with the inclusion of overlap and three‐center terms. The diatomic Coulomb and exchange integrals are estimated from accurate values for the H2 molecule by a modified London—Eyring—Sato procedure, while the three‐center integrals are approximated by simple formulas. A linear, symmetric saddle‐point configuration of minimum energy is found that has properties in approximate agreement, though not identical, with other estimates from theory and experimental rate data. The details of the surface are presented in terms of contour maps for a variety of distances and angles. Because of the inclusion of overlap and three‐center terms, a more realistic energy is expected for the nonlinear configurations than could be obtained from previous potential energy formulas. The utility of the present method for dynamical studies of reaction cross sections is indicated.

F. L. Minn

Papers

Potential Energy Surface for H3