Bruce C. Garrett

POLYRATE 4: A new version of a computer program for the calculation of chemical reaction rates for polyatomics

POLYRATE is a computer program for the calculation of chemical reaction rates of polyatomic species (and also atoms and diatoms as special cases). Version 1.1 was submitted to the CPC Program Library in 1987, and version 4.0.1 was submitted in 1992. Since that time many new capabilities have been added, old ones have been improved, and the code has been made more portable and user-friendly, resulting in the present improved version 6.5. The methods used are variational or conventional transition state theory and multidimensional semiclassical adiabatic and large-curvature approximations for tunneling and nonclassical reflection. Rate constants may be calculated for canonical or microcanonical ensembles or for specific vibrational states of selected modes with translational, rotational, and other vibrational modes treated thermally. Bimolecular and unimolecular reactions and gas-phase, solid-state, and gas-solid interface reactions are all included. Potential energy surfaces may be global analytic functions or implicit functions defined by interpolation from input energies, gradients, and force constants (Hessian matrices) at selected points on a reaction path. The data needed for the dynamics calculations may also be calculated from a global potential energy surface with more accurate calculations at stationary points. The program calculates reaction paths by the Euler, Euler stabilization, or Page-McIver methods. Variational transition states are optimized from among a one-parameter sequence of generalized transition states orthogonal to the reaction path. Tunneling probabilities are calculated by numerical quadrature, using either the centrifugal-dominant-small-curvature approximation, the large-curvature-version-3 approximation, and/or optimized multidimensional tunneling approximations. In the large-curvature case the tunneling probabilities may be summed over final vibrational states for exoergic reactions or initial vibrational states for endoergic reactions.

Criterion of minimum state density in the transition state theory of bimolecular reactions

We discuss two minimum‐density‐of‐states criteria for the location of generalized transition states for chemical reactions. One is due to Bunker and Pattengill; the other is due to Wong and Marcus. We prove that both provide upper bounds on the exact classical equilibrium rate constant. In addition, we show that for several‐dimensional systems both methods are exact at threshold, and in the limit of an infinite number of dimensions they agree with the variational theory of reactions of Wigner, Horiuti, and Keck. However, it is also shown that for a finite number of degrees of freedom both methods yield rate constants which are only as accurate as or less accurate than rate constants given by the variational theory of reactions. We note that, where tested by others for actual systems, the differences of the results obtained with the variational and Bunker–Pattengill criteria have been minor.

Variational transition state theory and tunneling for a heavy–light–heavy reaction using an ab initio potential energy surface. 37Cl+H(D) 35Cl→H(D) 37Cl+35Cl

Ab initio POL–CI calculations, augmented by a dispersion term, are used to predict the potential energy surface for the reaction Cl+HCl. The saddle point is found to be nonlinear. The surface is represented by a rotated‐Morse‐oscillator spline fit for collinear geometries plus an analytic bend potential. Variational transition state theory calculations, based on a linear reference path, are carried out, and they yield much smaller rate constants than conventional transition state theory, confirming that earlier similar results for this heavy–light–heavy mass combination were consequences of the small skew angle and were not artifacts of the more approximate potential energy surfaces used in those studies. Transmission coefficients are calculated using approximations valid for large‐reaction‐path curvature and the potential along the reference path is scaled so that the calculated rate constant agrees with experiment. The resulting surface is used to compute the H/D kinetic isotope effect which is in quali...

Vibrationally adiabatic models for reactive tunneling

The approximation of vibrational adiabaticity in curvilinear natural collision coordinates is investigated for tunneling in three‐atom collinear reactions. A validity criterion is derived which limits the adiabatic approximation to systems with small reaction‐path curvature. A general formalism is developed for systems which satisfy this criterion. A one‐dimensional Schrodinger equation is proposed which is sufficiently flexible so as to be adaptable to many different models of tunneling. We present three new methods for including reaction‐path curvature effects on multidimensional tunneling in reactive systems: a method based on a quantum mechanical vibrational average (VA) over degrees of freedom transverse to the minimum‐energy path; a method (called DA for dynamical‐path vibrational‐ average) that includes internal centrifugal effects in the description of the transverse vibrational motion (in this method the vibrational average is approximated as a quantal vibrational average about the dynamical path...

Semiclassical eigenvalues for nonseparable systems: Nonperturbative solution of the Hamilton–Jacobi equation in action‐angle variables

It is shown how the Hamilton–Jacobi equation for a multidimensional nonseparable system can be efficiently solved directly in action‐angle variables. This allows one to construct the total (classical) Hamiltonian as a function of the ’’good’’ action‐angle variables which are the complete set of constants of the motion of the system; requiring the action variables to be integers then provides the semiclassical eigenvalues. Numerical results are presented for a two‐dimensional potential well, and one sees that the semiclassical eigenvalues are in good agreement with the exact quantum mechanical values even for the case of large nonseparable coupling.

A least‐action variational method for calculating multidimensional tunneling probabilities for chemical reactions

We present a new method for calculating tunneling probabilities for chemical reactions with arbitrary curvature of the reaction path. The computational effort for obtaining a reaction probability at one energy consists of an integral over tunneling amplitudes for paths starting at various points on the reaction coordinate; for each point along the reaction coordinate, a one‐dimensional search is performed to find the optimal tunneling path starting at that point; and for each tunneling path, a one‐dimensional imaginary‐action integral is evaluated. The method is designed to be applicable and practical even for general polyatomic reactions where no other reliable approach is affordable. To ascertain the accuracy of the method we have applied it to a wide range of one‐ and three‐dimensional atom–diatom reactions on analytic potential energy surfaces for which accurate quantum mechanical rate constants are available. The accuracy, as compared to the accurate quantal calculations, is better than any previousl...

Photoelectron spectra of the hydrated iodine anion from molecular dynamics simulations

In this paper, we present the first calculations, based on molecular dynamics techniques, of vertical electron binding energies for the ionic clusters I−(H2O)n, (n=1–15). In these studies, we employ the polarizable water model developed recently by Dang [J. Chem. Phys. 97, 2659 (1992)]. We construct the ion–water potential so that the successive binding energies for the ionic clusters, the hydration enthalpy, and the structural properties of the aqueous ionic solution agree with the results obtained from experiments. The simulated vertical electron binding energies compare well with recent data from photoelectron spectroscopy experiments by Markovich, Giniger, Levin, and Cheshnovsky [J. Chem. Phys. 95, 9416 (1991)]. Interestingly, we obtain coordination numbers of 4 to 5 for the ionic clusters, I−(H2O)n, for n≥6. This result is smaller than the coordination number, based on the energetic properties predicted by Markovich et al. Possible reasons for this discrepancy are discussed in the paper. Furthermore,...

Generalized transition state theory calculations for the reactions D+H2 and H+D2 using an accurate potential energy surface: Explanation of the kinetic isotope effect

Rate constants are calculated for the reactions D+H2→DH+H and H+D2→HD+D and compared to measured values. An accurate potential energy surface, based on the ab initio calculations of Liu and Siegbahn, was used. Rates were calculated using both conventional transition state theory and canonical variational theory. In the former, the generalized transition state dividing surface is located at the saddle point; in the latter it is located to maximize the generalized free energy of activation. We show that, in the absence of tunneling corrections, locating the generalized‐transition‐state dividing surface variationally has an important quantitative effect on the predicted rate constants for these systems and that, when tunneling is included, most of the effect of using a better dividing surface can be included in conventional transition state theory for these systems by using a consistent transmission coefficient for quantal scattering by the vibrationally adiabatic potential energy curve. Tunneling effects ar...

The definition of reaction coordinates for reaction‐path dynamics

We present equations for generalized‐normal‐mode vibrational frequencies in reaction‐path calculations based on various sets of coordinates for describing the internal motions of the system in the vicinity of a reaction path. We consider two special cases in detail as examples, in particular three‐dimensional atom–diatom collisions with collinear steepest descent paths and reactions of the form CX3+YZ→CX3 Y+Z with reaction paths having C3v symmetry. We then present numerical comparisons of the differences in harmonic reaction‐path frequencies for various coordinate choices for three such systems, namely, H+H2→H2+H, O+H2→OH+H, and CH3+H2→CH4+H. We test the importance of the differences in the harmonic frequencies for dynamics calculations by using them to compute thermal rate constants using variational transition state theory with semiclassical ground‐state tunneling corrections. We present a new coordinate system for the reaction CH3+H2 that should allow for more accurate calculations than the Cartesian ...

Semiclassical transition state theory for nonseparable systems: Application to the collinear H+H2 reaction

Two different kinds of semiclassical approximations are used to evaluate a previously obtained quantum mechanical transition state theory rate expression. No assumptions, however, such as separability of the Hamiltonian, vibrationally adiabatic motion along a reaction coordinate, etc., are incorporated. Application is made to the collinear H+H2 reaction, and agreement with accurate quantum scattering calculations is found to be reasonably good. The results indicate that transition state theory—provided no assumptions of separability are included—is probably as accurate quantum mechanically as it has been found to be classically for describing the threshold of chemical reactions with an activation barrier.