Alan D. Isaacson

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.

Polyatomic canonical variational theory for chemical reaction rates. Separable‐mode formalism with application to OH+H2→H2O+H

A formalism for the application of variational transition‐state theory and semiclassical vibrationally adiabatic transmission coefficients to bimolecular reactions involving an arbitrary number of atoms is presented. This generalizes previous work on atom–diatom reactions. We make applications in this paper to the reactions OH+H2→H2O+H and OH+D2→HDO+D using the Schatz–Elgersma fit to the Walch–Dunning ab initio potential energy surface. For both reactions we find large differences between conventional and variational transition‐state theory and large effects of anharmonicity on the calculated rate constants. The effect of reaction‐path curvature on the calculated transmission coefficients and rate constants is also large. The final calculated values of the kinetic isotope effects are in good agreement with experiment at high temperature but too large at room temperature.

Statistical‐diabatic model for state‐selected reaction rates. Theory and application of vibrational‐mode correlation analysis to OH(nOH)+H2(nHH)→H2O+H

The state‐selected reaction rates OH(nOH = 0,1)+ H2(nHH = 0,1)→H2O+H are calculated by an extension of variational transiton state theory. The reactant vibrational modes are assumed to correlate diabatically with generalized normal modes of a generalized activated complex. Using the Walch‐Dunning‐Schatz‐Elgersma ab initio potential energy surface, the theory predicts that excitation of H2 is 19–68 times more effective than excitation of OH in promoting reaction at 300 K, where the range of values corresponds to different possible assumptions about the quantal effects on reaction‐coordinate motion. These values are in much better agreement with the experimental value (about 100) than is a calculation based on the conventional transition state, which yields 2×104.

Simple perturbation theory estimates of equilibrium constants from force fields

We propose and test a very simple method for calculating equilibrium constants from quartic force fields.

Tests of approximation schemes for vibrational energy levels and partition functions for triatomics: H2O and SO2

Various approximate schemes are used to obtain vibrational energy levels and partition functions for H2O and SO2. These results are then compared with accurate quantum mechanical values computed for the same original quartic force fields. The neglect of interaction force constants in internal coordinates and the use of a Morse model to describe stretching anharmonicity are both shown to provide reasonably accurate perturbation theory energy levels and partition functions, while the neglect of interaction force constants in normal coordinates is found to yield much less accurate results. In addition, the method of Pitzer and Gwinn to calculate partition functions without first calculating energy levels is shown to provide a good approximation to the accurate partition functions.

MORATE: a program for direct dynamics calculations of chemical reaction rates by semiempirical molecular orbital theory

Abstract We present a computer program, MORATE (Molecular Orbital RATE calculations), for direct dynamics calculations of unimolecular and bimolecular rate constants of gas-phase chemical reactions involving atoms, diatoms, or polyatomic species. The potential energies, gradients, and higher derivatives of the potential are calculated whenever needed by semiempirical molecular orbital theory without the intermediary of a global or semiglobal fit. The dynamical methods used are conventional or variational transition state theory and multidimensional semiclassical approximations for tunneling and nonclassical reflection. The computer program is conveniently interfaced package consisting of the POLYRATE program, version 4.5.1, for dynamical rate calculations, and the MOPAC program, version 5.03, for semiempirical electronic structure computations. All semiempirical methods available in MOPAC, in particular MINDO/3, MNDO, AM1, and PM3, can be called on to calculate the potential and gradient. Higher derivatives of the potential are obtained by numerical derivatives of the gradient. Variational transition states are found by a one-dimensional search of generalized-transition-state dividing surfaces perpendicular to the minimum-energy path, and tunneling probabilities are evaluated by numerical quadrature.

General method for removing resonance singularities in quantum mechanical perturbation theory

This paper presents a way of improving second‐order perturbation theory calculations by summing contributions of uncoupled excitations to infinite order. For problems involving molecular vibrations, the new theory is shown to give similar results to conventional second‐order perturbation theory when the system treated has no near resonances but also to give accurate and stable results even very close to resonance. The new theory is tested by comparison to converged variational calculations for vibrational energy levels of formaldehyde, formaldehyde‐d2, and two two‐dimensional model subsystems based on formaldehyde.

POLYRATE: a general computer program for variational transition state theory and semiclassical tunneling calculations of chemical reaction rates

Abstract We present a computer program for calculating rate constants of gas-phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction pathe and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.

Harmonic and anharmonic rate constants and transmission coefficients obtained from ab initio data

Recent ab initio information of Kraka and Dunning on the reaction OH+H2→H2O+H is used to construct a potential energy surface in the vicinity of the reaction path. The resultant energy surface reproduces the ab initio reactant and product properties and provides a good fit to the ab initio data in the interaction region. Anharmonic vibrational energy levels involving the bound degrees of freedom orthogonal to the reaction coordinate are obtained using perturbation theory through second order for cubic terms and first order for quartic terms, with resonance effects removed. These energy levels are used in the calculation of transmission coefficients and thermal rate constants over the temperature range from 200 to 2400 K. The results are compared with those obtained from harmonic vibrational energy levels.

The accuracy of the Pitzer–Gwinn method for partition functions of anharmonic vibrational modes

The Pitzer–Gwinn method is applied to calculate partition functions at 200–4000 K for 26 potential energy curves exhibiting various types and degrees of anaharmonicity. This method, when combined with a simple approximation to estimate the zero point energy, yields reasonably reliable results for all cases studied.