Yi Ping Liu

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.

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.

VARIATIONAL TRANSITION-STATE THEORY AND SEMICLASSICAL TUNNELLING CALCULATIONS WITH INTERPOLATED CORRECTIONS : A NEW APPROACH TO INTERFACING ELECTRONIC STRUCTURE THEORY AND DYNAMICS FOR ORGANIC REACTIONS

In variational transition-state theory (VTST) and semiclassical tunnelling calculations, especially those with semiempirical potential-energy surfaces, it is sometimes desirable to match the classical energies and vibration frequencies of some points (e.g. the reactant, saddle point, product, van der Waals complex, ion–molecule complex) along the minimum-energy path (MEP) and in the reaction swath with high-level results, as this can improve the accuracy. This can be accomplished by adding a correction function to the calculated energies or frequencies. In this paper, we introduce a three-point or zero-order interpolated correction method which is based on the correction at three points, in particular the saddle point and two stationary points, one on each side of the MEP. We use the corrections at these points to build a correction function for the classical energy and for each vibrational mode frequency along the MEP. The function is calibrated such that the corrected result matches the accurate values at these stationary points. The functional forms to be used depend on the shape of the MEP under consideration and the relative correction values at those points. Similar treatments are applied to the determinant of the moment of inertia tensor along the reaction path and to the potential-energy function in non-adiabatic regions of corner-cutting tunnelling paths. Once parameters in the functional forms are determined, we then use the corrected energy, frequency and moments of inertia information together with other MEP and reaction swath data, as obtained directly from the potential-energy surface, to perform new VTST calculations. Details of the implementation are presented, and applications to reaction rate calculations of the OH + CH4→ H2O + CH3 and CF3+ CD3H → CF3H + CD3 reactions are included.

Validation of trajectory surface hopping methods against accurate quantum mechanical dynamics and semiclassical analysis of electronic-to-vibrational energy transfer

The validity of the quasiclassical trajectory surface hopping method is tested by comparison against accurate quantum dynamics calculations. Two versions of the method, one including electronic coherence between hops and one neglecting this effect, are applied to the electronically nonadiabatic quenching processes Na(3p)+H2(ν=0, j=0 or 2) → Na(3s)+H2(ν′,j′). They are found to agree well, not only for quenching probabilities and final-state distributions, but also for collision lifetimes and hopping statistics, demonstrating that electronic coherence is not important for this system. In general the accurate quantum dynamical calculations and both semiclassical surface hopping models agree well on the average, which lends credence to applications of semiclassical methods to provide insight into the mechanistic details of photochemical processes proceeding on coupled potential surfaces. In the second part of the paper the intimate details of the trajectories are analyzed to provide such insight for the prese...

Use of an improved ion–solvent potential‐energy function to calculate the reaction rate and α‐deuterium and microsolvation kinetic isotope effects for the gas‐phase SN2 reaction of Cl−(H2O) with CH3Cl

We present calculations of the rate constants and secondary kinetic isotope effects for the gas‐phase SN2 reaction Cl−(H2O)+CH3Cl based on a new chloride–water potential‐energy function that has been specifically converged for heavy‐water isotope effects. The results are compared to new calculations employing five chloride–water potential‐energy functions that have been developed for simulations of aqueous solutions. In all calculations the ClCH3Cl− solute intramolecular potential is taken from a previous semiglobal fit to ab initio calculations including electron correlation. We also examine two different intramolecular water potentials, and we examine the effect of treating the CH3 internal rotation at the ClCH3Cl−(H2O) transition state as a hindered rotation. Both the CH3/CD3 (α‐deuterium) and H2O/D2O (microsolvation) kinetic isotope effects are studied.

Quantum steam tables. Free energy calculations for H2O, D2O, H2S, and H2Se by adaptively optimized Monte Carlo Fourier path integrals

Converged quantum mechanical vibrational–rotational partition functions and free energies are calculated using realistic potential energy surfaces for several chalcogen dihydrides (H2O, D2O, H2S, H2Se) over a wide range of temperatures (600–4000 K). We employ an adaptively optimized Monte Carlo integration scheme for computing vibrational–rotational partition functions by the Fourier path‐integral method. The partition functions and free energies calculated in this way are compared to approximate calculations that assume the separation of vibrational motions from rotational motions. In the approximate calculations, rotations are treated as those of a classical rigid rotator, and vibrations are treated by perturbation theory methods or by the harmonic oscillator model. We find that the perturbation theory treatments yield molecular partition functions which agree closely overall (within ∼7%) with the fully coupled accurate calculations, and these treatments reduce the errors by about a factor of 2 compared...

MORATE 6.5: A new version of a computer program for direct dynamics calculations of chemical reaction rate constants

Abstract MORATE (Molecular Orbital RATE calculations) is a computer program for direct dynamics calculations of unimolecular and bimolecular rate constants of gas-phase chemical reactions involving atoms, diatoms, or polyatomic species. The dynamical methods used are conventional or variational transition state theory and multidimensional semiclassical approximations for tunneling and nonclassical reflection. 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 multidimensional semiclassical algorithms, including the small-curvature and large-curvature tunneling approximations and the microcanonical optimized multidimensional tunneling approximation. The computer program is a conventiently interfaced package consisting of the POLYRATE program, version 6.5, for dynamical rate constant calculations, and the MOPAC program, version 5.05mn, for semiempirical electronic structure computations. In single-level mode, the potential energies, gradients, and higher derivatives of the potential are computed whenever needed by electronic structure calculations employing semiempirical molecular orbital theory without the intermediary of a global or semiglobal fit. All semiempirical methods available in MOPAC, in particular MINDO/3, MNDO, AM1, and PM3, can be called on to calculate the potential, gradient, or Hessian, as required at various steps of the dynamics calculations, and, in addition, the code has flexible options for electronic structure calculations with neglect of diatomic differential overlap and specific reaction parameters (NDDO-SRP). In dual-level mode, MINDO/3, MNDO, AM1, PM3, or NDDO-SRP is used as a lower level to calculate the reaction path, and interpolated corrections to energies and frequencies are added; these corrections are based on higher-level data read from an external file.