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Projection operator techniques for enforcing bond‐distance and bond‐angle constraints in reaction‐path dynamics calculations are presented. These techniques provide a systematic method for carrying out reduced‐dimensionality calculations in generalized normal mode coordinates with constrained values for selected internal coordinates. The methods are illustrated with generalized transition‐state theory and multidimensional semiclassical tunneling calculations for the reactions OH+H2→H2O+H and CH3+H2→CH4+H in which one or more bond lengths and/or bond angles is held fixed.

We have calculated the kinetic isotope effect of the reaction CF{sub 3} + CD{sub 3}H by a semiclassical method that gives insight into tunneling paths for hydrogen atom transfer. In particular, tunneling is treated by a new optimized multidimensional semiclassical method which is valid even for large curvature of the reaction path, and should have wide applicability. The method used in the dynamics calculations is variational transition state theory with ground-state transmission coefficients. The torsional vibrational mode of the transition state is treated as a hindered internal rotation. The calculations are made practical for a system with 27 degrees of freedom by employing the direct dynamics approach, i.e., the force field necessary for the dynamics calculations is evaluated `on the fly` by using the neglect of diatomic differential overlap (NDDO) molecular orbital theory with semiempirical specific-reaction parameters (SRP), which are based on the standard AM1 parametrization adjusted to improve the agreement between experiment and the calculated quantities such as the vibrational frequencies of reactants and products and the classical barrier height. The kinetic isotope effects are calculated by using two SRP force fields, and they are in good agreement with the experimental measurements. The picture of the corner cutting tunnelingmore » process that emerges is discussed graphically. 88 refs., 10 figs., 9 tabs.« less

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.

The primary kinetic isotope effect for the sigmatropic rearrangement reaction of cis-1,3-pentadiene is studied by the direct dynamics method. The calculations are carried out with the computer code MORATE, which combines the semiempirical molecular orbital package, MOPAC, and the polyatomic dynamics code, POLYRATE, developed previously by the authors' research group. Dynamics calculations are based on canonical variational transition-state theory including multidimensional tunneling corrections. The force field is obtained by molecular orbital theory with the AM1, PM3, and MINDO/3 parameterizations. The kinetic isotope effects calculated with the MINDO/3 and PM3 Hamiltonians agree with those calculated by AM1 within 13%, and the latter agree with experiment within 13%. The tunneling contributions to the kinetic isotope effects are analyzed, and the nature of the vibrationally assisted tunneling process is discussed. General features of the dynamics from all three parameterizations are similar, and the quantitative differences in the predictions of the three calculations can be understood in terms of global characteristics of the potential energy functions that they predict. 41 refs., 8 figs., 6 tabs.

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.

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.

A new approach is presented for performing geometry optimization for stationary points on potential energy hypersurfaces with equality constrainst on the internal coordinates of a polyatomic system. The working equations are the same as for unconstrained Newton-Raphson optimization in Cartesian coordinates except that projection operators are applied to the gradient and Hessian to enforce the constraints. Two reactive systems with different kinds of constraints are treated as examples

Classical trajectory simulations are used to study the intramolecular dynamics of isolated CF3H and the CF3H(H2O)3 cluster, by either exciting the CH stretch local mode to then=6 level or by adding an equivalent amount of energy to an OH stretch normal mode. Energy transfer from the CH local mode is statistically the same for CF3H(H2O)3 as for isolated CF3H, and agrees with previous experimental studies. Clusters excited with 6 quanta in the CH local mode are remarkably stable. Though the CF3H-(H2O)3 intermolecular potential is only 1.5 kcal/mol, only 1 of 26 clusters excited with 6 quanta in the CH local mode dissociate within 10 ps. The absorption linewidth for the CH local mode in CF3H(H2O)3 is related to IVR within CF3H and not to the unimolecular lifetime of the cluster. When an OH stretch normal mode of the cluster is excited, energy transfer to CF3H is negligible and nearly one half of the clusters dissociate within 10 ps.

Variational Transition state theory calculations with semiclassical transmission coefficients have been carried out for a prototype case of α-deuterium secondary kinetic isotope effects (KIEs) in a reaction involving the transformation of an sp 3 carbon to sp 2 , in particular for the reactions of CH 4 and CD 3 H with H and D. We also study the KIE for the reverse direction and for the reactions of CH 4 and CD 3 H with D. We find that the variational transition states lead to significantly different nontunneling KIEs than the conventional ones, e.g., 1.22 vs. 1.07, and the inclusion of multidimensional tunneling effects increases the discrepancy even more. The origins of these variational and tunneling effects are examined in detail in terms of structures, vibrational frequencies, and the curvature of the reaction path. The conclusions have wide implications for the validity of conventional treatments of kinetic isotope effects

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.

Molecules with isolated compound state resonances decompose with state specific unimolecular rate constants. In some cases, this state specificity can also be identified as mode specific decomposition. Mode specificity means there are exceptionally large or small state specific rate constants depending on which internal modes are excited in forming the resonance state. The ability to establish the modes excited requires that the energies, for resonance states yielding mode specific behavior, can be predicted by finding patterns in the positions of these states in the spectrum. Such patterns allow a zero-order Hamiltonian and basis set to be used to assign quantum numbers to the resonances and to define the type of mode specificity. A situation contrary to one where all the resonance states exhibit mode specificity is statistical state specificity. For this case there are no patterns in the positions of the resonances in the spectrum, so that all the resonance states are intrinsically unassignable. Small and large fluctuations of the state specific rate constants are simply random occurrences, and cannot be associated with any pattern. Statistical inaccuracies make it difficult to identify mode specificity from a distribution of nearest neighbor energy levels. For all types of state specificity (including mode specificity and statistical state specificity), a microcanonical ensemble of compound state resonances will usually not decay exponentially. However, a corresponding result is often not obtained by classical mechanical simulations. The nonexponential decay of a microcanonical ensemble of resonance states results in monoenergetic chemical activation and thermal Lindemann-Hinshelwood rate constants which deviate from those of RRKM theory.

The classical mechanics of intramolecular relaxation of benzene CH(D) local mode overtone states is studied with the molecular models HC3, DC3, and H3C3. These reduced dimensionality models provide one means to correct for the improper classical mechanical treatment of zero‐point motion in complete benzene models. They give significantly smaller homogeneous linewidths for the low energy CH(D) overtones than found from previous classical trajectory calculations for C6H6/C6D6 models. The n=3 and 5 linewidths for the DC3 model are less than 1 cm−1, while for the HC3 and H3C3 models these linewidths are approximately 5–10 cm−1. The energy transfer pathways for the deuterated and nondeuterated models are substantially different. A gradation of couplings are observed from the trajectories. For the low energy HC3/H3C3 overtones a CCH bend is initially the mode most strongly coupled to the excited CH bond, while for the higher overtones it is the B1 CC stretch. In the relaxation of the H3C3 overtones, five modes ...

Different distribution functions are used to describe fluctuations in state‐specific unimolecular rate constants, for states which lie within a narrow energy interval. The effect of these distributions on the reactant population vs time N(τ,E) and the time‐dependent unimolecular rate constant k(τ,E) are considered. Comparisons are made with the exponential decay predicts by RRKM (Rice–Ramsperger–Kassel–Marcus) theory of unimolecular kinetics. The collision‐averaged unimolecular rate constant k(ω,E) is also determined for each of the distributions of state‐specific unimolecular rate constants. Overall, k(ω,E) is found to be relatively insensitive to fluctuations in state‐specific unimolecular rate constants.

Zero‐point energy excitation has a profound effect on the relaxation of benzene CH and CD overtone states. Only adding a fraction of the zero‐point energy for each normal mode in the initial conditions results in smaller overtone relaxation rates. If no zero‐point energy is added to C6H6, the n=3 and 5 CH overtones do not relax within 1 ps. Adding zero‐point energy to different types of normal modes has nonequivalent effects on overtone relaxation. Zero‐point excitation of modes with HCC bend character is particularly effective in enhancing relaxation of the overtones.

A benzene fragment HC3/DC3 is used as a model for benzene in a quasiclassical trajectory study of the intramolecular decay of the n=3 overtone. The calculated linewidth (fwhm) for the CH overtone is ≈ 4 cm−1 and that for CD

Quasiclassical trajectory calculations have been performed to study intramolecular vibrational energy redistribution (IVR) from CH overtone states in benzene. The rate and extent of this redistribution is sensitive to details of the potential energy surface. A particularly important potential energy surface property is attenuation of the HCC bending frequency upon CH stretch excitation. This property gives rise to non‐irreversible IVR when the CH stretch is highly excited. An analog to quantum beats is observed in phase averaged quasiclassical trajectories.

Quasiclassical trajectory calculations have been performed to study intramolecular vibrational energy redistribution (IVR) from CH overtone states in benzene. The rate and extent of this redistribution is sensitive to details of the potential energy surface. A particularly important potential energy surface property is attenuation of the HCC bending frequency upon CH stretch excitation. This property gives rise to non‐irreversible IVR when the CH stretch is highly excited. An analog to quantum beats is observed in phase averaged quasiclassical trajectories.