Large-curvature Tunneling Research Articles

Predictions of rate constants and estimates for tunneling splittings of concerted proton transfer in small cyclic water clusters

We present transfer rates for the concerted hydrogen exchange in cyclic water clusters (H2O)n (n=3,4) based on ab initio hypersurfaces. The studied hydrogen exchange involves bond breaking and forming and is in contrast to flipping motions of “free” hydrogen atoms in a “chemical” reaction. The rates are calculated for gas-phase systems using canonical, variational transition state theory. Multidimensional tunneling corrections are included assuming both a small and a large reaction path curvature. Hybrid density functional theory [B3LYP/6-31+G(d)] was used to evaluate the potential energy hypersurface with interpolated corrections of second order perturbation theory [MP2/6-311++G(3pd,3df)] at the three stationary points for both systems. Large curvature tunneling corrections are included in dual-level direct ab initio dynamics for the cyclic tri- and tetramer of water. The ridge of the reaction swath serves as an estimate for the tunneling probability of various straight-line corner cutting paths. Our results suggest that the investigated species interconvert on a time scale of seconds. The ground-state tunneling splitting is proportional to the square root of the transition probability at the energy of the minima, which is available from the calculation of tunneling corrections. The associated tunneling splittings are estimated to be between 10−4 and 10−5 cm−1, which is close to the experimental resolution limit.

Theoretical Estimation of the Activation Energy for the Reaction HO• + H2O → H2O + •OH: Importance of Tunneling

Ab initio calculations for the potential barrier height for the symmetric H-atom exchange reaction HO• + H2O → H2O + •OH are reported. A value of 42.2 kJ mol-1 is found using the QCISD(T)/6-311+G(3df,2p) method. Multireference CISD calculations converge toward a similar value for the barrier provided that a Davidson correction is applied. The effect of quantum mechanical tunneling is investigated. Rate constants calculated by using conventional and small-curvature tunneling-corrected transition state theory with the UMP2/6-311G(d,p) transition structure and reaction path are compared for a wide range of temperatures. Tunneling reduces the Arrhenius activation energy, obtained from the temperature dependence of the calculated rate constants, by at least 20 kJ mol-1 at 300 K. The best theoretical estimate for the Arrhenius activation energy at 300 K is 21.2 kJ mol-1; the discrepancy between this and the experimental value of 17.6 ± 2 kJ mol-1 is likely to be due to neglect of large-curvature tunneling effects. The QCISD(T)/6-311+G(3df,2p) calculated enthalpy of association of HO• + H2O → HO•···HOH, the hydrogen-bonded precursor complex, is −8.9 kJ mol-1. The best theoretical estimate for the intrinsic barrier height for the symmetric H-atom exchange HO•···HOH → HOH···•OH is 25.1 kJ mol-1.

Dual-Level Direct Dynamics Calculations of Deuterium and Carbon-13 Kinetic Isotope Effects for the Reaction Cl + CH4

The kinetic isotope effects, KIEs, for hydrogen abstraction from the isotopologs CH4, 13CH4, CH3D, and CD4 by chlorine atoms have been studied by the dual-level direct dynamics approach with the MORATE computer program. Low-level calculations of the potential energy surface were carried out at the NDDO-SRP level (in particular the AM1-SRP level), using two different sets of specific reaction parameters labeled SRP4 and SRP13. High-level structural and energetic properties of the reactants, saddle point, and products were obtained at the MP2-SAC and MP2 levels using the 6-311G(2d,d,p) basis set and were used to interpolate corrections to the low-level calculations. The dual-level calculations were carried out using the ICL-Eckart improved interpolated corrections algorithm. Tunneling was included by the microcanonical optimized multidimensional tunneling (μOMT) method, and we find that large-curvature tunneling paths usually provide the dominant contribution, with significant participation of excited vibra...

ABCRATE: A program for the calculation of atom-diatom reaction rates

ABCRATE is a computer program for the calculation of atom-diatom chemical reaction rates for systems with collinear-dominated dynamics. The dynamical methods used are conventional or generalized transition state theory (GTST) and multidimensional semiclassical approximations for tunneling and nonclassical reflection. The GTST methods included in this version of the program are the canonical and improved canonical variational transition state theory (VTST) and the canonical unified statistical (CUS) method. Rate constants may be calculated for canonical ensembles or for specific vibrational states of selected modes with translational, rotational, and other vibrational modes treated thermally. The potential energy surface required by the program may be a global or semiglobal analytic function. The reaction path is calculated as the path of steepest descent in mass-scaled coordinates from a collinear saddle point, and vibrations transverse to the reaction path are treated by curvilinear internal coordinates. The vibrational modes are quantized, and anharmonicity may be included by various options, including the WKB approximation for bond stretches and the centrifugal oscillator approximation through quartic terms for the curvilinear bend coordinate. Tunneling probabilities are calculated by a variety of semiclassical methods, in particular zero-curvature tunneling (ZCT), small-curvature tunneling (SCT), large-curvature tunneling (LCT), least-action tunneling (LAT), and the microcanonical optimized multidimensional tunneling (μOMT) methods.

Large Curvature Tunneling Effects Reveal Concerted Hydrogen Exchange Rates in Cyclic Hydrogen Fluoride Clusters Comparable to Carboxylic Acid Dimers

Reaction rate constants for the concerted proton transfer in cyclic hydrogen fluoride clusters obtained by using a variational transition state theory approach with high-level data at three stationary points and with interpolated corrections based on semiempirical Hamiltonians specially parametrized for these systemsMP2/6-311++G(3df,3pd)///PM3-SRPare reported. For the first time multidimensional tunneling is included in the large curvature limit. The corresponding small curvature limit is benchmarked against higher level calculations. The ridge of the reaction swath is defined in a general way and serves together with an estimate of the barrier width as a validation of the potential energy hypersurfaces. Recent experimental and theoretical results concerning carboxylic acids, whose hypersurfaces are found to be very similar to those of the HF clusters, underline the relevancy of the investigated concerted proton exchange motion. A reaction rate constant k(300 K) = 2.86 × 109 s-1 is found for (HF)5, which is similar to carboxylic acid dimers, whose experimental k(300 K) lie near 1010 s-1.

A comparison of two methods for direct tunneling dynamics: Hydrogen exchange in the glycolate anion as a test case

Two methods for studying tunneling dynamics are compared, namely the instanton model and the approach of Truhlar and co-workers, which are based on the direct output of electronic structure calculations and thus are parameter free. They are employed to evaluate the zero-level tunneling splitting due to intramolecular hydrogen exchange in the glycolate anion. The first method was developed in a series of recent studies and presents a combination of the instanton theory with quantum-chemically computed potentials and force fields. For the compound at hand, which has 21 internal degrees of freedom, a complete potential-energy surface is generated in terms of the normal modes of the transition-state configuration. It is made up of the potential-energy curve along the tunneling coordinate and harmonic force fields at the stationary points. The level of theory used is HF/6–31++G**. All modes that are displaced between the equilibrium configuration and the transition state are linearly coupled to the tunneling mode, the couplings being proportional to the displacements in dimensionless units. These couplings affect the instanton trajectory profoundly and, depending on the symmetry of the skeletal modes, can enhance or suppress the tunneling. In the glycolate anion all modes have such displacements and thus are included in the calculation. Based on the similarity with malonaldehyde, it is argued that tunneling prevails in the studied process, and the zero-level tunneling splitting is predicted. The latter is found within the computational scheme developed earlier, which avoids explicit evaluation of the instanton path and thus greatly simpli-fies the tunneling dynamics. These results are tested by the method of large-curvature tunneling of Truhlar and co-workers implemented in a dual-level scheme. The potential energy surface needed for the dynamics calculations is generated at the semiempirical PM3 level of theory and then corrected by interpolation with high-level HF/6–31++G** results for the stationary points. The code corresponding to this approximation is in the package MORATE 6.5. The tunneling splittings found by the two approaches are in quantitative agreement. We have found that the computational scheme based on the instanton model is much less time consuming both in the static and dynamics part. This computational efficiency, also demonstrated in a number of earlier studies, merits future application of the method to fairly large systems of practical interest, such as clusters and organic compounds with excited-state proton transfer.

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

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.

Application of the large-curvature tunneling approximation to polyatomic molecules: Abstraction of H or D by methyl radical

The large-curvature semiclassical ground-state tunneling approximation, version 3 (abbreviated LCG3) has been implemented for variational transition state theory calculations on systems with more than three atoms. It is illustrated by applications to the hydrogen and deuterium atom transfer reactions of CH 3 with H 2, D 2, and HD and to a six-body model of the reaction of CH 3 with benzene to produce CH 4 and a phenyl radical.

Phenomenological manifestations of large-curvature tunneling in hydride-transfer reactions

An important consequence of recent dynamical theories of tunneling is that, because of large curvature of the reaction path in a typical H(+), or H(-) transfer, light-isotope transfer occurs in more extended nuclear frameworks than heavy-isotope transfer. This is now incorporated into the Marcus phenomenological theory relating reaction rate constants to equilibrium constants. It leads to Bronsted slope parameters that depend on the isotope transferred. The new theoretical formulation is tested on experimental data for hydride and deuteride transfer between nicotinamide adenine dinucleotide analogs and on computational data for hydrogen-atom and deuterium atom transfer between pseudo-atoms. The experimental kinetic isotope effects (KIE's) are shown to vary with reaction equilibrium constant (K/sub ij/) in a way that is quantitatively consistent with the theory. The critical configurations generated by the calculations vary from the saddle point and from each other in the way anticipated by the theory. However, the calculated KIE values are a rather scattered function of K/sub ij/, because the tunneling corrections are large and somewhat system specific. Overall, we believe that this combination of experimental and calculated results provides considerable support for the idea that large-curvature results provides considerable support for the idea that large-curvature tunneling needs to be more » considered in hydrogen transfer reactions. « less

Test of variational transition state theory with a large-curvature tunneling approximation against accurate quantal reaction probabilities and rate coefficients for three collinear reactions with large reaction-path curvature: Cl+HCl, Cl+DCl, and Cl+MuCl

The large-curvature ground-state model for the transmission coefficient of generalized transition state theory [presented in a previous paper by B. C. Garrett, D. G. Truhlar, A. F. Wagner, and T. H. Dunning, J. Chem. Phys. 78, 4400(1983)] is tested against accurate quantal calculations of the rate coefficients for collinear reactions with very large inertial effects, namely Cl+HCl→ClH+Cl, Cl+DCl→ClD+Cl, and Cl+MuCl→ClMu+Cl. The tests cover the temperature range 200–2400 K. The accurate rate calculations are based on reaction probabilities obtained by a new numerical method for solving Schrödinger’s equation in Delves’ coordinates. Improved canonical variational transition state theory predicts rate coefficients 5.0–18 times smaller than those predicted by conventional transition state theory for the H transfer; for the D transfer, the ratio is 2.0–3.4; and for Mu it is 22–2.8×107. The large-curvature model predicts transmission coefficients as large as 41, 8, and 206 for the H, D, and Mu-transfer cases at 200 K, decreasing to 1.2, 1.1, and 1.4 at 2400 K. Despite the large effect of variationally optimizing the transition state location and the large size of the tunneling effect and the wide variation of both effects with temperature, improved canonical variational transition state theory with large-curvature ground-state transmission coefficients (ICVT/LCG) is accurate within a factor of 1.7 over a temperature range of a factor of 8, 300–2400 K, for all three reactions. At 200 K, the ICVT/LCG model underestimates the rate coefficients, by factors of 2.3, 1.9, and 1.5 for H, D, and Mu, respectively.