Quantum Mechanics of the H+H2 Reaction: Exact Scattering Probabilities for Collinear Collisions

The H + H2 reaction is very important in theoretical chemical dynamics (1-4). A model that is often used to study this reaction is to restrict the atoms to lie on a nonrotating line throughout the collision and to consider that the system is electronically adiabatic, i.e., it remains the lowest electronic state throughout the collision. This reduces the problem to scattering of three particles on a potential energy surface which is a function of two linearly independent coordinates. This model has been studied classically (5-8), and Mortensen and Pitzer (9) have calculated exact quantum mechanical reaction probabilities at five relative translational energies E0. In this Communication, we present some results of our more extensive exact calculations on this model of the H + H2 reaction and show their consequences for the validity of approximate theories of chemical reactions. For the cases considered here, the assumption of electronic adiabaticity causes very little error (10)

Test of variational transition state theory against accurate quantal results for a reaction with very large reaction-path curvature and a low barrier

We present three sets of calculations for the thermal rate constants of the collinear reaction I+HI-->IH+I: accurate quantum mechanics, conventional transition state theory (TST), and variational transition state theory (VTST). This reaction differs from previous test cases in that it has very large reaction-path curvature but hardly any tunneling. TST overestimates the accurate results by factors of 2×10^10, 2×10^4, 57, and 19 at 40, 100, 300, and 1000 K, respectively. At these same four temperatures the ratios of the VTST results to the accurate quantal ones are 0.3, 0.8, 1.1, and 1.4, respectively. We conclude that the variational transition states are meaningful, even though they are computed from a reaction-path Hamiltonian with large curvature, which is the most questionable case

Army ants algorithm for rare event sampling of delocalized nonadiabatic transitions by trajectory surface hopping and the estimation of sampling errors by the bootstrap method

The most widely used algorithm for Monte Carlo sampling of electronic transitions in trajectory surface hopping (TSH) calculations is the so-called anteater algorithm, which is inefficient for sampling low-probability nonadiabatic events. We present a new sampling scheme (called the army ants algorithm) for carrying out TSH calculations that is applicable to systems with any strength of coupling. The army ants algorithm is a form of rare event sampling whose efficiency is controlled by an input parameter. By choosing a suitable value of the input parameter the army ants algorithm can be reduced to the anteater algorithm (which is efficient for strongly coupled cases), and by optimizing the parameter the army ants algorithm may be efficiently applied to systems with low-probability events. To demonstrate the efficiency of the army ants algorithm, we performed atom–diatom scattering calculations on a model system involving weakly coupled electronic states. Fully converged quantum mechanical calculations were performed, and the probabilities for nonadiabatic reaction and nonreactive deexcitation (quenching) were found to be on the order of 10^–8. For such low-probability events the anteater sampling scheme requires a large number of trajectories (~10^10) to obtain good statistics and converged semiclassical results. In contrast by using the new army ants algorithm converged results were obtained by running 10^5 trajectories. Furthermore, the results were found to be in excellent agreement with the quantum mechanical results. Sampling errors were estimated using the bootstrap method, which is validated for use with the army ants algorithm

The quantum dynamics of electronically nonadiabatic chemical reactions

Considerable progress was achieved on the quantum mechanical treatment of electronically nonadiabatic collisions involving energy transfer and chemical reaction in the collision of an electronically excited atom with a molecule. In the first step, a new diabatic representation for the coupled potential energy surfaces was created. A two-state diabatic representation was developed which was designed to realistically reproduce the two lowest adiabatic states of the valence bond model and also to have the following three desirable features: (1) it is more economical to evaluate; (2) it is more portable; and (3) all spline fits are replaced by analytic functions. The new representation consists of a set of two coupled diabatic potential energy surfaces plus a coupling surface. It is suitable for dynamics calculations on both the electronic quenching and reaction processes in collisions of Na(3p2p) with H2. The new two-state representation was obtained by a three-step process from a modified eight-state diatomics-in-molecules (DIM) representation of Blais. The second step required the development of new dynamical methods. A formalism was developed for treating reactions with very general basis functions including electronically excited states. Our formalism is based on the generalized Newton, scattered wave, and outgoing wave variational principles that were used previously for reactive collisions on a single potential energy surface, and it incorporates three new features: (1) the basis functions include electronic degrees of freedom, as required to treat reactions involving electronic excitation and two or more coupled potential energy surfaces; (2) the primitive electronic basis is assumed to be diabatic, and it is not assumed that it diagonalizes the electronic Hamiltonian even asymptotically; and (3) contracted basis functions for vibrational-rotational-orbital degrees of freedom are included in a very general way, similar to previous prescriptions for locally adiabatic functions in various quantum scattering algorithms

Exact and Approximate Quantum Mechanical Reaction Probabilities and Rate Constants for the Collinear H + H2 Reaction

We present numerical quantum mechanical scattering calculations for the collinear H+H2 reaction on a realistic potential energy surface with an 0.424 eV (9.8 kcal) potential energy barrier. The reaction probabilities and rate constants are believed to be accurate to within 2% or better. The calculations are used to test the approximate theories of chemical dynamics. The reaction probabilities for ground vibrational state reagents agree well with the vibrationally adiabatic theory for energies below the lowest threshold for vibrational excitation, except when the reaction probability is less than about 0.1. For these low reaction probabilities no simple one-mathematical dimensional theory gives accurate results. These low reaction probabilities occur at low energy and are important for thermal reactions at low temperatures. Thus, transition state theory is very inaccurate at these low temperatures. However, it is accurate within 40% in the higher temperature range 450–1250°K. The reaction probabilities for hot atom collisions of ground vibrational state reagents with translational energies in the range 0.58 to 0.95 eV agree qualitatively with the predictions of the statistical phase space theory. For vibrationally excited reagents the vibrational adiabatic theory is not accurate as for ground vibrational state reagents. The lowest translational energy of vibrationally excited reagents above which statistical behavior manifests itself is less than 1.0 eV

Computational chemistry

Computational chemistry has come of age. With significant strides in computer hardware and software over the last few decades, computational chemistry has achieved full partnership with theory and experiment as a tool for understanding and predicting the behavior of a broad range of chemical, physical, and biological phenomena. The Nobel Prize award to John Pople and Walter Kohn in 1998 highlighted the importance of these advances in computational chemistry. With massively parallel computers capable of peak performance of several teraflops already on the scene and with the development of parallel software for efficient exploitation of these high-end computers, we can anticipate that computational chemistry will continue to change the scientific landscape throughout the coming century. The impact of these advances will be broad and encompassing, because chemistry is so central to the myriad of advances we anticipate in areas such as materials design, biological sciences, and chemical manufacturing