Aron Kuppermann

Quantum mechanical reactive scattering for three‐dimensional atom plus diatom systems. I. Theory

A method is presented for accurately solving the Schrodinger equation for the reactive collision of an atom with a diatomic molecule in three dimensions on a single Born–Oppenheimer potential energy surface. The Schrodinger equation is first expressed in body‐fixed coordinates. The wavefunction is then expanded in a set of vibration–rotation functions, and the resulting coupled equations are integrated in each of the three arrangement channel regions to generate primitive solutions. Next, these are smoothly matched to each other on three matching surfaces which appropriately separate the arrangement channel regions. The resulting matched solutions are linearly combined to generate wavefunctions which satisfy the reactance and scattering matrix boundary conditions, from which the corresponding R and S matrices are obtained. The scattering amplitudes in the helicity representation are easily calculated from the body fixed S matrices, and from these scattering amplitudes several types of differential and int...

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.

Exact quantum, quasiclassical, and semiclassical reaction probabilities for the collinear F+H2 → FH+H reaction

Exact quantum, quasiclassical, and semiclassical reaction probabilities and rate constants for the collinear reaction F+D_2 → FD+D are presented. In all calculations, a high degree of population inversion is predicted with P^R_(03) and P^R(04) being the dominant reaction probabilities. In analogy with the F+H_2 reaction (preceding paper), the exact quantum 0→3 and 0→4 probabilities show markedly different energy dependence with PR03 having a much smaller effective threshold energy (E_T=0.014 eV) than P^R_(04) (0.055 eV). The corresponding quasiclassical forward probabilities P^R_(03) and P^R_(04) are in poor agreement with the exact quantum ones, while their quasiclassical reverse and semiclassical counterparts provide much better approximations to the exact results. Similar comparisons are also made in the analysis of the corresponding EQ, QCF, QCR, and USC rate constants. An information theoretic analysis of the EQ and QCF reaction probabilities indicates nonlinear surprisal behavior as well as a significant isotope dependence. Additional quantum results at higher energies are presented and discussed in terms of threshold behavior and resonances. Exact quantum reaction probabilities for the related F+HD → FH+D and F+DH → FD+H reactions are given and an attempt to explain the observed isotope effects is made.

Hyperspherical coordinates in quantum mechanical collinear reactive scattering

A new hyperspherical coordinate method for performing atom—diatom quantum mechanical collinear reactive scattering calculations is described. The method is applicable at energies for which breakup channels are open. Comparison with previous results and new results at high energies for H H2 are given. The usefulness of this approach is discussed.

Three-dimensional quantum mechanical reactive scattering using symmetrized hyperspherical coordinates

We report here the first three-dimensional (3D) reactive scattering calculations using symmetrized hyper-spherical coordinates (SHC). They show that the 3D local hyper-spherical surface function basis set leads to a very efficient computational scheme which should permit accurate reactive scattering calculations to be performed for a significantly large number of systems than has heretofore been possible.

Quantum mechanical reactive scattering: An accurate three‐dimensional calculation

Accurate three–dimensional (3–D) quantum–mechanical calculations of differential and total cross sections for the H + H2 exchange reaction on the Porter and Karplus potential energy surface have been performed. These are the first such calculations which are vibrationally and rotationally converged, and the results are believed to be accurate to 5% or better. They can serve as a comparison standard against which approximate methods can be tested.

A useful mapping of triatomic potential energy surfaces

Abstract We present in this paper a mapping of triatomic three-dimensional Born-Oppenheimer potential energy surfaces V for which all arrangement channels are represented evenhandedly. This representation is very useful for visualizing the geometrical and dynamical properties of such surfaces.

Large quantum effects in the collinear F + H2 → FH + H reaction

We have performed accurate quantum mechanical calculations of reaction probabilities for the collinear F+H2-->FH+H reaction as well as corresponding quasiclassical trajectory calculations. A comparison of these results shows that very significant quantum mechanical effects are present in this reaction.

The geometric phase effect shows up in chemical reactions

Abstract The persistent differences between the rotational state distribution measurements of Kliner, Adelman and Zare (J. Chem. Phys. 95, (1991) 1648) for the D + H 2 reaction and theory are shown to be almost entirely the result of the geometric phase effect. This effect is due to a conical intersection between the two lowest electronically adiabatic potential energy surfaces of this system. Using accurate quantum scattering calculations, we have identified it for the first time in a chemical reaction studied experimentally. Predictions of additional large dynamical effects are also made. This phase is apt to be important for many other systems displaying conical intersections.

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).