Michael J. Redmon

Quantum resonance structure in the three-dimensional F + H2 reaction

Abstract Evidence for a quantum resonance in the three-dimensional F + H 2 ( v = 0, i = 0) → FH( v = 2, all i ) + H reaction is presented. Relative to the collinear reaction, this resonance is much broader and is shifted by about 0.1 eV to higher energies. This resonance has not been predicted in previous quasiclassical trajectory computations, or in approximate quantum calculations.

Quantum dynamics of the F+H2 reaction: Resonance models, and energy and flux distributions in the transition state

Theoretical analysis is provided of quantum collinear scattering calculations on the F+H2 reaction. Modeling the 0→2 and 0→3 reaction probability curves by altering the vibrational energy correlation diagram illustrates the significance and necessity of wells in the v=2 and v=3 potential curves. Variation of the average vibrational energy and vibrational entropy in the interaction region clarifies the function of temporarily populated high lying vibrational levels during the reaction. Maps showing the probability density, flux, and phase of the scattering wavefunction clearly depict the quantum nature of the reaction dynamics. The vibrational entropy and average vibrational energy increase dramatically in the region of the potential surface where multipole quantum whirlpools are formed.

POLYRATE: a general computer program for variational transition state theory and semiclassical tunneling calculations of chemical reaction rates

Abstract We present a computer program for calculating rate constants of gas-phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction pathe and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.

Global potential energy hypersurface for dynamical studies of energy transfer in HF--HF collisions

The interaction energy of two HF molecules at 1332 individual points has been calculated with Moeller–Plesset (many–body) perturbation theory at the MP4‐SDTQ level using a 6‐311G** basis set. 293 of the points correspond to stretching of one HF molecule from its equilibrium geometry. No attempt was made to use a sufficiently fine grid to accurately describe the well region corresponding to hydrogen bonding. However, the location and minimum energy are consistent with experiment and other accurate theoretical results. An extensive global fit (rms error of 1 kcal/mol) is reported of 1319 points (below 10 eV of potential energy) using a modified London potential with corrections obtained using polynomials through four‐body interactions. A model electrostatic potential represents the long‐range interaction. In addition, the use of an expansion in products of three Legendre functions is discussed. It is shown that the latter approach, although accurately fitting the ab initio data, has difficulties interpolati...

Ab initio treatment of electronically inelastic K+H collisions using a direct integration method for the solution of the coupled‐channel scattering equations in electronically adiabatic representations

We calculate the adiabatic potential energy curves and nonadiabatic first‐derivative couplings for the X, A, and C 1Σ+ states of KH by an ab initio one‐electron pseudopotential formalism. The splitting of the X and A curves at the avoided crossing is in good agreement with experiment. The ab initio results are used to calculate the electronically inelastic transition probabilities and cross sections for K+H collisions at low energies by R matrix propagation in the adiabatic representation with exponential sector transformations. Since this method has never been applied before, we made an extensive study of its convergence properties and efficiency. We found it to be a convenient, accurate, and efficient method. The cross sections are changed by about a factor of two when the potential curves are changed by a different treatment of the KH+ core, but only by about 1% when the assumptions about the nonadiabatic second‐derivative coupling terms are altered. Our estimate of the 42P→ 42S quenching cross section...

Quantum-mechanical differential reaction cross sections for the F + H2(ν = 0) - FH(ν′= 2.3) + H reaction☆

Abstract Velocity scatterring angle intensity maps for the F + H2(ν = 0): j = 0)

Theoretical studies of vibrational excitation in collisions of O(3P) with H2O(1A1)

FH(ν′ = 2, 3: j′) + 11 reaction are predicted from quantum-mechanical J conserving, calculations. The extent of the shift in the angular distribution from backscattering at 1.8 kcal/mole to sideways scattering (intensity peak at 100°) at 3.0 kcal/mole is in quantitative agreement with recent crossed molecular beans experiments.

Quantum dynamics of the three‐dimensional F+H2 reaction. II. Scattering wave function density and flux analysis

The quasiclassical trajectory method is used to calculate cross sections for vibrational excitation in O(3P)+H2O(000) collisions. The potential surface is a Sorbie–Murrell fit to the ab initio MBPT calculation of Bartlett and Purvis. State‐to‐state transition probabilities are evaluated using the histogram method to discretize the H2O good action variables obtained from a classical perturbative treatment of the molecular Hamilton–Jacobi equation. Integral cross sections are presented for all one‐quantum excitations [(010), (100), and (001)] plus some multiquantum excitations. Rotational distributions for each final vibrational state indicate that significant rotational excitation accompanies vibrational excitation. The angular distributions for vibrationally excited final states indicate sidewards peaking. The resulting (001) cross section is in reasonable agreement with experimental shock tube results. The analogous (010) excitation cross section is larger than the corresponding experimental value. Altho...

Quantum dynamics of the three‐dimensional F+H2 reaction. I. Energy partitioning and entropy analysis in the collision complex

Further analysis of the quantum dynamics of the three‐dimensional F+H2→FH+H reaction for total angular momentum J=0 focuses on the properties of the total scattering wave function. After assembling the scattering wave function (as outlined in the previous paper), we study throughout the interaction region the wave function probability density and flux. In order to present 3D figures, two different 2D projections of the wave function are utilized—constant s planes and constant m planes. Salient topological features are noted and compared at system energies below, on, and above the 0.36 eV resonance. Quantum whirlpools (which are quite sensitive to the total energy) are located in the reactant and product valleys.

Collisional Excitation of H2O by O-Atom Impact: Classical Dynamics on an Accurate Ab Initio Potential Energy Surface

Analysis is presented of the quantum dynamics of the three‐dimensional F+H2→FH+H reaction for total angular momentum J=0. First, the method (coordinates, Hamiltonian, basis sets, close‐coupling method, and boundary conditions) of solving the Schrodinger equation is reviewed, with emphasis on numerical construction of the scattering wave function in the region of the collision complex. Then, four types of analysis of the collision complex are presented: (1) translational wave functions for the dynamically significant channels, (2) vibration‐rotation energy partitioning, (3) vibration‐rotation entropies, (4) variation with position along the reaction coordinate of the total scattering wave function density. Emphasis is placed upon variations in these quantities as the system passes through a quantum resonance (near total energy 0.36 eV). In paper II of this series, the total scattering wave function density and flux are analyzed in the region of the collision complex.