Gregory A. Parker

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. IV : Discrete variable representation (DVR) basis functions and the analysis of accurate results for F+H2

Accurate 3D coupled channel calculations for total angular momentum J=0 for the reaction F+H2→HF+H using a realistic potential energy surface are analyzed. The reactive scattering is formulated using the hyperspherical (APH) coordinates of Pack and Parker. The adiabatic basis functions are generated quite efficiently using the discrete variable representation method. Reaction probabilities for relative collision energies of up to 17.4 kcal/mol are presented. To aid in the interpretation of the resonances and quantum structure observed in the calculated reaction probabilities, we analyze the phases of the S matrix transition elements, Argand diagrams, time delays and eigenlifetimes of the collision lifetime matrix. Collinear (1D) and reduced dimensional 3D bending corrected rotating linear model (BCRLM) calculations are presented and compared with the accurate 3D calculations.

Accurate three-dimensional quantum probabilities and collision lifetimes of the H+O2 combustion reaction

Accurate 3D quantum state‐to‐state reaction probabilities and collision lifetimes for the H+O2→OH+O combustion reaction for total angular momentum J=0 are reported. The reaction probabilities are dominated by resonances, many of which overlap. The total reaction probability is not enhanced by vibrational or rotational excitation of the reactants. The first accurate final state distributions are presented, and probability is found to spread out into all open product vibrational and rotational channels, with a rather strong tendency to produce highly excited product rotational states. The first calculated collision lifetimes are presented, and resonances with lifetimes of 1–10 ps are found at most energies. Whether the reaction behaves statistically is discussed, and future extensions needed are also discussed.

The discrete variable–finite basis approach to quantum scattering

A discrete variable representation for scattering problems is developed. In this representation the potential matrix is diagonal, with elements being the potential evaluated at the proper quadrature points. The angular momentum operators may be treated exactly up to truncation of the basis set and provide the coupling in the coordinate‐labeled discrete variable representation. The definition of the inner product over the internal coordinates as quadratures rather than integrations allows a discrete matrix transformation to be used to diagonalize any potential matrix. This framework allows one to obtain approximate solutions in a particularly simple and efficient manner and is presented in detail for atom–diatom collisions. At large values of the scattering distance the coupled equations may be solved to a high degree of accuracy using the distorted wave approximation in the finite basis representation. At small values of the scattering distance an exactly analogous technique may be used to obtain an appro...

Accurate quantum probabilities and threshold behavior of the H+O2 combustion reaction

We report accurate 3D quantum reaction probabilities for the H+O2 combustion reaction and find that they are resonance dominated and rise linearly above threshold. The reaction probability is not enhanced by vibrational or rotational excitation of the reactants but does increase above the threshold for vibrationally excited products.

A detailed three‐dimensional quantum study of the Li+FH reaction

Accurate quantum reactive scattering calculations in the full three‐dimensional physical space have been carried out for the Li+FH reaction at zero total angular momentum using the adiabatically adjusting principal axis of inertia hyperspherical coordinate formalism. The procedures for fitting the potential energy surface, calculating the surface functions, and propagating the solutions in a coupled channel treatment are given and discussed. Features of the resulting reactive probability plots are analyzed, and simple explanations of a number of the quantum resonance and oscillatory features are found.

Empirical potential for the He+CO2 interaction: Multiproperty fitting in the infinite‐order sudden approximation

An empirical intermolecular potential for the interaction of He with CO2 is obtained via data reduction of phenomenological cross sections. The infinite order sudden approximation is used to calculate the total differential, total integral, and spectral line broadening cross sections, and diffusion, viscosity, thermal conductivity, thermal diffusion factors, and second virial coefficients. Second order Chapman–Cowling corrections were used to determine some of the transport coefficients, and quantum corrections to the classical virial coefficients were included. The empirical potential obtained simultaneously fits all nine different types of experimental data to within their experimental error and the computational accuracy.

A guide to rotations in quantum mechanics

To lay a foundation for the study and use of rotation operators in graduate quantum mechanics and in research, a thorough discussion is presented of rotations in Euclidean three space (R3 ) and of their effect on kets in the Hilbert space of a single particle. The Wigner D-matrices are obtained and used to rotate spherical harmonics. An extensive ready-reference appendix of the properties of these matrices, expressed in a consistent notation, is provided. Careful attention is paid throughout to various conventions (e.g. active versus passive viewpoints) that are used in the literature.

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. VI. Analytic basis method for surface functions

We continue development of the theory of reactive (rearrangement) scattering using adiabatically adjusting principal axes hyperspherical (APH) coordinates. The surface functions, functions of the APH hyperangles covering the surface of the internal coordinate sphere, are expanded in analytic basis functions centered in each of the arrangement channels. The rotational functions are associated Legendre polynomials, and the vibrational functions are harmonic functions of an ‘‘anharmonic’’ variable which covers an infinite range, allows accurate Gauss–Hermite quadrature, and includes effects of anharmonicity. Example calculations show that these functions provide an efficient basis which can markedly decrease the computational effort required to generate accurate surface functions.

Vibrationally and rotationally resolved angular distributions for F+H2→HF(ν,j)+H reactive scattering

Angular distributions for individually resolved ν, j states from the F+H2→HF(ν,j)+H chemical reaction are measured for the first time. Vibrational and rotational resolution is achieved simultaneously by applying laser+bolometer detection techniques to crossed-beam reactive scattering. In addition to backward-scattering HF(ν=1, j=6) and HF(ν=2, j=5), we also observe HF(ν=1, j=6) products scattered into the forward hemisphere. The results are in qualitative agreement with fully three-dimensional exact quantum reactive scattering calculations [Castillo et al., J. Chem. Phys. 104, 6531 (1996)] which were conducted on an accurate potential-energy surface [Stark and Werner, J. Chem. Phys. 104, 6515 (1996)]. However, the forward-scattered HF(ν=1, j=6) observed in this experiment is not reproduced by quasi-classical calculations [Aoiz et al., Chem. Phys. Lett. 223, 215 (1994)] on the same potential-energy surface.

Accurate 3D quantum reactive probabilities of Li+FH

Abstract Accurate three-dimensional quantum reactive scattering calculations have been carried out at zero total angular momentum ( J =0) for the “three-different-atom non-collinearly dominated” Li+HF reaction. The main features of the reactive probability for reactants in the ground vibrational state are discussed.