Russell T Pack

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory

The theory of reactive (rearrangement) scattering for three atoms in three physical dimensions using adiabatically adjusting, principal axes hyperspherical (APH) coordinates is given. The relationships of the APH coordinates to Delves and Jacobi coordinates are given, and the kinetic energy operator is shown to be relatively simple. Procedures for solving the equations via either an exact coupled channel (CC) method or an optimum centrifugal sudden (CSAPH) approximation are given as well as procedures for applying scattering boundary conditions. Surface functions of two angles are obtained using a finite element method with an optimized, nonuniform mesh, and the CC equations are solved using the efficient VIVAS method. Sample CC results are given for the H3 system. The present approach has the advantages that all arrangements are treated fully equivalently; it is a principal axis system, so that both axes and internal coordinates swing smoothly with the reactions; it is directly applicable to both symmetr...

Rotationally and vibrationally inelastic scattering in the rotational IOS approximation. Ultrasimple calculation of total (differential, integral, and transport) cross sections for nonspherical molecules

A simple, direct derivation of the rotational infinite order sudden (IOS) approximation in molecular scattering theory is given. Connections between simple scattering amplitude formulas, choice of average partial wave parameter, and magnetic transitions are reviewed. Simple procedures for calculating cross sections for specific transitions are discussed and many older model formulas are given clear derivations. Total (summed over rotation) differential, integral, and transport cross sections, useful in the analysis of many experiments involving nonspherical molecules, are shown to be exceedingly simple: They are just averages over the potential angle of cross sections calculated using simple structureless spherical particle formulas and programs. In the case of vibrationally inelastic scattering, the IOSA, without further approximation, provides a well‐defined way to get fully three dimensional cross sections from calculations no more difficult than collinear calculations. Integral, differential, viscosit...

Intermolecular potential surfaces from electron gas methods. I. Angle and distance dependence of the He–CO2 and Ar–CO2 interactions

Angle dependent intermolecular potential energy surfaces for the two states (2A′ and 2A″) that arise from the interaction of ground (X 2Π) state NO with Ar are calculated using the electron gas model to obtain the short range interactions. The average and difference of the two interaction energies are fit to analytic forms convenient for use in scattering calculations and joined smoothly onto the long range van der Waals potential previously determined. The results, which appear to be of useful accuracy, and the applicability of the electron gas model to such open shell–closed shell interactions are discussed.

Simple theory of diffuse vibrational structure in continuous uv spectra of polyatomic molecules. I. Collinear photodissociation of symmetric triatomics

A theory for the direct photodissociation of polyatomic molecules is presented, and it is shown that uv absorption spectra into simply dissociative upper electronic states can have considerable vibrational structure. This provides a simple interpretation of many of the ’’diffuse vibrational bands superimposed on continua’’ often seen in polyatomic spectra.

First quantum corrections to second virial coefficients for anisotropic interactions: Simple, corrected formulaa)

A simple formula for the first quantum correction to the second virial coefficient, valid for the interaction of any like or unlike combination of atoms, diatomics, spherical top, or symmetric top molecules is given. It is found that the commonly used formulas of Wang Chang contain an error that omits an anisotropic contribution. The sizes of the different contributions to the quantum correction are discussed. As examples, calculations for He–SF6 and He–CO2 are reported.

Anisotropic potentials and the damping of rainbow and diffraction oscillations in differential cross sections

Abstract Total differential cross sections are calculated using the IOSA and a new anisotropic 12-6 potential. Rainbows are damped solely by the well depth anisotropy; diffraction oscillations are damped by the well position anisotropy. This separation should aid in the empirical determination of anisotropic potentials.

Metastable states of ozone calculated on an accurate potential energy surface

A new potential energy surface for ozone is developed. It is based on high level ab initio data and includes an accurate description of the barrier region. Full quantum reactive scattering calculations using a coupled channel approach and hyperspherical coordinates are performed on this surface for various isotopic compositions of ozone. Collision lifetimes are obtained over a wide energy range, which gives the spectrum of rovibrational metastable states (scattering resonances). This spectrum is discovered to be very nonstatistical. The spectrum of resonances is dense below the isotopic zero-point-energy threshold and sparse above it. This feature is explained by the opening of additional dissociation channels at higher energies. This behavior is a general quantum mechanical effect that should occur in other triatomic molecules.

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.

Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. III. Small θ behavior and corrigenda

We continue development of the theory of reactive (rearrangement) scattering using adiabatically adjusting, principal axis, hyperspherical (APH) coordinates. The behavior of the solutions for small θ (oblate symmetric top) configurations is examined, and it is shown that the exact surface functions need not be continuous at θ=0. A procedure for testing the importance of the small θ region and the adequacy of the usual APH centrifugal sudden basis of surface functions is presented and illustrated by example calculations on the even parity, J=1, H3 system. A list of corrections to earlier papers in the series is also given.