R. T. Poe

Three-dimensional quantum mechanical study of the F + H2 reactive scattering

Abstract Three-dimensional quantum mechanical calculations for the exoergic reactive scattering of F + H 2 → FH + H are carried out in the framework of the distorted wave approximation. Vibration—rotation distributions of the product molecule obtained in the present calculation are discussed in terms of available experimental results.

Three‐dimensional quantum mechanical studies of D+H2→HD+H reactive scattering. IV. Cross sections and rate constants with rotationally excited target molecules

The body fixed formulation of the adiabatic distorted wave theory is used to study the reactive collisions of the (D,H2) system. Cross sections are obtained on the ab initio potential surface from the threshold to 0.5 eV in relative translation energy for the case where the target molecule is in the first rotationally excited state. The present results of the ortho‐hydrogen are qualitatively similar to but quantitatively different from the previous results of para‐hydrogen. The statistically weighted cross sections and product state distributions are found in general agreement with the molecular beam experiment. The reaction rates are obtained by integration over the distribution function. From 150 to 750°K where there are experimental data, the curvature in the Arrhenius plot of the calculated rate constants is in excellent agreement with experiment. However, the absolute magnitudes of the rate constants are smaller than the experimental ones.

Reactive scattering of rotationally excited target molecules with adiabatic theory

We present a formulation of the three‐dimensional quantum mechanical reactive scattering of an atom and a rotationally excited diatomic target molecule within the framework of adiabatic distorted wave theory. This is an extension of previous work where only the rotationally ground initial state was treated while the final molecule could be in any state. The importance of the present formulation lies in the fact that the population of the rotationally excited target molecules is significant under ordinary experimental conditions. A method of obtaining exact and approximate adiabatic wave functions and energies is developed through the use of the body‐fixed formulation of atom–diatomic molecule scattering. The integration in transition matrix with rotationally excited adiabatic wave function is again reduced to the three‐dimensional integral by separating out the angular variables for the rigid motion of the plane for the atom–molecule system. Explicit integration formula is presented for the reactive trans...

Theory of phonon inelastic atom–surface scattering. I. Quantum mechanical treatment of collision dynamics

We present a systematic formulation of the atom–surface scattering dynamics which includes the vibrational states of the atoms in the solid (phonons). The properties of the total scattering wave function of the system, a representation of the interaction potential matrix, and the characteristics of the independent physical solutions are all derived from the translational invariance of the full Hamiltonian. The scattering equations in the integral forms as well as the related Green functions were also obtained. The configurational representations of the Green functions, in particular, are quite different from those of the conventional scattering theory where the collision partners are spatially localized. Various versions of the integral expression of scattering, transition, and reactance matrices were also obtained. They are useful for introducing approximation schemes. From the present formulation, some specific theoretical schemes which are more realistic compared to those that have been employed so far...

Three dimensional quantum mechanical studies of D+H2 → HD+H reactive scattering. V. Cross sections and rate constants from the adiabatic T matrix theory

The adiabatic T matrix method is used to carry out a three dimensional quantum mechanical calculation for the reactive scattering of D+H2 on an ab initio potential surface. Total and differential cross sections as well as final state distributions are obtained. When compared with adiabatic distorted wave results, agreement is good except the present total cross section is larger. When compared with trajectory calculations, agreement is also good except for the threshold behavior and the final state distribution. The rate constants obtained from the present total reaction cross sections are in very good agreement with measurements. With the analysis of the center of mass to laboratory transformation for the trajectory calculations and the comparison between those results and present ones, differential cross sections and final state distributions obtained in the present calculation are also seen to be in agreement with the molecular beam experiment.

Coupled channel distorted wave method of atom–molecule reactive scattering: Application to para to ortho hydrogen molecule conversion

We present a three dimensional coupled channel distorted wave approach of the atom–molecule reactive scattering. The full entrance channel wave functions are obtained from the inelastic vibrational and rotational close‐coupling approximation, and reactive cross sections are evaluated with those wave functions employing the transition matrix (T matrix) method. Therefore, in contrast to the previous adiabatic distorted wave model of the reactive scattering, the present method allows for the target molecule to be dynamically distorted following the motion of the incident atom. The formulation of the approach and efficient computational procedures for obtaining the reactive T matrix elements are presented. The reactive scattering cross sections and the rate constants of the H+H2 para to ortho hydrogen molecule conversion have been evaluated to illustrate the computational aspects of the present method. The wave function obtained from the rotational close‐coupling approximation yields better results on the rea...

Theory of collisions between an atom and a diatomic molecule in the body‐fixed coordinate system.a) I. Coupled differential equation and asymptotic boundary conditions

The body‐fixed (BF) formulation for atom–diatom scatterings is developed to the extent that one can use it to perform accurate close‐coupling calculation, without introducing further approximation except truncating a finite basis set of the target molecular wave function, on the same ground as one use the space‐fixed (SF) formulation. In this formulation, the coupled differential equations are solved an the boundary conditions matched entirely in the BF coordinate system. A unitary transformation is used to obtain both the coupled differential equation and the boundary condition in BF system system from SF system. All properties of the solution with respect to parity are derived entirely from the transformation, without using the parity eignfunctions of the BF frame. Boundary conditions that yield the scattering (S) matrix and the reactance (R) matrix are presented for each parity in both the far asymptotic region (where the interaction and the centrifugal potentials are both negligible) and the near asym...

Quantum mechanical determination of product state distributions in the H + D2 → HD + D reaction

We present three-dimensional quantum mechanical calculations of the product state distributions in the H + D2 → HD + D reaction. The two-potential formalism of the distorted-wave Born approximation is used with the distorted potential taken to be the potential between the atom and the molecule when they are in the collinear configuration. The predicted vibrational and rotational distributions of HD molecules are compared with two new sets of experimental measurements and with quasi-classical calculations.

Theory of phonon inelastic atom–surface scattering. II. Approximate methods and applications to resonance and adsorption

Approximate theoretical schemes for the calculation of the phonon inelastic scattering were derived from the formulation in the preceding paper. They can be adopted to flexible input potentials and are more realistic compared to the schemes that have been employed so far and at the same time are capable of yielding effective ab initio computation. An iterative coupled integral equation method thus obtained is much more tractable than that of the coupled differential equation when the phonons are taken into account. In this approach, the multiphonon transitions are readily obtained as higher order processes with the potential matrix elements being limited to the dominant one‐phonon transitions. The S matrix elements of both elastic reflection and simultaneous diffraction and phonon transitions can also be obtained from the coupled channel transition matrix (CCTM) approach derived from the diffractive wave Green function where the coupling between the reciprocallattice points due to the atom–surface interac...

Adiabatic T matrix theory for three dimensional reactive scattering: Application to the (H, H2) system

We present an adiabatic transition matrix (T matrix) method of atom–molecule reactive scattering. In this method, the coupling between vibrational and rotational motions is taken into account for obtaining the adiabatic molecular wave functions. These wave functions are expanded in terms of the basis functions taken from the eigenfunctions of a double well potential. From the full potential surface in the linear configuration of three atoms, the double well potential is obtained. Convergence of the expansion is achieved for evaluating the adiabatic wave functions and two body atom–molecule interaction potential. Cross sections are computed with the T matrix method employing the converged adiabatic wave functions. Numerical results for the H+H2 reactive cross section on an ab initio potential surface are presented. Results on D+H2 reaction will be reported in a subsequent paper. The differential cross sections and final state distributions computed from the present adiabatic T matrix method are similar to ...