Akihiko Ohsaki

Hyperspherical coordinate approach to atom-diatom chemical reactions in the sudden and adiabatic approximations

Abstract The methodology and the basic physical idea of the sudden and the adiabatic approximations to deal with atom-diatom chemical reactions are reviewed. Reformulation of these approximations in terms of the collinear-type hyperspherical coordinates is presented together with numerical applications to some reactions systems. Practically useful formulae are derived for the evaluation of reaction cross sections and rate constants. Particular emphasis is placed on the power on the hyperspherical coordinate approach, clarification of the reaction mechanisms, and importance of the potential ridge in a reactive transition. Comparison with classical trajectory calculations clearly reveals quantum mechanical tunneling effects. A new approach to rotational transition in a reaction is also discussed briefly.

Quantum mechanical study of the light‐atom transfer reactions, O(3P)+XCl→OX+Cl (X=H,D). I. Reactions in the ground vibrational states

We present a three‐dimensional quantum mechanical study of the light‐atom transfer reaction O(3P)+XCl(vi=0)→OX(vf=0)+Cl(X=H,D), where vα represents the vibrational state in the α channel. The adiabatic‐bend approximation reformulated in terms of the hyperspherical coordinates is employed to calculate the cross sections and rate constants. The potential energy surface used here is the Persky–Broida’s LEPS‐I. The results are compared with the available experimental data and quasiclassical trajectory calculations. A discrepancy is found between the present results and the quasiclassical trajectory results at low collision energies (low temperatures). This is a clear manifestation of the quantum mechanical tunneling effect. The present results of the rate constants and the kinetic isotope effect are generally in better agreement with experiment. The previously proposed constant centrifugal potential approximation (CCPA) is directly demonstrated to work well.

Dynamics of collinear asymmetric light atom transfer reactions

The Rosen–Zener formula in its sophisticated form is shown to be applicable to asymmetric collinear light atom transfer reactions with near degeneracy of asymptotic vibrational levels. The formula is applied to simple model systems and is demonstrated to work well over a wide range of energy for both systems with and without reaction barrier. It is also discussed that effects of surface topology and masses on reaction dynamics are effectively investigated by hyperspherical coordinates.

A quantum-mechanical study of chemical reaction and charge-transfer processes in the (Ar + H2)+ system

Abstract A three-dimensional quantum-mechanical study of the (Ar + H 2 + system within the reactive infinite-order sudden approximation is presented. All four possible channels for chemical reaction and charge transfer were treated simultaneously. The various cross sections deviate by at most 50% from recent trajectory surface hopping results.

Reaction dynamics of D+H2→DH+H: Effects of potential energy surface topography and usefulness of the constant centrifugal potential approximation

Two findings are reported for the D+H2→DH+H reaction on the basis of the exact quantum mechanical calculation for J=0, where J is total angular momentum. First, with use of the Liu–Siegbahn–Truhlar–Horowitz (LSTH) surface and the Varandas surface, we demonstrate that a rather small difference in potential energy surface (PES) induces a surprisingly large effect on reaction dynamics. Two origins of the discrepancy are pointed out and analyzed: (1) Noncollinear conformation in the reaction zone contributes to the reaction significantly despite the fact that the minimum energy path and the saddle point are located in the collinear configuration. (2) A difference in the distant part of PES also causes a discrepancy in the reaction dynamics indirectly, although this effect is much smaller than (1). Secondly, we investigate the validity of the constant centrifugal potential approximation (CCPA) based on the accurate results for J=0. The use of CCPA to estimate total cross section and rate constant is again prov...

On the evaluation of cross section and rate constant of atom-diatom reactions in the sudden and adiabatic approximations

The constant centrifugal potential approximation is explicitly tested and its general usefulness is demonstrated. This method is directly applied to the model reaction systems Cl + H2, Cl + HBr and O + HCl in both the sudden (RIOS) and the adiabatic-bend reduced dimensionality approximations. These two approximations are employed using the collinear-type hyperspherical coordinates reported before. This constant centrifugal potential approximations saves considerable cpu time, because the orbital angular momentum l necessary to obtain converged cross sections can easily be more than 100, and what we have to evaluate in this approximation is only the l = 0 reaction probability as a function of collision energy. Brief discussion is also presented concerning the choice of the location where the constant centrifugal potential is evaluated.

Electron-Exchange Effect in Electron-Impact Excitation of the n=2 Fine-Structure Levels of Hydrogenic Ions

The electron-impact transitions between the n =2 fine-structure levels of hydrogenic ions are calculated by an improved close coupling scheme that accounts for the electron-exchange effect. It is f...

Approximate quantum mechanical treatment of light-atom transfer reactions

Abstract The use of collinear-type hyperspherical coordinates to investigate three-dimensional light-atom transfer reactions within the framework of the adiabatic approximation (with respect to rotational motion) originally devised by Bowman is proposed. In the cases of (1) symmetric light-atom transfer and (2) near-resonant asymmetric light-atom transfer reactions, explicit approximate analytical expressions available for collinear reaction probabilities are suggested to estimate directly the three-dimensional reaction cross sections and rate constants. It is also demonstrated that the Rosen-Zener formula is applicable to collinear asymmetric light-atom transfer reactions without introducing any diabatic representation of potentials.

Electron-impact excitations between the n = 2 fine-structure levels of hydrogenic ions

The electron-impact transitions of n =2 fine-structure levels in hydrogenic ions are treated employing two kinds of close coupling methods and the Coulomb–Born approximation. By using these methods together, a reduction of calculation labor is attempted. The obtained results considerably differ from those of a previous close coupling calculation by Zygelman and Dalgarno [Phys. Rev. A 35 (1987) 4085] at low energies.

Radial integrals in the Coulomb–Born approximation: Multipole transitions

Abstract This is the second series of the radial integrals in Coulomb–Born approximation, and describes a computer program package CRIMPT2W, which evaluates the radial integrals for the general multipole transitions. The integral expressions are given analytically in terms of Appell functions.