Reactive scattering with row-orthonormal hyperspherical coordinates. 3. Hamiltonian and transformation properties for pentaatomic systems

The Hamiltonian for triatomic and tetraatomic systems in row-orthonormal hyperspherical coordinates has been derived previously. However, for pentaatomic systems this derivation requires nontrivial generalizations. These are presented in this paper, together with the corresponding Hamiltonian. Each of the twelve operators that contribute to this Hamiltonian is kinematic-rotation invariant. As for the triatomic and tetraatomic cases, these pentaatomic demcocratic coordinates are particularly well suited for calculations of reactive scattering in five atom systems

Hyperspherical harmonics for tetraatomic systems

A recursion procedure for the analytical generation of hyperspherical harmonics for tetraatomic systems, in terms of row-orthonormal hyperspherical coordinates, is presented. Using this approach and an algebraic Mathematica program, these harmonics were obtained for values of the hyperangular momentum quantum number up to 30 (about 43.8 million of them). Their properties are presented and discussed. Since they are regular at the poles of the tetraatomic kinetic energy operator, are complete, and are not highly oscillatory, they constitute an excellent basis set for performing a partial wave expansion of the wave function of the corresponding Schrödinger equation in the strong interaction region of nuclear configuration space. This basis set is, in addition, numerically very efficient and should permit benchmark-quality calculations of state-to-state differential and integral cross sections for those systems

Scattering of thermal He beams by crossed atomic and molecular beams. I. Sensitivity of the elastic differential cross section to the interatomic potential

The ability of diffraction oscillations in atomic beam scattering experiments to uniquely determine interatomic potentials for highly quantal systems is examined. Assumed but realistic potentials are used to generate, by scattering calculations and incorporation of random errors, differential cross sections which are then treated as if they were ’’experimental’’ data. From these, attempts are made to recover the initial potential by varying the parameters of assumed mathematical forms different from the original one, until a best fit to the "experimental" results is obtained. It is found that the region of the interaction potential around the van der Waals minimum is accurately determined by the "measured" differential cross sections over a range of interatomic separations significantly wider than would be expected classically. It is also found, for collision energies at which the weakly repulsive wall is appreciably sampled, that the SPF–Dunham and double Morse–van der Waals types of potentials lead to accurate determinations of the interatomic potential, whereas many other mathematical forms do not. Analytical parameterizations most appropriate for obtaining accurate interatomic potentials from thermal DCS experiments, for a given highly quantal system, may depend on the collision energy used

Asymptotic analysis of state-to-state tetraatomic reactions using row-orthonormal hyperspherical coordinates

The state-to-state asymptotic analysis of tetraatomic reactions is presented. It is assumed that the four-atom time-independent partial wave Schrödinger equation has been solved subject to the condition that in the limit of very compact geometries the wave function vanishes. These solutions are initially obtained in body-fixed row-orthonormal hyperspherical coordinates and transformed in the asymptotic arrangement channel regions of nuclear configuration space to Jacobi body-fixed coordinates. From the latter, compact explicit expressions for the reactance (R) and scattering (S) matrices, useful for accurate numerical calculations, are obtained. The different systems of coordinates used and their interrelations are given. The approach described is particularly well suited for implementation on massively parallel architectures and is appropriate for the calculation of benchmark-quality state-to-state integral and differential cross sections on currently available computers

An optimal adiabatic-to-diabatic transformation of the 1 2A[prime] and 2 2A[prime] states of H3

Molecular reaction dynamics in the adiabatic representation is complicated by the existence of conical intersections and the associated geometric phase effect. The first-derivative coupling vector between the corresponding electronically adiabatic states can, in general, be decomposed into longitudinal (removable) and transverse (nonremovable) parts. At intersection geometries, the longitudinal part is singular, whereas the transverse part is not. In a two-electronic-state Born–Huang expansion, an adiabatic-to-diabatic transformation completely eliminates the contribution of the longitudinal part to the nuclear motion Schrödinger equation, leaving however the transverse part contribution. We report here the results of an accurate calculation of this transverse part for the 1 2A[prime] and 2 2A[prime] electronic states of H3 obtained by solving a three-dimensional Poisson equation over the entire domain [sans-serif U] of internal nuclear configuration space [script Q] of importance to reactive scattering. In addition to requiring a knowledge of the first-derivative coupling vector everywhere in [sans-serif U], the solution depends on an arbitrary choice of boundary conditions. These have been picked so as to minimize the average value over [sans-serif U] of the magnitude of the transverse part, resulting in an optimal diabatization angle. The dynamical importance of the transverse term in the diabatic nuclear motion Schrödinger equation is discussed on the basis of its magnitude not only in the vicinity of the conical intersection, but also over all of the energetically accessible regions of the full [sans-serif U] domain. We also present and discuss the diabatic potential energy surfaces obtained by this optimal diabatization procedure

Quantum Mechanics of the H+H2 Reaction: Exact Scattering Probabilities for Collinear Collisions

The H + H2 reaction is very important in theoretical chemical dynamics (1-4). A model that is often used to study this reaction is to restrict the atoms to lie on a nonrotating line throughout the collision and to consider that the system is electronically adiabatic, i.e., it remains the lowest electronic state throughout the collision. This reduces the problem to scattering of three particles on a potential energy surface which is a function of two linearly independent coordinates. This model has been studied classically (5-8), and Mortensen and Pitzer (9) have calculated exact quantum mechanical reaction probabilities at five relative translational energies E0. In this Communication, we present some results of our more extensive exact calculations on this model of the H + H2 reaction and show their consequences for the validity of approximate theories of chemical reactions. For the cases considered here, the assumption of electronic adiabaticity causes very little error (10)

Energy dependence of the differential photoelectron cross sections of molecular nitrogen

The angular distribution of photoelectron intensity for molecular nitrogen was studied using He I and Ne I resonance line discharge light sources. Studies of photoelectron angular distributions covering a range of photon energies, and thus a range of photoelectron energies, are possible using the weaker high order lines in each discharge as well as the principal lines. Peaks in three photoelectron bands of N_2 were studied at the photon energies 16.85, 19.78, 21.22, 23.09, and 23.74 eV, where possible. We find that the v′=0 peak of the X^ 2Σ^+_g band has abnormally high intensity and, at the higher photon energies, an abnormally low angular distribution asymmetry parameter, β. Several mechanisms for this anomaly are discussed, including autoionization, the variation of electric dipole transition moments with internuclear distance, and possible shape resonance phenomena. None of these explanations is completely in agreement with all theoretical and experimental evidence

Comment on "Theory of collisions between an atom and a diatomic molecule in the body-fixed coordinate system"

It is shown that the phase factor i^(J+j+I) omitted in a theory of atom‐diatom monreactive scattering formulated by schatz and kupperman but included in the Choi, Poe, and Tang theory does not lead to errors in the analysis of te (H,H_2) system

Nonmolecular nature of nitric-oxide-inhibited thermal decomposition of n-butane

The thermal decomposition of most organic molecules is generally accepted to occur at least in part via a free radical chain process. Since Hinshelwood and Staveley (1) discovered that small additions of nitric oxide reduced the rate of thermal decomposition, there has been much controversy (2) concerning the nature of the “residual” reaction remaining after further additions of inhibitor produce no further decrease in rate. Jach, Stubbs, and Hinshelwood (3) have shown this limiting rate to be independent of the inhibitor used and attribute this residual reaction to a nonchain molecular process in which the parent molecule breaks up, in a single step, into stable products

Vibrational deactivation on chemically reactive potential surfaces: An exact quantum study of a low barrier collinear model of H + FH, D + FD, H + FD and D + FH

We study vibrational deactivation processes on chemically reactive potential energy surfaces by examining accurate quantum mechanical transition probabilities and rate constants for the collinear H + FH(v), D + FD(v), H + FD(v), and D + FH(v) reactions. A low barrier (1.7 kcal/mole) potential surface is used in these calculations, and we find that for all four reactions, the reactive inelastic rate constants are larger than the nonreactive ones for the same initial and final vibrational states. However, the ratios of these reactive and nonreactive rate constants depend strongly on the vibrational quantum number v and the isotopic composition of the reagents. Nonreactive and reactive transition probabilities for multiquantum jump transitions are generally comparable to those for single quantum transitions. This vibrationally nonadiabatic behavior is a direct consequence of the severe distortion of the diatomic that occurs in a collision on a low barrier reactive surface, and can make chemically reactive atoms like H or D more efficient deactivators of HF or DF than nonreactive collision partners. Many conclusions are in at least qualitative agreement with those of Wilkin’s three dimensional quasiclassical trajectory study on the same systems using a similar surface. We also present results for H + HF(v) collisions which show that for a higher barrier potential surface (33 rather than 1.7 kcal/mole), the deactivation process becomes similar in character to that for nonreactive partners, with v→v−1 processes dominating