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A Wronskian formalism is developed for resonance tunnelling reactions. It is shown how the S matrix can be written in terms of Wronskians between solutions of the SchrSdinger equation representing incoming and outgoing waves. The method is an adaptation of the Jost function approach to elastic two-body scattering. Formal expressions are derived for the imaginary parts of the energy eigenvalues that arise from the application of complex boundary conditions used in a previous semiclassical analysis. When the imaginary parts are small, so that the resonance is sharp, the S matrix can be written in a Breit-Wigner resonance form. The theory unifies and extends the semiclassical analysis of resonance tunnelling reactions given previously.

Conical intersections in C,, C?,, and linear configurations for the 'A' states of the H2C1+ molecule are investigated with the help of a 10 x 10 model Hamiltonian matrix in a valence-bond basis. The line of intersection (linen) between states 2 and 3 is traced from one end point, an intersection between two states of 'B2 symmetry in a CZv configuration, to the other end point, an intersection between two 'C+ states in a linear H-H-CI configuration. The linea consists of 5 branches having symmetries C,y, C,,, C,,,, C1,, and C,. A litzea between states 3 and 4 starting at a crossing of 'C+ and 'n states in a linear C, , configuration consists of three branches (C,r, C2", CI) leading to the asymptotic region CI + HL The starting point of linea 314 is connected to the asymptotic region H + HCI via a linen in the linear configuration. Linene of C, symmetry could be found by examining the eigenvalues of the Hessian matrix of second derivatives along a line of intersection in a higher symmetry (C2" or linear), a useful method for locating accidental intersections that lends itself readily to nD initio calculations. The existence of the litleae could be related to physical properties of the molecule, such as the dipole moment, indicating that the model Hamiltonian does reflect the true physical behaviour.PHILIP

AbstractsThe relation of the straightforward Rayleigh-Schrodinger perturbation theory for the interaction of two atoms to the asymptotic exchange theory is described. The one-electron case of a hydrogen atom perturbed by a nucleus is examined in detail. It is shown that the asymptotic theory contains an infinite summation of terms in the Rayleigh-Schrodinger series. The nature of the branching between states and its implications for convergence is elucidated.On dkcrit le rapport entre la theorie des perturbations de Rayleigh-Schrodinger pour l'interaction de deux atomes et la thkorie d'kchange asymptotique. On hudie en dktail de cas d'un atome d'hydroghne perturb6 par un noyau. I1 est dimontri que la thkorie asymptotique contient une somme infinie de termes de la skrie de Rayleigh-Schrodinger. La bifurcation entre les itats est expliquke avec les implications en ce qui concerne la convergence.Die Beziehung der Rayleigh-Schrodinger'schen Storungstheorie fur die Wechselwirkung zwischen zwei Atomen zur asymptotischen Austauschtheorie wird beschrieben. Der Fall eines von einem Kern gestorten Wasserstoffatoms wird detailliert untersucht. Es wird gezeigt dass die asymptotische Theorie eine unendliche Summe von Gliedern der Rayleigh-Schrodinger'schen Reihe enthalt. Die Abzweigung zwischen den Zustanden und ihre Folgerungen fur die Konvergenz wird erlautert.

Articles you may be interested inCan quasiclassical trajectory calculations reproduce the extreme kinetic isotope effect observed in the muonic isotopologues of the H + H2 reaction? J. Chem. Phys. 135, 034310 (2011); 10.1063/1.3611400 Dynamical calculations for the H+para, orthoH2 reactions at low temperatures: Effect of rotational energy of reagent H2 molecule J. Chem. Phys. 95, 4154 (1991); 10.1063/1.460771 Effect of vibration on rotational energy transfer. A quasiclassical trajectory study of He+H2Quasiclassical trajectory studies of the H+H2 reaction on an accurate potential energy surface. II. Effect of initial vibration and rotation on reactivity A quasiclassical trajectory study of reagent vibrational excitation effects in the OH+H2→H2O+H reaction It is clear then that there are important dynamical effects in both Reactions (1) and (2). Earlier dynamical calculations are too approximate to allow a meaningful comparison with experiment. The trajectory calculation of North and Leventhal 12 used only a sum of two-body interactions as a model potential and allowed the H2 no initial vibration. The resulting dynamiCS were characteristic of successive twO-body encounters