Separation and semiclassical quantization of bending motion near linear geometries of a triatom

Abstract

It is shown that separation of internal bending motion from other degrees of freedom in the vicinity of li~ear confi~rations of a triatom leads to the one-dimensional Schr6dinger equation for the centnfugal OSCIllator for a very broad family of coordinate transformations. This feat~re makes the ap~roach especially attractive for semiclassical quantization of bending motIon, compared wIth the alternative, broadly used approach treating bending motion as two mutua~ly perpendic~lar bending modes. Significant errors due to the neglect of the quartic pote~tlal term coupl.mg th~ mutually perpendicular bending modes are demonstrated using bendmg ~esonances .m partIal cross ~ections for the H + H2 exchange reaction as an example.Another Important Issue addressed m the paper is how the choice of rotating axes affects the rotat~onal energy. It is shown th~t the correct expression for the rotational energy is obtained only If the body-fixed axes are dIrected along the principal inertia axes of the triatom in its accessible nearly linear configurations.

Functional Representation for the Born−Oppenheimer Diagonal Correction and Born−Huang Adiabatic Potential Energy Surfaces for Isotopomers of H3

“…The calculations were performed using the ABCRATE code . A general description of VTST for calculations of reaction rates in triatomic systems with collinear reaction paths is given elsewhere. , Specifically, we used the improved canonical variation theory, in which eigenvalues of the stretch mode (describing motion perpendicular to the reaction path) are computed by a WKB approximation, and energy levels for the doubly degenerate bends are computed by the centrifugal oscillator approximation, , where the bend potential is fitted to a harmonic−quartic potential . Quantum corrections for reaction coordinate motion are included by a multiplicative transmission coefficient that is computed from a normalized Boltzmann average of semiclassical tunneling probabilities .…”

Transition State Resonances in the Reaction Cl + H2 → HCl + H

“…s = 0 corresponds to the saddle point, V MEP is the Born−Oppenheimer potential energy along the minimum energy reaction path (MEP), and ε int is the vibrational energy of the modes excluding motion along the reaction coordinate. The VA curves are obtained by using the program ABCRATE wherein the MEP is calculated using the steepest descent method 35 on both sides of the saddle point, the quantized energies of the stretching modes are approximated by the WKB method, , and the quantized energies of the bends are obtained from a centrifugal oscillator treatment , using a quadratic-quartic fit to the two-dimensional potential for bending motions.…”

Rotational energy analysis for rotating–vibrating linear molecules in classical trajectory simulation

“…This model fails as soon as a molecule begins to rotate and vibrate as is evident from the results of high resolution spectroscopic studies. The traditional approach [11][12][13][14][15][16][17][18][19][20][21][22][23][24] to handle the rotation-vibration problem is to set up a moving coordinate system or an Eckart frame by imposing Sayvetz conditions. 9,25 The zeroth order term in the rotation-vibration interaction vanishes in that case, and the remainder is called the Coriolis energy.…”