Mark S. Child

Semiclassical mechanics with molecular applications

1. Introduction 2. Phase Integral Approximations 3. Quantization 4. Angle-Action Variables 5. Matrix Elements 6. Semiclassical Inversion Methods 7. Non-Separable Bound Motion 8. Wavepackets 9. Atom-Atom Scattering 10. The Classical S Matrix 11. Reactive Scattering Appendix A: Phase Integral Techniques Appendix B: Uniform Approximations and Diffraction Integrals Appendix C: Transformations in Classical and Quantum Mechanics Appendix D: The Onset of Chaos Appendix E: Angle-Action Transformations Appendix F: The Monodromy Matrix Appendix G: Solutions to Problems

Potential models and local mode vibrational eigenvalue calculations for acetylene

Two potential models for acetylene are developed and tested by comparison between variational calculations for the stretching vibrational term values and available spectroscopic data. The first model based on local bond potentials with harmonic interbond coupling gives root mean square deviations of 6 cm−1 for C2H2 and 3 cm−1 for C2D2. The second model is more ambitious, being designed to reproduce the dissociation characteristics of the molecules, and the calculated root mean square deviations from the experimental vibrational term values are larger, 32 cm−1 for C2H2 and 24 cm−1 for C2D2. The eigenvalue spectrum of C2H2 is shown to differ from that of C2D2 in showingmarked local mode features and this difference in behaviour is underlined by means of a correlation diagram. Finally it is shown how the known normal mode frequencies and anharmonic constants may be introduced into a simple model in order to predict the excited term values of C2H2, again with a root mean square deviation of 6 cm−1.

Predissociation and photodissociation of IBr: A case of intermediate coupling strength

The observed predominance of excited Br(2 P 1/2) atoms in the nearultra-violet photodissociation products of IBr is shown to be quantitatively consistent with an intermediate coupling regime in the visible absorption region, which invalidates the traditional interpretation of the B′(O +) state as a new Born-Oppenheimer state arising from a strongly avoided potential curve crossing. A general theory of predissociation at intermediate coupling, covering the positions, intensities and widths of the spectral lines, shows that both diabatic and adiabatic characteristics must be taken into account. The presence of a sharp level is predicted at any coincidence between an adiabatic and a diabatic term value with the same J value, and the spacing between neighbouring lines is shown to depend on an average between the diabatic and adiabatic rotational constants. The theory is successfully applied to the B(3Π o + ) and B′(O +) states of IBr, and potential curves for the two states are reported. The analysis is consi...

Rotational predissociation of the Ar⋅HCl van der Waals complex: Close‐coupled scattering calculations

We report an extensive computational study of rotationally predissociating metastable states of the Ar⋅HCl van der Waals complex, using a highly realistic empirical intermolecular potential recently proposed by Hutson and Howard. The states are characterized by fully converged, close‐coupled, scattering calculations. Resonance energies, widths, and partial widths are extracted by fitting the energy dependence of S matrices. Total angular momenta of 0 and 1 are studied, and the calculations span an energy range from 0 to 1400 cm−1. The resonance widths vary from <10−4 to ≳5 cm−1, and it is shown that the isolated narrow resonance approximation is of poor validity for the wider resonances. Comparison of the close‐coupling results with approximate calculations enables assignment of approximate quantum numbers to the metastable states. Physical explanations are suggested for the strong trends in resonance parameters as a function of the intermolecular stretching, diatom rotation, and molecule‐fixed angular mo...

Rydberg–Klein–Rees inversion of high resolution van der Waals infrared spectra: An intermolecular potential energy surface for Ar+HF (v=1)

A method is described for extraction of two‐dimensional (angular and radial) potential energy surfaces for triatomic rare gas–hydrogen halide van der Waals complexes. The approach relies on extensive J rotational term values obtained by high resolution infrared laser jet spectroscopy for a family of bending vibrational states to deduce the radial and angular dependence of the intermolecular potential. First, effective 1D radial potentials for a series of bending states are obtained by rotational RKR analysis of experimentally observed rotational progressions. These 1D potentials, which represent vibrational averages over different bending wave functions, are then inverted to determine the radially dependent coefficients of a Legendre expansion to the full surface, i.e., ∑lVl(R)Pl (cos θ). This relies on adiabatic angular motion with respect to radial degrees of freedom, the validity of which is discussed. This approach is tested with experimental data from the (100 0) (fundamental), (120 0) (HF parallel b...

A simple classical prediction of quantal resonances in collinear reactive scattering

Abstract Quantal collinear reactive scattering computations have shown that in the vicinity of thresholds of reactant or product vibrational states, one finds resonances in the state to state reaction probability. We find that these resonances can be explained classically in terms of energy transfer between adiabatic reactant and product channels. This transfer is attributable to resonant periodic orbits, resonating between reactants and products. The classical condition for a quantal resonance is that the action of the orbit over one period be an integer (in units of h ) and that the energy at which this occurs be lower than the adiabatic barrier heights of the resonating states. These conditions suffice for a prediction of the location of the quantal resonance within a 1% accuracy!

Time dependent quantum propagation in phase space

Numerical solutions of the quantum time-dependent integro-differential Schrodinger equation in a coherent state Husimi representation are investigated. Discretization leads to propagation on a grid of nonorthogonal coherent states without the need to invert an overlap matrix, with the further advantage of a sparse Hamiltonian matrix. Applications are made to the evolution of a Gaussian wave packet in a Morse potential. Propagation on a static rectangular grid is fast and accurate. Results are also presented for a moving rectangular grid, guided at its center by a mean classical path, and for a classically guided moving grid of individual coherent states taken from a Monte Carlo ensemble.

Multidimensional quantum propagation with the help of coupled coherent states

A previous initial value coupled coherent state (CCS) representation is applied to Gaussian wave packet propagation on multidimensional Henon Heiles potentials. Solutions of the time-dependent integro-differential Schrodinger equation are obtained in a basis of trajectory guided Frozen Gaussian Coherent States, with Monte Carlo sampling to ensure a unique capability for propagating multidimensional wave functions. Results, which are obtained for up to 14 D, are compared with those derived by the Herman–Kluk semiclassical initial value representation (IVR) wave packet method.

Local mode degeneracies in the vibrational spectrum of H2O

Abstract The development of progressively close local mode degeneracies in higher overtone stales is shown to be clearly demonstrable in the stretching vibrational spectrum of H 2 O and to be relatively little affected by the state of the bending vibration. Calculated vibrational term values derived from the Sorbie-Murrell potential surface are in good agreement with the experimental spectrum.

Local and normal stretching vibrational states of H2O

Classical and semiclassical features of the stretching vibrations on a realistic potential energy surface for the water molecule are examined at energies up to the dissociation limit, Ed ≏ 38000 cm-1. The relative importance of normal, local and irregular motions at different energies is assessed in terms of fractional phase areas in an appropriate Poincare surface of section. Two limits El ≏ 2200 cm-1 and Ec ≏ 30000 cm-1 are identified, marking the onset of local and irregular motions respectively. Below E L all motions are normal, in the range El < E < Ec the total growth in the phase space is attributed largely to local vibrations, and above Ec irregular motions begin to predominate largely at the expense of local trajectories. Some regular motion of the normal type persist above the dissociation limit. This division of the phase space area is in good agreement with the division of phase space volumes as revealed by the disposition of quantum eigenstates. A quantization procedure for the local motions ...