Rotational Sudden Approximation Research Articles

Rotational excitation of physisorbed molecules by resonant electron scattering

The resonant rotational excitation of physisorbed H 2 molecules by low energy electron impact is studied using the rotational sudden approximation. The rotational excitation efficiency is analysed as a function of the constraint imposed on the molecular rotation by the adsorption. This allows the description of the variation of the energy loss spectrum corresponding to rovibrational excitation as a function of the constraint on molecular rotation. This model study is then used to discuss the recent results by Svensson et al. [Phys. Rev. Lett. 83 (1999) 124] on the rovibrational excitation of H 2 molecules adsorbed at steps on Cu(5 1 0), in terms of quasi-2D rotor and of constrained 3D rotors.

Dynamical Lie algebraic treatment for the A+BC scattering

We report the study of translational-vibrational energy transfer in the A+BC scattering using the dynamical Lie algebraic approach combined with the intermediate picture. The rotational sudden approximation is applied to treat the rotational motion of the BC molecule, which is regarded as an anharmonic oscillator. The calculated results show that the transition probabilities increase with increasing rotational quantum number. Comparison with those obtained in the collinear collision of system A+BC manifests that the transition probabilities here increase indeed. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 214–221, 2001

Three-dimensional wavepacket calculation for the photodissociation of water in the [formula omitted] state

We present an exact three-dimensional wavepacket calculation for the photodissociation of water in the first absorption band using the ab initio potential energy surface of Staemmler and Palma. The results are compared with two-dimensional calculations in which the bending angle is frozen and (approximate) three-dimensional calculations in which the rotational degree of freedom of the product is treated within the rotational sudden approximation. It is found that the diffuse structures superimposed on the broad absorption spectrum become even more diffuse when the bending degree of freedom is treated exactly.

Validity of the rotational sudden approximation for vibrational relaxation in He + CO

Calculations of cross sections and rate constants are reported for the vibrational relaxation of CO in collision with 3He and 4He. Results computed using a semiclassical technique and a vibrational close-coupling, rotational infinite-order sudden method are compared.

He-HF vibrational inelasticity at low and intermediate energies from quantum collision theory

The rotational-sudden approximation (IOSA) has been applied to He-HF scattering at intermediate energies by using an ab initio computed potential-energy surface which explicitly included the dependence on the internal molecular coordinate. The vibrational degree of freedom has therefore been treated exactly by solving the coupled radial equations that were obtained after expanding the target vibrations over a large number of HO wavefunctions. The radial behaviour of the computed coupling matrix elements between lower-lying target states is analyzed at various relative orientations of the atom-to-target vector with respect to the molecular bond. The present results clearly show that the coupling strength and range can be directly related to the specific anisotropic behaviour of the potential surface and to the varying efficiency of (V, T) coupling as the He atom probes different molecular regions. The computed relaxation times are compared with experiments at various temperatures and with previous calculations performed via different surfaces and dynamical models and show satisfactory agreement with observations, thus markedly improving the quality of earlier computed cross sections.

An examination of the use of vibrationally adiabatic basis functions for the calculation of molecular collision cross sections

Comparison is made between the use of two different types of vibrational basis functions for the expansion of the total wave function in a vibrationally inelastic scattering problem. The calculations are performed within the framework of the sudden approximation for the rotational motion of the molecular fragments. The different basis functions that are compared are a vibrationally adiabatic set and the standardly used set of diabatic vibrational basis functions. The adiabatic vibrational basis functions are chosen so as to approximately diagonalize the matrix representation of the interaction potential at each value of the scattering coordinate. Nevertheless, they permit the formulation of analytic expressions for the nonadiabatic coupling terms of the kinetic energy operator that are present when an adiabatic basis is used. In order to provide a reference against which to judge the two different bases, the sets of coupled differential equations which arise in the rotational sudden approximation are solved for the He+H2 system, and fixed-angle S matrices are calculated at several scattering energies and different values of the total angular momenta. It is shown that if the customary diabatic basis is used in conjunction with first order distorted wave perturbation theory to calculate the fixed-angle S matrices, these do not agree well with the exactly computed S matrices to which they should correspond. In contrast, if an adiabatic vibrational basis is used, the distorted wave approximation yields fixed-angle S matrices which are in good agreement (within 15% or better) with the fully converged exact calculations.

Proton–H2 scattering on an a b i n i t i o CI potential energy surface. I. Vibrational excitation at 10 eV

A complete configuration interaction (CI) ground state surface for the H3+ system has been calculated using 5S and 3(Px,Py,Px) basis functions at each center. A total of 650 nuclear geometries has been considered which makes the new surface appropriate not only for scattering calculations, but also for the evaluation of the vibrational–rotational spectrum of the H3+ molecule. Significant deviations are found from the analytic Giese and Gentry potential used in many previous theoretical studies, especially for large and small nonequilibrium H–H separations which are important for vibrational excitation of the H2 molecule. Vibrational–rotational excitation cross sections have been calculated in the rotational sudden approximation where the vibrational degree of freedom is treated exactly by solving seven vibrationally coupled radial equations. The use of the new surface leads to increased vibrational excitation compared to previous calculations utilizing the same scattering approximation and to excellent agreement at 10 eV with the angle-dependent measurements of Hermann, Schmidt, and Linder.

Theoretical studies of vib-rotational excitation in Li +-H 2 collisions at intermediate energies

The rotational sudden approximation has been applied to Li +-H 2 scattering at 5.54 and 8.8 eV, for which few experimental data are available. The vibrational degree of freedom has been treated exactly by solving the coupled radial equations. In the energy range considered the integral cross sections for rotational excitation in the vibrational ground state decrease by 20–30%, while that for excitation of the first vibrational state summed over the final rotational distribution increases by a factor of 2.5. The agreement between theoretical and experimental vibrational transition probabilities for backward scattering is reasonable only at 8.8 eV but very poor at the lower energy, 5.54 eV. The differential cross sections for rotational excitation in the vibrational ground state as well as in the first excited state exhibit broad oscillations with an angular spacing of about Δθ ≈ 20°–30°. A twofold application of semiclassical arguments relates this structure to interferences between different atom-molecule orientations which are treated separately in the sudden approach. Responsible for this new type of interference effect is the strong anisotropy of the repulsive branch of the interaction potential, which becomes gradually more important when the energy is increased.

The rotational sudden approximation at low energies

The infinite-order sudden approximation is studied at low energies for a system with widely spaced energy levels to determine the limits of its validity. It is found that even under these extreme conditions it gives highly accurate results for cross sections summed over final rotational states. The elastic cross sections are also reasonably accurate in this approximation, though, for this worst case situation, the state to state cross sections for inelastic scattering are not even qualitatively correct for high Δj transitions. The high accuracy of the cross sections summed over final rotational states commends the sudden approximation for use in reducing the complexity of carrying rotational channels in the calculation of vibrational transitions. The use of the sudden approximation in studying expansions of interaction potentials is discussed.