The Born closure approximation for the scattering amplitude of an electron-molecule collision

When the fixed-nuclei (FN) approximation is applied to the calculation of electron scattering from a polar molecule, the resulting cross section diverges in the forward direction of scattering. This is due to the long-range nature of the interaction between the electron and the molecular dipole. To avoid this difficulty, a hybrid method is proposed for the calculation of the scattering amplitude. This method is based on the FN approximation for a close collision and the Born approximation for a distant collision. The present paper describes the detailed formulation of the method for practical applications. Furthermore the present approach is extended to other long-range interactions (due to quadrupole moment and/or polarization effect) and to a dipole-allowed vibrational excitation. In these cases, while no divergence occurs, it is often difficult to confirm the convergence of the partial-wave expansion. With the employment of the present approach, it is much easier to confirm the convergence and hence to obtain reliable cross sections. The formulas are given for diatomic molecules as well as for polyatomic ones. Received: 12 June 2000 / Accepted: 6 July 2000 / Published online: 24 October 2000     

Elastic scattering of electrons by H2 in the born approximation

This paper presents accurate computation of the differential cross sections for the elastic and vibrational excitation of ground state H₂ by fast electrons. The electronic matrix elements are evaluated at 20 internuclear separations and proper averaging over vibrational wavefunctions is carried out. The comparison to experiment yields excellent agreement. Different computational procedures appropriate for low and moderate values of momentum transfer are compared.     

On the calculation of the electron capture within the strong potential born approximation

A new method to perform the calculation the limits of the electron capture cross-section in the Strong Potential Born Approximation is presented. Within this approach, the high velocity limit is obtained by a simple algebraic procedure as an alternative derivation to the complex variable analysis used previously.     

An application of the refined born approximation to the solution of coupled equations involved in electron-ion and electron-atom scattering problems

A new approach to the solution of coupled equations involved in electron-ion and electron-atom scattering problems is proposed. This method is a combination of iteration and variation procedures. The main advantage of this method is that exchange terms can be calculated in a direct and straightforward manner. The method is based on the Lippmann-Schwinger equation and does not require trial functions satisfying appropriate boundary conditions. Using the Volterra formulation one can find the solution on an interval determined by the range of the exchange potential and the long-range potential terms can be taken into account by a projection procedure giving the asymptotic value of the reactance matrix. The method is tested on the case of electron-hydrogen atom scattering in the 1s-2s and 1s-2s-2p approximation.We have adapted the method proposed originally by Rayski to obtain solutions of coupled equations involved in electron-ion and electron-atom scattering. As mentioned in section 1 the construction of the method secures an automatic fulfilment of the boundary conditions. It allows an easy calculation of the exchange potential as well as an estimation of the introduced approximation. It gives also a possibility of detecting any spurious convergence. Moreover, it is important that this formalism can be applied in the case of normalized as well as unnormalized initial integral equations. This fact is of special importance in the case of long-range interactions. When the method is used for unnormalized (Volterra) equations it allows application of a very convenient projection procedure for treating the long-range terms in the direct potential.Electron-hydrogen atom collisions are investigated as a numerical illustration of the method. In the 1s-2s approximation the normalized equations were solved, while in the 1s-2s-2p approximation the solution was obtained with the help of Volterra equations and the long-range terms of the direct potential were taken into account by the projection procedure. In both cases the calculations were performed in the first iteration step and the obtained solutions agree fairly well with the results obtained by a numerical integration. It is not clear which set of results is more accurate. The numbers of parameters needed to obtain these results was not too large (not more than twenty in each channel) and decreased with the increase of the values of angular momentum and energy. The calculations were performed without weight functions, although the use of an appropriate weight function can improve the effectiveness of the method. This effectiveness could also be improved through a more lucky choice of trial functions.     

Bound and scattering states for a hyperbolic‐type potential in view of a new developed approximation

A new developed approximation is used to obtain the arbitrary l‐wave bound and scattering state solutions of Schrödinger equation for a particle in a hyperbolic‐type potential. For bound state, the energy eigenvalue equation and unnormalized wave functions in terms of Jacobi polynomials are achieved using the Nikiforov–Uvarov (NU) method. Besides, energy eigenvalues are calculated numerically for some states and compared with those given in the literature to check accuracy of our results. For scattering state, the wave function is found in terms of hypergeometric functions. Furthermore, scattering amplitude and phase shifts are achieved using scattering solutions. Also it is shown that the energy eigenvalue equation obtained from analytic property of scattering amplitude is same with one obtained using NU method. © 2015 Wiley Periodicals, Inc.     

Molecular structure and the born—Oppenheimer approximation

A discussion is attempted of the validity of the Born—Oppenheimer approximation which is characterized as an asymptotic analysis leading to a semiclassical theory of molecular structure. It is suggested that there are inherent defects in the resulting semiclassical theory which will limit its utility in the explanation of highly accurate experiments involving molecules.     

Derivation from coupled channel equations of the resonance raman scattering amplitude for a diatomic molecule

The coupled equations of molecular collision theory can be formulated in such a way as to yield the amplitude for resonance Raman scattering of light by a diatomic molecule. Two variants of the method can be adopted, characterized by different choices for the potential matrices. All molecular potentials, either analytical or numerical, are treated on the same footing. Tests of accuracy are presented for the case of harmonic potentials intersected by linear potentials, for which an exact analytical solution can be given.     

Neutron scattering from a deformed “vander Waals chain”-quasi Gaussian approximation

We calculate the neutron scattering form of an affinely deformed van der Waals chain, i.e., a labeled chain embedded in a network, whose deformation behavior can be described by an effective van der Waals equation in an effective Gaussian approximation. This provides microscopic information about the deformation behavior of van der Waals networks and complements the macroscopic information given by stress-strain relations.dedicated to Prof H.-G. Kilian on occasion of his 66th birthday     

A simple but fully nonlocal correction to the random phase approximation

The random phase approximation (RPA) stands on the top rung of the ladder of ground-state density functional approximations. The simple or direct RPA has been found to predict accurately many isoelectronic energy differences. A nonempirical local or semilocal correction to this direct RPA leaves isoelectronic energy differences almost unchanged, while improving total energies, ionization energies, etc., but fails to correct the RPA underestimation of molecular atomization energies. Direct RPA and its semilocal correction may miss part of the middle-range multicenter nonlocality of the correlation energy in a molecule. Here we propose a fully nonlocal, hybrid-functional-like addition to the semilocal correction. The added full nonlocality is important in molecules, but not in atoms. Under uniform-density scaling, this fully nonlocal correction scales like the second-order-exchange contribution to the correlation energy, an important part of the correction to direct RPA, and like the semilocal correction itself. For the atomization energies of ten molecules, and with the help of one fit parameter, it performs much better than the elaborate second-order screened exchange correction.     

The capture of inner-shell electrons in the strong-potential born (SPB) approximation

For the first time the capture of inner-shell electrons by protons is calculated by the SPB method without further approximation and using Hartree-Slater wavefunctions. The resulting cross-section has roughly the correct shape, but is much too large. The problem is traced to a loss of normalization caused by the SPB approximation. A suitably renormalized SPB gives close agreement with experiment.     

The parameterization and validation of generalized born models using the pairwise descreening approximation

Generalized Born Surface Area (GBSA) models for water using the Pairwise Descreening Approximation (PDA) have been parameterized by two different methods. The first method, similar to that used in previously reported parameterizations, optimizes all parameters against the experimental free energies of hydration of organic molecules. The second method optimizes the PDA parameters to compensate only for systematic errors of the PDA. The best models are compared to Poisson-Boltzmann calculations and applied to the computation of potentials of mean force (PMFs) for the association of various molecules. PMFs present a more rigorous test of the ability of a solvation model to correctly reproduce the screening of intermolecular interactions by the solvent, than its accuracy at predicting free energies of hydration of small molecules. Models derived with the first method are sometimes shown to fail to compute accurate potentials of mean force because of large errors in the computation of Born radii, while no such difficulties are observed with the second method. Furthermore, accurate computation of the Born radii appears to be more important than good agreement with experimental free energies of solvation. We discuss the source of errors in the potentials of mean force and suggest means to reduce them. Our findings suggest that Generalized Born models that use the Pairwise Descreening Approximation and that are derived solely by unconstrained optimization of parameters against free energies of hydration should be applied to the modeling of intermolecular interactions with caution.     

Complex model optical potential for electron scattering from oxygen

We report calculations of the total (elastic plus inelastic) cross-sections for the e-O system over a wide energy range 10–5000 eV. A local complex optical potential is calculated for the system using the atomic wavefunctions at the Hartree-Fock level. The real part of potential is composed of the attractive static, correlation polarisation and exchange potential. The imaginary component of the complex potential is a function of target charge density, incident electron energy and mean excitation energy. The resulting complex potential is treated in variable phase approach to yield complex phase shifts and total cross-sections. The total and elastic cross-sections are compared with the other available results. The agreement is excellent for total cross-sections with other theoretical work at energies greater than 100 eV. We have excellent agreement for elastic cross-sections with the experimental and theoretical results at all the energies. The elastic differential cross-sections are presented at 50 eV and 1000 eV. We fit the absorption cross-section values to Bethe asymptotic formula in high energy range (≥ 5500 eV). Ionisation cross-sections above 1000 eV are also deduced from the theory.     

Calculation of the potential energy surface of a polyatomic molecule in an adiabatic approximation

V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 6, pp. 1142–1144, November–December, 1995     

Calculation of the glory scattering with anisotropic molecule-atom interactions in sudden approximation

For specified rotational states glory phenomena are investigated in sudden approximation under influence of angle dependent terms in the intermolecular potential. The distance at which the intermolecular potential is probed by the anisotropic glory undulation is R ≈ 0.96 R_m, for LJ 12-6 potentials, i.e. the well defined probing distance nearly coincides with the classical turning point of the glory ray. For a specific choice of the ratio of anisotropy parameters, q_2,12/q_2,6, ≈ 1.5, the anisotropic glory changes sign. Quenching of the state averaged glories practically disappears for q_2,12/q_2,6 ≈ 2 (e.g. for NO-Ar). The method of calculation is tested against a full partial wave treatment.     

Calculation of the exciton green's function of a molecular crystal from a two-site dynamical coherent potential approximation

A new two-site dynamical coherent potential approximation for exciton-phonon interaction models corresponding to a homomorphic partition of the hamiltonian is described. The renormalization of both the site energy and the exciton bandwidth is accomplished in contrast to single-site CPA models.     

Quantum reactive scattering with a transmission-free absorbing potential

A recently derived transmission-free absorbing potential is applied to the study of atom-diatom chemical reactions. This absorbing potential only depends on a single parameter--the width of the absorbing region--and its reflection properties are guaranteed to improve as this parameter is increased. Converged results can therefore be obtained very easily, as we illustrate with time-dependent wave packet calculations on the H + H2,F + H2, and H + O2 reactions.