Effect of Interaction Potential on Laser-assisted e-Ar Scattering

The interaction potentials between electron and atom play an important role in electron-atom scattering. Using three potential models, the absolute differential cross section has been calculated by the second Born approximation theory. Results show that these model potentials are successful in the laser-assisted e-Ar scattering system. The influence of static potential, exchange potential and polarization potential on the absolute differential cross section is also analyzed and discussed.     

Volterra inverse scattering series method for one‐dimensional quantum barrier scattering

The Volterra inverse scattering series method is developed to obtain the interaction potential for one‐dimensional quantum barrier scattering problems. The Lippmann–Schwinger equation describing quantum barrier scattering is renormalized from a Fredholm to a Volterra integral equation. Employing the Born–Neumann series solution of the Lippmann–Schwinger Volterra equation and a related expansion of the interaction potential in orders of the data, we derive the Volterra inverse scattering series for the reflection and transmission amplitudes. Each term of the interaction potential is computed using the scattering amplitude and the Volterra Green's function. We do not consider the separate issue of extracting scattering amplitudes from quantum cross sections. The triangular nature of the Volterra Green's function significantly reduces computational effort. The Volterra series is then applied to several one‐dimensional quantum barrier scattering problems. Computational results show that the first few terms in the Volterra series can yield accurate interaction barriers. In addition, the potential barriers are calculated using the Born inverse scattering series based on the Lippmann–Schwinger Fredholm equation with the reflection amplitude. The comparison between the Born and Volterra results demonstrates that the Volterra inverse scattering series can provide a more accurate and more efficient method for determining the interaction potential.     

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.     

Atom-molecule scattering with the average wavefunction method

The average wavefunction method (AWM) is applied to atom-molecule scattering. In its simplest form the labor involved in solving the AWM equations is equivalent to that involved for elastic scattering in the same formulation. As an initial illustration, explicit expressions for the T-matrix are derived for the scattering of an atom and a rigid rotor. Results are presented for low-energy scattering and corrections to the Born approximation are clearly evident. In general, the AWM is particularly suited to polyatom scattering due to its reduction of the potential in terms of a separable atom-atom potential.     

A computational method for multi-channel scattering calculations. Applications to rotational excitation and long-lived states of He-N2

A computational scheme is reported which uses a reference potential approximation to provide an efficient numerical solution of the multi-channel Volterra integral equation. Applications to rotational inelastic scattering and quasi-bound states of the He-N₂ system are presented, together with a discussion of the effects of varying the number of closed channels.     

Dimensionality control of coupled scattering equations using partitioning techniques

A method of variable reduction of the dimensionality of the coupled equations for inelastic scattering is presented, based upon a projection operator P with a restricted range of orbital angular momentum states. For rotational states in the range O?j ?j^* and total angular momentum large, the coupled equations have dimensionality (j^* + 1) ? N ?(j^* + 1)², where the value of N is controlled by the choice of P. This is in contrast to conventional partitioning techniques which utilize further restrictions on the important molecular rotational states. The equations for the P subspace and its complementary Q subspace are decoupled by an approximation on the equation of motion of Qψ_scat. Information about scattering into the Q subspace is retained, within this degree of approximation, and is reintroduced at the end of the computation with little additional labor. The theory is developed in terms of atom-rigid-rotor scattering, although addition of vibrational modes would not in any way interfere with the basic techniques used.     

Fragment-based quantum mechanical methods for periodic systems with Ewald summation and mean image charge convention for long-range electrostatic interactions

We describe an Ewald-summation method to incorporate long-range electrostatic interactions into fragment-based electronic structure methods for periodic systems. The present method is an extension of the particle-mesh Ewald technique for combined quantum mechanical and molecular mechanical (QM/MM) calculations, and it has been implemented into the explicit polarization (X-Pol) potential to illustrate the computational details. As in the QM/MM-Ewald method, the X-Pol-Ewald approach is a linear-scaling electrostatic method, in which the short-range electrostatic interactions are determined explicitly in real space and the long-range Ewald pair potential is incorporated into the Fock matrix as a correction. To avoid the time-consuming Fock matrix update during the self-consistent field procedure, a mean image charge (MIC) approximation is introduced, in which the running average with a user-chosen correlation time is used to represent the long-range electrostatic correction as an average effect. Test simulations on liquid water show that the present X-Pol-Ewald method takes about 25% more CPU time than the usual X-Pol method using spherical cutoff, whereas the use of the MIC approximation reduces the extra costs for long-range electrostatic interactions by 15%. The present X-Pol-Ewald method provides a general procedure for incorporating long-range electrostatic effects into fragment-based electronic structure methods for treating biomolecular and condensed-phase systems under periodic boundary conditions.     

Total cross sections for electron scattering by polyatomic molecules at 10–1000 eV: C2H2, C2H4, C2H6, C3H6, C3H8 and C4H8

A model complex optical potential (composed of static, exchange, polarization and absorption terms) is employed to calculate the total (elastic and inelastic) electron-atom scattering cross sections from the corresponding atomic wave function at the Hartree-Fock level. The total cross sections (TCS) for electron scattering by their corresponding molecules (C₂H₂, C₂H₄, C₂H₆, C₃H₆, C₃H₈ and C₄H₈) are firstly obtained by the use of the additivity rule over an incident energy range of 10–1000 eV. The qualitative molecular results are compared with experimental data and other calculations wherever available, good agreement is obtained in intermediate-and high-energy region.     

Ultracold collisions and reactions of vibrationally excited OH radicals with oxygen atoms

We report a quantum dynamics study of O + OH (v = 1, j = 0) collisions on its ground electronic state, employing two different potential energy surfaces: the DIMKP surface by Kendrick and Pack, and the XXZLG surface by Xu et al. A time-independent quantum mechanical method based on hyperspherical coordinates has been adopted for the dynamics calculations. Energy-dependent probabilities and rate coefficients are computed for the elastic, inelastic, and reactive channels over the collision energy range E(coll) = 10(-10)-0.35 eV, for J = 0 total angular momentum. Initial state-selected reaction rate coefficients are also calculated from the J = 0 reaction probabilities by applying a J-shifting approximation, for temperatures in the range T = 10(-6)-700 K. Our results show that the dynamics of the collisional process and its outcome are strongly influenced by long-range forces, and chemical reactivity is found to be sensitive to the choice of the potential energy surface. For O + OH (v = 1, j = 0) collisions at low temperatures, vibrational relaxation of OH competes with reactive scattering. Since long-range interactions can facilitate vibrational relaxation processes, we find that the DIMKP potential (which explicitly includes van der Waals dispersion terms) favours vibrational relaxation over chemical reaction at low temperatures. On the DIMKP potential in the ultracold regime, the reaction rate coefficient for O + OH (v = 1, j = 0) is found to be a factor of thirteen lower than that for O + OH (v = 0, j = 0). This significantly high reactivity of OH (v = 0, j = 0), compared to that of OH (v = 1, j = 0), is attributed to enhancement caused by the presence of a HO(2) quasibound state (scattering resonance) with energy near the O + OH (v = 0, j = 0) dissociation threshold. In contrast, the XXZLG potential does not contain explicit van der Waals terms, being just an extrapolation by a nearly constant function at large O-OH distances. Therefore, long-range potential couplings are absent in calculations using the XXZLG surface, which does not induce vibrational relaxation as efficiently as the DIMKP potential. The XXZLG potential leads to a slightly higher reactivity (a factor of 1.4 higher) for O + OH (v = 1, j = 0) compared to that for O + OH (v = 0, j = 0) at ultracold temperatures. Overall, both potential surfaces yield comparable values of reaction rate coefficients at low temperatures for the O + OH (v = 1, j = 0) reaction.     

Long-range interactions between an atom in its ground S state and an open-shell linear molecule

Theory of long-range interactions between an atom in its ground S state and a linear molecule in a degenerate state with a nonzero projection of the electronic orbital angular momentum is presented. It is shown how the long-range coefficients can be related to the first and second-order molecular properties. The expressions for the long-range coefficients are written in terms of all components of the static and dynamic multipole polarizability tensor, including the nondiagonal terms connecting states with the opposite projection of the electronic orbital angular momentum. It is also shown that for the interactions of molecules in excited states that are connected to the ground state by multipolar transition moments additional terms in the long-range induction energy appear. All these theoretical developments are illustrated with the numerical results for systems of interest for the sympathetic cooling experiments: interactions of the ground state Rb((2)S) atom with CO((3)Π), OH((2)Π), NH((1)Δ), and CH((2)Π) and of the ground state Li((2)S) atom with CH((2)Π).     

Electron scattering with H2S and PH3 molecules

Calculated total, differential and momentum transfer cross sections are reported for the vibrationally elastic scattering of electrons from H₂S and PH₃ molecules in the range of energy 0.1–50 eV. The scattering process is approximated by two incoherent scatterings caused, separately, by a central field and a long-range electric dipole interaction. The central field is calculated with a spherical approximate molecular wave function, in which the exchange interaction is treated in two ways: (i) exactly within the accuracy of the molecular wave function; (ii) approximately by a local model potential. The scattering by the central field is calculated with partial wave expansion technique, while the scattering by the electric dipole potential is calculated by using the first Born approximation for a rotating dipole model with experimental values of the dipole moments of H₂S and PH₃. The total cross sections are approximated by the incoherent sum of the cross section due to the central potential and the cross section of 00→10 rotational transition caused by the electric dipole potential. The effects of the polarization interaction are also tested. The contribution of small-angle scattering to the integral cross section is analyzed for these weakly polar molecules with some quantitative comparison.     

Accuracy and convergence of higher order distorted wave perturbation theory

A distorted wave perturbation theory which allows for a different distortion potential for each channel is investigated. The method is closely related to a perturbative solution of close coupled equations. Improvement in first order is found. However, higher order terms are not significantly improved over other computationally more convenient approaches. For purposes of comparison, numerical results are given for the oscillator atom collinear collision. The convergence of series solutions is studied as a function of scattering parameters. The accuracy of several approximation schemes is also investigated.     

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     

A study of the valence interaction integrals in effective core potential applications

The valence interactions in two effective core potential (ECP) methods, the frozen orbital ECP and the method of Sakai and Huzinaga, are shown to yield atomic valence orbital Coulomb and exchange interaction integrals closely approximating all-electron calculations. The ECP approximation is studied in some detail with special application to the ScO molecule. The too short bond distance in ScO when the 3s. 3p orbitals are included in the core is shown to stem from a long-range attraction of the ECP.     

Nonlocal ion potential effects on the optical response of lithium clusters

We present a spherical symmetry model, containing explicitly nonlocal effects in the electron-ion interaction, to describe the electronic properties of lithium clusters. We assume either an optimized discrete ionic structure or a jellium structure. The model provides the nonlocal potential from which the random phase approximation with exact exchange is applied to calculate the optical response of Li clusters. The optical response of Li ₁₃₉ ⁺ obtained within this model is in good agreement with the measured giant dipole resonance. The same model is used to predict alkali-metal effective masses; the agreement with band structure calculations is emphasized.     

Energy conserving approximations to the quantum potential: dynamics with linearized quantum force

Solution of the Schrodinger equation within the de Broglie-Bohm formulation is based on propagation of trajectories in the presence of a nonlocal quantum potential. We present a new strategy for defining approximate quantum potentials within a restricted trial function by performing the optimal fit to the log-derivatives of the wave function density. This procedure results in the energy-conserving dynamics for a closed system. For one particular form of the trial function leading to the linear quantum force, the optimization problem is solved analytically in terms of the first and second moments of the weighted trajectory distribution. This approach gives exact time-evolution of a correlated Gaussian wave function in a locally quadratic potential. The method is computationally cheap in many dimensions, conserves total energy and satisfies the criterion on the average quantum force. Expectation values are readily found by summing over trajectory weights. Efficient extraction of the phase-dependent quantities is discussed. We illustrate the efficiency and accuracy of the linear quantum force approximation by examining a one-dimensional scattering problem and by computing the wavepacket reaction probability for the hydrogen exchange reaction and the photodissociation spectrum of ICN in two dimensions.     

SC Cellular multiple scattering in molecular electronic structure calculations

Recent advances in the statistical exchange approximation to the one-electron potential and in the use of general potentials in multiple scattering are studied numerically and combined in a cellular multiple scattering calculation of the electronic structure of molecules. The particular examples of these calculations are SF₆, H, and H₂, the results being compared with those of previous approximations and other techniques. It is first seen that the Xαβ approximation or a similar one based on the use of a universal parametrization of the statistical exchange (and some effects of correlation) part of the potential will provide the maximum of freedom in the partition of the real space of the molecules into cells. This avoids arbitrariness in the assumed value of the parameters to be used in every cell. The usefulness of the Xαβ approximation in a muffin-tin and in a cellular calculation is discussed. It is also found that the usual limitation to muffin-tin-like potentials, while simpler as a first approximation, can be removed without unduly increasing the computing effort. However, an accurate evaluation of the real self-consistent potential in each cell (or even in a muffin-tin) will increase the length of the program, the storage necessities and the computing time by a factor estimated to be between three and ten according to the geometry considered. It is concluded that the cellular multiple scattering method offers the best possibilities for a systematic use of multiple scattering techniques in molecular calculations.