Semiclassical self-consistent field perturbation theory for the hydrogen atom in a magnetic field

A recently developed perturbation theory for solving self-consistent field equations is applied to the hydrogen atom in a strong magnetic field. This system has been extensively studied using other methods and is therefore a good test case for the new method. The perturbation theory yields summable large-order expansions. The accuracy of the self-consistent field approximation varies according to field strength and quantum state but is often higher than the accuracy from adiabatic approximations. A new derivation is presented for the asymptotic adiabatic approximation, the most useful of the adiabatic approaches. This derivation uses semiclassical perturbation theory without invoking an adiabatic hypothesis. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 183–192, 1998     

Semiclassical theory for atom—surface scattering: Calculations on Ar + W(110)

By using a semiclassical approach we derive an effective potential which governs the motion of the colliding atom/molecule. The effective potential depends on the surface temperature and the phonon excitation during the collision. Numerical results on Ar + W(110) are discussed and compared with experimental data.     

Semiclassical exponential perturbation theory. An adiabatic approach for rotationally inelastic scattering

The exponential perturbation approximation is tested in the semiclassical perturbed stationary states frame, using spline functions for interpolation of the non-adiabatic couplings. An application is realized for the p-H₂ + ⁴He rotational cross sections.     

Semiclassical theory of atom-solid surface collisions: Elastic scattering

The elastic scattering of atoms from solid surfaces is examined within the semiclassical framework. Explicit expression for diffraction intensities are obtained which utilize classical trajectory information as the computational device. Effect of lattice disorder are examined.The results of Beeby and Weinberg are considered.An alternative method for extracting the surface atom displacements and the attractive well depth of the atom-surface interaction is discussed.     

Semiclassical theory for diatom-diatom collisions

A semiclassical approach to diatom-diatom collisions is presented. The method involves a classical treatment of the translational and rotational motion of both molecules. The vibrational degrees of freedom are quantized using a Morse oscillator approximation. The method is used to evaluate the accuracy of previous calculations based upon the energy-corrected harmonic-oscillator approach.     

Semiclassical scattering matrix for two-state exponential model

A semiclassical scattering matrix for the two-state problem with one non-adiabaticity region is discussed. The Stueckelberg phases for an exponential model are obtained and some limiting cases are considered.     

Atomic scattering factors for heavy atoms as investigated by small-angle gas electron diffraction

The experimental examination of the elastic and inelastic scattering factors for tin, iodine and mercury has been performed through the total-intensity     

Exponential perturbation theories for inelastic scattering

An Exponential Perturbation Theory (EPT) is derived whereby one calculates a phase-shift matrix by an nth order perturbation theory and then exponentiates it to obtain the scattering matrix. The theory has been developed to include high-order terms, closed channels and resonances. The radial wavefunctions used are WKB solutions which are generalized to cases where there are multiple turning points. The orbital angular momentum may be treated exactly or in the classical or sudden limits. Calculations are done for the rotationally inelastic scattering in He + H₂, Ar + N₂ and Ar + HCl. The first two systems give fair to good agreement with accurate calculations; the last case gives poor agreement. The first-order EPT is very much better than the first-order distorted-wave approximation.     

Differential cross sections from classical perturbation scattering theory. I. ion—dipole scattering

The formalism for calculating differential cross sections for atom—molecule scattering using classical perturbation scattering theory (CPST) is developed. The results are applied to the scattering of an ion by a dipolar molecule. The interaction potential used in the calculation consists of the ion—dipole and ion—induced dipole terms in the long-range expansion of the potential. Various approximate methods for calculating differential cross sections are also considered.     

Rotational transitions and diffraction in D2 scattering from the LiF(001) surface: theory and experiment

High probabilities of energy transfer from translation to molecular rotations are observed in the scattering of n-D(2) from LiF(001) at an incident beam energy of 85.3 meV. For the 100 incidence direction, close-coupling calculations yield ratios of the rotationally inelastic (j=0-->2) and (j=1-->3) peaks to the rotationally elastic specular peaks (G=0) that are in reasonable agreement with experiment, as are the ratios of the rotationally elastic diffraction peak intensities to the specular peak intensities. The agreement between theory and experiment is also quite good for the rotationally inelastic diffractive (-1-1) transitions for (j=1-->3), but rather poor for (j=0-->2). The calculations show that the interaction between the electrostatic field of the surface ions and the quadrupole moment of the D(2) molecule efficiently promotes the (j=0-->2) and (j=1-->3) transitions. If this electrostatic interaction is excluded from the potential model, the ratios of the (j=0-->2) and (j=1-->3) rotationally inelastic peaks to the corresponding specular peaks show a large discrepancy with experiment, underlining the importance of this interaction. The close-coupling calculations show a somewhat worse agreement with experiment for the 110 incidence direction. In particular, the sharp peaks observed experimentally in the ratios of the peak intensities of the rotationally inelastic G=0 (j=0-->2) and (j=1-->3) to the rotationally elastic G=0 transitions as a function of incident angle are not reproduced by the calculations. The theoretical ratios of the peak intensities of the rotationally elastic diffraction to G=0 transitions are shifted to lower incidence angles with respect to experiment. The rotationally inelastic diffractive (-10) transitions present an interesting resonance phenomenon for the (j=0-->2) rotational transition. This resonance is predicted by both theory and experiment, although at rather different incident angles.     

Bounds for Hartree-Fock perturbation theory

Upper and lower bounds for the second-order energy in both coupled and uncoupled Hartree-Fock perturbation theories are derived. Using these bounds inequalities are derived for the error in the geometric approximation.     

Coupled-channel calculations and the accuracy of the sudden approximation for atom—surface scattering

Exact coupled-channel calculations are presented for the scattering of Ne from W(110) and He from LiF(001), using symmetry to partly decouple the scattering equations. The results are used to test the recently proposed sudden approximation. For Ne/W(110), typical of all metals, the sudden approximation gives excellent quantitative accuracy. For the very unfavorable system He/LiF(001) good semiquantitative agreement is found with the exact results. It is concluded that the sudden approximately provides an efficient and accurate tool for atom—surface scattering calculations.     

Hyperthermal Ar atom scattering from a C(0001) surface

Experiments and simulations on the scattering of hyperthermal Ar from a C(0001) surface have been conducted. Measurements of the energy and angular distributions of the scattered Ar flux were made over a range of incident angles, incident energies (2.8-14.1 eV), and surface temperatures (150-700 K). In all cases, the scattering is concentrated in a narrow superspecular peak, with significant energy exchange with the surface. The simulations closely reproduce the experimental observations. Unlike recent experiments on hyperthermal Xe scattering from graphite [Watanabe et al., Eur. Phys. J. D 38, 103 (2006)], the angular dependence of the energy loss is not approximated by the hard cubes model. The simulations are used to investigate why parallel momentum conservation describes Xe scattering, but not Ar scattering, from the surface of graphite. These studies extend our knowledge of gas-surface collisional energy transfer in the hyperthermal regime, and also demonstrate the importance of performing realistic numerical simulations for modeling such encounters.     

Explicitly correlated second-order perturbation theory calculations on molecules containing heavy main-group elements

Slater-type geminals (STGs) have been used as explicitly correlated two-electron basis functions for calculations on the hydrides of N–As and Sb (as well as on the hydrides of O–Se and F–Br with similar, not reported results) in various one-electron basis sets of Gaussian atomic orbitals. The performance of the explicitly correlated theory has been assessed with respect to the exponent of the STG, for example, by using different exponents for individual pair correlation functions and pair energies. It is shown that a correlation factor with an exponent of ${\gamma = 1.4 a_{0}^{-1}}$ can give reliable results within 1% from the basis-set limit for all investigated molecules in an aug-cc-pVQZ basis set for the valence shells, using fixed amplitudes for the STGs in a diagonal orbital-invariant formulation of the theory. The use of relativistic effective core potentials (RECPs) in explicitly correlated second-order perturbation theory has been investigated.