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A method to compute two-electron integrals over arbitrary regions of space is introduced and particularized to the basins appearing in the quantum theory of atoms in molecules. The procedure generalizes the conventional multipolar approach to account for overlapping densities. We show that the approach is always convergent and computationally efficient, scaling as N(4) in the worst, two-center case. Several numerical results supporting our claims are also presented.

Wave functions for one-electron diatomic molecules such as H2+ and HeH2+ are analyzed by Bader’s atoms in molecules method. The locations of the degenerate axial critical points in the electron density generated from sigma states arising from the n=1–6 united atom manifolds are shown to correspond well with the boundaries of domains obtained solely from a classical description of the electron motion. The relationship clarifies the connection between the atomic and molecular regimes of classical trajectories and the quantum description of the states. In particular, the classical transition from atomic to molecular character roughly corresponds to the appearance of a critical point in the electron density located on the internuclear axis between the nuclei. The global aspects of the relationship between the classical and quantum descriptions helps to demonstrate the classical framework of the quantum picture.

The existence of integral (Hi¯) in the surplus function variational quantum Monte Carlo approach is discussed and a method is proposed for avoiding the infinity in the calculation of Hi¯. A rigid model of nucleus was adopted to avoid the infinity appearance of r−i. Discussion of a new solution for Schrodinger’s equation of hydrogen atom, which may make the calculation of the Hi¯ value more accurate is also presented.

We present a quantum theory of scattering of an atom from a solid surface. The formalism is constructed by assuming that the solution of two simpler problems is known; one of them is scattering of the atom by the average lattice potential; the other is the motion of the lattice in the absence of the scattering atom. The theory includes the effect of the thermal motion of the surface atoms as well as multiphonon energy transfer processes. The derivation assumes that the thermal fluctuations of the projectile–lattice potential and the energy of the distortion of the lattice by the projectile can be treated as perturbations.

A more general description of the Cotton—Mouton effects in atoms and molecules is presented. By use of a time‐dependent double perturbation approach, closed and spectral expansion expressions of required molecular parameters are derived. The method is applied to the hydrogen atom to generate accurate Cotton—Mouton dispersion curves for a wide range of wavelengths, including the first two lines of the Lyman series.