Threesimulated expressions are suggested regarding the Z-dependence of groundstate energies of neutral atoms at the Hartree-Fock, exact nonrelativistic and relativistic levels. The Hartree-Fock-level Z^−1/3-expansion contains three previously derivedplus two newly derived terms, the latter signifying exchange corrections from the ‘inner core’ and the ‘core mantle’ of the Lieb atom. This leads to better agreement than any previous expression, with every coefficient being physically transparent. The Z-dependence of the correlation energy is obtained from a semiempirical Wigner-type correlation potential while the relativistic correction is taken to be in between the values suggested separately by Scott and Schwinger. Agreement with reference values is again better than before. It appears, however, that the atomic Z^−1/3-expansion should not proceed beyond terms O(Z).

Gas-surface scattering is speculated as a meaningful problem for understanding the physics of fractals. Fractal behaviour can be associated with a self-similar geometry on a solid surface. The interaction potential for a gas atom or molecule approaching the lattice depends primarily on local factors but a parametric dependence of the cross-section data on the fractal dimension can be conceived. Such a dependence on the self-similar character of a multi-centred target is more explicit when multiple scattering is included. Application of approximation schemes like the previously developed average wavefunction method to this problem is suggested.

Density functional theory (DFT) has not been applied on a large scale to time-dependent problems and problems involving excited states. Atomic and molecular collisions involving both these types of phenomena remain outside the purview of DFT. An amalgamation of quantum fluid dynamics (QFD) with DFT considerably broadens the range of applicability of traditional (ground-state) DFT. Ion-atom collisions have been studied by jointly using DFT and QFD.

It is shown that molecular hardness can be expressed as the geometric mean of the hardness values for constituent atoms. Using this principle the hardness values for several molecules have been calculated from the pertinent atomic data obtained through a five-point finite difference formula. Finally, gradation of several acids and bases into hard, border-line and soft categories has been made on the basis of their calculated hardness values.