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Large scale CI calculations of frequency-dependent dipole polarizabilities (FDPs) of ground state BH at the experimental distance of R = 2.329a0 have been performed using two sets of contracted GTO functions involving up to 316 × 106 symmetry-adapted Slater determinants, comparing recently developed interpolation and variational techniques. Final calculation of BH–BH dispersion coefficients was done using the larger basis set of 268 AOs in the frozen-core FCI approximation and the lower bounds resulting from the variational approach.

The solution of the asymptotic quantum mechanical differential equations in the neighbourhood of singular points is suggested to overcome some complexities occurring with the technique of the indicial equations. After separation of the variables, the differential equations are solved in their asymptotic regions, the general regular solutions in the whole interval being then found by replacing integration constants by functions of the variables and finding the differential equations determining these functions. The resulting differential equations are now free from singularities and can be solved by the usual series expansion, giving simple polynomial solutions for the harmonic oscillator and the hydrogen atom and more complicated solutions for H 2 + .

In a previous paper on the Keesom effect, we presented a procedure for the evaluation of the average potential energy of interaction between two dipoles of strength μ a distance R apart in the limit of small temperature T . The resulting expansion in terms of the dimensionless T -dependent parameter a = − μ 2 / R 3 kT was then proved by us to be an asymptotic one. Here we reformulate our method in a simplified form, extending it to include the quantum effects which must be taken into account in the low-temperature regime. The resulting formulae show explicitly the transition from the quantum regime to the classical one as a function of temperature.

A self-consistent theory of the linear response previously developed by one of us is applied to the dipole–dipole dispersion interaction of two ground state H atoms in the united atom (He) limit, using a Sellmeier representation of the polarizability in terms of pseudostates. Numerical calculations show that a truncated 12-term expansion out of the N = 22 H(1s) dipole pseudospectrum built from STOs with orbital exponent c = 0.985 gives a result exceeding by no more than 5% the variational result for the He dispersion energy.

Frozen-core full-CI calculations of frequency-dependent dipole polarizabilities (FDPs) of ground state BeH 2 at the experimental distance of R = 2.506 a 0 have been performed using an extended set of 208 contracted GTO functions [9s9p5d3f] on Be and [9s8p6d] on H involving about 58 × 10 6 symmetry-adapted Slater determinants. The Casimir–Polder integral was then evaluated analytically using eight optimized imaginary frequencies chosen according to a recently developed interpolation technique which allows for the evaluation of the three dipole dispersion constants for the BeH 2 –BeH 2 homodimer, from which isotropic C 6 and anisotropy γ 6 coefficients are derived for the first time.

Fluctuation theory techniques are used to evaluate short-range interactions in ground state H 2 + by calculating in a direct way small energy differences taken with respect to the ground state of the united atom He + . Appropriate coordinate transformation allows to obtain inner and outer Hermitean eigenvalue equations, which are then solved perturbatively in positive powers of the internuclear distance R choosing He + as unperturbed problem. The separation constants are deduced from the regularity conditions on the functions. Next, the function endowed with the right symmetry is constructed by solving an integral equation in a perturbative way. A second-order approximation gives short-range interaction coefficients which are exact up to R 5 .

An elementary technique has been developed to intercept available values of a given atomic or molecular multipole dynamic polarizability through an expression providing a faithful representation for its dependence on the imaginary frequency. The explicitation of the implied interpolative parameters is obtained by imposing that the available data ought to be exactly intercepted. Numerical tests concerning a ground state hydrogen atom have confirmed the reliability of such interpolative procedure for extracting continuous trends from some initial estimates performed on multipole polarizabilities and for evaluating dispersion constants.

Ordinary LCAO-MO theory allows for the ab-initio definition of α and β parameters occurring in the Huckel theory including overlap of simple σ homonuclear systems. One- and two-electron terms not included in Huckel theory are explicitly considered. When such correction terms are neglected in the very spirit of Huckel theory, simple calculation in the hydrogenic approximation for the ground states of H2+, H2, He2+, He2 at the corresponding bond lengths shows semiquantitative agreement with experimental or accurate theoretical results for the bond energies, providing a simple and clear physical picture of the nature of the chemical bond.

Small well-shaped basis sets have been used to perform highly accurate variational-perturbative evaluations of dynamic (frequency-dependent) multipole polarizabilities for a hydrogen atom in its ground state. Their structure has been suggested by the ab initio polynomial power expansion we have recently developed to get correspondingly exact results within a finite range covering the region of low frequencies. The frequency-dependent coefficients of the optimized linear combinations of the excited pseudostate orbitals were obtained by diagonalizing the representative matrix of the excitation operator from the ground state. High levels of accuracy have been observed over a set of frequencies now covering the complete real and imaginary ranges.

A recently proposed exact power expansion for the dynamic (frequency-dependent) multipole polarizabilities of a ground-state hydrogen atom has been improved keeping its simple polynomial structure substantially unaffected and enlarging its range of convergence. The improvement is performed by adding unexpanded frequency terms taken from the formal expression of the polarizability as a sum-over-states and subtracting their corresponding power expansions. The enlarged range of convergence obtained in this way covers all real frequencies of physical importance and the related imaginary frequencies.

The Guillemin-Zener wavefunction for the ground and excited states of H + 2 is improved in terms of a separate double expansion in powers of confocal spheroidal coordinates. Variational optimization by the Ostrowski method shows that no more than 15 linear coefficients are needed to yield for both states practically exact interaction energies over the whole range of nuclear separations.

The bond-orbital approach to short-range intermolecular interactions is extended to include polarization and delocalization effects using second-order perturbation theory. Ab initio calculations on H 4 show that results based on a nonorthogonal BO SCF wavefunction closely approach the full MO ones, whereas different orthogonalizatkm procedures give corrections which depend heavily on the accuracy of the one-configuration result.

A generalised London formula is presented for the one-centre calculation of dispersion coefficients of spherically symmetric atoms in S-states in terms of the static multipole polarisabilities and the related orbital excitation energies of the individual atoms. The results obtained for the C6, C8, C10 coefficients for H2 and for the C6 coefficients for He2, Li2, Be2 and their mixtures are highly encouraging.

For many-electron atoms (molecules) the calculation of long-range interactions by the variation-perturbation method is ambiguous when the eigenfunction ψ 0 describing separate non-interacting atoms is not accurately known. Double-perturbation theory is suggested as a systematic way of evaluating small corrections due to intra-atomic electron repulsion and correlation, after the largest contribution to the interaction energy has been obtained from a rigorously bounded variational calculation in an independent-particle model. Preliminary calculation of the London C 6 coefficient for two He atoms are presented using a single-term Hylleraas function to describe intra-atomic correlation.

A simple scheme for obtaining well-localized non-orthogonal Wannier-type orbitals (WTOs) for periodic systems is discussed. (The WTOs corresponding to the same cell are orthogonal but the WTOs of different cells are generally not.) The method uses the Magnasco–Perico localization criterion based on Mulliken's population analysis: Mulliken's net population corresponding to the elementary cell is extremized. The calculations require the system's density and overlap matrices which are assumed to be known from a conventional band calculation but no explicit reference is made to the Bloch orbitals. The viability of the method is illustrated with the example of 6-31G calculations for polyacetylene and polyglycine.

The construction of non-orthogonal localized molecular orbitals (Wannier functions of extended systems) with maximal degree of localization according to the Magnasco-Perico localization criterion derived from Mulliken's population analysis is discussed and several forms of the equations giving these orbitals are presented. A partial orthogonality property of these orbitals permits an easy determination of the effective orthogonal atomic orbitals characterizing the actual state of the atom in the molecule; this helps to find connections between large-scale ab initio SCF calculations and traditional atomic orbital concepts. Calculations indicate full agreement with the traditional AO picture: for all ‘ordinary’ compounds one gets as many molecular orbitals appreciably localized on the given atom as are contained in the classical ‘minimal basis’ for that atom.