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Direct ab initio calculation of long-range induction and dispersion interactions expended up to R−8 and evaluated at the SCF intermolecular separation for the complexes of He and Ne with HF shows that the angular shapes of such van der Waals atom-dipolar molecule dimers are determined by the absolute minima of the induction interaction.

Ab initio MG-FSGO calculations on H2H2 with increasingly accurate floating Gaussian bases show that fully optimized wavefunctions of intermediate size do describe quite accurately the intermolecular interactions in short range and their orientation dependence.

The importance of geminal interactions in determining rotational barriers is analyzed to order S2 in occupied inter-orbital overlap. For molecules carrying a lone pairs of electrons at both ends of the rotation axis, the inclusion of geminal interactions is found to be essential to ensure the correct angular behaviour of the total enery.

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.

Improved bond-orbital calculations of the differential stability of cis—trans isomers in N 2 H 2 , NF and N 2 F 2 show that the general trend along the series appears to be largely due to σ geminal delocalization. favouring the cis isomer and enhanced by F substitution. The effect is characteristic of molecules possessing σ lone pairs at both ends of the central bond. Both σ and π vicinal delocalizations contribute little.

6-31G calculations of linear H-bonding in (HF)2, (H2O)2, FH ⋯ NH3, H2O ⋯ HF, geometrical isomerism in N2H2 and rotation barriers in CH3OH, N2H4 show that the split-valence bond-orbital method works well in the intermolecular case but not in the intramolecular one, where the second-order barriers are normally different from the SCF ones.

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.

The topology of the period doubling attractor at the onset of chaos, and its implications for the structure of the power spectrum are discussed. The presence of a seemingly anomalous peak at a non 2n frequency is explained in terms of a topological invariant of the attractor whose systematics is shown to be universal. An experiment on an electronic circuit is performed, and its results are shown to be fully consistent with the theory.

Ab initio STO-3G bond-orbital (BO) studies of the angular geometry in CH 4 , NH 3 , H 2 O, CH 2 O, CH 3 F, CH 2 F 2 show that the small second-order delocalization between non-orthogonal SCF BOs is essential to give reasonably accurate results when lone pairs are present on the central atom.

Second order variational calculations of static multipole polarizabilities are reported for the ground states of H, He, Li and Be using Hartree—Fock Ψ 0 and the whole atomic Hamiltonian as H 0 . Correlation is admitted in the valence shell of He and Be for both the ground and the excited states. The calculations make use of gaussian bases and are devised to follow the lines of our previous work done with a Slater basis. Use of 2-term optimized gaussian orbitals including scale factors for Li and Be gives ab initio results which are close to those obtained with a single optimized Slater orbital for each excited pseudostate. Polarizabilities and excitation energies allow for the one-centre calculation of the C 2 n dispersion coefficients between all pairs of interacting atoms with an absolute accuracy which is the same as that obtained in the corresponding STO calculations.

A finite representation of spherical Bessel functions followed by contour integration in the complex plane allows a new unified evaluation of the k integral occurring in the generalized multipole expansion of rab−1 based on a Fourier transform. In addition to the well known asymptotic formulae, a simple closed-form expression is obtained for the overlap region of intermediate separations.

Ab initio STO-3G calculations of rotation barriers in six single-rotor molecules have shown the inadequacy of the Mulliken approximation in the Surjan formula which expresses barriers as a sum of bond-bond pair interactions. Following our early work, expansion to order S2 followed by pair delocalization is suggested as a possible alternative to semi-empirical advance.

Additive (pairwise) and nonadditive contributions to the rotation barrier in ethane are explicitly evaluated with ab-initio calculations based on two approximate separations of the electron-nucleus potential. Nonadditive effects beyond three-body are seen to be negligible, a result which can be very useful for applications to larger molecules.

The contributions to rotational barriers in ethane, propane and butane are discussed with reference to a theoretical model based on the additivity of the intramolecular penetration energy between pairs of different bonds.

Rabbit morulae were treated with specific indirect immunofluorescence and immunoperoxidase histochemical techniques. The first antibody in both systems was rabbit anti-human chorionic gonadotropin (hCG) beta-subunit. Negative controls revealed a complete absence of reaction. All morulae incubated with the double-antibody system showed a positive reaction. Rabbit morulae thus present a substance with antigenic determinants similar to the beta-subunit of hCG. The physiologic role of this substance is unknown.

It is shown how E MSMA 2 can be calculated from the extrema of a single functional. Then bounds can be deduced from this property.

Ab initio calculations on twenty van der Waals dimers of small polar molecules at the experimentally observed intermolecular separation R, using Hartree-Fock molecular moments, show that the minima in the electrostatic interaction expanded up to R−6 converges to angular structures which are close to those observed experimentally for such complexes.

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.