Accurate ab initio potential energy curve of F2. II. Core-valence correlations, relativistic contributions, and long-range interactions.

The nonrelativistic, valence-shell-only-correlated ab initio potential energy curve of the F(2) molecule, which was reported in the preceding paper, is complemented by determining the energy contributions that arise from the electron correlations that involve the core electrons as well as the contributions that are due to spin-orbit coupling and scalar relativistic effects. The dissociation curve rises rather steeply toward the energy of the dissociated atoms because, at larger distances, the atomic quadrupole-quadrupole repulsion and spin-orbit coupling counteract the attractive contributions from incipient covalent binding and correlation forces including dispersion.

Accurate ab initio potential energy curve of F2. III. The vibration rotation spectrum.

An analytical expression is found for the accurate ab initio potential energy curve of the fluorine molecule that has been determined in the preceding two papers. With it, the vibrational and rotational energy levels of F(2) are calculated using the discrete variable representation. The comparison of this theoretical spectrum with the experimental spectrum, which had been measured earlier using high-resolution electronic spectroscopy, yields a mean absolute deviation of about 5 cm(-1) over the 22 levels. The dissociation energy with respect to the lowest vibrational energy is calculated within 30 cm(-1) of the experimental value of 12 953+/-8 cm(-1). The reported agreement of the theoretical spectrum and dissociation energy with experiment is contingent upon the inclusion of the effects of core-generated electron correlation, spin-orbit coupling, and scalar relativity. The Dunham analysis [Phys. Rev. 41, 721 (1932)] of the spectrum is found to be very accurate. New values are given for the spectroscopic constants.

Molecule intrinsic minimal basis sets. I. Exact resolution of ab initio optimized molecular orbitals in terms of deformed atomic minimal-basis orbitals.

A method is presented for expressing the occupied self-consistent-field (SCF) orbitals of a molecule exactly in terms of chemically deformed atomic minimal-basis-set orbitals that deviate as little as possible from free-atom SCF minimal-basis orbitals. The molecular orbitals referred to are the exact SCF orbitals, the free-atom orbitals referred to are the exact atomic SCF orbitals, and the formulation of the deformed "quasiatomic minimal-basis-sets" is independent of the calculational atomic orbital basis used. The resulting resolution of molecular orbitals in terms of quasiatomic minimal basis set orbitals is therefore intrinsic to the exact molecular wave functions. The deformations are analyzed in terms of interatomic contributions. The Mulliken population analysis is formulated in terms of the quasiatomic minimal-basis orbitals. In the virtual SCF orbital space the method leads to a quantitative ab initio formulation of the qualitative model of virtual valence orbitals, which are useful for calculating electron correlation and the interpretation of reactions. The method is applicable to Kohn-Sham density functional theory orbitals and is easily generalized to valence MCSCF orbitals.

Molecule intrinsic minimal basis sets. II. Bonding analyses for Si4H6 and Si2 to Si10.

The method, introduced in the preceding paper, for recasting molecular self-consistent field (SCF) or density functional theory (DFT) orbitals in terms of intrinsic minimal bases of quasiatomic orbitals, which differ only little from the optimal free-atom minimal-basis orbitals, is used to elucidate the bonding in several silicon clusters. The applications show that the quasiatomic orbitals deviate from the minimal-basis SCF orbitals of the free atoms by only very small deformations and that the latter arise mainly from bonded neighbor atoms. The Mulliken population analysis in terms of the quasiatomic minimal-basis orbitals leads to a quantum mechanical interpretation of small-ring strain in terms of antibonding encroachments of localized molecular-orbitals and identifies the origin of the bond-stretch isomerization in Si4H6. In the virtual SCF/DFT orbital space, the method places the qualitative notion of virtual valence orbitals on a firm basis and provides an unambiguous ab initio identification of the frontier orbitals.

Mean Wiener numbers and other mean extensions for alkane trees

The "Wiener number" (the sum over intersite graph distances of a structure) as averaged over all alkane structural isomers of a fixed number N of carbon atoms is considered. This and several other measures of average graphical "extension" of N-site alkanes are computed for N up to 90 (where there are over 10(35) such isomers). Fits are then made for several surmised or derived asymptotic forms, and a heuristic argument is made relating these results to geometric extensions of a random mix of (N-site) alkanes.

Chemical sub-structural cluster expansions for molecular properties.

Abstract The correlation of different molecular sub-structures with various molecular properties has a long history, of over a century. And currently such structural characterizations still remain of central interest in chemistry. Thus a general formalism to analyze a property or activity in terms of sub-structural contributions is of interest, and is pursued here. The approach may indeed be viewed as a formalization and extension of standard bond-energy ideas as arise even in introductory chemistry courses. The present formalism allows for: • a more complete and comprehensive formulation, with higher-order corrections to achieve greater accuracy; • a more general form for the class of sub-structures appearing in the expansion, thereby allowing more general (e.g., "multiplicative") properties to be expanded; and • a more general form for the expansion functions, thereby allowing more rapid convergence rates for the expansions. An illustrative example for the structure/property correlation of conjugated-hydrocarbon π-energy is made. Some comments on the use for describing bio-activities, and in particular toxicities, are made.