Atomic spectral-product representations of molecular electronic structure: metric matrices and atomic-product composition of molecular eigenfunctions

Recent progress is reported in development of ab initio computational methods for the electronic structures of molecules employing the many-electron eigenstates of constituent atoms in spectral-product forms. The approach provides a universal atomic-product description of the electronic structure of matter as an alternative to more commonly employed valence-bond- or molecular-orbital-based representations. The Hamiltonian matrix in this representation is seen to comprise a sum over atomic energies and a pairwise sum over Coulombic interaction terms that depend only on the separations of the individual atomic pairs. Overall electron antisymmetry can be enforced by unitary transformation when appropriate, rather than as a possibly encumbering or unnecessary global constraint. The matrix representative of the antisymmetrizer in the spectral-product basis, which is equivalent to the metric matrix of the corresponding explicitly antisymmetric basis, provides the required transformation to antisymmetric or linearly independent states after Hamiltonian evaluation. Particular attention is focused in the present report on properties of the metric matrix and on the atomic-product compositions of molecular eigenstates as described in the spectral-product representations. Illustrative calculations are reported for simple but prototypically important diatomic (H_2, CH) and triatomic (H_3, CH_2) molecules employing algorithms and computer codes devised recently for this purpose. This particular implementation of the approach combines Slater-orbital-based one- and two-electron integral evaluations, valence-bond constructions of standard tableau functions and matrices, and transformations to atomic eigenstate-product representations. The calculated metric matrices and corresponding potential energy surfaces obtained in this way elucidate a number of aspects of the spectral-product development, including the nature of closure in the representation, the general redundancy or linear dependence of its explicitly antisymmetrized form, the convergence of the apparently disparate atomic-product and explicitly antisymmetrized atomic-product forms to a common invariant subspace, and the nature of a chemical bonding descriptor provided by the atomic-product compositions of molecular eigenstates. Concluding remarks indicate additional studies in progress and the prognosis for performing atomic spectral-product calculations more generally and efficiently

Hydrogen Bond Energies in Carboxylic Acids

A question of interest to the study of the chemisorption of carbon monoxide on iron is whether the carbon is desorbed with the same oxygen to which it was bonded prior to the adsorption. A mixture of C13O and CO18 in the desorbed gas in amounts greater than expected from normal abundance ratios shows that an intermolecular oxygen exchange occurs

Responses to Familiar and Unfamiliar Humans by Belugas (Delphinapterus leucas), Bottlenose Dolphins (Tursiops truncatus), & Pacific White-Sided Dolphins (Lagenorhynchus obliquidens): A Replication and Extension

Previous research has documented that cetaceans can discriminate between humans, but the process used to categorize humans still remains unclear. The goal of the present study was to replicate and extend previous work on the discrimination between familiar and unfamiliar humans by three species of cetaceans. The current study manipulated the familiarity and activity level of humans presented to 12 belugas (Delphinapterus leucas) housed between two facilities, five bottlenose dolphins (Tursiops truncatus), and six Pacific white-sided dolphins (Lagenorhynchus obliquidens) during free-swim conditions. Two measures of discrimination were coded from video recordings of each trial: lateralized visual processing and gaze duration. No clear lateralization effects emerged at the species level, primarily due to extensive individual variability. The results also indicated that activity level influenced gaze durations across species, and for some individuals, the interaction between human familiarity and activity level influenced gaze durations and eye preferences. Unexpectedly, bottlenose dolphins had longer gaze durations for familiar humans whereas belugas and Pacific white-sided dolphins had longer gaze durations for unfamiliar humans. All three groups displayed longer gaze durations for active humans as compared to neutral humans, and belugas and bottlenose dolphins had significantly longer gaze durations than Pacific white-sided dolphins. These results indicate that the cetaceans can discriminate between unfamiliar and familiar humans and preferred active humans. However, discrimination of humans via lateralized visual processing did not appear at the group level, but rather at the individual level which countered previous research. This study is discussed within the contexts of attention and individual differences across animals of different species