Theoretical study of binding energy and electronic energy levels in small clusters of metal atoms

Abstract

The theme of this research has been to investigate the structural and some of the electronic properties of various isomers for aggregates consisting of up to nine univalent atoms. The study presents a classification, by group-theoretical methods, of some of the energy levels for these systems and highlights the stability of the linear configuration. The latter result emphasizes an important difference between classical and quantum bonding theories; in the former, maximization of the number of bonds entails greatest stability.

The cause of the gradual change from the linear to the three-dimensional structures, as the most stable configuration for larger clusters, was also investigated and appears to be a consequence of the increasing ratio of volume to surface atoms for the latter isomers. The variation of ionization potential with cluster size and shape was studied through qualitative analysis of the charge distribution in the highest occupied orbital of each system. The predicted trend for small linear complexes was found to fit into the general pattern determined by experiment.

Two distinct, but complementary, approaches have been adopted in this study. The first of these, the ENERGY formulation, analysed each system in terms of its total energy or, when detailed information concerning a particular phenomenon was desired, in terms of the appropriate component of the total energy. This approach involved the setting up of a simplified model, chosen by systematic approximations of the Hartree-Fock and Phillips-Kleinmann theories, and was used in deriving potential curves for the dimer, the trimer (equilateral triangular form) and quadramer (square and tetrahedral forms).

On the other hand, the CHARGE DENSITY formulation viewed the formation of an aggregate in terms of the accompanying redistribution of the valence charge. Symmetry arguments were used to obtain a pictorial description of this redistribution and, along with the electro-static theory of Hellmann and Feynman, formed the basis of a qualitative Molecular Orbital theory by which the relative stability of different isomeric forms was studied.

An interesting by-product of the shift in emphasis away from purely energetic considerations and to the gross properties of the charge distribution, is the suggestion that the absence of core-electrons indirectly accounts for the non-metallic bulk properties of hydrogen. This hypothesis may be compared with the resonance theory of the Valence Bond explanation of metallic bonding.