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Geometrically active atomic states and the formation of molecules in their normal shapes

✍ Scribed by Cleanthes A. Nicolaides; Yannis Komninos

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
167 KB
Volume
67
Category
Article
ISSN
0020-7608

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✦ Synopsis

We present a theory of molecular formation according to which the shape of polyhedral or coordination compounds is fixed to a very good approximation by Ž . the shape of a particular state or states of the central atom, which is activated by spin and spacial coupling of optimal strength between this state, called the geometrically active Ž . atomic state GAAS and the state of the ligands. For a molecule with a central atom, spacial coupling of optimal strength, means that the shape of the GAAS fixes the position of the ligands according to the maximum overlap principle of the Heitler᎐London, Slater, and Pauling theory of covalent bonding, whereby much of the energy lowering from the free atom limit is obtained by the maximization of the contribution of the exchange integrals. Hence, a direct causal relationship between the shape of the GAAS and the shape of the molecular state at equilibrium seems to exist. This relationship implies a picture of diabatic connection between the geometrically asymptotic region and the equilibrium region, which is driven by the coupled GAAS and provides the ''why'' of Ž molecular shape. Since the latter is fixed by the shape of the GAAS in cases of electronic complexity or of molecular instability it is possible that more than one GAAS contribute . simultaneously , prediction of the shape of certain large systems can be made based on the a priori recognition of the corresponding GAAS. The concept of the shape of atomic states defined and computed quantum mechanically from the probability distribution Ž .

Dcos

of the angle that the position vectors of two electrons form in the given 12 12 atomic state. Specifically, it is deduced from the distribution's maxima which provide the w most probable values of . As shown previously Y. Komninos and C. A. Nicolaides, 12 Ε½ .x Ε½ . Phys. Rev. A 50, 3782 1994 , D cos is obtainable directly from the state-specific 12 expression for the Coulomb interaction, where the R k integrals are replaced by Legendre polynomials P , multiplied by normalization constants and radial overlaps. The theory is k

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