Equivalent Orbitals and the Shapes of Excited Species

Abstract

The electron distributions in the ground states of C?H?, HCO, and NH?, and in one excited state of each species, have been considered by transforming the sinlple molecular orbitals into equivalent ones. I n the light of these considerations, the shapes and dimensions of the above species in these states have been discussed. I t is found that a considerable degree of understanding can be achieved though there is uncertainty in the interpretation in some cases. INTRODUCTIONThe object of this paper is to discuss some ways in which the shapes of n~olecules and radicals in their ground and excited states are decided by their electronic structures. The molecule C2Hp and the radicals HCO and N H 2 will be co~lsidered as examples. An extensive treatment of this type of problem has been given by Walsh (lo), his approach being that of simple molecular orbital (M.O.) theory. This method, in its simple form, implies that the total energy can be represented to a satisfactory approximation by the sum ol a number of one-electron energies of values corresponding to the orbitals that are occupied. Clearly this is an overapproximation, for interelectronic effects arising both from their charge and from the consequences of the Pauli principle (i.e. effects of multiplicity) are ignored. T o some extent, of course, in drawing diagrams in his papers, Walsh has taken account of these effects, for the graphs of energy against angle are not computed from a number of one-electron calculations but are derived on a more enlpirical basis.Simple A11.O. theory, because interelectronic effects are ignored, is clearly an oversii~lplification. This may be particularly serious in the discussion of shapes, for these are, to a large extent, decided by the mutual effects of electrons on one another. For example, inethane is tetrahedral because the Pauli principle requires that four electrons with parallel spins in the 2s and three 2 p orbitals of carboil will be, with greatest probability, a t the corners of a regular tetrahedron (11). Moreover charge effects favor this shape also. Also NH3 is pyramidal because of the presence of the lone pair and of the interaction of this with the bonding pairs (7). Consideration of shapes should therefore include interelectron effects as well as one-electron effects, and consequently the simple M.O. procedure is not wholly satisfactory.The approach used in this paper will be that based on the representation of the molecular wave function in terms of equivalent orbitals which are linear combinations of the basic one-electron molecular orbitals, for these allow an easier appreciation of the electron distribution, and a more reasonable assessment of the effects of electron interactions. This procedure has been used previously by the author to discuss the bonding in the ground and some excited states of the diatomic molecules and ions formed by carbon, nitrogen, and oxygen (5). Equivalent orbitals of this type are to be preferred when electron distributioils are being considered (4). I t was found that the fo...

An Appraisal of Valence-bond Structures and Hybridization in Compounds of the First-row elements.

“…The electronic structure of CO has been examined theoretically (186,203), and it suggested that the bonding hybrid from carbon is approximately a tetrahedral hybrid (203); this estimate places 75 per cent s character in the orbital occupied by the lone pair on carbon. The electronic structure of N2 has been compared with those of CO (219,222) and C2H2 (178). A close similarity is observed in the computed molecular orbitals for N2 and CO (260) and in the derived electron overlap populations (219,221).…”

“…In the previous section, the valence electrons about an atom in a molecule wore pictured in localized orbitals. The advantages of partitioning the electron cloud of a molecule into localized, nonoverlapping parts, called in molecular orbital theory equivalent, orbitals, have been discussed by several authors (48,112,120,161,163,178,247,271). Two types of localized orbitals are frequently encountered: orbitals occupied by unshared, nonbonding electrons, and orbitals occupied by bonding or shared electrons.…”