Orbital crossing

Solid line gives values calculated for Langevin orbiting cross-sections. 

When molecular orbital cross sections oi are available, photoionization intensities are more conveniently obtained as (11,12)... 

Orbitals. Atomic orbitals represent the angular distribution of electron density about a nucleus. The shapes and energies of these amplitude probability functions are obtained as solutions to the Schrodinger wave equation. Corresponding to a given principal quantum number, for example n = 3, there are one 3s, three 3p and five 3d orbitals. The s orbitals are spherical, the p orbitals are dumb-bell shaped and the d orbitals crossed dumb-bell shaped. Each orbital can accomodate two electrons spinning in opposite directions, so that the d orbitals may contain up to ten electrons. 

Figure 12 Splitting of the frontier orbitals in the open face of a DSD transition state. One function is symmetric (S) with respect to the conserved mirror plane, the other is antisymmetric (A). Their energies change in opposite senses and lead to an orbital crossing...

Using MS-SCF-X(x compositions and atomic-orbital cross sections from Schofield (1976). /Perry and Jolly (1974 ). 

The concepts discussed regarding the symmetry restrictions and their removal can be described in a number of ways. Complete correlation diagrams can be constructed and the forbiddenness illustrated by sharp orbital crossings 20). Although definitive, this approach would not as clearly illustrate the nature of the restraints to reaction. 

The restrictions associated with four-coordinate complexes are reversed when the band of d orbitals is filled with metal valence electrons (e.g., d systems). In these situations, ligand field restrictions are encountered from the tetrahedral complex and not the square planar. This departure from the quaUtative picture based on pure d orbitals is primarily due to hybridization factors in these systems. The square planar complex requires an empty d orbital (in the plane) to construct the four hybrid orbitals in the square plane. The [2-f2] transformation from the square planar complex thus returns two valence electrons (formally from a p orbital) to this orbital generating a filled d band in the process. The process proceeds without an orbital crossing. The tetrahedral system, in contrast, starts with a filled d band. The [2- -2] process formally moves a pair of d electrons into a p orbital. This process thus involves an orbital crossing and therefore encounters ligand field restrictions. 

Fig. 3. A schematic representation of two-electron orbitals crossing as a function of nuclear coordinate. The curve is redrawn from Dunlap and Mei (1983) where it was the crossing of the doubly degenerate 7r and 2a in the region of internuclear separation 1.0-4.5 bohr, and for occupations corresponding to the Z and A, states which are degenerate in spatial symmetry-restricted Xa-like methods. The one-electron energy scale is from —4 to — 14eV.

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