Spinor Bonds in Diatomic Molecules

Concepts such as a and n bonds, and bonding and antibonding orbitals, are derived from the consideration of diatomic molecular orbitals. The ideas of directional bonds originate in the hybridization of atomic orbitals to form orbitals with the optimal spatial properties for bonding. More generally, the use of symmetry, molecular or local, helps us to classify orbitals into various bonding types. 

In the following discussion, we consider only the large-component 2-spinors, because the small-component density is negligible for the valence spinors and would only complicate the picture. We analyze the spinors in terms of the a and components, which can be represented in terms of nonrelativistic orbitals. The normalization is neglected because we are seeking a qualitative rather than a quantitative description. The molecular axis is taken to be the z axis. The two atomic spinors are considered to be on different centers, and the positive combination is given first, followed by the negative combination. 

For homonuclear diatomic molecules, we can only make spinor combinations that preserve the inversion symmetry. The simplest combinations are those between spinors with i = nij for j = I + j, for which the first three are given here  

These combinations therefore give pure bonding and antibonding diatomic molecular spinors, which also have pure spin. For homonuclear diatomic molecules, the spinors have a definite inversion symmetry a = ofg, a = a , ti = 7i , n = Ttg, and so on. The Kramers partners of these spinors are found by interchanging the spin parts. The first one is 

The next example is the set of spinors with (o = mj = j for the p shell. Here, both spin-orbit components are represented  

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MOLECULAR BONDING AND STRUCTURE 461 Spinor Bonds in Diatomic Molecules... 

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