Spinors hybridization

Here indexes a = 1,2 numerate spinor components. Because we ignore direct hopping of d-electrons on the lattice, in the Hamiltonian (10) a quadratic term with the A -operators is absent, and A -operators enter linearly via the hybridization term. However in the second order perturbation with respect to hybridization such a term should appear it describes the induced hopping on the lattice. 

In organic chemistry, s-p hybridization is an important qualitative concept in the description of chemical bonds. Optimum orbitals for bonding in linear, planar trigonal, and tetrahedral configurations are formed by sp, sp, and sp hybrids. We have previously discussed how hybridization may be influenced by spin-free relativistic effects. With the involvement of p spinors that may be highly spin-orbit split, hybridization will also be influenced by the spin-orbit coupling. 

For linear molecules, we can form sp hybrids from the spinors ... 

The capability for relativistic hybridization is present for molecules of other than linear symmetry. The symmetry spinors for groups lower than cubic can be classified in terms of the m.j quantum numbers for spinors at the high symmetry point (or axis). Since the j quantum number is not part of the classification, relativistic hybridization can always take place. For example, in Dih the fermion irreps are e /2, e ji, and es/2, for which the Kramers partners have Tw modb = 1/2, 3/2, 5/2, respectively. The i and j = l + j spinors for a given rtij both belong to the same irrep. In... 

The simple bonding picture based on spinors and relativistic or spin-orbit hybridization is an appealing explanation of the effect of spin-orbit interaction on bonding, but it is by no means the only one. It is the natural explanation when spinors are the starting point, but it is also possible (and common) to start from a spin-free model and introduce spin-orbit effects at the post-SCF stage of the calculation. Now the bonding picture is a multi-electron picture that involves the interaction of states of different spin and symmetry. 

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