Large component inversion symmetry

For a relativistic Hamiltonian with inversion symmetry, it can be shown that the large and small components of the spinor have different parity. We do this by writing the spinor, 1 , as a column vector of large and small components... 

In the absence of other external fields, V is totally symmetric under the operations of the molecular symmetry group because it defines the symmetry group. 2c and E are numbers, which by definition are totally symmetric. B and its inverse are therefore totally symmetric. Moreover, the equation involving only the large component, above tells us that the operator (a-p) (totally symmetric, because... 

It remains to determine the symmetry relation between the large and the small component. To do this, we can use the remaining equation from the elimination of the small component, which provides us with a connection between and The inverse operator is totally symmetric, so the relations are determined by the operator c(or p), which in terms of symmetry can be represented as... 

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