Molecular orbital method and sum-over-states perturbation theory

1 Molecular orbital method and sum-over-states perturbation theory 

A magnetic parameter in tensor form can be evaluated as a sum of two contributions the first term expressed over the ground-state wave function and the second term involving transition moments between the ground-state and excited-state wave functions 

In the molecular orbital method the ground-state determinantal wave function f o) = f (0,0 0) is constructed from the set of occupied molecular spin-orbitals cpi).Then tne matrix elements of the one- and two-electron operators can be evaluated by utilising the Slater rules. The expectation value of a one-electron operator is 

Within the LCAO approximation, when the molecular orbitals are expanded over the basis set of atomic orbitals xM) 

Then the expectation value of a one-electron spinless operator becomes 

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