Relativistic MC-SCF in terms of DPT

The generalization from relativistic Hartree-Fock to relativistic MC-SCF can be considered at various levels of complexity. 

The simplest case is that the Cl expansion coefficients are fixed and not effected by relativity. Then one can essentially use the same formalism as in section 7.5, except that the one-particle density matrix is no longer idempotent and that the two-particle density matrix is not simply related to the one-particle density matrix. 

The next case is that relativity does affect the Cl expansion coefficients, but does not split the degeneracy. Then one still gets the simple result (518) for E2, but coupled HF must be replaced by coupled MC-SCF. 

In the general case there is degeneracy at the non-relativistic level, which is split by relativity. Then one must, after having performed the nonrel-ativistic calculation, extend the active space at orbital level by including all spin orbitals equivalent by symmetry. One then needs a matrix representation of the operator H2 in this basis to get the perturbation-adapted unperturbed states by diagonalizing this matrix representation. 

For details the reader is referred to the original literature [83]. Applications have so far been limited to the lowest level of approximation [92]. 

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