Multi-configuration linear response approach and random phase approximation

Multi-configuration linear response approach cind random phase approximation 

In the framework of response theory the lowest order contribution to the parity violating potential Vpy is given by the linear response function (denoted by ((. .))a J [106] 

In the MCSCF approximation the reference state 0), which is not necessarily the electronic ground state (see [47]), is expanded in a basis of configuration state functions (CSF) according to 

As in common MCSCF calculations, the response equations are solved in the subspace generated by the orbital excitation and de-excitation operators and g, with = a Ug, p q and by the state transfer operators Rf and Ri with R = z) (0 and i) denoting the orthogonal complement of the reference state 0) (see [128]). 

In our case, where we have static perturbations (o i = 0), a singlet reference state and operators inducing a coupling to the triplet manifold (see [129-131] for this special type of operators), the general equation (6.7) of reference [128] reads (see [106]) 

---