If the method is not variational, the APC-embedded site energies E F a F in Equation ( ) should formally be replaced by F a F H F F a F , while Equation ( ) should additionally contain F b F H F F a F . This is seen in the first two equations in expression 14.1.7 in Ref. 15. These matrix elements can be evaluated from the site-specific 1-and 2-particle (transition) density matrices. Hence, the ECI formulas could be expanded to fit any electronic structure method used for the site-state generation, although in this case the evaluation of the matrix elements might be more expensive due to the handling of the 2-particle densities. As a matter of fact, employing the replacements given in the previous paragraph, the ECI formulas hold generally. In other words, any set of (proper quantum-mechanical) functions of N F el variables can be used as the set of site states, i.e., the site states do not even have to be approximations of the eigenstates of the site Hamiltonians. This property allows one to, e.g., employ site-specific diabatic states as the site states in the ECI, if those are available and one wishes to avoid the (presumably expensive) calculation of the adiabatic site states.