Those states can be obtained by an electronicstructure calculation of fragment F with the APCs of all other fragments G included as external point charges (i.e., like in electrostatic embedding). Clearly, F a F and E F a F parametrically depend on the APCs of all other fragments. In the following, we will refer to all quantities related to those states as APC-embedded quantities (e.g., ˆ H F is the APC-embedded site Hamiltonian, F a F is an APC-embedded site state, and E F a F is an APC-embedded site energy), denoted by a tilde.