In the following, only the most important ideas are presented and discussed with a focus on the PERI-CC2 model. The essential concept is the introduction of an environment coupling operator
(**D***CC*)

(DCC) |
= | es + pol(DCC) |
(9.24) |

with the electrostatic contribution

es |
= | Θ^{(k)}_{m, pq}Q_{m}^{(k)} |
(9.25) |

and the polarization contribution

pol(DCC) |
= | Θ^{(1)}_{u, pq}μ_{u}ind(DCC) . |
(9.26) |

Here,
*Θ*^{(k)}_{m, pq}
are multipole interaction integrals of order *k*
and
*μ*_{u}*ind*
are the induced dipoles which can be obtained from the electric field
**F**_{u}
and the polarizability
*α*_{u}
at a site ** u**
:

μ_{u}ind = F_{u}_{u} |
(9.27) |

Because the induced dipoles depend on the electron density and *vice versa*, their computations enter the self-consistent part of the HF cycle. Introducing
**( DCC)**
into standard equations for the HF reference state and the CC2 equations leads to a general PE-CC2 formulation. To maintain efficiency, a further approximation has been introduced which makes the operator only dependent on a CCS-like density term. These general ideas define the PERI-CC2 model and allow to formulate the corresponding Lagrangian expression

from which all PERI-CC2 equations including the linear response terms may be derived. Note that the dependency on the density couples the CC amplitude and multiplier equations for the ground state solution vector.