Polarizable embedding
In this section we will include polarizable contributions, such that
where is the set of permanent charges in MM region, is the set of induced dipoles in MM region, the and are potential components are generated by electrons and nuclei in MM region, and are potential components are generated by electrons and nuclei in MM region. The converts to additional contribution to external potential Kohn–Sham equations
where and electrostatic interaction tensors of first and second order. In the above equation, induced dipoles in the MM region explicitly depend on electron density in the QM region and thus need to be determined for each step of the SCF procedure. Furthermore, the induced dipoles are the only MM region contribution explicitly entering response calculations of molecular properties and consequently account for this contribution is crucial in any QM/MM calculations of spectroscopic properties.