Embedding potentials

The hybrid QM/MM approach for multiscale modeling of complex systems was recognized with the Nobel Prize in chemistry in 2013. This model partitions the molecular system into a small quantum mechanical (QM) region containing up to a few hundred atoms and (typically) a larger molecular mechanical (MM) region containing up to several tens of thousands of atoms.

Full or partial interactions (electrostatics, induction, dispersion, short-range repulsion) are accounted for in between the QM and MM parts of the system, resulting in a Hamiltonian of the form

\[ \hat{H} = \hat{H}_\mathrm{QM} + \hat{H}_\mathrm{MM} + \hat{H}_\mathrm{QM/MM} \]

and an associated energy

\[ E = E_\mathrm{QM} + E_\mathrm{MM} + E_\mathrm{QM/MM} \]

Force fields describing the MM part with parameters, such as point charges, higher-order charge moments, and distributed polarizabilities, are determined empirically or using quantum chemistry methods. Two categories of embedding models exist

• non-polarizable

• polarizable

as presented in the subsequent sections of this book.