Mean field QM/MM method: Average position approximation

The average position mean field combined quantum mechanical (QM) and molecular mechanical (MM) method, denoted as QMMM, is described. This method can drastically reduce the QMMM molecular dynamics simulation time to a level similar to pure MM methods, enabling the sampling of millions of configurations. A rigorous analysis shows that there is a general and significant error (up to 7 kcalmol) in mean field QMMM methods arising from the loss of instantaneous polarization of the QM electronic wavefunction. To reach high level of accuracy and efficiency, polarizable force field should be used to represent the QM region in mean field QMMM methods.