A Hamiltonian electrostatic coupling scheme for hybrid Car-Parrinello molecular dynamics simulations

We present a fully Hamiltonian and computationally efficient scheme to include the electrostatic effects due to the classical environment in a Car-Parrinello mixed quantum Mechanics/molecular mechanics (QM/MM) method. The polarization due to the MM atoms close to the quantum system is described by a Coulombic potential modified at short range. We show that the functional form of this potential has to be chosen carefully in order to obtain the correct interaction properties and to prevent an unphysical escape of the electronic density to the MM atoms (the so-called spill-out effect). The interaction between the QM system and the more distant MM atoms is modeled by a Hamiltonian term explicitly coupling the multipole moments of the quantum charge distribution with the classical point charges. Our approach remedies some of the well known deficiencies of current electrostatic coupling schemes in QM/MM methods, allowing molecular dynamics simulations of mixed systems within a fully consistent and energy conserving approach.