DRF Theory

Within the Discrete Solvent Reaction Field model the QM/MM operator is

H_QM/MM = ∑_i v^DRF (r_i,ω) = ∑_i [v^el (r_i) + v^pol (r_i,ω)

where the first term, v^el, is the electrostatic operator and describes the Coulombic interaction between the QM system and the permanent charge distribution of the solvent molecules. The second term, v^pol, is the polarization operator and describes the many-body polarization of the solvent molecules, i.e. the change in the charge distribution of the solvent molecules due to interaction with the QM part and other solvent molecules. The charge distribution of the solvent is represented by atomic point charges and the many-body polarization by induced atomic dipoles at the solvent molecules. The induced atomic dipole at site s is found by solving a set of linear equations

μ^ind_s,α(ω) = α_s,αβ [F^init_s,β(ω) + ∑_t≠s T⁽²⁾_st,βγ μ^ind_t,γ(ω)],

where α_s,αβ is a component of the atomic polarizability tensor at site s The screened dipole interaction tensor is given by

T⁽²⁾_st,βγ = 3f^T_stR_st,αR_st,β/R⁵_st - f^E_stδ_αβ/R³_st

where the damping functions f^T_st and f^E_st have been introduced, see also [146]. A smeared-out point charge model [147] is used for short-range damping of the QM/MM operator

1/R_st → 1/S_st = erf(R_st)/R_st

The scaled distance, S_st, then replaces the normal distance, R_st, in the QM/MM operator.