Hybrid quantum mechanical/molecular mechanical (QM/MM) approach is now considered as an accurate tool for treating properties and mechanism of chemical reactions in condensed phase.1-4 Among those, enzymatic reactions occupy a central place due to their heterogeneous biologic environment difficultly approximable by an implicit representation.5-7 The method allows qualitative interpretation of such processes and quantitative values can be obtained and confronted to experiment. In some cases, the QM/MM approach fails at clearly determining chemical properties or it can be assumed that the method give errors which does not allow for direct comparison to experimental data. This can be due to several reasons. One of them is the neglect of polarization of the MM part, which is especially important when the reaction implies charged or significantly polar intermediates.2
There are several ways to include polarizability at MM level.8-10 The most prominent ones are induced dipoles,11 fluctuating charges12 and Drude oscillators (DO).13 The later is used in this study and is also called charge-on-spring14 or shell model.15,16 In the DO model,13 a mobile charge, called drude particle (DP), is linked to a polarizable atom by a spring. A fixed charge of same magnitude but opposite sign is added at the atom position thus forming a dipole with the DP. Polarization arises from the electrostatic interaction of the DP with the rest of the system.
We have first included this model in the QM/MM framework using the GROMOS charge-on-spring force field.17 The CHARMM DO model was also interfaced18 and we proposed an improvement using a three polarizable layer approach to include long range electrostatic and allow more efficient computation.19 As the para...
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...larization due to the close distance in between polarizable centers, a damping function is used. Thole proposed different shape for this function and additional parameters have usually to be included in the parameterization.27,31 Following his formalism, the product T_ij µ_j in (2) is extended by 〖 γ〗_ij, the damping function acting on interactions with bonded atoms.
The proper induced dipole moments of N polarizable atoms for a given configuration of the system can be obtained by solving the following linear system of equations.
〖(α〗^(-1) γT)μ=E^0 (3)
Where T is a 3N x 3N tensor containing the T_ij’s, α^(-1) is a diagonal tensor containing the inverse of the atomic polarizability tensors, γ accounts for Thole damping functions for bonded intereactions,