Classical Polarization in Hybrid QM/MM Methods

Abstract

We have presented a method for modeling polarization in hybrid QM/MM calculations. The method, which expresses the induced dipoles as a set of "induced" charges, is based on the induced dipole approach and methodology for calculating potential-derived point charges from distributed multipole series. The method has the advantage that the same methodology can be used to determine the induced charges and the potential derived charges and so both sets of charges are rigorously defined within the same framework. This underlying link with the wave function makes the method particularly suitable for use in hybrid QM/MM calculations. Here we assess the importance of explicit polarization in the classical part of a QM/MM system with regard to improving the classical description and the consequent effects on the quantum description. The main advantages of the induced charge approach are that the method is readily interfaced with quantum mechanical methods and that induced charges are more readily interpreted than induced dipoles. The ease of interpretation is illustrated by analysis of the charges involved in dimeric and trimeric hydrogen bonded systems. The method for treating the MM polarization has been validated by a regression analysis of the charges induced in both the QM and MM systems against those derived from full quantum mechanical calculations. The method has also been validated using two energy decomposition approaches, which show that MM polarization makes a significant and reliable contribution to the QM - MM interaction energy in a hybrid system. The distance dependency of the induced charges is investigated in calculations on methylsuccinyl-Ala-Ala-Pro-Ala chlormethyl ketone interacting with human neutrophil elastase and propranolol interacting with asparagine residues in a model of the beta(2)-adrenergic receptor.

Coupling density functional theory to polarizable force fields for efficient and accurate Hamiltonian molecular dynamics simulations

“…As is schematically indicated by the lower dashed arrow in Figure 3, at l = 1 the point charges q j and induced point dipoles p j of the individual atoms j are considered to be the sources of the potential. The associated expansion coefficients (21) are essentially given by the nth rank tensors 47 ∂ (n) (1/r). Here, the prefactor 1 − δ np , in which δ is the Kronecker symbol, ensures that the expansion is of comparable accuracy for the atomic charges and dipoles.…”

“…7 There are notable exceptions which combined a polarizable force field for the MM fragment with semiempirical quantum chemistry for the QM fragment. [8][9][10][11][12] Combinations of higher-level QM treatments (density functional a) Electronic mail: gerald.mathias@physik.uni-muenchen.de theory 13,14 (DFT) or ab initio quantum chemistry) with PMM force fields were either restricted to the energetics of static systems, [15][16][17][18][19][20][21][22][23] to small molecular clusters, [24][25][26][27][28][29] or describe the dynamics only in parts of the simulation system. 30,31 Other approaches augment DFT atoms with self-consistent polarization terms (SCP-DFT) to correct the deficiencies of the longrange electrostatics and dispersion description within certain exchange-correlation functionals.…”

Many-body effects and simulations of potassium channels

“…While if point charges alone are used to recreate polarization effects, there exists a geometrical restriction in polarization inherent to the location of the points. Although the use of additional off-atom charges provides a potential solution to this, this itself presents an issue of parametrization (Illingworth et al 2006). QM-based models perhaps provide a better alternative, although they do not quite fit the ideal of incorporating polarization into a classical system.…”

“…In common with the fluctuating charge model, polarization is here included without the addition of dipoles or additional off-atom charges, potentially allowing for easy incorporation into modelling software. This method has successfully been applied to energy calculations in both small-molecule (Illingworth et al 2006) and enzymatic (Illingworth et al 2008b) systems, and to the problem of ligand docking (Illingworth et al 2008a). …”

Simulation of Adsorption Processes at Metallic Interfaces: An Image Charge Augmented QM/MM Approach

“…Self-consistent techniques are available for the inclusion of polarization effects in QM/MM simulations of bioorganic molecules [28][29][30] , but there is no such method, to our knowledge, available for metallic interfaces. This motivates us to adapt the Siepmann-Sprik approach to a QM/MM scheme.…”