CHAPTER 9 FORMALISMS FOR THE EXPLICIT INCLUSION OF ELECTRONIC POLARIZABILITY IN MOLECULAR MODELING AND DYNAMICS STUDIES PEDRO E. M. LOPES 1 , EDWARD HARDER 2 , BENO ˆ IT ROUX 2 , AND ALEXANDER D. MACKERELL, JR. 1 1 Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland, 20 Penn Street, Baltimore, MD 21230, USA, e-mail: amackere@rx.umaryland.edu 2 Department of Biochemistry and Molecular Biology, Center for Integrative Science, University of Chicago, Chicago, Illinois, 60637 Abstract: Current methodologies for modelling electronic polarization effects in empirical force fields are presented. Emphasis is placed on the mathematical details of the methods used to introduce polarizability, namely induced dipoles, Drude oscillators or fluctuating charge. Overviews are presented on approaches used to damp short range electrostatic interactions and on Extended Langrangian methods used to perform Molecular Dynamics simulations. The final section introduces the polarizable methods under development in the context of the program CHARMM Keywords: Empirical force field, Electronic polarization, Polarizability, Force field, Inducible dipoles, Drude oscillators, Fluctuating charge, Molecular dynamics, CHARMM 9.1. INTRODUCTION Molecular mechanical (MM) force fields (FF) are widely used in molecular modeling studies of systems with thousands on up to millions of atoms. To date they have proved to be surprisingly accurate in many applications despite their simplified functional forms. This accuracy is, to some extent surprising, due to the number of approximations in FFs, the biggest of which is typically the method by which the charge distribution of the molecules is treated. In additive force fields, which represents the bulk of current FFs [1, 2] this is done by assigning partial fixed charges to the atoms, thus creating a force field whose electrostatic properties are not capable of reacting to changes in the environment. Additive force fields common for biomolecular simulations [3–6] share the same general functional form: 219 D.M. York and T.-S. Lee (eds.), Multi-scale Quantum Models for Biocatalysis, 219–257. DOI 10.1007/978-1-4020-9956-4 9, © Springer Science+Business Media B.V. 2009