Force Field Treatment of Proton and Hydrogen Transfer in Molecular Systems

Proton and hydrogen-bonded motifs are amongst the most widely occurring patterns in chemistry and biology. Besides their intrinsic chemical significance, they also display a fascinating range of dynamical effects including highly quantum behavior or strong coupling between inter and intramolecular degrees of freedom. In chemical and biological systems, rates for proton transfer (PT) or hydrogen transfer (HT) can cover the picosecond to millisecond range, which corresponds to a few kilocalories per mole up to 20 kcal mol−1. From a computational perspective, this implies that the energetics along a specific motif has to be extensively sampled in order to converge the experimental observables. Possible approaches to treat the energetics include ab initio molecular dynamics (AIMD) simulations, mixed quantum mechanical/molecular mechanics (QM/MM) calculations, and more or less empirical parameterizations of the intermolecular interactions based on model potentials or parameterized fits to rigorous quantum chemical calculations. In this chapter, we discuss QM/MM embedding schemes into an empirical force field based on fitting high-quality (Moller–Plesset perturbation theory (MP2) with a large basis set) quantum chemical calculations, which allows the explicit treatment of the long-time dynamics. The essential feature of this procedure is its accuracy, flexibility, and suitability for either QM or classical treatments of the nuclear dynamics. The present chapter discusses the theory, implementation, and applications of this embedding scheme and discusses it with regard to other existing ways to treat PT or HT in strongly and weakly coupled systems. PT and HT reactions are fundamental in chemistry and biology. Although the famous Grotthuss shuttling mechanism [1] was introduced more than 200 years ago, notable progress in understanding atomistic details underlying the process has only been achieved recently with modern spectroscopic techniques and high-performance computer simulations [2]. From an experimental point of view, infrared (IR) studies [3–5] were successful in probing the vibrational dynamics of hydrogen bonds. However, a complete assignment/interpretation of the spectra