Classical force fields, polarization

METHODS TO INCLUDE POLARIZATION IN CLASSICAL FORCE FIELDS... 

The QM/MM and ab initio methodologies have just begun to be applied to challenging problems involving ion channels [73] and proton motion through them [74]. Reference [73] utilizes Hartree-Fock and DFT calculations on the KcsA channel to illustrate that classical force fields can fail to include polarization effects properly due to the interaction of ions with the protein, and protein residues with each other. Reference [74] employs a QM/MM technique developed in conjunction with Car-Parrinello ab initio simulations [75] to model proton and hydroxide ion motion in aquaporins. Due to the large system size, the time scale for these simulations was relatively short (lOps), but the influences of key residues and macrodipoles on the short time motions of the ions could be examined. 

The energy with both repulsion and polarization removed as above, E. If no coupling exists, such as in fully classical force-fields, the equation... 

Several approaches for calculating excited states in protein environments were proposed to improve the ordinary QM/MM description. The effect of polarization was included as a classical force field [27], and the excitation energy calculated for bacteriorhodopsin (bR) was 0.34 eV less than that from a fixed-charge non-polarizable QM/MM method [27]. Later, a triple-layer QM1/QM2/MM approach was proposed, and DFT(PBEO) calculations were performed for the QM2 layer, which consisted of the amino acids 4 A from the retinal PSB [28]. The calculated excitation energy of bR was only 0.08 eV smaller than that obtained using the ordinary QM/MM method [28]. In another study, an empirical polarization model combined with the QM/MM calculation produced a red shift of 0.14-0.17 eV [29]. However, these pioneering studies neglected the CT effects between the retinal and the protein environments. 

In associating liquids the molecular dipole moments increase by 40-60% compared to the isolated molecule. These solvents will therefore strongly affect the chemical reactivity of solute molecules. Classical force field simulations neglecting polarization will not be able to capture these changes. 

In the previous Section we obtained the formula for junction between quantum and classical subsystems Eq. (13). The control for the types of interactions which are taken into account is an important characteristic of particular QM/MM scheme. The authors of Ref. [110] have proposed a classification of hybrid schemes based on the interaction between fragments. According to it, the simplest type of model is mechanical embedding (examples of this type of modelling are the IMOMM [38] and IMOMO [59] schemes by Morokuma) when both QM and MM systems are not polarized by each other and their interaction is represented by classical force fields only. In this context the choice of parameters of intersystem interaction can be crucially important, so, they are frequently optimized [97,118]. More elaborated model is that including polarization of the QM subsystem. This polarization can be covered by including the MM charges into one-electron part of the Hamiltonian of the QM subsystem ... 

Many problems in force field investigations arise from the calculation of Coulomb interactions with fixed charges, thereby neglecting possible mutual polarization. With that obvious drawback in mind, Ulrich Sternberg developed the COSMOS (Computer Simulation of Molecular Structures) force field [30], which extends a classical molecular mechanics force field by serai-empirical charge calculation based on bond polarization theory [31, 32]. This approach has the advantage that the atomic charges depend on the three-dimensional structure of the molecule. Parts of the functional form of COSMOS were taken from the PIMM force field of Lindner et al., which combines self-consistent field theory for r-orbitals ( nr-SCF) with molecular mechanics [33, 34]. 

Both of the above approaches rely in most cases on classical ideas that picture the atoms and molecules in the system interacting via ordinary electrical and steric forces. These interactions between the species are expressed in terms of force fields, i.e., sets of mathematical equations that describe the attractions and repulsions between the atomic charges, the forces needed to stretch or compress the chemical bonds, repulsions between the atoms due to then-excluded volumes, etc. A variety of different force fields have been developed by different workers to represent the forces present in chemical systems, and although these differ in their details, they generally tend to include the same aspects of the molecular interactions. Some are directed more specifically at the forces important for, say, protein structure, while others focus more on features important in liquids. With time more and more sophisticated force fields are continually being introduced to include additional aspects of the interatomic interactions, e.g., polarizations of the atomic charge clouds and more subtle effects associated with quantum chemical effects. Naturally, inclusion of these additional features requires greater computational effort, so that a compromise between sophistication and practicality is required. 

Piquemal J-P, Chelli R, Procacci P, Gresh N (2007) Key role of the polarization anisotropy of water in modeling classical polarizable force fields. J Phys Chem A 111 8170... 

The total electric field, E, is composed of the external electric field from the permanent charges E° and the contribution from other induced dipoles. This is the basis of most polarizable force fields currently being developed for biomolecular simulations. In the present chapter an overview of the formalisms most commonly used for MM force fields will be presented. It should be emphasized that this chapter is not meant to provide a broad overview of the field but rather focuses on the formalisms of the induced dipole, classical Drude oscillator and fluctuating charge models and their development in the context of providing a practical polarization model for molecular simulations of biological macromolecules [12-21], While references to works in which the different methods have been developed and applied are included throughout the text, the major discussion of the implementation of these models focuses... 

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