Force field models, empirical parameters

In this study the authors develop simplified equations relating equilibrium fractionations to mass-scaling factors and molecular force constants. Equilibrium isotopic fractionations of heavy elements (Si and Sn) are predicted to be small, based on highly simplified, one-parameter empirical force-field models (bond-stretching only) of Sip4, [SiFJ, SnCl4, and [SnCl,] -. 

Electrostatic interactions can be most simply modeled as the Coulomb interaction between partial atomic charges, while the repulsion-dispersion part is usually described by a Lennard-Jones or, more accurately, an exp-6 form, each of which contains parameters that must be fixed. High-quality empirically fitted parameter sets have been developed, where the atom-atom interactions are parameterized to reproduce the structures, sublimation enthalpies and, sometimes, further observable properties of organic molecular crystals [73,74]. Their use has been very effective in CSP. Nonempirical approaches to fitting intermolecular force fields, where the parameters are derived from quantum mechanical calculations, have occasionally been applied for CSP [75-78], but these are currently limited to small molecules, so currently lack relevance for typical pharmaceutical molecules. 

In this chapter we refer to recent reports describing the successful development and application of NMR-based techniques to study lipids in various contexts, to develop new methods to study recombinant proteins and peptides in artificial lipid membranes and last, but not least, to validate other methods such as all-atomistic force field and empirical models on the basis of NMR parameters. 

In the past, force fields were parameterized based only on experimental data nowadays, most modem force fields include substantial quantum chemical information. According to the nature of the data used for parameterization, force fields can be classified as ab initio, semi-empirical, and empirical. Simple potentials, e.g., for argon, which require few parameters, can be fitted exclusively to macroscopic experimental data however, more complex force fields have numerous parameters and thus depend heavily on ab initio data. This chapter gives an introduction to the present state-of-the-art in this field. Attention is given to the way modeling and simulation on the scale of molecular force fields interact with other scales, which is mainly by parameter inheritance. Parameters are determined both bottom-up from quantum chemistry and top-down from experimental data. 

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

The approach presented above is referred to as the empirical valence bond (EVB) method (Ref. 6). This approach exploits the simple physical picture of the VB model which allows for a convenient representation of the diagonal matrix elements by classical force fields and convenient incorporation of realistic solvent models in the solute Hamiltonian. A key point about the EVB method is its unique calibration using well-defined experimental information. That is, after evaluating the free-energy surface with the initial parameter a , we can use conveniently the fact that the free energy of the proton transfer reaction is given by... 

The polarizable fluctuating charge model in CHARMM results from the work of Patel, Brooks and co-workers [92, 214], The water model is based on the TIP4P-FQ model of Rick, Stuart and Berne [17], In the development of the force field the electronegativities and hardnesses were treated as empirical parameters and do not have any association with experimental or QM values, for example, from ionization energies and electron affinities of single atoms. 

Infrared spectra are straightforward to predict theoretically, demanding development of a force field (FF) to determine frequencies and dipole derivatives for intensities. These parameters were initially obtained using empirically fitted force constants and simple models for transition dipoles (Krimm and Bandekar, 1986 Torii and Tasumi, 1996). 

The various types of successful approaches can be classified into two groups empirical model calculations based on molecular force fields and quantum mechanical approximations. In the first class of methods experimental data are used to evaluate the parameters which appear in the model. The shape of the potential surfaces in turn is described by expressions which were found to be appropriate by semiclassicala> or quantum mechanical methods. Most calculations of this type are based upon the electrostatic model. Another more general approach, the "consistent force field method, was recently applied to the forces in hydrogen-bonded crystals 48> 49>. 

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