Empirical force field parameter

Table 1 Types and Sources of Target Data Used m the Optimization of Empirical Force Field Parameters...

In this section we will discuss in some detail the relationship between molecular mechanics force field parameters and real physical parameters. As mentioned before, the fundamental difference between spectroscopic and molecular mechanics force fields is that the former are molecule-specific while the latter are general. Empirical force field parameters can be used for the calculation of unknown structures and their strain energies, and for the prediction of vibrational frequencies of new compounds. However, the parameters themselves generally have limited meaning. 

Clearly, the issues of first principles and transferability are more pertinent to an essentially academic book such as the present one, while production details are more aptly included in internal technical manuals (heaven knows how much vital information is secreted in confidential company reports and thus hidden from the scientific community). The matter can be reformulated as follows the value of a parametric theory is directly proportional to the extension of the factual landscape to which it applies, and inversely proportional to the effort made in its development. Atom-atom formulations cannot yet be beaten in this respect. They apply with success to a wide scope of different problems and can give reliable theoretical estimates of crystal sublimation enthalpies and liquid evaporation enthalpies. And yet they are limited by their intrinsically scarce adherence to first principles, with a lack of contact between parameters and the implied physics. For these reasons, the future is not in their direction, and different paths must be sought, presumably in the direction of closer relationships between empirical force field parameters and quantum chemical data, considering that many molecular properties are nowadays more cheaply... 

Equation (7) implies that the molecular response to an external field depends, in addition to the field itself, on the derivatives with respect to the nuclear coordinates of the molecular multipole moments. These derivatives are the intrinsic molecular observables that should translate into the empirical force field parameters. 

Diversity of protein structure and function is enhanced by the different chemical functional groups seen in the 20 common amino acids. This variety, however, complicates the development of empirical force field parameters for proteins. For simplicity we will simply list a number of the model compounds used for the different amino acids. This is presented in Table 1. The selection of appropriate model compounds is based on a balance between the size of the compound and the available target data. For example, a large number of gas and condensed phase data are available for methanol however, sole use of that compound for the sidechains of serine or threonine avoids accurate tests of parameters associated with the covalent connection of the sidechain to the backbone. This is overcome by the use of larger compounds such as ethanol and isopropanol. Increases in computational resources will allow for ab initio calculations on larger model compounds. However, as discussed in the previous section, care... 

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]. 

Tliroughout this chapter and in Table 1 the inclusion of QM results as target data is evident, with the use of such data in the optimization of empirical forces fields leading to many improvements. Use of QM data alone, however, is insufficient for the optimization of parameters for condensed phase simulations. This is due to limitations in the ability to perform QM calculations at an adequate level combined with limitations in empirical force fields. As discussed above, QM data are insufficient for the treatment of dispersion... 

Foloppe N, MacKerell AD (2000) All-atom empirical force field for nucleic acids I. Parameter optimization based on small molecule and condensed phase macromolecular target data. J Comput Chem 21 (2) 86-104... 

Figure 4. Schematic illustration of force-constant parameters used in Modified Urey-Bradley Force-Field (MUBFF) vibrational modeling (Simanouti (Shimanouchi) 1949). The MUBFF is a simplified empirical force field that has been used to estimate unknown vibrational frequencies of molecules and molecule-like aqueous and crystalline substances. Here, three force constants (K, H, and describe distortions of a tetrahedral XY molecule, [Cr04] due to bond stretching (Cr-O), bond-angle bending (Z O-Cr-O), and repulsion between adjacent non-bonded atoms (0..0). Less symmetric molecules with more than one type of bond or unequal bond angles require more parameters, but they will belong to the same basic types.

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,] -. 

The conformational energies of the lower members of POM, 2,4-dioxapentane and 2,4,6-trioxaheptane are estimated by the empirical force field method. The gauche states of the Internal rotation around the skeletal C—0 bonds are successfully predicted to be of lower energies in both molecules. In order to calculate the unperturbed dimension and dipole moment of POM, RIS approximations are made by using the results obtained from the force field calculations on 2,4,6-trioxaheptane. Although these parameters are significantly different from those estimated earlier, they reproduce the observed values fairly well. 

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