Potential energy function parametrization

A short presentation of the Consistent Force Field is given, with emphasis on parametrization and optimization of energy function parameters. For best possible calculation of structure, potential energy functions with parameter values optimized on both structural and other properties must be used. Results from optimization with the Consistent Force Field on alkanes and ethers are applied to glucose, gentiobiose, maltose and cellobiose. Comparison is made with earlier and with parallel work. The meaning and use of conformational maps is discussed shortly. 

A series of simplified force fields was created by Rasmussen et al. [56, 57]. The PEF400 [58] and PEF300 (potential energy function) and variants here of are used for the calculation of disaccharides and monosaccharides (cf. below). The parametri-sation of this force field program includes atomic charges which (in variant PEF422) differ for the anomeric carbon and the other carbon atoms. The parametrization is obtained from ab initio calculations. 

Some theoretical purists tend to view molecular mechanics calculations as merely a collection of empirical equations or as an interpolative recipe that has very little theoretical Justification. It should be understood, however, that molecular mechanics is not an ad hoc approach. As previously described, the Born-Oppenheimer approximation allows the division of the Schrodinger equation into electronic and nuclear parts, which allows one to study the motions of electrons and nuclei independently. From the molecular mechanics perspective, the positions of the nuclei are solved explicitly via Eq. (2). Whereas in quantum mechanics one solves, which describes the electronic behavior, in molecular mechanics one explicitly focuses on the various atomic interactions. The electronic system is implicitly taken into account through judicious parametrization of the carefully selected potential energy functions. 

Starting point is QM calculation within the framework of density-functional theory (DFT) (Hohenberg and Kohn, 1964 Kohn and Sham, 1965 Payne et al., 1992). DFT-based energy calculations can be used to evaluate the parameters of classical interatomic interaction potentials, which can be used to perform MS, MC, and MD simulations such ab initio potential parametrization is a key to improving the transferability of the classical force field. In Fig. 1, an interatomic potential energy function for Si-H interactions is given as an example of such a parametrization (Ohira et al., 1995). 

The descriptions of molecular dynamics and the theory of chemical reactions in gas and condensed phases are based on the concept of potential energy function (hypersurface) [1,2] rooted in the Bom-Oppenheimer (BO) approach [3]. The parametric dependance of the electronic wave function with respect to nuclear coordinates is the basic idea on which the BO framework rest. In this paper, a different approach is taken. The electronic state functions are taken to be independent from the instantaneous nuclear positions. As a first step, we consider molecular systems which are characterized by stationary nuclear configurations belonging to particular symmetry groups. The corresponding electronic stationary states must always transform according to given irreduci-... 

The eigenfunctions depend parametrically on the choice of intemuclear separation R = R — Rb. The K-dependent eigenvalues k(R) act as potential energy functions for nuclear vibrational motion when the Born-Oppenheimer separation of nuclear and electronic motions is valid. 

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