Conformational energies methods

Conceptually related to the molecular mechanics approach are the so-called empirical or conformational energy methods (Scheraga, 1977 Ra-machandran and Sasisekharan, 1968). These treat molecules as a collection of subunits (e.g., peptides) and usually investigate only internal rotational degrees of freedom. Somewhat akin to the empirical methods is the so-called hard-sphere or contact distance method (Ramachandran and Sasisekharan, 1968). This rapid method assumes all atoms are impenetrable balls and can be used to differentiate possible and impossible conformations. No energies are calculated. Space-filling, hand-held molecular models give the same type of information, but less quantitatively. 

Empirical conformational energy program for peptides (ECEPP) is the name of both a computer program and the force field implemented in that program. This is one of the earlier peptide force fields that has seen less use with the introduction of improved methods. It uses three valence terms that are fixed, a van der Waals term, and an electrostatic term. 

In Chapter 2, a brief discussion of statistical mechanics was presented. Statistical mechanics provides, in theory, a means for determining physical properties that are associated with not one molecule at one geometry, but rather, a macroscopic sample of the bulk liquid, solid, and so on. This is the net result of the properties of many molecules in many conformations, energy states, and the like. In practice, the difficult part of this process is not the statistical mechanics, but obtaining all the information about possible energy levels, conformations, and so on. Molecular dynamics (MD) and Monte Carlo (MC) simulations are two methods for obtaining this information... 

Ah initio calculations of polymer properties are either simulations of oligomers or band-structure calculations. Properties often computed with ah initio methods are conformational energies, polarizability, hyperpolarizability, optical properties, dielectric properties, and charge distributions. Ah initio calculations are also used as a spot check to verify the accuracy of molecular mechanics methods for the polymer of interest. Such calculations are used to parameterize molecular mechanics force fields when existing methods are insulficient, which does not happen too often. 

In the following, the method itself is introduced, as are the various techniques used to perform normal mode analysis on large molecules. The method of normal mode refinement is described, as is the place of normal mode analysis in efforts to characterize the namre of a protein s conformational energy surface. 

Calculations on larger molecules have been carried out using molecular mechanics techniques and the Merck force field.- This method has proven to be suitable for the calculation of equilibrium geometries and conformational energy differences. 

The literature in this field is confusing because of a somewhat haphazard method of nomenclature that has arisen historically. This is compounded by some mistakes in structure determination, reported in early papers, and which are occasionally quoted. The first part of this chapter deals with nomenclature and with a brief overview of early work. Subsequent sections deal with the formation and metabolism of di-D-fructose dianhydrides by micro-organisms, and the formation of dihexulose dianhydrides by protonic and thermal activation. In relation to the latter topic, recent conclusions regarding the nature of sucrose caramels are covered. Other sections deal with the effects of di-D-fructose dianhydrides upon the industrial production of sucrose and fructose, and the possible ways in which these compounds might be exploited. An overview of the topic of conformational energies and implications for product distributions is also presented. 

Conformation analysis methods. In many cases in the process of building a 3D structure from scratch, decisions have to be made between multiple alternatives with similar energy. A typical example is an sp -sp torsion angle with similar energies for the alternatives of -i-60°, -60° and 180°. In many cases, rules are used to decide (e.g. stretch an open chain portion as much as possible to avoid clashes). Sometimes, the best result cannot be determined without a conformation analysis (e.g. complex ring systems with exocycHc substituents). Despite conformation analysis being a topic of its own covered in the next chapter, many automatic 3D structure generators have to fall back in certain situations to a limited conformation search in order so solve a specific problem and to come up with a reasonable solution. 

Gundertofte, K., Liljefors, T., Norrby, P.-O., Pettersson, I. A comparison of conformational energies calculated by several molecular mechanics methods. 

DG was primarily developed as a mathematical tool for obtaining spahal structures when pairwise distance information is given [118]. The DG method does not use any classical force fields. Thus, the conformational energy of a molecule is neglected and all 3D structures which are compatible with the distance restraints are presented. Nowadays, it is often used in the determination of 3D structures of small and medium-sized organic molecules. Gompared to force field-based methods, DG is a fast computational technique in order to scan the global conformational space. To get optimized structures, DG mostly has to be followed by various molecular dynamic simulation. 

Topol, I. A., and S. K. Burt. 1993. The calculations of small molecular conformation energy differences by density functional method. Chem. Phys. Lett 204,611. 

The molecular mechanics technique has been called by many different names, including Westheimer method, strain-energy method, conformational energy calculations, empirical potential energy calculations, atom-atom pair potential method, and force field calculations. Empirical force field is widely used, but somewhat long, and many authors omit empirical, leading to confusion with spectroscopic force field calculations. Molecular mechanics (11) now appears to be favored (10a) and is used (abbreviated as MM) throu out this chapter. 

Conformational studies on monocyclic Cg to Cn ketones have been reviewed with reference to the MM method (184 see also ref. 89). Extensive comparisons of the conformational energies of trans-... 

In 1963, V.S.R. Rao undertook a more ambitious task the prediction of the likely conformations of polysaccharides from a computerized survey of model structures ( ). As a result of atomic overlap, some model conformers had higher energies than others, a criterion by which most models could be rejected. These predictions were not accompanied by experimental data for the subject molecules, leaving to experimentalists the task of corroboration or refutation. Although many advances in computers and methods have occurred in the intervening decades, predicting polysaccharide conformations based upon relative conformational energies continues to be of substantial interest. 

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