Possible conformation

The number of possible conformations rises dramatically with increasing ring size. Therefore, large ring systems carmot be handled by the methods applied to small rings. However, in rigid polymacrocyclic structures for example, an overall... 

As the number of conformations increases exponentially with the number of rotatable bonds, for most molecules it is not feasible to take all possible conformations into account. However, a balanced sampling of the conformational space should be ensured if only subsets arc being considered. In order to restrict the number of geometries output, while retaining a maximum of conformational diversity, ROTATE offers the possibility of classifying the remaining conformations, i.c., similar conformations can be combined into classes. The classification is based on the RMS deviation between the conformations, either in Cartesian (RMS y 7if [A]) or torsion space in [ ], The RMS threshold, which decides whether two... 

Possible conformations of the calix[4]arene systems. (Figure adapted from Fischer S, P D J Groothenuis, roenen, PV P van Hoorn, F C j M van Geggel, D N Reinhoudt and M Karplus 1995. Pathways for mational Interconversion of Calix[4]arenes. Journal of the American Chemical Society 117 1611-1620.)... 

The most ambitious approaches to the protein folding problem attempt to solve it from firs principles (ab initio). As such, the problem is to explore the coirformational space of th molecule in order to identify the most appropriate structure. The total number of possibl conformations is invariably very large and so it is usual to try to find only the very lowes energy structure(s). Some form of empirical force field is usually used, often augmente with a solvation term (see Section 11.12). The global minimum in the energy function i assumed to correspond to the naturally occurring structure of the molecule. 

The level of theory necessary for computing PES s depends on how those results are to be used. Molecular mechanics calculations are often used for examining possible conformers of a molecule. Semiempiricial calculations can give a qualitative picture of a reaction surface. Ah initio methods must often be used for quantitatively correct reaction surfaces. Note that size consistent methods must be used for the most accurate results. The specific recommendations given in Chapter 18 are equally applicable to PES calculations. 

Polymers can be crystalline, but may not be easy to crystallize. Computational studies can be used to predict whether a polymer is likely to crystallize readily. One reason polymers fail to crystallize is that there may be many conformers with similar energies and thus little thermodynamic driving force toward an ordered conformation. Calculations of possible conformations of a short oligomer can be used to determine the difference in energy between the most stable conformer and other low-energy conformers. 

As a consequence of these various possible conformations, the polymer chains exist as coils with spherical symmetry. Our eventual goal is to describe these three-dimensional structures, although some preliminary considerations must be taken up first. Accordingly, we begin by discussing a statistical exercise called a one-dimensional random walk. 

Fig. 7. Formation of a supramolecular aggregate composed of a compound containing nine melamine rings (the three-layered nonamelamine derivative A) and nine molecules of neohexylisocyanurate (B). Of the 16 possible conformers that can result, two are shown The first has the nine molecules of B arranged in three rosettes of three molecules each, stacked atop each other in the second, the rosettes are staggered with respect to each other such that the rosettes in the first and third layers of A are aligned with each other, but not with the rosette in the second layer. The supramolecular assembly is stabilized...

For any given protein, the number of possible conformations that it could adopt is astronomical. Yet each protein folds into a unique stmcture totally deterrnined by its sequence. The basic assumption is that the protein is at a free energy minimum however, calometric studies have shown that a native protein is more stable than its unfolded state by only 20—80 kj/mol (5—20 kcal/mol) (5). This small difference can be accounted for by the favorable... 

As the ring size increases, the number of possible conformations increases further so that many alternative diamond-lattice conformations are available. ... 

STO-3G calculations find the corresponding transition state to be more stable than other possible conformations by several kilocalories per raole. The origin of the preference for this transition-state conformation is believed to be a stabilization of the C=0 LUMO by the a orbital of the perpendicularly oriented substituent. 

The stereoselectivity of alkylation of 3-acetylbutyrolactone is influenced by additional alkyl substituents on the ring at C-4 and C-5. Analyze possible conformations of the enolate and develop an explanation of the stereoselectivity. 

The model (23) is simple to study, but unfortunately not very widely applicable. In general, one is more interested in situations where the interfaces are free to fold around and to assume every possible conformation. A second possible approach is to switch over to a lattice formulation. This has been done by a number of groups [231-233]. The resulting models are very... 

FIGURE 6.3 Many of the possible conformations about an -carbon between two peptide planes are forbidden because of steric crowding. Several noteworthy examples are shown here. 

Christian Anfmsen s experiments demonstrated that proteins can fold reversibly. A corollary result of Anfmsen s work is that the native structures of at least some globular proteins are thermodynamically stable states. But the matter of how a given protein achieves such a stable state is a complex one. Cyrus Levinthal pointed out in 1968 that so many conformations are possible for a typical protein that the protein does not have sufficient time to reach its most stable conformational state by sampling all the possible conformations. This argument, termed Levinthal s paradox, goes as follows consider a protein of 100 amino acids. Assume that there are only two conformational possibilities per amino acid, or = 1.27 X 10 ° possibilities. Allow 10 sec for... 

Figure 11.S Possible conformations of N2H4 with pyramidal N. Hydrazine adopts the gauche C l form with N N 145 pm, H-N- II 108°. and a twist angle of 95 as shown in the lower diagram.

Notice molecular symmetry at work. The Huckel rr-electron model is in many ways a blunt instrument, because we would get exactly the same answers for either of the following possible conformers of hexatriene (Figure 7.3). 

Deriving such heat of formation parameters requires a large body of experimental Ai/f values. For many classes of compound there are not sufficient data available. Only a few force fields, notably MM2 and MM3, attempt to parameterize also heats of formation. Most force fields are only concerned with reproducing geometries and possibly conformational relative energies, for which the steric energy is sufficient. 

Fig. 8-1. Schematic representations of the interaction of the (R)NapEtNH enantiomer guest with a chiral pyridine-18-crown-6 host (S,S)-1 and possible conformations of the (R)NapEt com-...

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