Conformation, molecular

The problem is conventionally sidestepped by assuming that nuclear and electronic motions are decoupled, but despite many efforts this condition has never been shown to yield a rigid molecular shape either. The insurmountable problem is permutational invariance. In molecular-orbital calculations that decouple electronic from nuclear motion the nuclei are identified in order to support the definition of molecular structure, but then permutation of identical nuclei implies rearrangement of bonds and a new set of calculated electronic energies. There is little hope of ever overcoming these problems  

The discussion of stereochemistry in Chapter 2 implicitly assumed that molecules are as rigid as the physical models or two-dimensional pictorial representations that we use to study them. Our current understanding of quantum mechanics, thermodynamics, and spectroscopy tells us that molecules are in constant motion, however. At room temperature they vibrate and (in the liquid or gas phase) rotate. Not only may the entire molecule rotate, but bond rotations within a structure can change intramolecular spatial relationships. 

The term conformation generally refers to one of the spatial arrangements that a molecule can achieve by rotation about single bonds. If a molecule has several bonds about which rotation can occur, then the shape of the molecule can change significantly. Even though they ordinarily cannot be isolated, conformations that correspond to energy minima are known as conformers, a contraction of conformational isomers. Occasionally they are called rotamers, a shortened form of rotational isomers. 

A conformation can be identified by a dihedral angle, which is the angle made by two bonds on adjacent atoms when the adjacent atoms are eclipsed in a Newman projection. Consider a C—C unit with substituent A on one carbon atom and substituent B on the other. The dihedral angle is the angle between the lines A-C and C-B in the Newman projection. The angle is considered positive if the arrow drawn from the near bond line curves clockwise toward the second bond line and negative if the arrow curves counterclockwise. 

Perspectives on Structure and Mechanism in Organic Chemistry, Second Edition By Felix A. Carroll Copyright 2010 John Wiley Sons, Inc. 

If the dihedral angle A-C-C-B is near 60°, near 120°, near 240° or near 300°, then one of the substituents is said to be clinal (inclined or slanted) with respect to the other. The notation for conformations with dihedral angles of 30° to 90° is -I- syn-clinal (-j- sc) 90° to 150° is + anti-clinal (+ ac) 210° to 270° is -anti-clinal -ac) and 270° to 330° is -syn-clinal (—sc). 

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Harder P, Grunze M, Dahint R, Whitesides G M and Laibinis P E 1998 Molecular conformation in oligo(ethylene glycol)-terminated self-assembled monolayers on gold and silver surfaces determines their ability to resist protein adsorption J. Rhys. Chem. B 102 426-36... 

The free energy differences obtained from our constrained simulations refer to strictly specified states, defined by single points in the 14-dimensional dihedral space. Standard concepts of a molecular conformation include some region, or volume in that space, explored by thermal fluctuations around a transient equilibrium structure. To obtain the free energy differences between conformers of the unconstrained peptide, a correction for the thermodynamic state is needed. The volume of explored conformational space may be estimated from the covariance matrix of the coordinates of interest, = ((Ci [13, lOj. For each of the four selected conform-... 

C.D. Maranas, IP. Androulakis and C.A. Floudas, A deterministic global optimization approach for the protein folding problem, pp. 133-150 in Global minimization of nonconvex energy functions molecular conformation and protein folding (P. M. Pardalos et al., eds.), Amer. Math. Soc., Providence, RI, 1996. 

G. Ramachandran and T. Schlick. Beyond optimization Simulating the dynamics of supercoiled DNA by a macroscopic model. In P. M. Pardalos, D. Shal-loway, and G. Xue, editors. Global Minimization of Nonconvex Energy Functions Molecular Conformation and Protein Folding, volume 23 of DIM ACS Series in Discrete Mathematics and Theoretical Computer Science, pages 215-231, Providence, Rhode Island, 1996. American Mathematical Society. 

Soc. 1974, 96, 4S34--i842. pi3] D. Weininger, SMILES - a language for molecules and reactions, in Handbook of Chemoinformatics, J. Gasteiger (Ed.) Wiley-VCH, Weinheim, 2003, Chapter 11, Section 3. pi4] G. M. Crippen, T.F. Havel, Distance geometry and molecular conformations, in Chemometrics Research Studies Series 15 D. Bawden (Ed.), Research Studies Press (Wiley), New York, 1988. 

Reynolds C A, J W Essex and W G Richards 1992. Atomic Charges for Variable Molecular Conformations. Journal of the American Chemical Society lli 9075-9079. 

Jorgensen W L and J K Buckner 1987. Use of Statistical Perturbation Theory for Computing Solven Effects on Molecular Conformation. Butane in Water. Journal of Physical Chemistry 91 6083-6085. 

G. M. Crippen, T. F. Havel, Dutanee Geometry and Molecular Conformation John Wiley Sons, New York (1988). 

It may be desirable to predict which crystal structure is most stable in order to predict the products formed under thermodynamic conditions. This is a very difficult task. As of yet, no completely automated way to try all possible crystal structures formed from a particular collection of elements (analogous to a molecular conformation search) has been devised. Even if such an effort were attempted, the amount of computer power necessary would be enormous. Such studies usually test a collection of likely structures, which is by no means infal-... 

Stereochemistry. Cyclohexane can exist ia two molecular conformations the chair and boat forms. Conversion from one conformation to the other iavolves rotations about carbon—carbon single bonds. Energy barriers associated with this type of rotation are low and transition from one form to the other is rapid. The predominant stereochemistry of cyclohexane has no influence ia its use as a raw material for nylon manufacture or as a solvent. 

Fig. 2. Molecular modeling of dopamine D2 receptor agonists used to define the molecular conformation needed for selective high affinity binding.

The melting points, optical rotations, and uv spectral data for selected prostanoids are provided in Table 1. Additional physical properties for the primary PGs have been summarized in the Hterature and the physical methods have been reviewed (47). The molecular conformations of PGE2 and PGA have been determined in the soHd state by x-ray diffraction, and special H and nuclear magnetic resonance (nmr) spectral studies of several PGs have been reported (11,48—53). Mass spectral data have also been compiled (54) (see Mass spectrometry Spectroscopy). 

J. Kleia, Molecular Conformation and Dynamics of Macromolecules in Condensed Systems, Elsevier, Amsterdam, 1988, p. 333. 

To extract the conformational properties of the molecule that is being studied, the conformational ensemble that was sampled and optimized must be analyzed. The analysis may focus on global properties, attempting to characterize features such as overall flexibility or to identify common trends in the conformation set. Alternatively, it may be used to identify a smaller subset of characteristic low energy conformations, which may be used to direct future drug development efforts. It should be stressed that the different conformational analysis tools can be applied to any collection of molecular conformations. These... 

Figure 6 A schematic representation of two clustering methods, m which each point represents a single molecular conformation and the circles are the similarity cutoff distances used to define the clusters, (a) Three clusters are defined when overlapping clusters are grouped together, (h) Five clusters are defined when the overlaps are removed from one of the overlapping clusters.

As stated earlier, the main motivation for using either PCA or PCA is to construct a low-dimensional representation of the original high-dimensional data. The notion behind this approach is that the effective (or essential, as some call it [33]) dimensionality of a molecular conformational space is significantly smaller than its full dimensionality (3N-6 degrees of freedom for an A-atom molecule). Following the PCA procedure, each new... 

Fortunately, it was found that in polypeptide systems the effective dimensionality of conformational spaces is significantly smaller than the dimensionality of the full space, with only a few principal axes contributing to the projection [38-41]. In fact, in many cases a projection quality of 70-90% can be achieved in as few as tliree dimensions [42], opening the way for real 3D visualization of molecular conformational space. Figure 8... 

GM Crippen, TF Havel. Distance Geometry and Molecular Conformation. Taunton, England Research Studies Press, 1988. 

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