Dihedral torsion

The conformational distance does not have to be defined in Cartesian coordinates. Eor comparing polypeptide chains it is likely that similarity in dihedral angle space is more important than similarity in Cartesian space. Two conformations of a linear molecule separated by a single low barrier dihedral torsion in the middle of the molecule would still be considered similar on the basis of dihedral space distance but will probably be considered very different on the basis of their distance in Cartesian space. The RMS distance is dihedral angle space differs from Eq. (12) because it has to take into account the 2n periodicity of the torsion angle. 

The other syntax for supplying molecular structures to Gaussian 94 is the Z-matrix. A Z-matrix specifies the locations of and bonds between atoms using bond lengths, bond angles, and dihedral (torsion) angles. 

A fourth atom bonded to either end of the previous chain, and the value of the dihedral (torsion) angle formed by the four atoms. 

Some authors refer to improper dihedrals when discussing dihedral torsion where we would not normally expect full rotation, for example, any of the C-C-C-C linkages in the benzene ring of aspirin. Many MM force fields treat... 

Frickenhaus, S., Kannan, S., Zacharias, M. Efficient evaluation of sampling quality of molecular dynamics simulations by clustering of dihedral torsion angles and sammon mapping. J. Comput. Chem. 2009, 30, 479-92. 

The torsional potential may be expressed as a truncated Fourier series, as shown in [Eq. (12)], where the summations is over all n unique bond dihedrals (torsions), co. Usually, the first three terms are sufficient to describe the torsional energy adequately. Higher terms may improve the fit between experimental data and calculation. Inclusion of Vi and V2 terms has improved the agreement between experi-ement and calculations. "" Radom, Hehre, and Pople had given a physical explanation to the torsional terms. The onefold term, Fi, is a dipole-dipole interaction. The twofold term, V2, arises from hyperconjugation. The threefold term, F , has a steiic origin. 

The third term in eq. [8.112] is the interaction energy between solvent molecules. It is usually approximated by the molecular mechanics force field, which in general contains bond stretching, angle bending, dihedral torsion andnon-bonded terms (see Section 8.4.5). 

Forcefield-A set of parameterized analytical expressions used in molecular mechartics for evaluating the contributions to the total potential energy of a molecular system forcefields typically, but not always, include contributions for bond stretching, angle bending, dihedral torsion, van der Waals, and Coulombic interactions. 

Glycosidic bonds as seen in Figure 3 can be energetically defined by their dihedral torsional angles, ( ), /, and o) and by the intramolecular hydrogen bonds (indicated by the... 

Bonded interactions depend on the deviations of the chemical bond lengths and bond angles from their equilibrium values, as well as on the values of the dihedral (torsion) angles. The simplest and most often used approach is to represent the bonded energy as a sum of three separate contributions, described below ... 

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