Dihedral torsion angle

The dihedral angle or torsional energy interaction in MM-t is of the general form of equation (12) on page 175 but explicitly includes n=l, 2, and 3 with a phase angle (j) =0 ... 

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. 

Next come the dihedral angles (or torsions), and the contribution that each makes to the total intramolecular potential energy depends on the local symmetry. We distinguish between torsion where full internal rotation is chemically possible, and torsion where we would not normally expect full rotation. Full rotation about the C-C bond in ethane is normal behaviour at room temperature (although 1 have yet to tell you why), and the two CH3 groups would clearly need a threefold potential, such as... 

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 excited dibromide executes this vibrational mode and the vibrational coherence persists as some trajectories find the C Br bond-cleavage exit channel, a reaction favored when the dihedral angle is close to 60°. The proper phasing of two vibrations, the BrCCC dihedral-angle-modifying torsional mode and the C—Br stretching vibration, leads to the cleavage of the C Br bond. 

Let US first examine current practice in nomenclature of the phenom-menon of internal rotation. Standard textbooks on conformational analysis on the one hand and those on spectroscopy on the other hand deal differently with the basic definitions. Internal rotation is measured by one or more torsion angles (dihedral angles, azimuthal angles). In the simple cases of e.g. a 1,2-disubstituted ethane the potential energy associated with the internal rotation may be written in a formal sense as a truncated Fourier expansion ... 

In the vast majority of MD applications a further simplification is made by using effective pair-wise additive potentials for atomic interactions. In simulations which contain flexible molecules, it is common practice to add terms which represent chemical bonds, bond angles, improper torsions and dihedrals. Interactions between atoms of molecules are represented by effective pair-wise additive potentials. This empirical approach splits the total potential energy of the system into a bonded (inter-molecule) and non-bonded (intra-molecular) part. 

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