Torsion barrier

This barrier (torsional strain) causes the potential energy of the ethane molecule to rise to a maximum when rotation brings the hydrogen atoms into an eclipsed conformation. 

To calculate N (E-Eq), the non-torsional transitional modes have been treated as vibrations as well as rotations [26]. The fomier approach is invalid when the transitional mode s barrier for rotation is low, while the latter is inappropriate when the transitional mode is a vibration. Hamionic frequencies for the transitional modes may be obtained from a semi-empirical model [23] or by perfomiing an appropriate nomial mode analysis as a fiinction of the reaction path for the reaction s potential energy surface [26]. Semiclassical quantization may be used to detemiine anliamionic energy levels for die transitional modes [27]. 

To account for barriers of rotation about chemical bonds, i.e., the energetics of twisting the 1,4-atoms attached to the bonds formed by the atoms 2-3, a three-term torsion energy function like that in Eq. (24) is used, in the given form or slightly modified, in almost every force field. 

The origin of a torsional barrier can be studied best in simple cases like ethane. Here, rotation about the central carbon-carbon bond results in three staggered and three eclipsed stationary points on the potential energy surface, at least when symmetry considerations are not taken into account. Quantum mechanically, the barrier of rotation is explained by anti-bonding interactions between the hydrogens attached to different carbon atoms. These interactions are small when the conformation of ethane is staggered, and reach a maximum value when the molecule approaches an eclipsed geometry. 

It is noteworthy that it is not obligatory to use a torsional potential within a PEF. Depending on the parameterization, it is also possible to represent the torsional barrier by non-bonding interactions between the atoms separated by three bonds. In fact, torsional potentials and non-bonding 1,4-interactions are in a close relationship. This is one reason why force fields like AMBER downscale the 1,4-non-bonded Coulomb and van der Waals interactions. 

An sp sp- single bond where each of the central atoms is in Group VIA (for example, hydrogen peroxide) has a two fold barrier with optirn iitn torsional an glc of 90 degrees, as described by V2=-2,0 kcal/tnol. 

In each of the cases abttvc the total barrier heights are tlivitled by the total II iini her of torsion s counted. For example, ethan e uses a parameter V3=2.0/6 for each ofits six torsions, leading to a total barrier of 2.0 hcal/mol. 

Fhe van der Waals and electrostatic interactions between atoms separated by three bonds (i.c. the 1,4 atoms) are often treated differently from other non-bonded interactions. The interaction between such atoms contributes to the rotational barrier about the central bond, in conjunction with the torsional potential. These 1,4 non-bonded interactions are often scaled down by an empirical factor for example, a factor of 2.0 is suggested for both the electrostatic and van der Waals terms in the 1984 AMBER force field (a scale factor of 1/1.2 is used for the electrostatic terms in the 1995 AMBER force field). There are several reasons why one would wish to scale the 1,4 interactions. The error associated wilh the use of an repulsion term (which is too steep compared with the more correct exponential term) would be most significant for 1,4 atoms. In addition, when two 1,4... 

The barriers in Fig, 4-10 are high because it is difficult to twist ethylene out of its normal planar conformation. The energy is the same at the midpoint and the end points in Fig, 4-10 because, on twisting an ethylene molecule 180" out of its normal conformation, one obtains a molecule that is indistinguishable from the original. The molecule has 2-foid torsional syinnteiry. 

It is generally recognized that the flexibility of a bulk polymer is related to the flexibility of the chains. Chain flexibility is primarily due to torsional motion (changing conformers). Two aspects of chain flexibility are typically examined. One is the barrier involved in determining the lowest-energy conformer from other conformers. The second is the range of conformational motion around the lowest-energy conformation that can be accessed with little or no barrier. There is not yet a clear consensus as to which of these aspects of conformational flexibility is most closely related to bulk flexibility. Researchers are advised to first examine some representative compounds for which the bulk flexibility is known. 

The functional form for dihedral angle (torsional) rotation is identical to that shown in equation (13) on page 175. The barrier heights are in kcal/mol and are in the file pointed to by the Fouri-erTorsion entry for the parameter set in the Registry or the chem. ini file, usually called tor.txt(dbf). If more than one term is... 

An sp3-sp2 or sp -sp - single bond where the atom connected to the central sp (sp -5) atom is not another sp (sp - ) atom, as in the H-C-C-H torsion of propene, is described by a three-fold barrier V3=2.0 kcal/mol. 

Torsional barriers are referred to as n-fold barriers, where the torsional potential function repeats every 2n/n radians. As in the case of inversion vibrations (Section 6.2.5.4a) quantum mechanical tunnelling through an n-fold torsional barrier may occur, splitting a vibrational level into n components. The splitting into two components near the top of a twofold barrier is shown in Figure 6.45. When the barrier is surmounted free internal rotation takes place, the energy levels then resembling those for rotation rather than vibration. 

Table 6.7 gives a few other examples of torsional barrier heights. That for ethylene is high, typical of a double bond, but its value is uncertain. The barriers for methyl alcohol and ethane are three-fold, which can be confirmed using molecular models, and fhose of toluene and nifromefhane are six-fold. The decrease in barrier heighf on going fo a higher-fold barrier is fypical. Rofafion abouf fhe C—C bond in toluene and fhe C—N bond in nifromefhane is very nearly free. 

Figure 6.45 Torsional potential function, V(4>), showing a two-fold barrier...

Table 6.7 Barrier heights V for some torsional vibrations...

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