Energy, Torsional

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. 

Th e dih edral an gle or torsional energy interaction in MM-t- is of th e general form ofec naiion (12) on page 175 but explicitly includes... 

Fig. 4.S Variation in torsional energy (AMBER force field) with O-C-C-0 torsion angle (to) for OCH -CHjO fragment. The minimum energy conformations arise for to = 60° and 300°.

The value of the torsional energy increment has been variously estimated, but TORS = 0.42 kcal mol was settled on for the bond contribution method in MM3, In the full statistical method (see below), low-frequency torsional motion should be calculated along with all the others so the empirical TORS inererneut should be zero. In fact, TORS is not zero (Allinger, 1996). It appears that the TORS inererneut is a repository for an energy eiror or errors in the method that are as yet unknown. 

It is customary to shift the zero point of the potential by adding a factor of 1 to each term. Most rotational profiles resemble either the ethane or ethylene examples above, and a popular expression for the torsional energy is... 

The parameter redundancy is also the reason that care should be exercised when trying to decompose energy differences into individual terms. Although it may be possible to rationalize the preference of one conformation over another by for example increased steric repulsion between certain atom pairs, this is intimately related to the chosen functional form for the non-bonded energy, and the balance between this and the angle bend/torsional terms. The rotational banier in ethane, for example, may be reproduced solely by an HCCH torsional energy term, solely by an H-H van der Waals repulsion or solely by H-H electrostatic repulsion. Different force fields will have (slightly) different balances of these terms, and while one force field may contribute a conformational difference primarily to steric interactions, another may have the... 

The multiple minima nature of the bending energy and the low barriers for interconversion resemble the torsional energy for organic molecules. An expansion of bend in tenns of cosine or sine functions of the angle is therefore more natural than a... 

Table 2.3 Comparison of functional forms used in common force fields. The torsional energy, [ors is in all cases given as a Fourier series in the torsional angle...

Table 2.3 gives a description of the functional form used in some of the common force fields. The torsional energy is written as a Fourier series, typically of order three, in all cases. Many of the force fields undergo developments, and the number of atom types increases as more and more systems become parameterized thus Table 2.3 may be considered as a snapshot of the situation when the data were collected. The universal type force fields, described in Section 2.3.3, are in principle capable of covering molecules composed of elements from the whole periodic table, these have been labelled as all elements . 

As reported in Table 5 and in other recent publications [399,491 ], polymers with very low Tg are expected when the inherent skeletal flexibihty of poly-phosphazenes is coupled with fluorinated alcohols of low dimensions and/or of high chain mobility. In fact, the Tg values for POPs substituted with fluorinated alcohols vary between -50 °C and -90 °C, confirming the extreme chain mobility of these polymers and the existence in them of very low torsional energy barriers. 

Werpetinski, K. S., Cook, M., 1997, A New Grid-Free Density Functional Technique Application to hie Torsional Energy Surfaces of Ethane, Hydrazine, and Hydrogen Peroxide , J. Chem. Phys., 106, 7124. 

Figure 4. Schematic of torsional energy levels in Si electronic state of phenylsilane and Do electronic state of phenylsilane+. The torsional state symmetry labels arise under the molecular symmetry group G12.

Assignment of these spectra involves solution of a highly redundant, interlocking puzzle. We seek assignments consistent with all available information. We can calculate the torsional energies and wavefunctions for various one-dimensional... 

Certain physical properties show that rotation about the single bond is not quite free. For ethane there is an energy barrier of about 3 kcal mol-1 (12 kJ mol-1). The potential energy of the molecule is at a minimum for the staggered conformation, increases with rotation, and reaches a maximum at the eclipsed conformation. The energy required to rotate the atoms or groups about the carbon-carbon bond is called torsional energy. Torsional strain is the cause of the relative instability of the eclipsed conformation or any intermediate skew conformations. 

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