Potential torsion

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. 

Figure 7-10. Two examples of torsional potentials plotted using Eq, (24) with the parameters rt = 2, V = 5.0, y = Fi (solid line), and n = 3. = 3.0, y = 0 (broken line). All other V, ...

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

Fig. 4.7 Torsional potential varies as shown for different values of V , n and 7.

Many of the torsional terms in the AMBER force field contain just one term from the cosine series expansion, but for some bonds it was found necessary to include more than one term. For example, to correctly model the tendency of O-C—C-O bonds to adopt a gauche conformation, a torsional potential with two terms was used for the O—C—C—O contribution ... 

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... 

In molecular mechanics, the dihedral potential function is often implemented as a truncated Fourier series. This periodic function (equation 10) is appropriate for the torsional potential. 

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. 

The most useful general form of the torsional potential function V(4>) is... 

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

It is important to mention that for most applications the special form of the force field is not as important as the actual values of the parameters. These parameters are determined in a number of ways, mainly by comparison with experiments, e.g., vibrational spectroscopy. Torsional potentials, which are crucial for polymer configurations and dynamics of polymers, can... 

In a class of reahstic lattice models, hydrocarbon chains are placed on a diamond lattice in order to imitate the zigzag structure of the carbon backbones and the trans and gauche bonds. Such models have been used early on to study micelle structures [104], monolayers [105], and bilayers [106]. Levine and coworkers have introduced an even more sophisticated model, which allows one to consider unsaturated C=C bonds and stiffer molecules such as cholesterol a monomer occupies several lattice sites on a cubic lattice, the saturated bonds between monomers are taken from a given set of allowed bonds with length /5, and torsional potentials are introduced to distinguish between trans and "gauche conformations [107,108]. 

Tetrhedral intermediate, 172 Thermodynamic cycles, 186 Thermolysin, zinc as cofactor for, 204 Thrombin, 170 Torsional potential, 111 Transition states, 41-42,44, 45,46, 88, 90-92 in amide hydrolysis, 219-221 oxyanion hole and, 181 stabilization of, 181,181 carbonium ion, 154,155,156-161, 167-169 for gas-phase reactions, 43... 

H2S2 (hydrogenpersulfide), the smallest member of the polysulfane series [15], has been studied extensively by molecular spectroscopy and theoretical calculations [16] (and references therein). By now, accurate knowledge of its structure, torsional potential and vibrational modes has been established. Ab initio calculations readily reproduce these properties [17]. The value of the SSH angle in hydrogen disulfide was a subject of controversies for some time. However, recent experiments led to a different value which is in favour of the ab initio calculated value [17]. 

Torsional Potentials of Common Liquid Crystals and Fragments... 

Fig. 12. Torsional potential and molecular dipole for 22-difluoro biphenyl...

An even more serious problem concerns the corresponding time scales on the most microscopic level, vibrations of bond lengths and bond angles have characteristic times of approx. rvib 10-13 s somewhat slower are the jumps over the barriers of the torsional potential (Fig. 1.3), which take place with a time constant of typically cj-1 10-11 s. On the semi-microscopic level, the time that a polymer coil needs to equilibrate its configuration is at least a factor of the order larger, where Np is the degree of polymerization, t = cj 1Np. This formula applies for the Rouse model [21,22], i. e., for non-... 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

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