Torsional terms

Much work remains to be done in the development of this approach to explore the advantages and limitations of the method. The method will be extended to force fields that include torsional terms large systems such as biological macromolecules will also be treated. 

A typical force field model for propane contains ten bond-stretching terms, eighteen angle-bending terms, eighteen torsional terms and 27 non-bonded interactions. 

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 ... 

V these three functional forms, the improper torsion definition is most widely used as it can then be easily included with the proper torsional terms in the force field. However, the... 

The computational effort is significantly increased if three-body terms are included in the model. Even with a simple pairwise model, the non-bonded interactions usually require by far the greatest amount of computational effort. The number of bond, angle and torsional terms increases approximately with the number of atoms (N) in the system, but the number of non-bonded interactions increases with N. There are N(N —l)/2 distinct pairs of... 

In the case of ethylene, because of 2-fold symmetry, odd terms drop out of the series, V3, V5,... = 0. In the case of ethane, because of 3-fold symmeti-y, even temis drop out, V2, V4,... = 0. Terms higher than three, even though permitted by symmetry, are usually quite small and force fields can often be limited to three torsional terms. Like cubic and quaitic terms modifying the basic quadratic approximation for stretching and bending, terms in the Fourier expansion of Ftors (to) beyond n = 3 have limited use in special cases, for example, in problems involving octahedrally bound complexes. In most cases we are left with the simple expression... 

Addition of a [ Icnn (Fig. 4-13) lo the. V, V2. and V Icmi (Fig. 4-1 T) has Ihc effect t.)f raising the eciilral maximum and liie twt.) symmetrical minima witii(.)tit ciianging the energy of tlie stable ami forni, so producing a potential eneigy function that shows tlie cjualitative form of Fig, 4-1 2, In this context, tlie V j term is called a low-order torsional term. 

MM2. A Hydrocarbon Force Field Utilizing Vj and Va Torsional Terms... 

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... 

Allinger NL. Conformational analysis. 130. MM2. A hydrocarbon force field utilizing VI and V2 torsional terms. 7 Am Chem Soc 1977 99 8127-34. 

Another modification is concerned with the torsional term, which has to describe the full torsional range of 360°. (The quadratic terms in Eq. (2) and (4) are, of course, only valid in the vicinity of e.) Trigonometric expressions are usually chosen ... 

The explicit incorporation of torsional terms is necessary, even if nonbonded interactions are considered for pairs of atoms which are separated by a chain of only three bonds (see Section 2.1.5.). 

Exhaustive catalytic hydrogenation of triptycene affords an equilibrium mixture of perhydrotriptycene isomers. As expected, Boyd s force field (37) calculations, with a modified torsional constant, reproduced the observed composition fairly well (Table 6). All important conformations were taken into account for each isomer. The most stable conformations agree with the results of the X-ray analysis (131) and have the characteristic that the cyclohexane rings are invariably either boat or deformed chair. The most stable conformation of all is 20 (ttt). The predominant conformation of ccc, in which all cyclohexane rings are boat, has an enthalpy only 2.56 kcal/mol above that of 20. The difference is virtually all due to angle and torsional terms. 

Rasmussen s efforts to adopt CFF to saccharides merit special attention (32). His latest version (34), which virtually eliminated the torsional term, awaits critical examination. Tvaroska and Bleha (183) performed partial relaxation MM calculations on dimethoxymethane... 

To illustrate the different complexities, CHARMM s energies arising from torsional terms depend only on the two central atoms, and there is only one cosine term. For MM2 and MM3, there are three cosine terms for each four-atom sequence that defines a torsion angle. MM2 treats lone pairs of electrons on hydroxyl and ether oxygen atoms as separate "atoms that also must be parameterized. Therefore, many more parameters must be used with the MM2 and MM3 programs than the CHARMM program. (The parameters for all the atomic sequences in glucose, and many other molecules, are furnished with MM2 and MM3.)... 

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