Torsion, force fields

It remains to find out whether a similar treatment can be developed for the torsion force fields habitually indexed by quadruples of atomic types and thus posing most problems in the prescription of parametrization. One can also think about following problem setting, namely of designing a set of MINDO/3 or NDDO parameters selected for using with the formulae of either of the approximations of the DMM family. In this case, the entire parameter set can be indexed by the only atomic types as no parameters indexed by pairs and even more by triples or quadruples of atomic types are previewed in a semiempirical setting. 

Atomistically detailed models account for all atoms. The force field contains additive contributions specified in tenns of bond lengtlis, bond angles, torsional angles and possible crosstenns. It also includes non-bonded contributions as tire sum of van der Waals interactions, often described by Lennard-Jones potentials, and Coulomb interactions. Atomistic simulations are successfully used to predict tire transport properties of small molecules in glassy polymers, to calculate elastic moduli and to study plastic defonnation and local motion in quasi-static simulations [fy7, ( ]. The atomistic models are also useful to interiDret scattering data [fyl] and NMR measurements [70] in tenns of local order. 

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. 

The PEF is a sum of many individual contributions, Tt can be divided into bonded (bonds, angles, and torsions) and non-bonded (electrostatic and van der Waals) contributions V, responsible for intramolecular and, in tlic case of more than one molecule, also intermoleculai interactions. Figure 7-8 shows schematically these types of interactions between atoms, which arc included in almost all force field implementations. 

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. 

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. 

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. 

An atom lhai hassp h yhridi/alion lends lo be coplanar wilh its attached aloms. This effect isaccoiinled for by improper torsions in Olher force fields and by oiil-of-plane-bending inlcraclions in... 

Th c values of V I, V2, and V3, in keal/tnol, are listed in mmp-tor.txtfdbf). fhc MM+ force field uses special values for the torsional force constants when the atoms are in a four-member ring. 

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 ... 

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°.

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... 

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 force-field model for ethanol contains C-O and O—H bond-stretching contributions in ethane thiol these are replaced by C—S and S—H parameters. Similarly, in ethanol there will be angle-bending terms due to C—O—H, C—C—O and H—C—O angles in ethane thiol these will be C—S—H, C—C—S and H—C—S. The torsional contribution will be modified appropriately, as will the van der Waals and electrostatic interactions (both those within the... 

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