Torsion interactions, force fields

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. 

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. 

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. 

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

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... 

Stretching, bond bending, torsions, electrostatic interactions, van der Waals forces, and hydrogen bonding. Force fields differ in the number of terms in the energy expression, the complexity of those terms, and the way in which the constants were obtained. Since electrons are not explicitly included, electronic processes cannot be modeled. 

The molecular structure input requires atom types to be assigned, which are not the same from one force field to the next. The input also includes a list of bonds in the molecule. There is not a module to automatically assign atom types. Most of the modules use a Cartesian coordinate molecular structure, except for a few that work with torsional space. The same keyword file is read by all the executables. A little bit of input is obtained by the program either interactively or from an ASCII file piped to standard input, which makes for a somewhat cryptic input file. This system of common input files and the user choosing which executables to run give TINKER the ability to run very sophisticated simulations while keeping the input required for simple calculations fairly minimal within the limitations mentioned here. 

An atom that has sp hybridization tends to be coplanar with its attached atoms. This effect is accounted for by improper torsions in other force fields and by out-of-plane-bending interactions in... 

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... 

In a similar way the potential constant method as described here allows the simultaneous vibrational analysis of systems which differ in other strain factors. Furthermore, conformations and enthalpies (and other properties see Section 6.5. for examples) may be calculated with the same force field. For instance, vibrational, conformational, and energetic properties of cyclopentane, cyclohexane and cyclodecane can be analysed simultaneously with a single common force field, despite the fact that these cycloalkanes involve different distributions of angle and torsional strain, and of nonbonded interactions 8, 17). This is not possible by means of conventional vibrational spectroscopic calculations. 

The simple cycloalkanes (CH2)n with n = 5 to 12 are the compounds most frequently studied by force field calculations (8, 9, 11, 12,17, 21). This preference results from their simple structure, from the abundant available experimental material (structural (46), thermo-chemical (47) and vibrational spectroscopic (27, 48, 49) data), and from the fact that, apart from bond length deformations, all other strain factors (angle deformations, unfavourable torsion angles, strongly repulsive nonbonded interactions) are important for the calculation of their properties. The cycloalkanes are thus good candidates for testing force fields. For a more detailed discussion we choose cyclodecane, a so-called medium-ring compound. 

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