Molecular mechanics torsion

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. 

You can add restraints to any molecular mechanics calculation (single point, optimization or dynamics). These might be NMR restraints, for example, or any situation where a length, angle, or torsion is known or pre-defined. Restraints with large force constants result in high frequency components in a molecular dynamics calculation and can result in instability under some circumstances. 

Arestraint (not to be confused with a Model Builder constraint) is a user-specified one-atom tether, two-atom stretch, three-atom bend, or four-atom torsional interaction to add to the list of molecular mechanics interactions computed for a molecule. These added interactions are treated no differently from any other stretch, bend, or torsion, except that they employ a quadratic functional form. They replace no interaction, only add to the computed interactions. 

One of the major difficulties with molecular mechanics procedures (MMh- or otherwise) is that they almost always fail. That is, you find that force constants are not available for the molecule of interest. This is both the strength and weakness of molecular mechanics it uses atom types to introduce specific chemical environments for the atoms within a molecule (to obtain accuracy in the calculations) but then requires knowledge of force constants specific to that chemical environment (as specific as stating that an atom is in a five-member ring containing one oxygen and one carbon, for example). As the number, N, of atom types rises the number of force constants needed to describe all possible occurrences of these atom type becomes very large. For torsions, for... 

Conversely, processes which convert carbons to sfp- carbons are more favorable for five-membered than for six-membered rings. This can be illustrated by the data for acetolysis of cyclopentyl versus cyclohexyl tosylate. The former proceeds with an enthalpy of activation about 3kcal/mol less than the latter." A molecular mechanics analysis found that the difference was largely accounted for by the relief of torsional strain in the cyclopentyl case." Notice that there is an angle-strain effect which is operating in the opposite direction, since there will be some resistance to the expansion of the bond angle at the reaction center to 120° in the cyclopentyl ring. 

All the structural models in this book are computer-drawn. To make sure they accurately portray bond angles, bond iengtiis, torsional interactions, and steric interactions, the most stable geometry of each molecule has been calculated on a desktop computer using a commercially available molecular mechanics program based on work by N. L. Allinger of the University of Georgia. 

Murphy et al. [34,45] have parameterized and extensively tested a QM/MM approach utilizing the frozen orbital method at the HF/6-31G and B3LYP/6-31G levels for amino acid side chains. They parameterized the van der Waals parameters of the QM atoms and molecular mechanical bond, angle and torsion angle parameters (Eq. 3, Hqm/mm (bonded int.)) acting across the covalent QM/MM boundary. High-level QM calculations were used as a reference in the parameterization and the molecular mechanical calculations were performed with the OPLS-AA force... 

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