Angle Bending Interactions

the most common functional form to model the angle interactions is a harmonic expression  

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The angle bending interactions of ethylene and ethane in cis or trans position with a common bond have been analyzed by Shimanouchi as an evidence of the flexibility of the C-C and C=C bonds. He used this investigation to obtain an estimation of Young s modulus of bonds (Shimanouchi, 1957). 

Angle bending interactions occur when an angle formed by three cmisecutive sites is perturbed from its equilibrium value. Several potentials are employed to describe this energy contribution. However, the majority of force fields is based on the harmonic potential [54]... 

The term representing the covalent bond-angle bending interaction reads... 

The term representing the harmonic, so-called improper (out-of-plane, out-of-tetrahedral configuration) dihedral-angle bending interaction reads... 

In addition to these basic term s. force fieldsoften h ave cross term s that combine the above interactions. For example there may be a term which causes ati angle bend to interact with a bond stretch term (opening a bond angle may tend to lengthen the bonds in volved). 

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

In a Urey-Bradley force field, angle bending is achieved using 1,3 non-bonded interaction rather than an explicit angle-bending potential. The stretch-bond term in such a forci field would be modelled by a harmonic function of the distance between the 1,3 atoms ... 

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... 

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

Here is a constant that depends on the nature of atoms A, B and C. Not only that, both MM-f and MM2 allow for coupling between bond-stretching and angle-bending. Electrostatic interactions are accounted for by the interaction of bond dipoles rather than point charges. 

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... 

Molecular mechanics calculations use an empirically devised set of equations for the potential energy of molecules. These include terms for vibrational bond stretching, bond angle bending, and other interactions between atoms in a molecule. All of these are summed up as follows ... 

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