Angle bending term

SISM Treatment of Bond Stretching and Angle Bending Terms... 

MM-i- also includes a sevtic angle bending term. The final form for the angle bending energy is ... 

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

SHAPES angle-bending term is very similar ... 

Three-body and higher terms are sometimes incorporated into solid-state potentials. The Axilrod-Teller term is the most obvious way to achieve this. For systems such as the alkali halides this makes a small contribution to the total energy. Other approaches involve the use of terms equivalent to the harmonic angle-bending terms in valence force fields these have the advantage of simplicity but, as we have already discussed, are only really appropriate for small deviations from the equilibrium bond angle. Nevertheless, it can make a significant difference to the quality of the results in some cases. 

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... 

When the same energy terms are used in two force helds, it may be acceptable to transfer bond-stretching and angle-bending terms. These are fairly stiff motions that do not change excessively. The force constants for these terms vary between force helds, much more than the unstrained lengths and angles. 

The quadratic angle bending term in MM+ is identical to that of equation (12) on page 175, apart from a factor 1/2. Three Gq values... 

Also, the angle-bending term is modified from... 

Within MM, a POS or ligand-ligand repulsion scheme removes the angle-bend term at the metal and thus reference 9q values are not required. This approach has been adopted by Hambley and Comba in their MOMEC program (17) and we have followed suit (18). 

Angle-bend terms spanning coordination and ligand regions... 

UaB = 5 s,AB( AB — e,AB)2 Also, the angle-bending term is modified from... 

Parameterizing the Angle Bending Term From Eq. 3.3, a plot of Ebend against (a-aeq)2 should be linear with a slope of kbemj. From STO-3G calculations on bending the H-C-C angle in ethane we get (cf. Table 3.1 and Fig. 3.7)... 

The strategies employed by CHARMM and MM3 in the formulations of bond stretch terms are repeated in the formulation of angle bending terms. Thus, CHARMM uses simple harmonic terms, whereas MM3 uses an expansion up to sextic terms. 

In the early 1990s, Nicholas and coworkers proposed an MM force field for modeling siliceous zeolites. In their model the framework steric energy was described as a sum of a harmonic Si-O bond term, O-Si-O and Si-O-Si angle bending terms, and an Si-O-Si-0 dihedral angle term. The Lennard-Jones (12-6) and Coulombic terms represented nonbonded interactions. Their force field was successfully applied for calculation of the structures and infrared spectra of the siliceous sodalite and silicalite lattices. ... 

The nonbonded interactions term. This represents the change in potential energy with distance apart of atoms A and B that are not directly bonded (as in A-B) and are not bonded to a common atom (as in A-X-B) these atoms, separated by at least two atoms (A-X-Y-B) or even in different molecules, are said to be nonbonded (with respect to each other). Note that the A-B case is accounted for by the bond stretching term stretch> and the A-X-B term by the angle bending term bend. but the nonbonded term nonbond is, for the A-X-Y-B case, superimposed upon the torsional term torsion we can think of lorsion as representing some factor inherent to resistance to rotation about a (usually single) bond X-Y (MM does not attempt to explain the theoretical, electronic basis of this or any other effect), while for certain atoms attached to X and Y there may also be nonbonded interactions. 

The bond-stretching and angle-bending terms are often regarded as hard degrees of freedom, in that quite substantial energies are required to cause significant deformations from... 

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