Angle terms

Fig. 4. The average end-to-end-distance of butane as a function of timestep (note logarithmic scale) for both single-timestep and triple-timestep Verlet schemes. The timestep used to define the data point for the latter is the outermost timestep At (the interval of updating the nonbonded forces), with the two smaller values used as Atj2 and At/A (for updating the dihedral-angle terms and the bond-length and angle terms, respectively).

MM+ is iiiiipne among the force fields in ihe way it treats bonds and angles. Both the bond and angle terms can contain higher... 

Atoms with unusual hybridizations can be particularly dihicult to include. Most organic force helds describe atoms with hybridizations whose bond angles are all equivalent (i.e., sp, sp, and sp hybridizations with bond angles of 180, 120, and 109.5°, respectively). In contrast to this, a square planar atom will have some bond angles of 90° and some angles of 180°. In this case, it may be necessary to dehne the bond and angle terms manually, modify the software, or hold the bond angles hxed in the calculation. 

The OPLS atom types are a superset of the AMBER united atom types and the bonding parameters are just those of AMBER, supplemented where needed by the OPLS developers. The bond stretch, angle bending, dihedral angle and improper dihedral angle terms are identical to those of AMBER. Unlike AMBER, different combination rules are used for the van der Waals parameters, no hydrogen bonding term is used and no lone pairs are used. 

Non-bonded interactions are usually excluded between atoms which are already interacting by a bond or bond angle term (first and second neighbors) and are often modified for the end atoms of dihedral angles (third neighbors). 

Eq. 12 is modified by a contact angle term that is dependent on the surface energies of the interfaces among the substrate, crystal, and amorphous phases ... 

The program and force field SHAPES, developed for transition metal complexes and tested for square planar geometries, uses a single Fourier term (Eq. 2.19), which is similar to the torsional angle term in many molecular mechanics programs (see Section 2.2.3 periodicity = m, phase shift = Fourier force constant kg is related to that of the harmonic potential, kg (Eq. 2.7) by Eq. 2.20. 

Generally, gemma effects are only modeled via valence angle terms, i.e., nonbonded interactions are only considered for 1,4- and higher interactions. 

The characteristic ratio takes into account both the steric hinderance and valence angle terms. It is a good indicator of the stillness of the chain. Typical values of a and Coo are listed in Table 15.2. It is clear that the stifiness decreases with increasing temperature and that large side groups increase the stifiness. 

An alternative approach to modeling the L-M-L angles is to set the force constants to zero and include nonbonded 1,3-interactions between the ligand atoms. In most force fields, 1,3-interactions are not explicitly included for any atoms, instead they are taken up in the force constants for the valence angle terms. This is an approximation because the 1,3-interactions are most often repulsive and thus the function used to calculate the strain energy arising from valence angle deformation should be asymmetric. It was shown that the nonbonded 1,3-interactions around the metal atom are in many cases a major determinant of the coordination... 

There is a strong correlation between the parameters of different potential energy functions so that they should not be developed or refined in isolation. For example, the barrier to rotation about a bond can be modified by changing the explicit torsion angle term or by changing the nonbonded interactions. Thus, the effect of any change on a force field parameter needs to be tested extensively, i.e.,... 

We now determine the hole sizes of the various conformers of sar. Prepare the files of the six conformers of [Co(sar)]3+ by selecting the six Co-N bonds (Tools/ Build Selections) in each file to set up the constraints for the Energy calculations. Use the. out files but rename them as. hin. As outlined above, the strain energy vs. metal-donor-distance plots for the computation of the hole sizes need to be metal ion independent. Thus, you need to activate the option Without Energy of Selected Terms in the Energy setup window. Also, the donor-metal-donor valence angle term needs to be switched off, since this is also metal ion dependent. You can do that in the Edit/View/Force Field/Atom Type Parameters menu or in the Edit/View/Parameter Array window. Both options have been used before in this tutorial. 

The angle term in equation (10.31) gives positive values, except when 6 > 55° but 9 < 125°. At these values of angle 9, the induced shifts will be in the opposite direction of normal shifts, (i.e.) upheld for Eu and downheld for Pr. The reversal in the direction of the shifts is due to the term (3 cos2 0 — 1) becoming negative for these angles. 

Figure 2 Sample matrix patterns for (a) block diagonal and (b-e) sparse unstructured. Pattern (b) corresponds to the Hessian approximation (preconditioner) for a potential energy model from the local energy terms (bond length, bond angle, and dihedral angle terms), and (c) is a reordered matrix pattern that reduces fill-in during the factorization. Pattern (d) comes from a molecular dynamics simulation of super-coiled DNA36 and describes pairs of points along a ribbonlike model of the duplex that come in close contact during the dynamics trajectory pattern (e) is the associated reordered structure that reduces fill-in.

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