Nonbonded interactions estimated

Figure I. Nonbonded interactions estimated by hard-sphere calculations (1) to be present in the substituted cyclohexyl a- and fi-D-glycopyranosides (Compounds 4 to 9) as a function of the H torsion angle. The point for a specific H angle corresponds to the conformation for which the H angle provided the minimum...

Fig. 2.5. Possible applications of a coupling parameter, A, in free energy calculations, (a) and (b) correspond, respectively, to simple and coupled modifications of torsional degrees of freedom, involved in the study of conformational equilibria (c) represents an intramolecular, end-to-end reaction coordinate that may be used, for instance, to model the folding of a short peptide (d) symbolizes the alteration of selected nonbonded interactions to estimate relative free energies, in the spirit of site-directed mutagenesis experiments (e) is a simple distance separating chemical species that can be employed in potential of mean force (PMF) calculations and (f) corresponds to the annihilation of selected nonbonded interactions for the estimation of e.g., free energies of solvation. In the examples (a), (b), and (e), the coupling parameter, A, is not independent of the Cartesian coordinates, x. Appropriate metric tensor correction should be considered through a relevant transformation into generalized coordinates...

An even stronger case of intramolecular RAHB coupling is provided by the maleate ion (HOOCCH=CHCOO-), whose H-bonded and open conformers are shown in Fig. 5.22. Skeletal bond lengths and bond orders of these conformers are compared in Table 5.18. As shown in Fig. 5.22, the H-bonded conformer is favored in this case by more than 26 kcalmol-1, which is indicative of a powerful intramolecular no aoH interaction (estimated second-order stabilization 104 kcalmol-1) that is sufficient to overcome the severe steric repulsion of the extremely short H- -O nonbonded distance ( 1.3 A).56... 

The sizes of the dendrimers have been determined by calculating the molecular volumes, as defined by the van der Waals radii of the atoms, and by calculating the radii of gyration for several configurations of the dendrimers, as obtained from a molecular dynamics simulation at room temperature. The solvent influence on the calculated radii was estimated by scaling the nonbonded interactions between the atoms. Molecular volumes and average radii for ensembles of 500 conformations of the BAB-dendr-(NH2)D dendrimers have been collected in Table 26.2. 

A modified boat conformation of cyclohexane, known as the twist boat (Figure 1.9), or skew boat, has been suggested to minimize torsional and nonbonded interactions. This particular conformation is estimated to be about 1.5kcal mol-1 (bklmol-1) lower in energy than the boat form at room temperature. 

The main reason why nonbonded interactions involving metal ions have not been included in most force fields is a lack of good estimates for the parameters. As discussed in Chapter 2, Section 2.3, values for the van der Waals radius and the polarizability (e) are required. In the case of metal complexes it is difficult to obtain estimates for the van der Waals radius because the metal ion is generally buried inside an organic sheath and does not make close contacts with atoms free to move away from it. In a few cases close contacts to M(II) metal ions have been observed and these are consistent with van der Waals radii in the range 1.5-1.7 A. Where nonbonded interactions to the metal ions have been included in a force field, the van der Waals radius used has typically been more than 2.2 A[32]. 

Figure 1.9 Estimated values for nonbonding interactions and anomeric effects in aqueous solution. Interactions (1)-(6) are nonbonding interactions, and interactions (7)-(9) arise from anomeric effects.

As a general rule, the best approach when developing a force field for a metal complex is to use, without modification, the nonbonded interaction terms developed for organic compounds. The best known and most popular is the MM2 force field and this has been extended and adapted for modeling metal complexes by a number of groups1113 1161. Force fields developed for organic molecules do not have parameters for some of the elements present in metal complexes but reasonable estimates are available for most of theset57 59,65 96 120 123 13... 

It has been shown by X-ray crystallographic and NMR studies of aldehyde-Lewis arid complexes that a Lewis arid does not coordinate along the C=0 bond axis [76, 85], Moreover, according to the nature of the Lewis acid and the stoichiometry, several types of complexes can be generated [85, 86], When considering the nucleophilic attack on complexed carbonyl compounds, the various interactions at transition state must be estimated. Indeed, the presence of the Lewis acid can provide new nonbonded interactions with the incoming reagent. 

A, a reasonable estimate for the Ir-O bond, and the bond angles and lengths about the phosphorus center are invariant, the O-M-O bond angle would be decreased to 69°, much more strained than the angle subtended at the Co(III) center. If these critical bond angles, O-M-O and O-P-O, were increased to relieve the strain the metal-phosphorus nonbonded interaction would increase. 

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