Nonbonded interactions. See

Many force fields use a Lennard-Jones 6-12 potential71 to reproduce nonbonded interactions, see Equation 7. As two atoms approach one another, the steepness or hardness of the energy curve is proportional to r 12. The use of an exponential term instead of the r12 term in force field equations better reproduces experimental data for organic structures, and it is more consistent with quantum chemical calculations. 

In LN, the bonded interactions are treated by the approximate linearization, and the local nonbonded interactions, as well as the nonlocal interactions, are treated by constant extrapolation over longer intervals Atm and At, respectively). We define the integers fci,fc2 > 1 by their relation to the different timesteps as Atm — At and At = 2 Atm- This extrapolation as used in LN contrasts the modern impulse MTS methods which only add the contribution of the slow forces at the time of their evaluation. The impulse treatment makes the methods symplectic, but limits the outermost timestep due to resonance (see figures comparing LN to impulse-MTS behavior as the outer timestep is increased in [88]). In fact, the early versions of MTS methods for MD relied on extrapolation and were abandoned because of a notable energy drift. This drift is avoided by the phenomenological, stochastic terms in LN. 

United atom force fields (see United versus All Atom Force Fields on page 28) are sometimes used for biomolecules to decrease the number of nonbonded interactions and the computation time. Another reason for using a simplified potential is to reduce the dimensionality of the potential energy surface. This, in turn, allows for more samples of the surface. 

HyperChem supplements the standard MM2 force field (see References on page 106) by providing additional parameters (force constants) using two alternative schemes (see the second part of this book. Theory and Methods). This extends the range of chemical compounds that MM-t can accommodate. MM-t also provides cutoffs for calculating nonbonded interactions and periodic boundary conditions. 

Examine space-filling models for the two conformers and identify any likely unfavorable nonbonded interactions. Based on steric effects, which conformer would you anticipate would be the more stable Compare energies of anti-1,2-ethanediol and gauche-1,2-ethanediol to see if you are correct. Is this the same ordering of conformer energies as seen for n-butane (see Chapter 5, Problem 3)7... 

See also Energy minimization methods computer program for, 130-132 Nonbonded interactions, 56,61 Normal modes analysis, 117-119 computer program for, 132-134... 

First, one of the strongest piece of evidence in support of the existence of a thianorcaradiene intermediate is the steric effect of the substituents at C-2 and C-7 of a thiepin. Substantial stability gained by 2,7-di-tert-butyl substitution on thiepin implies that these groups force the nonbonding interaction in the thianorcaradiene structure to be large and hence the thiepin structure will be favored (see Section 4-1, 4-3 and 4-4). 

Fig. 7.5 Illustration of how dispersion forces affect gauche (G) conformations. Compared to structures with gauche forms devoid of dispersion forces (i.e., HF-optimized), structures with gauche forms subject to dispersion forces (MP2 optimized) contract in such a way that the 1. ..5 nonbonded interactions in an attractive part of the van der Waals potential are shortened. Thus, in GG-pentane (shown above), MP2-optimized torsional angles are contracted by several degrees compared to the HF-optimized geometry, causing a reduction in the 1...5 nonbonded distances by several tenths of an A. For additional details and the numerical values see R. F. Frey, M. Cao, S. Q. Newton, and L. Schafer, J. Mol. Struct. 285 (1993) 99.

The explicit incorporation of torsional terms is necessary, even if nonbonded interactions are considered for pairs of atoms which are separated by a chain of only three bonds (see Section 2.1.5.). 

In a similar way the potential constant method as described here allows the simultaneous vibrational analysis of systems which differ in other strain factors. Furthermore, conformations and enthalpies (and other properties see Section 6.5. for examples) may be calculated with the same force field. For instance, vibrational, conformational, and energetic properties of cyclopentane, cyclohexane and cyclodecane can be analysed simultaneously with a single common force field, despite the fact that these cycloalkanes involve different distributions of angle and torsional strain, and of nonbonded interactions 8, 17). This is not possible by means of conventional vibrational spectroscopic calculations. 

The above conclusions are general for all Y2A molecules where Y has available sigma np lone pairs. In subsequent sections, we shall see that the nonbonded interaction between sigma lone pairs is of paramount importance in controlling bond angles in molecules. 

Sigma lone pair nonbonded interaction in 1,2-difluorocyclopropane presents a similar situation to that observed in 1,2-difluoroethane (see Pattern b Scheme 1). Specifically, sigma nonbonded attraction may favor the trans isomer. This can be seen in the results of CNDO/2 calculations shown above where it appears that the sigma nonbonded interaction is repulsive in the cis isomer. 

The complexation of the base with the oxirane in nonpolar solvents drives the fi-deprotonation to occur from the syn face (see above), but also influences its regio- and stereochemistry. During the aggregation step, two conformational structures can be formed depending on which lone pair of the oxygen is used as the donor site. The relative stabilities of these complexes are largely influenced by nonbonded interactions between the base and the syn substituents on the epoxide (Scheme 16). 

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