Strain nonbonded interaction

In addition to torsional strain (eclipsing interaction) and steric strain (nonbonded interaction), the compression of internal bond angles in ring systems leads to an additional type of strain angle strain. 

One of the essential factors governing the products of acetalation is the disposition of available hydroxyl groupings of the conceivable products obtained at equilibrium, the relative free-energies of the isomers will be decisive. This, in turn, will involve a consideration of ring strain, nonbonded interactions, and repulsions. 

Use of a P2O5 to promote cyclization of steroidal backbones was also accomplished by Ireland and co-workers." In this case, the tram product 59 proved to dominate the product mixture. The preference was suggested to be due to a combination of A-strain and torsional strain-nonbonding interactions during the cyclization. The stereochemistry of the starting alcohol 58 had no impact on the ratio of the products. 

Nonbonded interactions are the forces be tween atoms that aren t bonded to one another they may be either attractive or repulsive It often happens that the shape of a molecule may cause two atoms to be close in space even though they are sep arated from each other by many bonds Induced dipole/induced dipole interactions make van der Waals forces in alkanes weakly attractive at most distances but when two atoms are closer to each other than the sum of their van der Waals radii nuclear-nuclear and electron-electron repulsive forces between them dominate the fvan derwaais term The resulting destabilization is called van der Waals strain... 

The medium-size rings (7 to 12 ring atoms) are relatively free of angle strain and can easily take a variety of spatial arrangements. They are not large enough to avoid all nonbonded interactions between atoms. 

Terms representing these interactions essentially make up the difference between the traditional force fields of vibrational spectroscopy and those described here. They are therefore responsible for the fact that in many cases spectroscopic force constants cannot be transferred to the calculation of geometries and enthalpies (Section 2.3.). As an example, angle deformation potential constants derived for force fields which involve nonbonded interactions often deviate considerably from the respective spectroscopic constants (7, 7 9, 21, 22). Nonbonded interactions strongly influence molecular geometries, vibrational frequencies, and enthalpies. They are a decisive factor for the transferability of force fields between systems of different strain (Section 2.3.). 

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. 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

The simple cycloalkanes (CH2)n with n = 5 to 12 are the compounds most frequently studied by force field calculations (8, 9, 11, 12,17, 21). This preference results from their simple structure, from the abundant available experimental material (structural (46), thermo-chemical (47) and vibrational spectroscopic (27, 48, 49) data), and from the fact that, apart from bond length deformations, all other strain factors (angle deformations, unfavourable torsion angles, strongly repulsive nonbonded interactions) are important for the calculation of their properties. The cycloalkanes are thus good candidates for testing force fields. For a more detailed discussion we choose cyclodecane, a so-called medium-ring compound. 

The extent of substitution of the carbon atoms a to the C=C bond is the same in 132 as in 130a, but some nonbonded interactions are removed by ring closure in 132, and the C=C torsion angle is only 11.8° with R(C=C) 134.9 pm (194) in good agreement with calculations (187). The strain energies in 131b and 132 were calculated to be 41.58 and 60.67 kcal/mol, respectively. 

Polynitro derivatives of pentacyclo[5.4.0.0 .0 °.0 ]undecane have attracted interest as potential high-energy explosives. Molecular strain in this caged system could arise from both the constrained norbomyl moiety and the cyclobutane ring. Additional strain would be expected from nonbonding interactions if the S-endo and 1 l-endo positions were substituted with gm-dinitro groups. 

A number of intramolecular cycloadditions of alkene-tethered nitrile oxides, where the double bond forms part of a ring, have been used for the synthesis of fused carbocyclic structures (18,74,266-271). The cycloadditions afford the cis-fused bicyclic products, and this stereochemical outcome does not depend on the substituents on the alkene or on the carbon chain. When cyclic olefins were used, the configuration of the products found could be rationalized in terms of the transition states described in Scheme 6.49 (18,74,266-271). In the transition state leading to the cis-fused heterocycle, the dipole is more easily aligned with the dipolarophile if the nitrile oxide adds to the face of the cycloolefin in which the tethering chain resides. In the trans transition state, considerable nonbonded interactions and strain would have to be overcome in order to achieve good parallel alignment of the dipole and dipolarophile (74,266). 

Possible conformations for cycloheptane include the comfortable appearing chair form, 7. However, this form has eclipsed hydrogens at C4 and C5 as well as nonbonded interactions between the axial-like hydrogens on C3 and C6. The best compromise conformation is achieved by a 30°-40° rotation around the C4-C5 bond to relieve the eclipsing of the hydrogens. This spreads the interfering hydrogens at C3 and C6 and results in a somewhat less strained conformation called the twist chair. The twist chair, 8, is very flexible and... 

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