Angle strain calculation

Table 6. Values of Angle Strain Calculated According to Equation (1) from Enthalpies of Hydrogenation [kcal/mole]...

Aimulene offers a particularly significant test of the Hiickel rule. The internal cavity in [18]annulene is large enough to minimize steric interactions between the internal hydrogens in a geometry that is free of angle strain. Most MO calculations find the delocalized structure to be more stable than the polyene. ... 

When this stereoelectronic requirement is combined with a calculation of the steric and angle strain imposed on the transition state, as determined by MM-type calculations, preferences for the exo versus endo modes of cyclization are predicted to be as summarized in Table 12.3. The observed results show the expected qualitative trend. The observed preferences for ring formation are 5 > 6, 6 > 7, and 8 > 7, in agreement with the calculated preferences. The relationship only holds for terminal double bonds. An additional alkyl substituent at either end of the double bond reduces the relative reactivity as a result of a steric effect. 

The reason for the minimum energy conformer of 6 cannot be as simple as that proposed for 5, as the former is far more puckered than what is necessary for minimizing the H- - -H nonbonded repulsions. Valence angle strain is another factor that might be important in this case. The similarity to the chair conformer of cyclohexane is striking, although the calculated [6]radialene conformation is less puckered. 

The boat-boat (417) and the twist-boat-boat (418) have low torsional strains but severe non-bonded repulsions, which, as usual, are transferred to internal angle strains. However, heteroatoms can modify these repulsions and certain transannular interactions can drastically reduce them. Even so, the boat-boat family is relatively unimportant as its energy is calculated to be quite high (12 kj mol-1) in cyclooctane. It probably serves as an intermediate for certain conformational interconversions of the boat-chair, especially when the twist-boat-chair pseudorotation itinerary is of high energy. In cyclooctane the boat-boat and its twisted partner have nearly the same energies and are not separated by a significant barrier. 

Type B azapentalenes behave as one ring, but aromatic character in systems such as 485 seems to be more localized in the ring that lacks the heteroatom X. The nature of X is important, since sulfur derivatives are the most stable this is probably due to a reduction of angle strain and/or to the participation of -orbitals. Physicochemical measurements, chemical reactivity, and quantum-mechanical calculations show... 

Exercise 12-3 Figure 5-8 indicates that the difference in energy between the conformation of butane with eclipsed methyls and the gauche form is about 5 kcal mole-1. Use this number to estimate the contribution of eclipsing to the instability of planar cyclohexane. Then calculate the instability of planar cyclohexane by including the angle strain from Exercise 12-2 in your estimate. 

Molecular mechanics calculations14 ) of the strain in adamantane support this interpretation. Since such calculations are based on empirically derived parameters, however, a unique set of parameters for the representation of physical reality cannot be derived. Nevertheless, all available conformational analysis calculations demonstrate that the strain in adamantane may be quantitatively accounted for in terms of angle strain, which implicitly includes strain due to... 

Last not least, force field, 52 1S4) and semiempirical106 l44) quantummechanical calculations have been used to calculate structural parameters and enthalpies of formation of angle strained cycloalkynes. These calculations are at present the only way to obtain quantitative estimates of ring strain in transient cycloalkynes, such as cycloheptyne 1S2). 

Since for most angle strained cycloalkynes, particularly for those which are not isolable, structural data is lacking, calculations have been carried out. The structural parameters and strain energies of cyclononyne (6)152 154,160>, cyelooctyne (14) 152,154,106,144), cycloheptyne (16) 152,154), cyclohexyne (20)1S4) and cyclopentyne (18) 154) were calculated. Some values for strain energies and C—C s C bond angles are given in Tables 3 and 4. 

Table 3. Calculated Strain Energies of Some Angle Strained Cycloalkynes...

Table 4. Calculated C—C=C Bond Angles in Some Angle Strained Cycloalkynes [°]...

PE spectra of the two angle strained cyclopolyynes 1,5-cyclooctadiyne (35)177) and the twelve membered tetraacetylene (43)88) have been measured and interpreted with the aid of semiempirical and ab initio molecular orbital calculations. In both compounds evidence for through-space and through-bond interactions between the acetylene moieties has been found 88,177). The compound (43) has been described on the basis of these results as weakly antiaromatic88). 

---