Section 22.4.4.3. Crystallographic conformations and energies

Crystallographic conformations obviously represent energetically accessible forms. However, for use in molecular-modelling applications, the key question must be asked: Are the condensed-phase crystallographic observations a good guide to conformational preferences in other phases? The indications are that the answer is `yes' from the types of studies exemplified or cited in the previous section: there appears to be a clear qualitative relationship between crystallographic conformer distributions and the low-energy features of the appropriate potential energy hypersurface, although the estimation of absolute energies from the relative populations of these distributions is not appropriate (Bürgi & Dunitz, 1988).

Allen, Harris & Taylor (1996) addressed this question in a systematic manner for a series of 12 one-dimensional (univariate) conformational problems. All of the chosen substructures [simple derivatives of ethane, involving a single torsion angle (τ) about the central C—C bond] were expected to show one symmetric (anti, τ ≃ 180°) energy minimum and two symmetry-related asymmetric (gauche, τ ≃ ±60°) minima. For each substructure, the crystallographic torsional distribution was determined from the CSD and compared with the 1D potential-energy profile, computed using ab initio molecular-orbital methods and the 6–31G* basis set. Close agreement was observed between the experimental condensed phase results and the computed in vacuo data. Taken over all 12 substructures, the ab initio optimized values of the asymmetric (gauche) torsion angle vary from <55° to >80°, and a scatter plot of these optimized values versus the mean crystallographic values for gauche conformers is linear, with a correlation coefficient of 0.831. Two other results of the study were that: (a) torsion angles with higher strain energies (>4.5 kJ mol⁻¹) are rarely observed in crystal structures (<5%); and (b) taken over many structures, conformational distortions due to crystal packing appear to be the exception rather than the rule.