Investigation of the Structural Conformation of Biphenyl by Solid State 13 C NMR and Quantum Chemical NMR Shift Calculations Dewey H. Barich, † Ronald J. Pugmire, ‡ and David M. Grant* ,† Departments of Chemistry and of Chemical and Fuels Engineering, UniVersity of Utah, Salt Lake City, Utah 84112 Robbie J. Iuliucci Department of Chemistry, Washington and Jefferson College, Washington, PennsylVania 15301 ReceiVed: NoVember 28, 2000; In Final Form: April 16, 2001 The principal values of the 13 C chemical-shift tensor (CST) for biphenyl have been determined with the FIREMAT experiment. The internal dihedral angle between the benzene rings in biphenyl is estimated to fall between 10 and 20° on the basis of quantum mechanical calculations of the CST principal values. A composite model of motion in the system, with contributions both from internal jumping between enantiomeric structures and from overall molecular librations, yields the smallest variance between predicted and measured values for an internal twist angle of 15° between the rings and a mean libration angle of (12° from the most favored molecular orientation. The composite model is clearly preferred to a motionless model (with >98% probability) and is also preferred over either of the isolated contributing dynamics, i.e., only libration or only internal jumping. Introduction The structure of biphenyl varies depending upon the mate- rial’s phase. The primary structural difference is the twist angle between the two phenyl rings. For example, biphenyl has a twist angle of 44.4° in the gas phase. 1,2 In solution estimates range from 19° to 32° for the parent molecule in various media. 3,4 This inter-ring angle also changes as a function of ortho substitution. The angle may be even smaller in the solid because crystal packing forces could contribute to the torsion barrier of the two phenyl rings relative to one another. High-temperature X-ray studies 5-12 (110-298 K) report a planar structure with space group P2 1 /a in which the midpoint of the phenyl-phenyl linkage lies at a crystallographic inversion center. While many of the early X-ray studies assumed a rigid planar model, Charbonneau and Delugeard 12 proposed in 1977 that the unusually large mean libration vibration (λ av 2 ) 109.17° 2 ) around the long molecular axis suggests that the observed planar structure is in fact the statistical aVerage over two equivalent twisted conformations about the phenyl-phenyl linkage creating a double-well potential. Heat capacity measure- ments by Atake et al. 13 have shown that the crystal experiences a displacive phase transition near 40 K. At 22 K 14 the biphenyl crystal structure has been determined to belong to space group Pa. In both of these low temperature structures the two connected rings are permanently twisted from one another by approximately 10°, destroying the aforementioned crystal- lographic inversion center observed at room temperature. This loss of an effective inversion center doubles the unit cell axis length associated with the long axis of biphenyl. Similar features are observed 15 for other polyphenyls such as p-terphenyl 16,17 and p-quaterphenyl. 18,19 The chemical-shift tensors (CST) of polycyclic aromatic compounds have received considerable attention in the past decade. 20-24 Most of these molecules are static in the crystal structure, as they exhibit rigid molecular structures. Biphenyl is unusual in that the phenyl-phenyl linkage has a rotational degree of freedom not present in most polycyclic aromatic compounds. Regrettably, NMR cannot observe translation effects where no change in orientation with respect to the magnetic field occurs. Hence, the displacive phase transitions observed at very low temperatures cannot be addressed in this work. However, CSTs provide the opportunity to investigate rotational modes that occur in the crystal system independently of the displacive effects. The measured CST principal values reported here demonstrate that the room-temperature crystal structure of biphenyl indeed undergoes constrained rotational averaging about the phenyl-phenyl linkage. Quantum chemical predictions of the full CST (both principal values and orienta- tions) provide the means to demonstrate the importance of rotational motion. The experimental tensor orientations and averages derived from reliable full tensor calculations properly considered with the dynamical models are discussed below. The tensor averaging of two mirror-image twisted biphenyls elimi- nates some off-diagonal elements and changes the principal values of the final, effective tensor. Because of the small range of values for the isotropic chemical shifts of the protonated carbons (125.5-129.8 ppm) and the large line widths (ca. 2 ppm), there is a considerable amount of overlap in that region of the 13 C spectrum. This † Department of Chemistry. ‡ Department of Chemical and Fuels Engineering. 6780 J. Phys. Chem. A 2001, 105, 6780-6784 10.1021/jp004314k CCC: $20.00 © 2001 American Chemical Society Published on Web 06/21/2001