The crystal structure of benzene at — 3°C

Abstract
A new X -ray analysis has confirmed that the space group is Pbca, with four molecules per unit cell, and a = 7⋅460, b = 9⋅666 and c = 7⋅034 Å. 284 structure factors have been measured from oscillation photographs using CuKα radiation. The structure suggested by Cox (1932) was refined by the Fourier transform method and by two-dimensional Fourier and difference syntheses. The co-ordinates derived from the projections were refined by three-dimensional differential syntheses in which isotropic thermal parameters were used and termination of series errors corrected by the backshift method. After five differential cycles, electron density and difference maps calculated in the mean molecular plane revealed appreciable angular oscillations of the molecules about their senary axes. The refinement was continued by means of three-dimensional differential syntheses with anisotropic thermal parameters for the carbon atoms, and difference syntheses computed in the plane of the molecule and adjacent parallel planes. The criterion finally used to determine the anisotropic parameters was the equality of the observed and calculated atomic peak curvatures, the scale factor being adjusted to give the corrected integrated number of electrons in the molecule. The r. m. s. amplitude of angular oscillation about the senary axis is approximately 7⋅9°. An important consequence of the molecular angular oscillation is that the mean C—C bond length is increased by 0⋅015 Å to 1⋅392 Å, the likely limits o f error being not less than 0⋅010 Å. The result agrees satisfactorily with other determinations o f the C—C distance in benzene, notably Langseth & Stoicheff’s value (1956) of 1⋅3974 ± 0⋅001 Å from the Raman spectrum of the gas. The carbon ring is accurately planar, individual co-ordinates being only 0⋅0013 Å from the mean plane. The final value of the residual R was 9⋅9%. During the refinement, an attempt was made to derive an accurate difference synthesis from which conclusions about bonding electrons could be drawn. The experimental data did not prove sufficiently reliable, and only very tentative conclusions have been obtained. Detailed examination of the crystal structure has shown that the molecules pack together like sheets of six-toothed gear wheels. This allows an easy in-phase oscillation o f the molecules about their senary axes, and explains the large r. m. s. amplitudes observed. Occasional rotations of molecules in groups are probably responsible for the narrowing of the nuclear magnetic resonance line above 120°K.