Bond-length corrections for external and internal vibrations in urea

Bond-length corrections for external and internal vibrations of the urea molecule were carried out at 293 and 123 K. The corrections for the external vibrations were performed by means of the rigid-body model after the vibration tensors of the internal vibrations had been subtracted from the observed vibration tensors. The corrections for the internal vibrations were calculated from the vibration and coupling tensors for urea which were recently determined by a spectroscopic analysis. If the external and internal vibrations in the crystal are not mixed, as is likely for the small urea molecule, the total correction can be calculated as the sum of the external and internal corrections. Since the internal vibrations contribute strongly to the vibrations of the H atoms, large total corrections for the N--H bonds are found; 0.030 and 0.027 Å for 293 K. The agreement of the corrected bond lengths for the C-N and N--H(1) bonds at 293 and 123 K is excellent (within 0.003 Å), for the N--H(2) bond (within 0.005 Å) and the C-O bond (within 0.010 Å) it is a little less satisfactory. The corrected N--H lengths are also in good agreement (within 0.003-0.005 Å) with those in the free ammonia molecule determined by gas electron diffraction and infrared spectroscopy. The correction with the rigid- body model alone, applied to the observed vibration tensors obtained from diffraction data, cannot be considered to be a satisfactory substitute for the correction obtained by the joint analysis. The riding model provides better corrections, but they are still too small for the N--H bonds. Most of the corrected bonds with terminal H atoms reported in the crystallographic literature were probably determined too short by about 0.01 Å or even more.