The shape of urea

The shape of the urea molecule has been studied by analysing the microwave spectra of several isotopic species, yielding r_s coordinates of all atoms except that of C, the latter being derived from first-moment equations, and by ab initio molecular-orbital calculations at the {MP2 }/{6-311 ⁺⁺G(d,p)} level. The derived bond lengths and angles are: r(CO), 1.22 ₁ Å; r( _CN), 1.37 ₈ Å; r(NH ₍₅₎), 0.99 ₈ Å; r(NH ₍₆₎), 1.02 ₁ Å; ∠NCN, 114.7°; sum of pyramidal angles around N, 350.6°. The conformer of lowest energy is predicted to be nearly planar with C ₂ symmetry, a second minimum for a shape of C ₈ symmetry being higher in energy by 421 cm ^-1. However, these are separated by a barrier estimated to be no higher than about 130 cm ^-1. Thus the two shapes are likely to be parts of the potential energy surface domain that is associated with the most stable shape of urea, i.e. one in which the zero-point vibration covers both C ₂ and C _s geometries, the most probable ( r_p) geometry being C ₂. Computed ab initio frequencies and their eigenvectors (harmonic approximation) imply that the lowest frequency vibration is a CN torsion, in conflict with King's assignment of NH ₂ wag. However, the substantial anharmonicity of the large-amplitude motion (LAM) associated with the interconversion between the C _s and C ₂ forms seems likely to perturb the v = 1 level of this LAM so that its 1 ← 0 transition becomes lowest in frequency, so removing the apparent conflict in assignment.