Solid-State Modeling. VI. 2,3-Diketopiperazine: the Integration of Crystallographic and Spectroscopic Evidence

2,3-Diketopiperazine (2,3-piperazinedione) crystallizes in the monoclinic space group P2₁/c with a = 5.941 (3), b = 10.080 (3), c = 8.282 (2) Å and β = 95.87 (3)°. The six-membered ring adopts a skew-boat conformation with Q = 0.467 (3) Å, θ = 64.6 (3)° and φ = 269.8 (4)°. Ab initio calculations show that the perfect skew-boat with its C₂ symmetry is broken by the formation of two intermolecular N—H...O bonds, involving only one of the C=O groups of the 2,3-diketopiperazine molecule. Vibrational spectra were recorded in solution and in the solid state. The assignment of the normal vibrations is proposed based on comparison with spectra of similar molecules and spectral changes due to deuteration. Ab initio calculations for the isolated molecule and the solid-state structure were used to calculate differences in the molecular geometry in the gas phase and crystalline state. Using these reference structures we calculated the stretching frequencies for the C=O groups. We predict an IR shift for C=O of 130 cm⁻¹, when the molecule goes from the gas phase to the solid state. The observed shift is 110 cm⁻¹. The differences between the C=O moieties in the solid state produce a calculated Δν of 55 cm⁻¹, which matches satisfactorily the observed value of 49 cm⁻¹.