Single crystal to single crystal topochemical photoreactions: Measuring the degree of disorder in the [2 + 2] photodimerization of trans-cinnamic acid using single-crystal ¹³C NMR spectroscopy

A single crystal of α-trans-cinnamic acid was synthesized with a ¹³C-label at the β-carbon position and photoreacted to yield the [2 + 2] cycloaddition product, α-truxillic acid. ¹³C{ ¹H} cross-polarization (CP) single-crystal NMR experiments were performed on the unreacted and sequentially photoreacted samples for different goniometer orientations, and the spectra were simulated using the SIMMOL and SIMPSON software packages. Atomic coordinates from single-crystal X-ray diffraction data were used as inputs in the simulations, which allowed the chemical shift tensor to be precisely measured and related to the unit cell (or molecular) reference frame of cinnamic acid. The line widths of the ¹³C resonances observed at different goniometer rotations were utilized to estimate the orientational dispersion of the cinnamic acid species, which ultimately provides a measure of disorder in the single crystal. The photoreacted sample, a solid solution of cinnamic and truxillic acids, maintained its single-crystal nature, even up to 44% conversion to truxillic acid, keeping its P2₁/n symmetry. Upon photoirradiation, however, a slight loss of order was observed in the cinnamic acid species as evidenced by an increase in the ¹³C NMR line widths, demonstrating that NMR can be used to monitor subtle orientational imperfections in single crystal to single crystal photoreactions.