Domino Tunneling

Matrix-isolation experiments near 3 K and state-of-the-art quantum chemical computations demonstrate that oxalic acid [<b>1</b>, (COOH)₂] exhibits a sequential quantum mechanical tunneling phenomenon not previously observed. Intensities of numerous infrared (IR) bands were used to monitor the temporal evolution of the lowest-energy O–H rotamers (<b>1cTc</b>, <b>1cTt</b>, <b>1tTt</b>) of oxalic acid for up to 19 days following near-infrared irradiation of the matrix. The relative energies of these rotamers are 0.0 (<b>1cTc</b>), 2.6 (<b>1cTt</b>), and 4.0 (<b>1tTt</b>) kcal mol^–1. A <b>1tTt</b> → <b>1cTt</b> → <b>1cTc</b> isomerization cascade was observed with half-lives (<i>t</i>_1/2) in different matrix sites ranging from 30 to 360 h, even though the sequential barriers of 9.7 and 10.4 kcal mol^–1 are much too high to be surmounted thermally under cryogenic conditions. A general mathematical model was developed for the complex kinetics of a reaction cascade with species in distinct matrix sites. With this model, a precise, global nonlinear least-squares fit was achieved simultaneously on the temporal profiles of nine IR bands of the <b>1cTc</b>, <b>1cTt</b>, and <b>1tTt</b> rotamers. Classes of both fast (<i>t</i>_1/2 = 30–50 h) and slow (<i>t</i>_1/2 > 250 h) matrix sites were revealed, with the decay rate of the former in close agreement with first-principles computations for the conformational tunneling rates of the corresponding isolated molecules. Rigorous kinetic and theoretical analyses thus show that a “domino” tunneling mechanism is at work in these oxalic acid transformations