Quantum Tunneling in Organic Chemistry Mark O’Dair University of Utah

Quantum Tunneling Overview: Tunneling is a phenomenon of Quantum Mechanics in which particles, with a small amount of probability, are able to “tunnel” or travel through a large, finite potential energy (PE) barrier instead of traveling over the barrier as Classic Mechanics dictates should occur. In a crude life-sized analogy, one could compare this to a boulder traveling over (classical) a hill (PE barrier) to the other side verses the same boulder tunneling through (quantum) the hill to the other side. This effect is in part possible due to the wave-particle duality of quantum-sized matter. Tunneling can occur in chemical reactions as depicted in the energy coordinate diagram. Wiki Page: http://en.wikipedia.org/wiki/Quantum_tunnelling Other References: Anslyn, E. and Dougherty, D. Modern Physical Organic Chemistry, University Science Books, 2003.

Quantum Tunneling Tunneling Requirements: Tunneling is highly dependent upon the mass of the particle and the width of the barrier. The barrier could be a physical distance. The less massive the particle and the narrower the barrier, the greater likelihood that tunneling will occur. This means that light particles such as electrons and hydrogen atoms – and in rarer cases heavier atoms – may influence a reaction and reaction rates through tunneling if reagents are held in close enough proximity. Wiki Page: http://en.wikipedia.org/wiki/Quantum_tunnelling Other References: Anslyn, E. and Dougherty, D. Modern Physical Organic Chemistry, University Science Books, 2003.

Examples in Organic and Biochemistry Organic Chemistry Below are two examples of rearrangements observed and studied by the Schreiner group in 2011 which are performed through carbon and hydrogen tunneling. Additional examples include the following: - Tunneling effects on hydrogen bonding - Nitrogen inversion - Kinetic Isotope Effects that are larger that theoretic maxima REFERENCES: Org. Lett., 2011, 13 (13), pp 3526–3529

Examples in Organic and Biochemistry Biochemistry: Enzymes It has been shown that the reaction mechanism of many enzymes involve tunneling, often hydrogen tunneling. For instance, the oxidation of an alcohol via the enzyme alcohol dehydrogenase has been shown to involve hydride tunneling (mechanism shown below). Other examples on enzymes and proteins known the utilize tunneling include the following: - Amine Oxidases - Lipoxygenase - Electron Transport Chain in respiration and photosynthesis (electron tunneling) REFERENCES: Acc. Chem. Res., 1998, 31 (7), pp 397–404, Biochemistry, 2014, 53 (14), pp 2212–2214, Elsevier, 2006, 1757(9–10), pp 1096–1109, Nature, 1999, 399, 496-499

Problems As mentioned in an earlier example, many enzymes have evolved to take advantage of tunneling in their reaction mechanisms. Using your knowledge of how enzymes work to catalyze reactions on substrates and your new understand of tunneling, explain why enzymes are so ideally suited to utilize tunneling. (HINT: Think of how active sites operate.) Kwart and colleagues studied the following E2-like reaction – Selenoxide Elimination. By substituting the colored hydrogen atom with deuterium, the researchers noticed a very substantial change in reaction rate. Which substitution results in a faster rate and why? Why is the rate difference so large (×74) between the two? Explain the premise of your answer. REFERENCES: J. Am. Chem. Soc., 1981, 103 (5), pp 1232–1234

Solutions Through various non-covalent interactions between functional groups, an enzyme’s active site positions the substrate in an optimal orientation to facilitate the reaction. This includes positioning atoms that need to form bonds with each other in close proximity. This increases the chance for tunneling by narrowing the barrier that a particle must transverse. For example, in proton and hydride transfers, the relevant hydrogen in most likely suited very close to the group that will extract it. In the case of alcohol dehydrogenase, the hydride is likely placed close to the NAD+ group. The hydrogen substitution is 74 times faster mainly due to quantum tunneling. The reason includes the mass differences of the substituents. In both cases, the extracting oxygen and the hydrogen/deuterium are very close (0.82 Å compared to 1.10 Å for a normal sp3 C–H bond) which makes tunneling probability much higher. Hydrogen substitution is so much faster because it is half the mass of deuterium causing hydrogen tunneling to occur much more than deuterium thus allowing hydrogen substitution to accelerate the reaction. In reality, X–H cleavage is general faster than X–D cleavage due to another nuance of quantum mechanics known as Kinetic Isotope Effect (KIE). However, in cases where tunneling occurs, as in the example given in the problem, tunneling causes X–H cleavage to occur much faster that the theoretical maximum that KIE can explain. REFERENCES: J. Am. Chem. Soc., 1981, 103 (5), pp 1232–1234

Contributed by: Mark O’Dair, Undergraduate University of Utah, 2014