Analytic Route to Tunneling Splittings Using Semiclassical Perturbation Theory.

We present an efficient, analytical, and simple route to approximating tunneling splittings in multidimensional chemical systems, directly from ab initio computations. The method is based on the Wentzel-Kramers-Brillouin (WKB) approximation combined with the vibrational perturbation theory. Anharmonicity and corner-cutting effects are implicitly accounted for without requiring a full potential energy surface. We test this method on the following three systems: a model one-dimensional double-well potential, the isomerization of malonaldehyde, and the isomerization of tropolone. The method is shown to be efficient and reliable.

Hydrogen tunnelling in the rearrangements of carbenes: the role of dynamical calculations.

Tunnelling controlled chemical reactions are those which preferably proceed through pathways with high but narrow potential energy barriers, via quantum tunnelling, resulting in a product that would be disfavoured classically. These reactions are very sensitive to barrier width, height and temperature and so dynamical theoretical methods are required to describe these processes. Recent experimental work on charge-tagged phenyl pyruvic acid derivatives has found, in contrast to similar systems, no evidence of tunnelling control. Using semiclassical transition state theory, we rationalise these results and find tunnelling is significant in this system.

New Developments in Semiclassical Transition-State Theory.

This Feature Article describes some recent developments and applications of the Semiclassical Transition-State Theory (SCTST) for treating quantum tunneling in chemical reactions. A reduced dimensional form of the SCTST is discussed and is shown to be particularly efficient, as the required number of electronic structure calculations is reduced to an absolute minimum. We also describe how an alternative formulation of SCTST developed by Hernandez and Miller [ Chem. Phys. Lett. 1993 , 214 , 129 ], the SCTST-θ, has advantages in allowing for straightforward applications of the SCTST for any form of the potential expansion at the transition state. We also illustrate the power of SCTST in applications to more complex systems. We show how polyatomic modes such as internal rotations and torsions can be treated efficiently in SCTST calculations. We also describe some applications of the method to hydrogen atom tunneling in unimolecular reactions including the degradation of chemical nerve agents and the decay of the atmospherically important Criegee intermediates.

Catalysis and tunnelling in the unimolecular decay of Criegee intermediates.

The unimolecular decay of Criegee intermediates is the major producer of OH radicals in the atmosphere. Here, Semi-Classical Transition State Theory (SCTST) in full and reduced dimensions is used to determine thermal rate constants for their unimolecular decay, as well as their decay catalysed by a single water molecule. These reactions shed light on the applicability of SCTST for catalysed hydrogen transfer reactions.