This Feature Article describes some recent developments and applications of the Semiclassical Transition State Theory (SCTST) for treating quantum tunnelling 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, called 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.
Ingo Fischer opened a general discussion of the paper by Anne Zehnacker: You also presented data on the structure of the ionic dipeptide and discuss the relative stability of the isomers in terms of the CH-p and NH-p bonds in the ion. But in the ion you also have ion-multipole interactions. Can you comment on their role for the structure and stability of the dipeptide isomers? Anne Zehnacker-Rentien responded: Actually, the CH and NH p-bonds disappear in the ionic "folded-extended" structure. Indeed, most of the charge is borne by the extended aromatic ring. Therefore, the interaction between the charged benzene ring and the NH becomes repulsive. This is why the extended ring undergoes a rotation upon ionisation, to favour an interaction between CO and the aromatic ring. However, I agree that this interaction is probably more of a dipole/charge interaction than a COp interaction. Ingo Fischer added: You point out that the NH-p bond is weaker in the c-LL isomer than in the c-LD isomer, while for the CH-p bond you observe the opposite trend. Do you have a simple picture that explains this result? Anne Zehnacker-Rentien replied: In general, steric constraints due to the cyclic nature of the dipeptide add to chirality effects and make these effects more prominent. This is the case for example for 1-amino-2-indanol in which the (R,S) and (R,R) diastereomers show much more structural differences than linear 1,2 amino alcohols. 1 In the cyclo Tyr-Tyr studied here, the cyclic nature of the peptide backbone is also responsible for the differences in interactions. Because of the different position of the extended aromatic ring in the "folded/extended" geometry of the two diastereomers (axial for L and equatorial for D), the CH-p
We present an efficient, analytical and simple route to approximating tunnelling splittings in multidimensional chemical systems, directly from ab initio computations.The method is based on the WKB approximation combined with vibrational perturbation theory. Anharmonicity and corner cutting effects are implicitly accounted for without requiring a full potential energy surface. We test this method on three systems; a model one-dimensional double well potential, the isomerisation of malonaldehyde, and the isomerisation of tropolone. The method is shown to be efficient and reliable.
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