Analytic Route to Tunneling Splittings Using Semiclassical Perturbation Theory

Abstract

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.

Upper and lower bounds for tunneling splittings in a symmetric double-well potential

“…5 The WKB approach has been applied successfully to several model potentials, such as one-and multidimensional symmetric double-wells, [16][17][18] onedimensional asymmetric potentials, 19 ring-puckering vibrations, 15 and in combination with vibrational perturbation theory. 20 A path-integral molecular dynamics method was used for double-well potentials in ref. 21.…”

Simple models for the quick estimation of ground state hydrogen tunneling splittings in alcohols and other compounds

“…The estimation of the torsional wavenumber from the harmonic normal mode treatment might be a major source of error and thus a good starting point for improvement. 31 In this context, it might be interesting to explore the performance of more sophisticated methods and models on the collated benchmark data as well as to investigate whether the proposed simple models might be applied as well to other series of compounds.…”

“…As one example, the result for nitrogen inversion is shown in Fig. 9 and the result of the regression is given in eqn (31).…”

“…9 Correlation between the experimental inversion splittings of fully N-deuterated and N-protiated amines and amides. The outlier from vinylamine is not considered in the regression, whose result is given in eqn (31). The value of the inversion splitting of deuterated vinylamine has been questioned before.…”

“…30 More affordable and somewhat more accessible, but also more approximate, are models which explore the tunneling along a one-dimensional pathway. [31][32][33] For the latter the release of software is acknowledged which makes the computation of half-lives for tunneling reactions broadly accessible. 34 From the perspective of a spectroscopist (such as the author of the present article), a supplementation with even more approximate methods for quickly and straightforwardly attainable estimations is desirable.…”