A Century of Semiclassics - Tunneling and Quantization

Abstract

Two quantum effects have had a big impact on Chemistry. Arguably the most important one is the quantization of vib-rotational energy levels, an effect which challenges classical mechanics computations of molecular dynamics and is at the basis of molecular spectroscopy. The second is quantum tunneling which is especially important when considering light atom transfer, especially hydrogen atoms and proton transfer. Tunneling was reported for the first time by Hund in 1927 in his paper which was submitted on Nov. 19, 1926. The quantization of energy levels was one of the major building blocks of the new quantum theory, the semiclassical quantization condition was formulated in the summer of 1927 by Brillouin, Wentzel and Kramers. In retrospect, a century later, we have learned much about the two effects, yet surprisingly, the giants who discovered and formulated the relevant semiclassical theories left us with some challenges. Some of these have been answered during the past five years and these are the main emphasis of this review, which is not a review of 100 years of semiclassics, a project which calls for books, rather than short review articles. At the same time, we point out some remaining challenges which have not been answered, and which demonstrate, that there is always something new to learn even when considering well established theories.