Abstract
The present article is an attempt to draw attention to a seminal work by Andrew Liehr “Topological aspects of conformational stability problem” [1, 2] issued more than half century ago. The importance of this work stems from two aspects of static Jahn-Teller and pseudo-Jahn-Teller problems fully developed by the author. First, the work of Liehr offers an almost complete overview of adiabatic potential energy surfaces for most known Jahn-Teller problems including linear, quadratic and higher-order vibronic couplings. Second, and most importantly, it identifies the factors defining the structure of Jahn-Teller surfaces. Among them, one should specially mention the minimax principle stating that the distorted Jahn-Teller systems tend to preserve the highest symmetry consistent with the loss of their orbital degeneracy. We believe that the present short reminiscence not only will introduce a key Jahn-Teller scientist to the young members of the community but also will serve as a vivid example of how a complete understanding of a complex problem, which the Jahn-Teller effect certainly was in the beginning of 1960s, can be achieved.
Highlights
After the publication of the Jahn-Teller theorem in 1937 [3, 4], there was a period of almost two decades during which the Jahn-Teller effect practically did not attract attention except via a few albeit very important publications [5, 6, 7, 8]
Adiabatic potential energy surfaces of Jahn-Teller problems In the paper comprising the treatment of static JahnTeller (Part I) [1], Liehr derived the analytical expressions for adiabatic potential energy surfaces (APES) of almost all Jahn-Teller systems
We emphasize that there are no minima mixing nuclear coordinates of different subsets (e.g., e and t2) when the linear vibronic coupling only is considered. This is a general feature of linear Jahn-Teller problems with several different sets of active nuclear coordinates, which always allows to consider the Jahn-Teller problem with individual subsets when the minima of APES are investigated (e.g., T ⊗ e and T ⊗ t2 instead of T ⊗ (e ⊕ t2)). This means that we always deal with Jahn-Teller problems with one single set of nuclear vibrations when investigate the minima of APES, to which the Liehr’s minimax principle perfectly applies
Summary
After the publication of the Jahn-Teller theorem in 1937 [3, 4], there was a period of almost two decades during which the Jahn-Teller effect practically did not attract attention except via a few albeit very important publications [5, 6, 7, 8]. 2. Adiabatic potential energy surfaces of Jahn-Teller problems In the Part I [1], Liehr derived the analytical expressions for APES of almost all Jahn-Teller systems.
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