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The adiabatic‐to‐diabatic transformation angle and the berry phase for coupled jahn–teller/renner–teller systems: The F + H 2 as a case study
Author(s) -
Das Anita,
Mukhopadhyay Debasis,
Adhikari Satrajit,
Baer Michael
Publication year - 2011
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.23272
Subject(s) - diabatic , adiabatic process , geometric phase , chemistry , mixing (physics) , quantum mechanics , coupling (piping) , dirac (video compression format) , jahn–teller effect , function (biology) , coupling constant , transformation (genetics) , physics , mathematical physics , atomic physics , ion , biology , mechanical engineering , biochemistry , gene , engineering , evolutionary biology , neutrino
The approach to calculate improved, two‐state, adiabatic‐to‐diabatic transformation angles (also known as mixing angles), presented before (see Das et al., J Chem Phys 2010, 133, 084107), was used here while studying the F + H 2 system. However, this study is characterized by two new features: (a) it is the first of its kind in which is studied the interplay between Renner–Teller (RT) and Jahn–Teller (JT) nonadiabatic coupling terms (NACT); (b) it is the first of its kind in which is reported the effect of an upper singular RT‐NACT on a lower two‐state (JT) mixing angle. The fact that the upper NACT is singular (it is shown to be a quasi‐Dirac δ‐function) enables a semi‐analytical solution for this perturbed mixing angle. The present treatment, performed for the F + H 2 system, revealed the existence of a novel parameter, η, the Jahn–Renner coupling parameter (JRCP), which yields, in an unambiguous way, the right intensity of the RT coupling (as resembled, in this case, by the quasi‐Dirac δ‐function) responsible for the fact that the final end‐of‐the contour angle (identified with the Berry phase) is properly quantized. This study implies that the numerical value of this parameter is a pure number (independent of the molecular system): η = $ 2\sqrt 2 /\pi $ (= 0.9003) and that there is a good possibility that this value is a novel characteristic molecular constant for a certain class of tri‐atomic systems. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011