A tri-atomic Renner-Teller system entangled with Jahn-Teller conical intersections

• Published in: The Journal of chemical physics 2013-01, Vol.138 (2), p.024113-024113
• Main Authors: Csehi, A, Bende, A, Halász, G J, Vibók, Á, Das, A, Mukhopadhyay, D, Baer, M
• Format: Article
• Language: English
• Subjects: Algorithms; Models, Chemical; Quantum Theory; Thermodynamics
• ISSN: 0021-9606; 1089-7690
• DOI: 10.1063/1.4773352

The present study concentrates on a situation where a Renner-Teller (RT) system is entangled with Jahn-Teller (JT) conical intersections. Studies of this type were performed in the past for contours that surround the RT seam located along the collinear axis [see, for instance, G. J. Halász, Á. Vibók, R. Baer, and M. Baer, J. Chem. Phys. 125, 094102 (2006)]. The present study is characterized by planar contours that intersect the collinear axis, thus, forming a unique type of RT-non-adiabatic coupling terms (NACT) expressed in terms of Dirac-δ functions. Consequently, to calculate the required adiabatic-to-diabatic (mixing) angles, a new approach is developed. During this study we revealed the existence of a novel molecular parameter, η, which yields the coupling between the RT and the JT NACTs. This parameter was found to be a pure number η = 22/π (and therefore independent of any particular molecular system) and is designated as Renner-Jahn coupling parameter. The present study also reveals an unexpected result of the following kind: It is well known that each (complete) group of states, responsible for either the JT-effect or the RT-effect, forms a Hilbert space of its own. However, the entanglement between these two effects forms a third effect, namely, the RT/JT effect and the states that take part in it form a different Hilbert space.