Abstract
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.
Highlights
This article is one additional link in a series of articles1–4 devoted to the problem of revealing rigorous, efficient, and accurate methods to construct diabatic potential energy surfaces (PES) for multi-state, poly-atomic molecular systems
The main difficulty is associated with the single-valuedness of these diabatic PESs, which is difficult to guarantee even for simple configuration space (CS) such as planes once they extend to large sizes
The literature contains numerous studies based on these matrices in connection with various different, tri-atomic, tetra-atomic, and poly-atomic molecular systems.6(a), 9, 11, 15,16(a), 17, 18. These studies are divided into two general categories based on the type of non-adiabatic coupling terms (NACT) included in the study: (a) adiabatic-to-diabatic transformation (ADT) matrices formed by Jahn-Teller (JT) NACTs;6(a),9,11,15 (b) ADT matrices formed by a mixture of both Renner-Teller (RT) NACTs and JT NACTs.16(a), 17,18(b), 18(c) This partitioning is somewhat artificial
Summary
This article is one additional link in a series of articles devoted to the problem of revealing rigorous, efficient, and accurate methods to construct diabatic potential energy surfaces (PES) for multi-state, poly-atomic molecular systems. The literature contains numerous studies based on these matrices in connection with various different, tri-atomic, tetra-atomic, and poly-atomic molecular systems.6(a), 9, 11, 15,16(a), 17, 18 These studies are divided into two general categories based on the type of non-adiabatic coupling terms (NACT) included in the study: (a) ADT matrices formed by Jahn-Teller (JT) NACTs;6(a), (b) ADT matrices formed by a mixture of both Renner-Teller (RT) NACTs and JT NACTs.16(a), 17,18(b), 18(c) This partitioning is somewhat artificial (in particular the existence of “pure” JT NACTs) This situation opened up the way for a theoretical/ mathematical study according to which these NACTs are up to a normalization factor, pure Dirac δfunctions.19,21(b) The theoretical findings of this study are incorporated in the present study The only problem encountered here is that these calculated NACTs are extremely spiky—reminiscent of the Dirac δ-function (see, e.g., Fig. 2 in Ref. 21(a))—and their correct shape is frequently missed
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