Renner-Teller/Jahn-Teller intersections along the collinear axes of polyatomic molecules: C2H2+ as a case study

Abstract

Some time ago we published our first article on the Renner-Teller ͑RT͒ model to treat the electronic interaction for a triatomic molecule ͓J. Chem. Phys. 124, 081106 ͑2006͔͒. The main purpose of that Communication was to suggest considering the RT phenomenon as a topological effect, just like the Jahn-Teller phenomenon. However, whereas in the first publication we just summarized a few basic features to support that idea, here in the present article, we extend the topological approach and show that all the expected features that characterize a three ͑multi͒ state RT-type'3 system of a triatomic molecule can be studied and analyzed within the framework of that approach. This, among other things, enables us to employ the topological D matrix ͓Phys. Rev. A 62, 032506 ͑2000͔͒ to determine, a priori, under what conditions a three-state system can be diabatized. The theoretical presentation is accompanied by a detailed numerical study as carried out for the HNH system. The D-matrix analysis shows that the two original electronic states 2 A 1 and 2 B 1 ͑evolving from the collinear degenerate ⌸ doublet͒, frequently used to study this Renner-Teller-type system, are insufficient for diabatization. This is true, in particular, for the stable ground-state configurations of the HNH molecule. However, by including just one additional electronic state-a B state ͑originating from a collinear ⌺ state͒-it is found that a rigorous, meaningful three-state diabatization can be carried out for large regions of configuration space, particularly for those, near the stable configuration of NH 2 . This opens the way for an accurate study of this important molecule even where the electronic angular momentum deviates significantly from an integer value.

An intraline of conical intersections for methylamine

“…͑1͒ In all previous studies [1][2][3][4][5][6][7][8]14,15,28,34 the seams are located outside the planes ͑e.g., the g-h plane, which is defined as the perpendicular plane to the seam 7͑a͒ ͒ that contain the moving test particle ͑which in the present case is the HC-NHH plane͒. In other words the methylamine creates a phenomenon where the two interacting states i.e., 1AЈ and 1AЉ, are coupled by a continuous line of cis formed by one single moving atom where all other ͑six͒ atoms of the molecule are fixed in configuration space.…”

“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] In the present article we consider a much larger system, the methylamine molecule, CH 3 NH 2 , consisting of seven atoms. The structure of the molecule is given in Fig.…”

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

“…25 This connection was found to be valid for all reported numerical studies of molecular systems with two quasi-isolated states. 4,[15][16][17]21(a), [26][27][28] In case the two-state system forms a Hilbert subspace the topological phase becomes an integer multiple of π (or zero). In the Introduction, we already mentioned that the necessary and sufficient condition that the diabatic potentials, formed by Eq.…”

“…Comment: As already mentioned in the Introduction, we also studied systems affected by both, JT-NACTs and RTNACTs 16(a), 17,18 where the contours surround the RT seams (and therefore do not intersect them) so that the resulting RT NACTs are not of the Dirac δ-function type and the need for η-type parameters becomes redundant.…”

“…As is well known, 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), 9,11,15 (b) ADT matrices formed by a mixture of both Renner-Teller (RT) NACTs and JT NACTs. 16 because molecular systems always contain both types of NACTs.…”