Molecular Symmetry Properties of Conical Intersections and Nonadiabatic Coupling Terms: Theory and Quantum Chemical Demonstration for Cyclopenta-2,4-dienimine (C5H4NH)
Date
2010-03-10
Authors
Al-Jabour, S.
Baer, M.
Deeb, O.
Leibscher, M.
Manz, J.
Xu, X.
Zilberg, S.
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Abstract
This paper discovers molecular symmetry (MS) properties of conical intersections (CIs) and the related
nonadiabatic coupling terms (NACTs) in molecules which allow large amplitude motions such as torsion, in
the frame of the relevant molecular symmetry group, focusing on groups with one-dimensional (1-d) irreducible
representations (IREPs). If one employs corresponding MS-adapted nuclear coordinates, the NACTs can be
classified according to those IREPs. The assignment is supported by theorems which relate the IREPs of
different NACTs to each other, and by properties of the NACTs related to the CIs. For example, planar
contour integrals of the NACTs evaluated along loops around the individual CIs are equal to +π or -π,
depending on the IREP-adapted signs of the NACTs. The + or - signs for the contour integrals may also be
used to define the “charges” and IREPs of the CIs. We derive various general molecular symmetry properties
of the related NACTs and CIs. These provide useful applications; e.g., the discovery of an individual CI
allows one to generate, by means of all molecular symmetry operations, the complete set of CIs at different
symmetry-related locations. Also, we show that the seams of CIs with different IREPs may have different
topologies in a specific plane of MS-adapted coordinates. Moreover, the IREPs impose symmetrical nodes of
the NACTs, and this may support their calculations by quantum chemical ab initio methods, even far away
from the CIs. The general approach is demonstrated by application to an example. Specifically, we investigate
the CIs and NACTs of cyclopenta-2,4-dienimine (C5H4NH) which has C2V(M) molecular symmetry with 1-d
IREPs. The results are confirmed by quantum chemical calculations, starting from the location of a CI based
on the Longuet-Higgins phase change theorem, until a proof of self-consistency, i.e., the related symmetryadapted
NACTs fulfill quantization rules which have been derived in [Baer, M. Beyond Born-Oppenheimer:
Electronic non-Adiabatic Coupling Terms and Conical Intersections; Wiley & Sons Inc.: Hoboken, NJ, 2006].