Jahn-Teller effects in molecular cations studied by photoelectron spectroscopy and group theory.

TLDR: This investigation of the methane cation represents the first experimental characterization of the JT effect in a threefold degenerate electronic state and shows how the pseudo-Jahn-Teller effect in the cyclopentadienyl cation causes electronic localization and nuclear delocalization.

Abstract: The traditional "ball-and-stick" concept of molecular structure fails when the motion of the electrons is coupled to that of the nuclei. Such a situation arises in the Jahn-Teller (JT) effect which is very common in open-shell molecular systems, such as radicals or ions. The JT effect is well known to chemists as a mechanism that causes the distortion of an otherwise symmetric system. Its implications on the dynamics of molecules still represent unsolved problems in many cases. Herein we review recent progress in understanding the dynamic structure of molecular cations that have a high permutational symmetry by using rotationally resolved photoelectron spectroscopy and group theory. Specifically, we show how the pseudo-Jahn-Teller effect in the cyclopentadienyl cation causes electronic localization and nuclear delocalization. The fundamental physical mechanisms underlying the vaguely defined concept of "antiaromaticity" are thereby elucidated. Our investigation of the methane cation represents the first experimental characterization of the JT effect in a threefold degenerate electronic state. A special kind of isomerism resulting from the JT effect has been discovered and is predicted to exist in all JT systems in which the minima on the potential-energy surface are separated by substantial barriers.

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ETH Library
Jahn-Teller effects in molecular
cations studied by photoelectron
spectroscopy and group theory
Journal Article
Author(s):
Wörner, Hans Jakob; Merkt, Frédéric
Publication date:
2009-08-17
Permanent link:
https://doi.org/10.3929/ethz-a-010782632
Rights / license:
In Copyright - Non-Commercial Use Permitted
Originally published in:
Angewandte Chemie. International Edition 48(35), https://doi.org/10.1002/anie.200900526
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Jahn-Teller effects in molecular cations studied by photoelectron
spectroscopy and group theory
∗
Hans Jakob W¨orner and Fr´ed´eric Merkt
Laboratorium f¨ur Physikalische Chemie, ETH-Z¨urich,
8093 Z¨urich, Switzerland
28th March 2009
wave number / cm
-1
101740 101760 101780 101800 101820 101840
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∗
dedicated to Prof. Martin Quack on the occasion of his 60
th
birthday
1

Understanding the structure and dynamics of molecules is the most fundamental goal of
chemistry. The traditional ”balls-and-sticks” concept of molecular structure fails when the mo-
tion of the electrons is coupled to that of the nuclei. Such a situation arises in the Jahn-Teller
(JT) effect which is very common in open-shell molecular systems, such as radicals or ions. The
JT effect is well known to chemists as a mechanism that causes the distortion of an otherwise
symmetric system. Its implications on the dynamics still represent unsolved problems in many
molecules. This article reviews recent progress in understanding the dynamic structure of molec-
ular cations having a high permutational symmetry using rotationally resolved photoelectron
spectroscopy and group theory. The JT effect profoundly modifies their electronic structure and
renders them fluxional. Specifically, we show how the Pseudo-JT effect in the cyclopentadienyl
cation causes electronic localization and nuclear delocalization. The fundamental physical mech-
anisms underlying the vaguely defined concept of ”antiaromaticity” are thereby elucidated. Our
investigation of the methane cation represents the first experimental characterization of the JT
effect in a threefold degenerate electronic state. A special kind of isomerism resulting from the
JT effect has been discovered and is predicted to exist in all JT systems in which the minima
on the potential energy surface are separated by substantial barriers. The JT effect can also
induce chirality which results in an interesting case of stereomutation dynamics.
1 Introduction
The Jahn-Teller (JT) and Pseudo-Jahn-Teller (PJT) effects arise from the coupling of electronic
and nuclear degrees of freedom in manifolds of degenerate or near-degenerate states and affects
the structural and dynamical properties of molecules, transition metal complexes and solids.
The variety of its physical and chemical implications is extremely rich [1, 2]. In electronically
degenerate states of molecules and transition metal complexes, the JT effect lowers the potential
energy for configurations of the nuclei having a reduced symmetry. If the corresponding JT
stabilization energy is large compared to vibrational energy intervals, the JT effect results in a
distortion of the molecule. In organic molecules, the JT effect is essential in the interpretation
of photochemistry and in the definition of antiaromaticity. In solids, the JT effect has been
invoked to explain phenomena like superconductivity and colossal magnetoresistance [1]. The
JT effect occurs in species with unpaired electrons, i.e. radicals, biradicals, etc. Such molecules
are usually highly reactive and play an important role as reaction intermediates, in combustion
chemistry, atmospheric chemistry and the chemistry of the interstellar medium.
2

The first advances in the investigation of the JT effect were of theoretical nature. Hermann
Jahn and Edward Teller used group theory to prove that a nonlinear molecule in an orbitally
degenerate state undergoes a geometric distortion [3, 4]. Longuet-Higgins [5, 6] calculated the
vibronic energy level structure resulting from the interaction of a doubly degenerate (E) elec-
tronic state with one doubly degenerate (e) vibrational mode, which is called the E⊗e JT effect.
He predicted the band shapes of optical absorption spectra and pointed at the first observ-
able manifestations of the JT effect in optical spectroscopy. A molecule subject to a JT effect
can distort along several equivalent vibrational modes giving rise to equivalent minima on the
potential energy surface. Bersuker recognized that this situation leads (in most cases) to a split-
ting of the lowest vibronic levels by tunneling [7].
¨
Opik and Pryce investigated the interaction
of triply degenerate electronic states (T) and doubly (e) and triply (t) degenerate vibrational
modes in molecules of the cubic point groups known as the T⊗(e+t
2
) effect and considered
for the first time the vibronic coupling between nondegenerate electronic states, also called the
Pseudo-Jahn-Teller (PJT) effect [8].
The most detailed experimental characterization of the JT effect has been achieved in high-
resolution optical and photoelectron spectroscopy. Optical spectroscopy has been applied to
elucidate the JT effect in several open-shell species including Na
3
and Li
3
. The
˜
A
2
E
00
state
of these species represents the prototype of the E⊗e JT effect [9]. The next higher electronic
state
˜
B
2
A
1
0
is subject to a PJT effect [10, 11]. Photoelectron spectroscopy has been used to
characterize the JT effect in a wide range of molecular cations. For instance, the analysis of
rotationally resolved PFI-ZEKE photoelectron spectra of C
6
H
6
has proven that the minima
of the ground state potential energy surface of C
6
H
+
6
, which is subject to the E⊗e JT effect,
correspond to a D
2h
geometry with two acute C-C-C bond angles, although the rovibronic
photoionization selection rules are adequately described in D
6h
(M) symmetry [12, 13].
Currently, the E⊗e JT effect is the best understood case and its ramifications are well
known [1, 14–18]. Much less is known about other cases, especially about molecules of higher
symmetry, where the electronic states can have threefold or higher degeneracies [19], primarily
because of the scarcity of high-resolution spectroscopic data that would permit the determination
of the structure and dynamics of such species.
The present review focuses on recent experimental and theoretical progress at the frontier
of the field. It demonstrates how rotationally resolved photoelectron spectroscopy permits the
investigation of molecular cations that are highly fluxional in their ground electronic state as a
consequence of the JT or PJT effects. This article also introduces a group theoretical formalism
3

Frequently asked questions

Q1. What is the effect of a distortion along an e′y component?

A distortion along an e ′ x component conserves C2v symmetry, whereas a distortion along an e′y component lowers the symmetry to Cs. 

Q2. What are the contributions in this paper?

In this paper, the authors present a review of the recent advances in the investigation of the Jahn-Teller ( JT ) effect in high-resolution optical and photoelectron spectroscopy. 

Q3. How can the ionizing transitions be detected?

the photoionizing transitions to specific cationic states can be detected with almost 100 % efficiency by measuring electrons. 

Q4. What is the motion connecting equivalent minima of a given set of six structures?

The motion connecting equivalent minima of a given set of six structures corresponds to a cyclic permutation of three hydrogen atoms also known as pseudorotation. 

Q5. How is the tunneling splitting in CH4 expected to be?

In the ground state of CH4, the tunneling splitting resulting from this motion is expected to be very small because of the very high barrier (≥ 35000 cm−1) for stereomutation [72]. 

Q6. What is the symmetry of the distorted structure?

Since the molecule is rigid and in its ground vibrational state, it must be classified in the point group of the distorted structure and the vibronic symmetry is the same as its electronic symmetry. 

Q7. What can be used to treat non-Jahn-Teller fluxional systems?

They can also be applied to rovibronic states, are useful in the construction of correlation diagrams [41, 61] and may be used to treat non-Jahn-Teller fluxional systems. 

Q8. What are the main aspects of the JT effect in highly symmetric molecules?

This review concentrated on two fundamental cations, the methane cation and the cyclopentadienyl cation, which are representative examples of the diversity of spectral, structural and dynamical manifestations of the JT effect in highly symmetric molecules. 

Q9. What is the rovibronic symmetries of the methane?

The first technique, that the authors call ”ZEKE-dip” spectroscopy (by analogy with ion-dip spectroscopy [46]) was applied to assign the rovibronic symmetries of the levels of the methane cation. 

Q10. How is the maximum of the reaction path similar to the one described in Ref.?

The maximum of the reaction path corresponds to a structure of Cs geometry that is very26similar to the one described in Ref. [35]. 

Q11. What can be done to reduce the symmetry of the electronic potential energy surfaces?

They allow one to reduce the permutational symmetry and remove the energetic equivalence of potential energy minima without affecting the nature of the electronic potential energy surfaces. 

Q12. What are the important parameters to describe the JT effect in a molecule?

These data are essential parameters to describe the JT effect in a molecule, but are in general insufficient to predict the coupled nuclear and electronic dynamics and the rovibronic energy level structure of a molecule. 

Q13. What is the number of equiv-11alent structures of a given symmetry?

The number of equiv-11alent structures of a given symmetry is determined by the ratio of the orders of the CNPI group of the molecule and the point group of the structure.