A study of the quadratic p2 ⊗ h Jahn–Teller system
TL;DR: In this article, a Jahn-Teller (JT) coupling model for doubly charged C 60 2 -dianion was developed. But the model was not applied to the Coulombic interactions between the two electrons.
About: This article is published in Journal of Molecular Structure.The article was published on 2007-07-16. It has received 9 citations till now. The article focuses on the topics: Vibronic coupling & Jahn–Teller effect.
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TL;DR: The dynamical Jahn-Teller effect on fullerene sites in insulating Cs(3)C(60) is investigated fully ab initio and the corresponding exchange model is derived and predicts the Néel temperature for A15 Cs(-1), close to experiment.
Abstract: The dynamical Jahn-Teller effect on fullerene sites in insulating ${\mathrm{Cs}}_{3}{\mathrm{C}}_{60}$ is investigated fully ab initio. The vibronic excitations of rotational type are at $\ensuremath{\ge}65\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$, while the net kinetic contribution to the Jahn-Teller stabilization energy constitutes approximately 90 meV. This means that no localization of distortions by intermolecular interactions is possible in these fullerides; therefore, free rotations of deformations take place independently on each ${\mathrm{C}}_{60}$. The latter destroy the orbital ordering and establish a conventional exchange interaction between $S=1/2$ on fullerene sites. The corresponding exchange model is derived and predicts the N\'eel temperature for A15 ${\mathrm{Cs}}_{3}{\mathrm{C}}_{60}$ close to experiment.
22 citations
TL;DR: In this paper, a pseudo vector spin is evoked to represent degenerate JT-distorted states when the quadratic JT coupling is considered, and the differential operator technique is used in effective field theory within the Ising approach.
Abstract: Fullerene molecules adsorbed on surfaces often show macroscopic average distortions. As charged ions C
60
are known to be Jahn-Teller (JT) active, it is suggested that these distortions could be a manifestation of cooperative JT effects (CJTE) due to interactions between neighbouring fullerene ions. In order to understand the distortion properties it is necessary to take correlations between different distortions into account. However, this can’t easily be done in the mean field approximation usually used to describe the CJTE. We therefore propose an alternative procedure to describe 2D mesoscopic islands of C60 ions in which a pseudo vector spin $$\vec S$$
is evoked to represent degenerate JT-distorted states when the quadratic JT coupling is considered. This approach is analogous to methods used for 2D magnetic systems. We then use the differential operator technique in effective field theory within the Ising approach. We include the effects of weak surface interactions and dynamic motion between equivalent distortions via terms equivalent to anisotropy and a transverse field
in magnetism respectively. For distortions to D
5d
symmetry, we determine single site correlations as a function of temperature, the macroscopic average distortion describing a structural phase transition, and the isothermal response function. Phase diagrams are
presented for relevant cases of the system parameters.
14 citations
TL;DR: In this article, a simple idea involving a symmetry analysis and Huckel molecular orbital theory can be used to understand observed STM images without need for the more usual but more complicated density functional calculations.
Abstract: Using scanning tunnelling microscopy (STM), it is possible to observe detailed structure of the molecular orbitals (MOs) of fullerene anions C−60. However, understanding the experimental observations is not straightforward because of the inherent presence of Jahn–Teller (JT) interactions, which (in general) split the MOs in one of a number of equivalent ways. Tunnelling between equivalent distortions means that any observed STM image will be a superposition of images arising from the individual configurations. Interactions with the surface substrate must also be taken into account. We will show how simple ideas involving a symmetry analysis and Huckel molecular orbital theory can be used to understand observed STM images without need for the more usual but more complicated density functional calculations. In particular, we will show that when the fullerene ion is adsorbed with a pentagon, hexagon or double-bond facing the surface, STM images involving the lowest unoccupied molecular orbital (LUMO) can be reproduced by adding together just two images of squares of components of the LUMO, in ratios that depend on the strength of the JT effect and the surface interaction. It should always be possible to find qualitative matches to observed images involving any of these orientations by simply looking at images of the components, without doing any detailed calculations. A comparison with published images indicates that the JT effect in the C−60 ion favours D3d distortions.
10 citations
16 Oct 2015
TL;DR: In this article, the combined effects of Jahn-Teller (JT) coupling and interactions with a surface substrate on fullerene anions were investigated, and the implications of this on observed scanning tunneling microscopy (STM) images were discussed, and comparisons made with existing experimental data.
Abstract: We investigate the combined effects of Jahn-Teller (JT) coupling and interactions with a surface substrate on fullerene anions C$_{60}^{2-}$ to C$_{60}^{4-}$. JT coupling alone causes the C$_{60}$ ions to instantaneously distort from the icosahedral symmetry of the neutral molecule to a lower symmetry, with the molecule moving dynamically between a set of equivalent distortions. When adsorbed on a surface, the number of equivalent minimum-energy distortions is reduced. The implications of this on observed scanning tunneling microscopy (STM) images will be discussed, and comparisons made with existing experimental data. We show that a consistent interpretation of the images from all of the charge states of C$_{60}$ can only be obtained using a JT model in which the symmetry is further reduced by surface interactions. The comparison with experimental data also allows us to determine relationships between the quadratic Jahn-Teller coupling and surface interaction parameters.
9 citations
Cites background from "A study of the quadratic p2 ⊗ h Jah..."
...This yields an alternative form for the JT Hamiltonian [13, 37], which is what 180...
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...splitting between different terms, which must also be taken into account [13]....
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...Depending upon the values of quadratic coupling, there can be six D5d minima, ten D3d minima or 15 D2h minima for p 2 ⊗ h and p(4) ⊗ h (with a very small region with 30 C2h minima) [13], unless the Ag state is sufficiently lower in energy than the Hg state, in which case JT effects can be suppressed [14]....
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01 Jan 2009
TL;DR: In this article, the authors present a systematic investigation of the complications inherent in JT-related STM studies, to seek out possible JT signatures in such images and to guide further imaging towards identification and quantification of JT effects in molecules on surfaces.
Abstract: Scanning tunnelling microscopy (STM) is capable of imaging molecules adsorbed onto surfaces with sufficient resolution as to permit intra-molecular features to be discerned. Therefore, imaging molecules subject to the Jahn–Teller (JT) effect could, in principle, yield valuable information about the vibronic coupling responsible for the JT effect. However, such an application is not without its complications. For example, the JT effect causes subtle, dynamic distortions of the molecule; but how will this dynamic picture be affected by the host surface? And what will actually be imaged by the rather slow STM technique? Our aim here is to present a systematic investigation of the complications inherent in JT-related STM studies, to seek out possible JT signatures in such images and to guide further imaging towards identification and quantification of JT effects in molecules on surfaces. In particular, we consider the case of surface-adsorbed C60 ions because of their propensity to exhibit JT effects, their STM-friendly size and because a better understanding of the vibronic effects within these ions may be important for realisation of their potential application as superconductors.
8 citations
References
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01 Mar 2006TL;DR: The Jahn-Teller effect in spectroscopy has been studied in this article, where it has been shown that it can be used to solve solvable solutions of vibronic equations.
Abstract: 1. Introduction 2. Vibronic interactions 3. Formulation of Jahn-Teller problems. Adiabatic potentials 4. Pseudo Jahn-Teller, Product Jahn-Teller, and Renner-Teller effects 5. Solutions of vibronic equations. Energy spectra and Jahn-Teller dynamics 6. The Jahn-Teller Effect in spectroscopy: general theory 7. Geometry, spectra, and reactivity of molecular systems 8. Solid-state problems: local properties and cooperative phenomena Appendices Subject index Formula index.
712 citations
TL;DR: The electron-accepting ability of C 60, the archetypal fullerene, is its most characteristic chemical property and was anticipated in early molecular orbital calcula- tions 1 which place a low-lying unoccupied level about 2 eV above the HOMO level.
Abstract: Chem. Rev. 2000, 100, 1075−1120 Discrete Fulleride Anions and Fullerenium Cations Christopher A. Reed* and Robert D. Bolskar Department of Chemistry, University of CaliforniasRiverside, Riverside, California 92521-0403 Received June 22, 1999 Contents I. Introduction, Scope, and Nomenclature II. Electrochemistry A. Reductive Voltammetry B. Oxidative Voltammetry III. Synthesis A. Chemical Reduction of Fullerenes to Fullerides i. Metals as Reducing Agents ii. Coordination and Organometallic Compounds as Reducing Agents iii. Organic/Other Reducing Agents B. Electrosynthesis of Fullerides C. Chemical Oxidation of Fullerenes to Fullerenium Cations IV. Electronic (NIR) Spectroscopy A. Introduction B. C 60 n- Fullerides C. C 70 and Higher Fullerenes D. Fullerenium Cations E. Diffuse Interstellar Bands V. Vibrational Spectroscopy A. Infrared Spectroscopy B. Raman Spectroscopy VI. X-ray Crystallography A. Introduction B. [PPN] 2 [C 60 ] and Related C 602- Structures C. C 60 - Structures D. C 603- Structures E. Comparison of Discrete and Extended Structures VII. Magnetic Susceptibility and Spin States VIII. NMR Spectroscopy A. Introduction B. 13 C NMR Data in Solution C. Interpretation of Solution NMR Data D. 13 C NMR Data in the Solid State E. Knight Shift in A 3 C 60 F. 3 He NMR of Endohedral Fullerides G. 13 C NMR of Derivatized Fullerenes H. 13 C NMR of Fullerenium Cations IX. EPR Spectroscopy A. Introduction B. Features of the C 60 - Spectrum i. The Low g Value ii. Temperature Dependence of the Line Width (∆H pp ) X. XI. XII. XIII. iii. Anisotropy iv. Problem of the Sharp Signals v. Origins of Sharp Signals vi. The C 120 O Impurity Postulate vii. The Dimer Postulate C. Features of the C 602- EPR Spectrum D. Features of the C 603- EPR Spectrum E. Features of C 604- and C 605- EPR Spectra F. EPR Spectra of Higher Fullerides G. EPR Spectra of Fullerenium Cations Chemical Reactivity A. Introduction B. Fulleride Basicity C. Fulleride Nucleophilicity/Electron Transfer D. Fullerides as Intermediates E. Fullerides as Catalysts F. Fullerides as Ligands G. Fullerenium Cations Conclusions and Future Directions Acknowledgments References I. Introduction, Scope, and Nomenclature The electron-accepting ability of C 60 , the archetypal fullerene, is its most characteristic chemical property. It is a natural consequence of electronic structure and was anticipated in early molecular orbital calcula- tions 1 which place a low-lying unoccupied t 1u level about 2 eV above the h u HOMO: 2-4 Early in the gas-phase investigations of fullerenes, the electron affinity of C 60 was measured and found to be high (2.69 eV). 5-7 When the macroscopic era of C 60 chemistry began in 1990, this property was soon found to translate into the solution phase. 8 In a rather remarkable cyclic voltammogram (see Figure 1), the reversible stepwise addition of up to six electrons was soon demonstrated electrochemically. 9,10 10.1021/cr980017o CCC: $35.00 © 2000 American Chemical Society Published on Web 02/16/2000
579 citations
232 citations
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TL;DR: In this article, the effects of vibronic coupling in the icosahedral cluster model were studied analytically on an icosahedron model and the results were necessary in order to calculate further properties of the system, such as Jahn-Teller reduction factors.
Abstract: The ${\mathit{T}}_{1\mathit{u}}$\ensuremath{\bigotimes}${\mathit{h}}_{\mathit{g}}$ Jahn-Teller system is studied analytically on an icosahedral cluster model. This system is a model for the effects of vibronic coupling in the ${\mathrm{C}}_{60}$ molecule. Vibronic coupling is very important in this system because both the electronic and vibrational states are of high symmetry. The method employed is to apply a unitary transformation to the Hamiltonian for the system in order to obtain expressions for the states associated with minima in the potential-energy surface. Quadratic coupling terms are included in the Hamiltonian in order to obtain distinct minima located at either pentagonal (${\mathit{D}}_{5\mathit{h}}$) or trigonal (${\mathit{D}}_{3\mathit{h}}$) positions in Q space. These states are good eigenstates of the system as a whole in very strong coupling. For finite couplings, projection operator techniques are then used to obtain explicit expressions for the vibronic ground and inversion states from these basis states for both the pentagonal and trigonal cases. Expressions for the corresponding energies are then derived as a function of the coupling constants. These results are necessary in order to be able to calculate further properties of the system, such as Jahn-Teller reduction factors, which are in turn necessary to explain experimental data on these systems.
192 citations
TL;DR: In this paper, the electron-phonon coupling constants were derived from the intensity of the excitation of phonons in high-resolution photoemission spectra, which support superconductivity.
Abstract: A high resolution experimental photoemission spectrum of ${\mathrm{C}}_{60}^{\phantom{\rule{0ex}{0ex}}\ensuremath{-}}$ is compared with calculations including the Jahn-Teller effect and multiple phonon satellites. The spectra show discrete loss features due to the excitation of phonons. From the intensity of these features, electron-phonon coupling constants are derived, which support the electron-phonon mechanism for superconductivity. The systematic deviations from previously calculated coupling constants are discussed in detail.
170 citations