Nonadiabatic effects play an important role in many areas of physics and chemistry. The coupling between electrons and nuclei may, for example, lead to the formation of a conical intersection between potential energy surfaces, which provides an efficient pathway for radiationless decay between electronic states. At such intersections the Born-Oppenheimer approximation breaks down, and unexpected dynamical processes result, which can be observed spectroscopically. We review the basic theory required to understand and describe conical, and related, intersections. A simple model is presented, which can be used to classify the different types of intersections known. An example is also given using wavepacket dynamics simulations to demonstrate the prototypical features of how a molecular system passes through a conical intersection.

Beyond Born-Oppenheimer: molecular dynamics through a conical intersection.

Modern aspects of the Jahn-Teller effect theory and applications to molecular problems.

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

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Discrete fulleride anions and fullerenium cations.

The hydration reaction is defined as the transfer of an ion or neutral chemical species from the gaseous phase into water, M n+ (g) → M n+ (aq). In this process, water mole- cules bind to metal ions through ion-dipole bonds of mainly electrostatic character. The hy- dration reaction is always strongly exothermic with increa sing heat of hydration with in- creasing charge density of the ion. The structures of the hydrated metal ions in aqueous solution display a variety of configurations depending on the size and electronic properties of the metal ion. The basic configurations of hydrated metal ions in aqueous solution are tetrahedral, octahedral, square antiprismatic, and tricapped trigonal prismatic. This paper gives an overview of the structures of hydrated metal ions in aqueous solution with special emphasis on those with a non-regular coordination figure. Metal ions without d-electrons in the valance shell form regular aqua complexes with a coordination figure, allowing a maxi- mum number of water molecules to be clustered around the metal ion. This number is de- pendent on the ratio of the metal ion radius to the atomic radius of oxygen in a coordinated water molecule (1.34 A). The lighter lanthanoid(III) ions have a regular tricapped trigonal prismatic configuration with the M-O distance to the capping water molecules somewhat longer than to the prismatic ones. However, with increasing atomic number of the lan- thanoid(III) ions, an increasing distortion of the capping water molecules is observed, result- ing in a partial loss of water molecules in the capping positions for the heaviest lanthanoids. Metal ions with d 4 and d 9 valance shell electron configuration, as chromium(II) and cop- per(II), respectively, have Jahn-Teller distorted aqua complexes. Metal ions with low charge and ability to form strong covalent bonds, as silver(I), mercury(II), palladium(II), and plat- inum(II), often display distorted coordination figures due to the second-order Jahn-Teller ef- fect. Metal ions with d 10 s 2 valence shell electron configuration may have a stereochemically active lone electron pair (hemi-directed complexes) or an inactive one (holo-directed). The hydrated tin(II), lead(II), and thallium(I) ions are hemi-directed in aqueous solution, while the hydrated bismuth(III) ion is holo-directed. The structures of the hydrated cationic oxo- metal ions are reported as well.

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Hydrated metal ions in aqueous solution: How regular are their structures?

Pseudo-Jahn-teller effect--a two-state paradigm in formation, deformation, and transformation of molecular systems and solids.

Vibronic interaction effects constitute a new field of investigation in the physics and chemistry of molecules and crystals that combines all the phenomena and laws originating from the mixing of different electronic states by nuclear displacements This field is based on a new concept which goes beyond the separate descriptions of electronic and nuclear motions in the adiabatic approximation Publications on this topic often appear under the title of the lahn-Thller effect, although the area of application of the new approach is much wider: the term vibronic interaction seems to be more appropriate to the field as a whole The present understanding of the subject was reached only recently, during the last quarter of a century As a result of intensive development of the theory and experiment, it was shown that the nonadiabatic mixing of close-in-energy elec tronic states under nuclear displacements and the back influence of the modified electronic structure on the nuclear dynamics result in a series of new effects in the properties of molecules and crystals The applications of the theory of vibronic in of spectroscopy [including visible, ultraviolet, in teractions cover the full range frared, Raman, EPR, NMR, nuclear quadrupole resonance (NQR), nuclear gam ma resonance (NOR), photoelectron and x-ray spectroscopy], polarizability and magnetic susceptibility, scattering phenomena, ideal and impurity crystal physics and chemistry (including structural as well as ferroelectric phase transitions), stereochemistry and instability of molecular (including biological) systems, mechanisms of chemical reactions and catalysis"

Vibronic interactions in molecules and crystals

The vibronic origin of dynamic instability of molecular systems considered earlier, is here given a more complete and rigorous treatment. It is shown that the nonvibronic contribution to the curvature of the adiabatic potential arising due to nuclear displacements under fixed electronic density distribution, is always positive, and hence the only reason for dynamic instability is the pseudo Jahn-Teller effect. For some examples of special interest (planar equilateral NH3, planar square CH4 and linear H
 3
 +
 ) the molecular excited states, responsible for the instability of the ground state, are revealed by means of ab initio calculations.

On the origin of dynamic instability of molecular systems

The adiabatic potential surface for icosahedral systems having three-, four- and five-fold degenerate orbital states interacting with five-fold degenerate vibrations (T-v,U-v andV-v problems) is investigated. It is shown that for theT-v andV-v Jahn-Teller cases the potential surface possesses respectively a two- or three-dimensional equipotential continuum of minima. For theU-v problem the potential surface contains 15 equivalent minima. The nature of the extremum points on the adiabatic potential surfaces is elucidated. In the linear approximation to theV-v problem in the minima points the lowest potential surface is double degenerate due to the accidental occurrence of axial symmetry.

The Jahn-Teller effect in icosahedral molecules and complexes

We have investigated the T⊗t2 Jahn–Teller problem with linear and quadratic vibronic coupling including a fourth-order term. First, numerical calculations of the lowest vibronic states were carried out by direct diagonalization of the Hamiltonian. The results show that the energy level of the ground vibronic state, which is triply degenerate T for small quadratic coupling g values, intersects the next A level with increasing g, thus realizing the nondegenerate ground state at sufficiently large g values. This result reverses the long-standing belief that the ground vibronic state for the T⊗t2 system has the same degeneracy and symmetry T as the initial electronic state. To explain these results in terms of Berry phase requirements and conical intersections, the adiabatic potential energy surface of the system is analyzed, and the relationships among the type and number of minima, conical intersections, and relevant tunneling paths are revealed. Depending on the vibronic coupling parameter values, there ar...

Multiple lines of conical intersections and nondegenerate ground state in T⊗t2 Jahn–Teller systems

In a semi-review paper, we show that the local pseudo-Jahn–Teller effect (PJTE) in transition metal B ion center of ABO3 perovskite crystals, notably BaTiO3, is the basis of all their main properties. The vibronic coupling between the ground and excited electronic states of the local BO6 center results in dipolar distortions, leading to an eight-well adiabatic potential energy surface with local tunneling or over-the-barrier transitions between them. The intercenter interaction between these dipolar dynamic units results in the formation of the temperature-dependent three ferroelectric and one paraelectric phases with order–disorder phase transitions. The local PJTE dipolar distortion is subject to the presence of sufficiently close in energy local electronic states with opposite parity but the same spin multiplicity, thus limiting the electronic structure and spin of the B(dn) ions that can trigger ferroelectricity. This allowed us to formulate the necessary conditions for the transition metal perovskites to possess both ferroelectric and magnetic (multiferroic) properties simultaneously. It clarifies the role of spin in the spontaneous polarization. We also show that the interaction between the independently rotating dipoles in the paraelectric phase may lead to a self-assembly process resulting in polar nanoregions and relaxor properties. Exploring interactions of PJTE ferroelectrics with external perturbations, we revealed a completely novel property—orientational polarization in solids—a phenomenon first noticed by P. Debye in 1912 as a possibility, which was never found till now. The hindered rotation of the local dipole moments and their ordering along an external field is qualitatively similar to the behavior of polar molecules in liquids, thus adding a new dimension to the properties of solids—notably, the perovskite ferroelectrics. We estimated the contribution of the orientational polarization to the permittivity and flexoelectricity of perovskite crystals in different limiting conditions.

https://www.mdpi.com/2410-3896/5/4/68/pdf

Victor Z. Polinger

Papers

Vibronic interactions in molecules and crystals

On the origin of dynamic instability of molecular systems

The Jahn-Teller effect in icosahedral molecules and complexes

Multiple lines of conical intersections and nondegenerate ground state in T⊗t2 Jahn–Teller systems

Perovskite Crystals: Unique Pseudo-Jahn–Teller Origin of Ferroelectricity, Multiferroicity, Permittivity, Flexoelectricity, and Polar Nanoregions