Theory of the Jahn–Teller Effect

Köppel, Horst; Cederbaum, Lorenz S.; Mahapatra, S.

doi:10.1002/9780470749593.hrs060

Cited by 15 publications

(15 citation statements)

References 113 publications

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“…Our formal proposal is that unless the vibrational profiles of two or more transitions into electronic ionic states are not separate in the PES, then vibronic coupling should be assumed. [48][49][50] Measured vibrational separations will at best be perturbed values and are not directly comparable with the harmonic wavenumbers derived from theoretical equilibrium structures. As an indicator, a gap in the PES should occur, where the baseline is re-established, before a succeeding state is regarded as unperturbed.…”

Section: Discussionmentioning

confidence: 99%

The ionic states of difluoromethane: A reappraisal of the low energy photoelectron spectrum including ab initio configuration interaction computations

Palmer

Biczysko

Baiardi

et al. 2017

The Journal of Chemical Physics

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A new synchrotron-based study of the photoelectron spectrum (PES) of difluoromethane is interpreted by an ab initio analysis of the ionic states, which includes Franck-Condon (FC) factors. Double differentiation of the spectrum leads to significant spectral sharpening; the vibrational structure observed is now measured with greater accuracy than in previous studies. Several electronic structure methods are used, including equation of motion coupled cluster calculations with single and double excitations (EOM-CCSD), its ionization potential variant EOM-IP-CCSD, 4th order Møller-Plesset perturbation theory (MP4SDQ) configuration interaction (CI), and complete active space self-consistent-field (CASSCF) methods. The adiabatic ionization energies (AIEs) confirm the assignments as band I, one state 1B (12.671 eV); band II, three states, 1B (14.259) < 1A (15.030) < 1A (15.478 eV); and band III, three states, 2B (18.055) < 2A (18.257) < 2B (18.808 eV). The three ionizations in each of the bands II and III lead to selective line broadening of the PES structure, which is attributed to vibronic overlap. The apparent lack of a vibrational structure attributable to both the 1A and 2A states in the PES arises from line broadening with the preceding states 1B and 2B, respectively. Although these A states clearly overlap with their adjacent higher IE, some vibrational structure is observed on the higher IE. The effects of vibronic coupling are evident since the observed structure does not fit closely with the calculated Born-Oppenheimer FC profiles. Correlation of the lowest group of four AIEs in the PES of other members of the CHX group, where X = F, Cl, Br, and I, clearly indicate these effects are more general.

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Section: Discussionmentioning

confidence: 99%

The ionic states of difluoromethane: A reappraisal of the low energy photoelectron spectrum including ab initio configuration interaction computations

Palmer

Biczysko

Baiardi

et al. 2017

The Journal of Chemical Physics

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“…This has made the rotation-vibration spectra of much more complex molecules accessible to the full analysis of the rotational-vibrational fine structure and the frontier in this area of research is moving toward even larger polyatomic molecules. Several articles in this handbook discuss these experimental developments (see, for instance, : High-resolution Fourier Transform Infrared Spectroscopy, Snels et al 2011 In parallel to the experimental developments, there has been great progress in the theoretical understanding of the quantum mechanics of molecules on the basis of quantum chemical ab initio theory as well as quantum dynamics in general (see Yamaguchi and Boudon et al 2011: Spherical Top Theory and Molecular Spectra, Köppel et al 2011: Theory of the Jahn-Teller Effect and Field et al 2011: Effective Hamiltonians for Electronic Fine Structure and Polyatomic Vibrations, this handbook). Thus, many aspects of rotation-vibration spectroscopy are covered in great detail in the individual articles of this handbook.…”

Section: Introductionmentioning

confidence: 99%

Fundamentals of Rotation–Vibration Spectra

Albert

Hollenstein

et al. 2011

Handbook of High‐resolution Spectroscopy

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We provide a survey of fundamental aspects of rotation-vibration spectra. A basic understanding of the concepts is obtained from a detailed discussion of rotation-vibration spectra of diatomic molecules with only one vibrational degree of freedom. This includes approximate and exact separation of rotation and vibration, effective spectroscopic constants, the effects of nuclear spin and statistics, and transition probabilities derived from the form of the electric dipole moment function. The underlying assumptions and accuracy of the determination of molecular structure from spectra are discussed. Polyatomic molecules show many interacting vibrational degrees of freedom. Energy levels and spectra are discussed on the basis of normal coordinates and effective Hamiltonians of interacting levels in Fermi resonance, and in more complex resonance polyads arising from anharmonic potential functions. The resulting time-dependent dynamics of intramolecular energy flow is introduced as well. Effective Hamiltonians for interacting rotation-vibration levels are derived and applied to the practical treatment of complex spectra. Currently available computer programs aiding assignment and analysis are outlined.

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“…Special cases characterized by a high molecular symmetry, such as the "Renner-Teller" and "Jahn-Teller (JT) effects" are particularly interesting because they enable one to study the vibronic interactions in detail, thanks to symmetry selection rules. Comprehensive theories of vibronic coupling have been formulated (see Köppel et al 2011: angular momentum about the axis as shown in Figure 28. The two angular momenta couple to form a total vibronic angular momentum ± K with K = | ± Λ ± |.…”

Section: Vibronic Coupling: the Renner-teller And Jahn-teller Effectsmentioning

confidence: 99%

“…] and thus particularly interesting. We refer to Section 2.3.6, Köppel et al 2011: Theory of the Jahn-Teller Effect, this handbook and also to the bibliography, for more comprehensive and exhaustive treatments of the JT effect.…”

Section: Electronic Transitions and The Jahn-teller Effectmentioning

confidence: 99%

“…More advanced material is presented in other articles of this handbook: The determination of potential energy surfaces and rovibronic energy levels of polyatomic molecules by ab initio quantum chemical methods is the object of Yamaguchi and Schaefer 2011: Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy, Tew et al 2011: Ab Initio Theory for Accurate Spectroscopic Constants and Molecular Properties, Breidung Callegari and Ernst 2011: Helium Droplets as Nanocryostats for Molecular Spectroscopy-from the Vacuum Ultraviolet to the Microwave Regime and Eikema and Ubachs 2011: Precision Laser Spectroscopy in the Extreme Ultraviolet, this handbook. The Jahn-Teller (JT) effect and nonadiabatic effects in manifolds of near-degenerate electronic states are treated in Köppel et al 2011: Theory of the Jahn-Teller Effect, this handbook, the treatment of fine structure in electronically excited states using effective Hamiltonians is the subject of Field et al 2011: Effective Hamiltonians for Electronic Fine Structure and Polyatomic Vibrations, this handbook, and studies of ultrafast electronic processes taking place on the (sub)femtosecond timescale are reviewed in Wörner and Corkum 2011: Attosecond Spectroscopy, this handbook. The use of photoelectron spectroscopy to study the electronic states of molecular cations is described by : High-resolution Photoelectron Spectroscopy, this handbook.…”

Section: Introductionmentioning

confidence: 99%

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Fundamentals of Electronic Spectroscopy

Wörner

Merkt

2011

Handbook of High‐resolution Spectroscopy

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The basic principles of electronic spectroscopy of atoms and molecules in the gas phase are presented. In the first part, the elementary concepts necessary to describe the electronic structure of atoms, diatomic molecules, and polyatomic molecules are introduced in a systematic manner, with an effort to classify the different interactions (electrostatic, spin–orbit, hyperfine) and types of motions (electronic, vibrational, rotational), which determine the energy level structures. In the second part, electronic transitions are discussed, with their spin‐rovibrational structures. Examples ranging from the simple band structure of \documentclass{article}\usepackage{amsmath}\usepackage{amssymb}\usepackage{amsbsy}\pagestyle{empty}\begin{document}$\rm{\Sigma}^{+}_{{{\rm u}}}\leftarrow \rm{\Sigma}_{{{\rm g}}}^{+}$\end{document} electronic transitions of homonuclear diatomic molecules to the highly complex band structure of polyatomic molecules subject to strong vibronic interactions are used to illustrate the richness of electronic spectra.

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Theory of the Jahn–Teller Effect

Cited by 15 publications

References 113 publications

The ionic states of difluoromethane: A reappraisal of the low energy photoelectron spectrum including ab initio configuration interaction computations

The ionic states of difluoromethane: A reappraisal of the low energy photoelectron spectrum including ab initio configuration interaction computations

Fundamentals of Rotation–Vibration Spectra

Fundamentals of Electronic Spectroscopy

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