E. Haller

On the statistical behaviour of molecular vibronic energy levels

Abstract Electronic spectra of polyatomic molecules often exhibit a high density of complicated energy levels, making a detailed analysis of the individual levels unfavourable. In these cases, statistical tests provide an appropriate means for analysing the spectra. Fluctuation measures are presented and evaluated for calculated and experimental molecular spectra as examples. The results are compared with the predictions of random matrix theory.

The visible absorption spectrum of NO2: A three-mode nuclear dynamics investigation

Abstract The vibronic band origins of the visible absorption spectrum of NO2 are calculated theoretically with the aid of a simple model Hamiltonian for the coupled electronic and vibrational motions. Including all three vibrational modes in the calculation and using ab initio values of the relevant parameters, we obtain satisfactory qualitative agreement with experiment. In particular, the observed high density and irregular intensity distribution of the band origins is reproduced correctly by the calculation. The present results confirm unambiguosly that the anomalous vibronic structure of the 2 B 2 ← 2 A 1 transition is caused by strong nonadiabatic interactions between the 2B2 and 2A1 electronic states of NO2. They also show that simple deconvolution procedures, which are often used to deperturb irregular spectra, are not applicable to the 2 B 2 ← 2 A 1 transition of NO2. To further explore the strength of the nonadiabatic effects in NO2, we calculate the mixing of the different electronic species in the vibronic eigenstates and compare it to several relevant experimental quantities.

Multimode Jahn–Teller and pseudo‐Jahn–Teller effects in BF+3

The ionic states of BF3 exhibit striking vibronic coupling effects. These effects are investigated using ab initio calculated ionization energies and vibronic coupling constants. The two Jahn–Teller active modes show interference effects in all bands of E symmetry. In the 2A1′ ionic state single quanta of a degenerate vibration are excited. They borrow their intensities from the adjacent 2E′ state by means of a pseudo‐Jahn–Teller interaction. The symmetry of BF+3 in its nondegenerate ground state is predicted to be lowered due to two‐mode pseudo‐Jahn–Teller interaction with the second excited state. This interaction is surprisingly strong and leads to an interesting vibronic structure. The vibrational fine structure in all experimental spectra is reproduced satisfactorily. The earlier discrepancies in assigning the three lowest lying ionic states are explained.

The E⊗(ϵ + ϵ) Jahn-Teller effect

The interaction of an electronic E-term and two degenerate normal vibrations of the same symmetry, leading to the so-called two-mode E⊗(ϵ + ϵ) Jahn-Teller effect, is investigated. Absorption spectra are calculated numerically via the Lanczos algorithm and are shown to exhibit new interesting structures. These two-mode spectra are seen to differ markedly from the spectra obtained by simply convoluting the constituting one-mode E⊗ϵ Jahn-Teller spectra. To classify the spectra we introduce, in addition to the coupling strengths of the individual normal vibrations, a hopping parameter which serves as a measure for the interaction of the normal vibrations via the electronic state. An effective one-mode E⊗ϵ Jahn-Teller hamiltonian is introduced which reproduces the envelope of the two-mode Jahn-Teller spectrum to a high accuracy.

Jahn-Teller effect for very strong coupling

The strong coupling limit of the E⊗ζ Jahn-Teller effect is investigated. The high energy part of the JT band shape is shown to exhibit an oscillatory behaviour in this limit. The oscillations are interpreted by adiabatic and Franck-Condon calculations as arising from the vibrational levels of the upper potential energy surface. A new measure of the coupling strength is proposed which is related to the excitation strength of these levels. It is shown to govern the approach of the exact band shape to the semiclassical limit.

Two-mode jahn-teller effect in nh+3

Abstract The two-mode E ⊗ (ϵ + ϵ) Jahn-Teller effect in NH+3 is investigated theoretically. Using ab initio coupling constants, it is shown that the inclusion of the interaction between the degenerate stretching and bending vibrational modes is essential for understanding the experimental findings. An effective single-mode Jann-Teller hamiltonian is introduced to simulate the more complicated two-mode problem. Although such a hamiltonian cannot be expected to reproduce the details of the vibrational structure, it is generally found to reproduce the band shape of unresolved spectra most accurately.

Effective single-mode Hamiltonian for the calculation of multi-mode Jahn-Teller band shapes

Abstract The set of transformations is investigated which eliminates the linear coupling terms of ( N -1)-modes in the N -mode Jahn-Teller Hamiltonian. It is shown that the remaining single-mode Jahn-Teller Hamiltonian leads to highly accurate absorption band shapes. A comparison is made with the band shapes determined with the single-mode effective Hamiltonian known in the literature as the cluster Hamiltonian.

On the connection between irregular trajectories and the distribution of quantum level spacings

For a model system the distribution of spacings between adjacent levels in specified intervals of the energy spectrum is compared with a semiclassical distribution. This distribution (Berry and Robnik, 1984) depends on the size of the phase space volume filled with irregular trajectories. Good agreement is found between quantal and semiclassical spacing distributions. In particular, the transition from regularity to irregularity observed in the quantum calculation (Haller et al., 1984) is well reproduced by the semiclassical results.

Energy Level Statistics of Coupled Oscillators

We investigate the manifestation of classical chaos in the statistics of quantum energy levels of coupled oscillators. On variation of the coupling strength or energy these systems exhibit a transition from regular to fully chaotic classical motion which is reflected by a corresponding transition of quantum spectral fluctuations. Regular classical motion is associated with an uncorrelated level sequence, and chaotic motion is associated with spectral statistics of random matrix ensembles. To characterize spectral fluctuations we use the distribution of spacings between adjacent energy levels and the spectral rigidity (Δ3 statistic). These quantities measure short and long range spectral fluctuations, respectively, and are found to respond in a different way to the underlying classical motion.