Mise au point. Theorie des effets de couplage vibronique multimodes. Probleme a 2 etats. Couplage vibronique mettant en jeu des modes et des etats degeneres. Effets du couplage vibronique multimodes en spectroscopie. Comportement statistique des niveaux d'energie vibroniques. Intersections coniques et evolution temporelle de la fluorescence

Multimode molecular dynamics beyond the Born-Oppenheimer approximation

In this paper we consider a theory for intramolecular radiationless transitions in an isolated molecule. The Born–Oppenheimer zero‐order excited states are not pure in view of configuration interaction between nearly degenerate zero‐order states, leading to the broadening of the excited state, the line shape being Lorentzian. The optically excited state can be described in terms of a superposition of molecular eigenstates, and the resulting wavefunction exhibits an exponential nonradiative decay. The linewidth and the radiationless lifetime are expressed in terms of a single molecular parameter, that is the square of the interaction energy between the zero‐order state and the manifold of all vibronic states located within one energy unit around that state. The validity criteria for the occurrence of an unimolecular radiationless transition and for exponential decay in an isolated molecule are derived. Provided that the density of vibrational states is large enough (i.e., exceeds the reciprocal of the interaction matrix element) radiationless transitions are expected to take place. The gross effects of molecular structure on the relevant molecular parameters are discussed.

Intramolecular Radiationless Transitions

Multimode Molecular Dynamics Beyond the Born‐Oppenheimer Approximation

It is shown that the dynamical Jahn-Teller effect in a complex having orbital degeneracy may partially quench spin-orbit interaction, the orbital parts of the Zeeman and hyperfine interactions, and other orbital operators governing response to perturbations such as strain or applied electric fields. Such dynamical quenching thus decreases the value of orbital reduction factors usually attributed in paramagnetic resonance studies to covalent bonding, without necessarily causing anisotropy in the spectrum of an individual complex. The dynamical Jahn-Teller effect may also substantially enhance various second-order effects. Such dynamic effects thus may make important changes in the parameters of the spin Hamiltonian without changing its symmetry. It is shown that the dynamical Jahn-Teller effect accounts qualitatively for unusual features in the spectra of interstitial transition-metal ions ${\mathrm{Cr}}^{0}$, ${\mathrm{Mn}}^{+}$, ${\mathrm{Mn}}^{0}$, and ${\mathrm{Fe}}^{+}$ in silicon and that it is probably of importance equal to or greater than that of covalent bonding in the interpretation of the spectrum of ${\mathrm{Fe}}^{2+}$ in MgO and CaO. A mathematical analysis of the dynamical effects is given for an orbital triplet state in interaction with a doublet or triplet vibrational mode, and some results are given also when the coupling is with the phonon continuum.

Dynamical Jahn-Teller Effect in Paramagnetic Resonance Spectra: Orbital Reduction Factors and Partial Quenching of Spin-Orbit Interaction

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

This paper examines the vibronic energy levels of a symmetrical non-linear molecule in a spatially doubly degenerate electronic state which is split in first order by a doubly degenerate vibrational mode. The vibronic levels are classified by a quantum number, which in certain cases is formally related to the combined angular momentum of electronic and vibrational motion, and numerical values are obtained for the energies of these levels as functions of this quantum number and a dimensionless parameter measuring the magnitude of the electronic-vibrational coupling. It is shown that the selection rules for transitions from these vibronic levels to those of a non-degenerate electronic state allow changes in vibrational energy of any integral number of quanta, as though the Jahn-Teller effect were equivalent to a distortion which makes allowed vibrational transitions which would otherwise be forbidden. Numerical values are given for the oscillator strengths of vibronic absorption or emission bands involving transitions between a Jahn-Teller distorted state and an electronically non-degenerate state. It is found that in transitions from the latter to the former the vibrational structure of the electronic band exhibits two intensity maxima if the distortion is large.

R. A. Sack

Papers

Studies of the Jahn-Teller effect .II. The dynamical problem