I. B. Bersuker

The Jahn—Teller Effect in Dipole (Multipole) Moments and Polarizabilities of Molecules

Publisher Summary This chapter discusses the results obtained in the applications on the concept of vibronic interactions and the investigations of electric properties of molecules, like dipole and multipole moments and polarizabilities. In the study of the electric properties of molecules, it is assumed that the electron and nuclear dynamics cannot destroy the molecular symmetry, and hence, the individual characteristics of molecules are conceptually determined by the symmetry of the nuclear framework only. This statement is based on the assumption that the charge distribution (either classical or quantic) is totally symmetric (with respect to the nuclear configuration)— that is, it transforms itself under the operations of the point symmetry group of the molecule. In the cases in which the electronic state of the molecule is nondegenerate, the preceding considerations are correct, and they remain the same in both the classical and quantum descriptions. In each of the states of the degenerate term or in their linear combinations, the charge distribution is not invariant with respect to all the operations of the assumed symmetry of the molecule. Therefore, all the conclusions based on the assumption of a totally symmetric charge distribution in the case of degeneracy become invalid. Additionally, in the case of electronic degeneracy the nuclear configuration, following the Jahn-Teller theorem, is not appropriate to the minimum of the adiabatic potential, and hence, the system is unstable with respect to nuclear displacements lowering the symmetry of the molecule.

Pseudo Jahn–Teller origin of formaldehyde molecular geometry in excited states

Abstract The pseudo Jahn–Teller effect is employed to explain the origin of the out-of-plane displacement of the oxygen atom (bending of the C–O group) in the excited singlet 1 A 2 and triplet 3 A 2 electronic states of formaldehyde which is planar in the ground state. The ground state, the excited 1 A 2 and 3 A 2 states, and several higher excited 1 B 2 and 3 B 2 states formed by one-electron MO excitations are calculated in a single-transition approximation and by including configuration interaction with single and double excitations using the GAMESS program. With these data the corresponding pseudo Jahn–Teller coupling constants and the contribution of the B 2 states to the instability of the A 2 states with respect to the oxygen out-of-plane displacements is estimated, and an explanation of both the larger instability of the triplet state as compared with the singlet state and the elongation of the C–O bond in the bent states is obtained.

A comparative study of the pseudo Jahn–Teller instability of linear molecules Ag3 and I3 and their positive and negative ions

Abstract In confirmation of the general idea of pseudo Jahn–Teller origin of instability of high-symmetry configurations of polyatomic systems that determines their geometry, a series of six molecules, Ag3n and I 3 n , n=−1,0,+1, were investigated. The electronic structure of the ground state of all the six molecules in the linear configuration was calculated by the extended-Huckel method with atomic charge and electron configuration self-consistency, while the excited state energy levels and wavefunctions were estimated in the single transition approximation. Then, the orbital vibronic constants, bare force constants and the vibronic contribution of the appropriate excited states to the instability of the linear configuration were evaluated. The obtained results show that in both series, silver and iodine, the curvature of the adiabatic potential of the linear configuration, in the direction of the bending distortions, decreases from the negative ions to the neutral atoms to the positive ions and becomes negative in the latter two cases, thus explaining the origin of the experimentally observed geometries. The numerical data give a detailed insight into: (1) the origin of the linear→bent distortions as being due to the additional covalency created by the σ–π overlap in the bent configuration; (2) the specific excited states that contribute to this process of geometry formation; and (3) the difference between the silver and iodine series.

Rayleigh and hyper-Rayleigh magnetic optical activity of molecular systems with orbital degeneracy

Linear and non-linear light scattering in static magnetic fields by molecules with orbitally degenerate ground states is investigated. The temperature dependent circular intensity difference (CID) spectrum induced by the orientational mechanism is calculated by taking into account the rotational diffusion. It is shown that the presence of degeneracy is a sufficient condition for temperature dependent CID occurrence both in Rayleigh and hyper-Rayleigh scattering; the selection rules determining the appropriate symmetry of the molecular ground states are obtained. The differences between two cases, the spin-only (Kramers) degeneracy and the orbital degeneracy, are discussed; the temperature dependent optical activity in light scattering is possible even if the antisymmetric scattering is neglected. The role of spin-orbit coupling in the generation of optical activity of molecules with G 3/2 ground terms is discussed. Examples of molecular systems are suggested, in which the new phenomena revealed in this wo...

Anomalous magnetic field-induced birefringence in molecular systems with the Jahn-Teller effect

It is shown that spherical-top molecules in orbitally degenerate states possess anomalous anisotropy of electric and magnetic properties leading to temperature-dependent birefringence induced by a static magnetic field. The Cotton-Mouton constant mC is expressed in terms of anisotropic tensors of the molecular polarizability, magnetic susceptibility, magnetic moment and magneto-electric hyperpolarizability. The resulting temperature dependence of mC is different from that (quadratic in T -1) expected without the Jahn-Teller effect. This difference is defined by introducing in this paper temperature-dependent reduction factors of electronic operators, which at low temperatures coincide with the usual ones. Reduction factors are calculated for systems with G 3/2 ground electronic terms. For these cases approximate analytical expressions are obtained taking into account the vibronic coupling with e and t 2 vibrations. Numerical estimation of the expected Cotton-Mouton constant in the case of the ReF6 molecul...

Interpretation of the indirectly induced field at nonmagnetic atoms in Fe-Y garnets

The indirectly induced magnetic fields at Sn4+ replacing Fe3+ in octahedral positions are derived in the MO LCAO [molecular orbitals by linear combinations of atomic orbitals] semiempirical approximation, with self-consistent charges on the atoms, for a part of the crystal containing Sn4+ and Fe3+ (in tetrahedral positions), the two being linked via oxygen ions. The absence of conduction is due to the very restricted overlap between the MO of the parts. The results explain the observed induced field and also predict certain possible effects, in particular unpaired spin density on other lattice ions.