Dipole polarizability transition moments

The symbol p is a transition moment operator, of which there are various kinds, namely, those corresponding to changes in electric or magnetic dipoles, higher electric or magnetic multipoles, or polarizability tensors. 

Dispersion interactions increase with the polarizability of the two molecules. The optical properties enter in the form of the excitation frequencies. Expression (6.9) only considers one term of a series over dipole transition moments. Usually, however, this term is by far the most dominant one. 

In the complexes [Ln(H20)y]3+, [Ln(oda)3]3, the dynamic polarization first-order electric dipole transition moment is minimized by negative interference due to the out-of-phase relation between the contributions of the [ML3] and [ML6] ligand sets [109,110]. For [Ln(oda)3]3 and other D3 complexes, only the anisotropic polarizability contributions are non-zero for AMj = 1 transitions in the [Eu(H20) ]3+ and [Eu(oda)3]3 complexes the contribution of the cross-term to the dipole strength of the 7Fo —> 5D2 and5 Do — 7F2 transitions has a magnitude comparable with that of the dominant crystal field or dynamic polarization contribution [111]. 

The dipole polarizability can be used in place of the dipole moment function, and this will lead to Raman intensities. Likewise, one can compute electrical quadrupole and higher multipole transition moments if these are of interest. 

X specifies the experimental angle between the external electric field and the light polarization at frequency p, and h is Planck s constant. The scalars and S, and the vectors R and R are functions of the transition moment polarizability and hyperpolarizability tensors, m is a unit vector oriented along the transition dipole moment and F is the internal electric field at the molecule, which depends on the externally applied field such that... 

An atom or molecule distorts under the action of an external field, the measure of distortion being expressed through a second-order electrical quantity called the (dipole) polarizability a, which we define in terms of a transition moment /q from state i//0 to t/q and an excitation energy s, as ... 

The electrostatic effects associated with the relative orientation of the chromophores show a specific connection with the corresponding electronic excited states and dipole transition moments that can, in turn, be related to changes in the hyperpolarizabilities via summation-over-states (SOS) expressions [1 3]. When the molecules interact, the electronic excited states split. In the case of a collinear arrangement, the intensities (oscillator strengths) are shifted to the red, that is, to the states of lower energies, whereas for a side by side and parallel configuration, the intensities are shifted to the blue. Furthermore, since the excited state polarizabilities are usually larger than the... 

Induction forces, on the other hand, may be responsible for the enchanced V y intensity. The squared transition moment expected for the dimer with two independent ethylene partners is twice that of the monomer. Inspection of Table 1 shows that the observed probability is somewhat higher than this. Vibration in each molecule induces oscillations in the polarizable charge distribution of the partner, leading to an enhanced dipole moment derivative. Numerical results for bound to a polarizable atom show that this enhancement is of the same magnitude as that observed (17). 

Here SI is the matrix of the dipole transition strength which is spin and number conserving.127 Therefore, the poles of (114) provide the singlet-singlet excitation energies and the corresponding residues are the transition moments. The static ( -independent) and dynamic ( -dependent) electric dipole polarizabilities per unit cell are then given by... 

---