Electric transition dipoles

Ground to excited state Transition electric dipole moments (Au) ... 

IR absorptions involve elastic or Rayleigh45 or constant-energy scattering of light in more detail, the electric field vector E of the input light must couple with the transition electric dipole moment fi,f as E fi,f. If E Lp,if, then no IR transition is seen. Allowed IR transitions require that the transition moment vector fii be nonzero—i.e., that is, that the static electric dipole moment fi of the molecule change during the IR absorption. 

The Ta <— So transition moments to particular spin sublevels for the three lowest triplet states of the ozone molecule, 3B2,3 A2 and 3B, were calculated by the MCQR method in ref. [70] using CASSCF wave functions. Table 7 recapitulates results for electric dipole radiative activity of different S-T transitions in ozone [70]. The type of information gained form this kind of spin-orbit response calculations are viz. transition electric dipole moments and oscillator strengths for each spin sublevel T , their polarization directions (7), radiative lifetimes (r ) and excitation energies (En). The most prominent features of the Chappuis band are reproduced in calculations, which simulate the photodynamics of ozone visible absorption [78, 79]. Because the CM (M2) state cannot be responsible for the Wulf bands, the only other candidates ought to... 

The result analogous to the dynamic contribution (37) is written down immediately on substituting transition electric dipoles by and electric... 

Raman spectroscopy is complementary to the corresponding absorption process because different selection rules are involved. For an absorption of a photon to take place there must be a change in the dipole moment of the molecule in the course of the transition (a non zero transition electric dipole moment). In Raman spectroscopy, however, the requirement for scatering to occur is that there is a change in the molecular polarizability (a second rank tensor) in the course of the transition. 

The light absorption by a molecule is the result of the resonance interaction between the electric field vector of the light and the transition electric dipole of the molecule. This fact tells us that, if the orientation of the molecular electric dipole responsible for the light absorption is aligned and ordered on an electrode surface and if one can control the electric field of the light at the position of the dipole, the optical signal includes information on the molecular orientation. This allows one to estimate the molecular orientation. 

The other is the use of the Stark effect. The Stark effect arises from the interaction of transition electric dipole with the static electric field at the electrified interface, resulting in a change of the absorption spectrum. Details are given in the following two subsections. 

The Stark effect is the change of absorption spectrum of a dye molecule due to the interaction between the static electric field and the transition electric dipole. The strength of the static electric field at an electrode/solution interface at a certain condition may exceed 10 V m , which is strong enough for the Stark effect to be observed. As for the linear Stark effect, a shift in the absorption spectral band is observed and can be expressed as... 

Electrochemical Stark effect As described already in Section 2.10.2, the Stark effect is based on the interaction of the interfacial static electric field with the transition electric dipole or molecular polarizability. The Stark effect may give rise to the first (or sometimes second) derivative of the absorption spectmm, depending on the type of interaction with the electric field. It is important to note that the ER signal due to the Stark effect should have the same frequency dependence as the ac change of the static electric field insofar as orientation change does not take place simultaneously, because the Stark effect is a field effect. In fact, this has been experimentally confirmed by frequency domain analysis [82]. 

The Raman components of the scattered waves have frequencies different from, and unrelated in phase to, the incident wave, so the polarizability tensors given above must be replaced by corresponding transition tensors which take account of the different initial and final molecular states. It is possible to generalize the previous treatment by invoking a transition electric dipole moment between initial and final molecular states fs y and [9,10,12], and this leads to the following general-... 

The transition electric dipole moment in eqn [57] can be developed by invoking the Born-Oppenheimer approximation to express the total molecular wave function as a product of electronic and vibrational parts. (Rotational wave functions do not have to be included here since eqn [57] refers to an isotropic system. That is, the equation is a result of a rotational average which is equivalent to a summation over all the rotational states involved in the transition.) A general molecular state can now be expressed as the product of vibrational and electronic parts. Assuming that the initial and final electronic states are the ground state jcg). 

Let us consider the simple case of two ions, each with one excitable electronic state separated from its electronic ground state by nearly equal energy. With suitable interaction between the two electronic systems, the excitation will jump from one ion to the other before a quantum of fluorescence is emitted. The systems interact by Coulomb interactions of the Van der Waals type. Forster (1948), who first treated such a case by quantum-mechanical theory, considered the dipole-dipole interactions. He assumed that the interaction is strongest if, for both transitions, electric-dipole transitions are allowed (Forster 1960). The interaction energy (//sa) is then proportional to the inverse of the third power of the interionic distance, and the transfer probability is given by... 

In the usual discussion of optical properties, exponentials, as in Equation (II-l), are set equal to 1. This gives the relation between absorption, polarizability and transition electric dipole moments. 

As we need to know the transition electric dipole vectors and not just their dot product, we must work with oriented molecules and measure the absorption for polarized light incident along different... 

Squared transition electric dipole moments for a number of vibrational states were computed and used to evaluate the ab initio DMSs against experiment, which appeared to be reasonably good. The effect of adding the relativistic corrections was investigated. 

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