Transitions electric dipole possibilities

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-... 

State I ) m the electronic ground state. In principle, other possibilities may also be conceived for the preparation step, as discussed in section A3.13.1, section A3.13.2 and section A3.13.3. In order to detemiine superposition coefficients within a realistic experimental set-up using irradiation, the following questions need to be answered (1) Wliat are the eigenstates (2) What are the electric dipole transition matrix elements (3) What is the orientation of the molecule with respect to the laboratory fixed (Imearly or circularly) polarized electric field vector of the radiation The first question requires knowledge of the potential energy surface, or... 

For many years, investigations on the electronic structure of organic radical cations in general, and of polyenes in particular, were dominated by PE spectroscopy which represented by far the most copious source of data on this subject. Consequently, attention was focussed mainly on those excited states of radical ions which can be formed by direct photoionization. However, promotion of electrons into virtual MOs of radical cations is also possible, but as the corresponding excited states cannot be attained by a one-photon process from the neutral molecule they do not manifest themselves in PE spectra. On the other hand, they can be reached by electronic excitation of the radical cations, provided that the corresponding transitions are allowed by electric-dipole selection rules. As will be shown in Section III.C, the description of such states requires an extension of the simple models used in Section n, but before going into this, we would like to discuss them in a qualitative way and give a brief account of experimental techniques used to study them. 

Provided that a transition is forbidden by an electric dipole process, it is still possible to observe absorption or emission bands induced by a magnetic dipole transition. In this case, the transition proceeds because of the interaction of the center with the magnetic field of the incident radiation. The interaction Hamiltonian is now written as // = Um B, where is the magnetic dipole moment and B is the magnetic field of the radiation. 

In this example, we will roughly estimate the order of magnitude for the intensity ratio of the electric dipole to magnetic dipole transitions. Of conrse, we will assnme that both processes are allowed (which, as shown below, is not possible for a given transition) and that the same excitation intensity is nsed. 

There are, however, certain selection rules for electric dipole transitions which considerably reduce the number of possible transitions. They are extensively discussed and proved in reference and for diatomic molecules consist essentially of the following three rules ... 

The crystal field model may also provide a calciflation scheme for the transition probabilities between levels perturbed by the crystal field. It is so called weak crystal field approximation. In this case the crystal field has little effect on the total Hamiltonian and it is regarded as a perturbation of the energy levels of the free ion. Judd and Ofelt, who showed that the odd terms in the crystal field expansion might connect the 4/ configuration with the 5d and 5g configurations, made such calculations. The result of the calculation for the oscillator strength, due to a forced electric dipole transition between the two states makes it possible to calculate the intensities of the lines due to forced electric dipole transitions. 

The other model is also principally possible. Europium initially enters the barite lattice as Eu" ", which oxidizes to Eu + at 700 °C. The relatively small difference between the Ba " and the Eu" ionic radii (1.5 and 1.7 A) makes this substitution possible. The luminescence of Eu was still not observed in minerals, but is known in luminofors (Gorobets et al. 1968). Eu has 6s electron configuration and the mostly probable are electric-dipole electron transitions 6s -6p, taking place between uneven and even 2,3,4 Ps,4,5 terms. 

As stated in an earlier paragraph, the sharp emission and absorption lines observed in the trivalent rare earths correspond to/->/transitions, that is, between free ion states of the same parity. Since the electric-dipole operator has odd parity,/->/matrix elements of it are identically zero in the free ion. On the other hand, however, because the magnetic-dipole operator has even parity, its matrix elements may connect states of the same parity. It is also easily shown that electric quadrupole, and other higher multipole transitions are possible. 

If the rare-earth ion is immersed in a crystal field, the perfect symmetry of the free ion is destroyed, leaving parity in some cases not quite a good quantum number. Under this circumstance, electric-dipole transitions become quite possible. It was Van Vleck (25), in his classic 1937 paper The Puzzle of Rare Earth Spectra, who first pointed out that the weak electric dipole emission was due to this mixing of states of opposite parity by the crystal field. 

It is possible to distinguish the electric dipole and electric quadrupole transitions from the magnetic dipole ones using the following selection rules (for a detailed treatment of the selection rules see ref. 556—560). 

While the fine structure transitions are inherently magnetic dipole transitions, it is in fact easier to take advantage of the large A = 1 electric dipole matrix elements and drive the transitions by the electric resonance technique, commonly used to study transitions in polar molecules.37 In the presence of a small static field of 1 V/cm in the z direction the Na ndy fine structure states acquire a small amount of nf character, and it is possible to drive electric dipole transitions between them at a Rabi frequency of 1 MHz with an additional rf field of 1 V/cm. 

Only one of these (Elu) contains a representation to which the electric dipole moment operator belongs. Therefore only one of the three possible transitions is symmetry allowed, and for this one the radiation must be polarized in the (x, v) plane (see Table 5.2). 

With infrared reflection absorption spectroscopy (IRRAS), it is possible to obtain information about the orientation of enzyme molecules adsorbed on flat metal surfaces (3,4). Electric dipole-transition moments oriented perpendicular to a flat metal surface show enhanced IR absorbance. IR bands due to vibrations of groups with transition moments oriented parallel to the surface are not observed. The IR-beam component which is polarized perpendicular to the plane of incidence (parallel to the surface) contains no information and can be eliminated by using a polarizer. 

Crystal field, or d-d, transitions are defined as transitions from levels that are exclusively perturbed d orbitals to levels of the same type. In other words, the electron is originally localized at the central metal ion and remains so in the excited state. When the system has ( symmetry, Laporte s rule says that an electric-dipole allowed transition must be between a g state and an u state, i.e., u - g. Since all the crystal field electronic states are gerade ( g ), no electric-dipole allowed transitions are possible. In short, all d-d transitions are symmetry forbidden and hence have low intensities. The fact that the d-d transitions are observed at all is due to the interaction between the electronic motion and the molecular vibration. We will discuss this (vibronic) interaction later (Section 8.10). 

Six types of spectra are theoretically possible in minerals of the orthorhombic, monoclinic and triclinic systems (McClure, 1959). However, for electric dipole transitions only three spectra are usually distinguished. These are the a, P and y spectra obtained when light is polarized along each of the three indicatrix axes, which in orthorhombic minerals such as olivine and orthopyroxene correspond to the three crystallographic axes. The majority of the spectra of minerals described in chapters 4 and 5 consist of polarized spectra measured in the three mutually perpendicular directions corresponding to a, P and y polarized light... 

For the evaluation of probabilities for spin-forbidden electric dipole transitions, the length form is appropriate. The velocity form can be made equivalent by adding spin-dependent terms to the momentum operator. A sum-over-states expansion is slowly convergent and ought to be avoided, if possible. Variational perturbation theory and the use of spin-orbit Cl expansions are conventional alternatives to elegant and more recent response theory approaches. 

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