Dipole moment allowed transition

It is apparent from Eq. (106) that transitions from the state 0,1V) to the dressed states of the manifold below are allowed only if the dipole moments are not parallel. The transitions occur with significantly reduced rates, proportional to (1 — cosO), giving very narrow lines when 0 0°. For parallel dipole moments the transitions to the state 0,N) are allowed from the dressed states of the manifold above, but are forbidden to the states of the manifold below. Therefore, the state 0, N) is a trapping state such that the population can flow into this state, but cannot leave it resulting in the disappearance of the fluorescence from the driven atom. The nonzero transition rates to the state 10,1V) are proportional to a and are allowed only when A 0. Otherwise, for A = 0, the state 0,1V) is completely decoupled from the remaining dressed states. In this case the three-level system reduces to that equivalent to a two-level atom. 

The assessment of the oscillator strengths for electronically allowed bands is quite straightforward all one need do is compute the transition dipole moment or transition probability, e[Pg.242]

Explain in your own words why electronic transitions are considered dipole-moment allowed. 

For two states that have a nonzero transition dipole moment, a transition between them is predicted to occur with the absorption or emission of a photon. Such a transition is called an allowed transition. A transition between two states that have a zero transition dipole moment is predicted not to occur, and is called a forbidden transition. A mle that tells which transitions are allowed is called a selection rule. The selection rules that we give in this chapter are generally obtained with approximate wave functions using first-order perturbation theory. Most of the selection rules are therefore not exactly obeyed. Forbidden transitions frequently do occur, but generally with lower probabilities than allowed transitions. 

The intensity of the band depends on the probability of the absorption, that is to say of the interaction between the incident radiation and the electrons of the system. The excitation of a molecule changes its electronic distribution and this gives rise to a dipole moment connected with the transition itself, that is proportional to its probability. A high absorption of light is possible for transitions with an high probability, that is to say with transitions that induce high variations in the dipole moment. These transitions are called allowed while low probability transitions are called forbidden and they present low absorptions values. 

If one of the components of this electronic transition moment is non-zero, the electronic transition is said to be allowed if all components are zero it is said to be forbidden. In the case of diatomic molecules, if the transition is forbidden it is usually not observed unless as a very weak band occurring by magnetic dipole or electric quadnipole interactions. In polyatomic molecules forbidden electronic transitions are still often observed, but they are usually weak in comparison with allowed transitions. 

Equation (6.8), to (d /dx)g. Figure 6.1 shows how the magnitude /r of the dipole moment varies with intemuclear distance in a typical heteronuclear diatomic molecule. Obviously, /r 0 when r 0 and the nuclei coalesce. For neutral diatomics, /r 0 when r qg because the molecule dissociates into neutral atoms. Therefore, between r = 0 and r = oo there must be a maximum value of /r. Figure 6.1 has been drawn with this maximum at r < Tg, giving a negative slope d/r/dr at r. If the maximum were at r > Tg there would be a positive slope at r. It is possible that the maximum is at r, in which case d/r/dr = 0 at Tg and the Av = transitions, although allowed, would have zero intensity. 

For vibrational transitions to be allowed in the infrared specttum there is an additional requirement that there must be an accompanying change of dipole moment and, in the... 

In the case of H2O it is easy to see from the form of the normal modes, shown in Figure 4.15, that all the vibrations Vj, V2 and V3 involve a change of dipole moment and are infrared active, that is w=l-0 transitions in each vibration are allowed. The transitions may be labelled Ig, 2q and 3q according to a useful, but not universal, convention for polyatomic molecules in which N, refers to a transition with lower and upper state vibrational quantum numbers v" and v, respectively, in vibration N. 

It follows from Equation (6.58) that the 1q, 2q and 3q transitions of H2O are allowed since Vj, V2 and V3 are Ui, and 2 vibrations, respectively, as Equation (4.11) shows. We had derived this result previously simply by observing that all three vibrations involve a changing dipole moment, but the rules of Equation (6.57) enable us to derive selection rules for overtone and combination transitions as well. 

Figure 5 shows a collection of S j -S0 R2PI spectra near the origin. The weak bands at low frequency are pure torsional transitions. We can extract the barrier height and the absolute phase of the torsional potential in S, from the frequencies and intensities of these bands. The bands labeled m7, wIq+, and are forbidden in the sense that they do not preserve torsional symmetry. In the usual approximation that the electronic transition dipole moment is independent of torsion-vibrational coordinates, band intensities are proportional to an electronic factor times a torsion-vibrational overlap factor (Franck-Condon factor). These forbidden bands have Franck-Condon factors m m") 2 that are zero by symmetry. Nevertheless, they are easily observed in jet-cooled spectra. They are comparably intense in many spectra, about 1-5% of the intensity of the allowed origin band. 

In order to determine the structural factors maximizing 2PA cross section values, we analyze (8) from Sect. 1.2.1. For all cyanine-like molecules, symmetrical and asymmetrical, several distinct 2PA bands can be measured. First, the less intensive 2PA band is always connected with two-photon excitation into the main absorption band. The character of this 2PA band involves at least two dipole moments, /

symmetry forbidden for centro-symmetrical molecules, such as squaraines with C, symmetry due to A/t = 0, and only slightly allowed for polymethine dyes with C2V symmetry (A/t is small and oriented nearly perpendicular to /t01). It is important to note that a change in the permanent dipole moment under two-photon excitation into the linear absorption peak, even for asymmetrical D-a-A molecules, typically does not lead to the appearance of a 2PA band. 2PA bands under the main absorption peak are typically observed only for strongly asymmetrical molecules, for example, Styryl 1 [83], whose S0 —> Si transitions are considerably different from the corresponding transitions in symmetrical dyes and represent much broader, less intense, and blue-shifted bands. Thus, for typical cyanine-like molecules, both symmetrical and asymmetrical, with strong and relatively narrow, S (I > S) transitions, we observe... 

Experimental plot Ahv"/ versus/(fio, oj allows to calculate with (20) a change of dipole moments zip during electronic transition. Figure 8 presents such plot for... 

Excited states formed by light absorption are governed by (dipole) selection rules. Two selection rules derive from parity and spin considerations. Atoms and molecules with a center of symmetry must have wavefunctions that are either symmetric (g) or antisymmetric (u). Since the dipole moment operator is of odd parity, allowed transitions must relate states of different parity thus, u—g is allowed, but not u—u or g—g. Similarly, allowed transitions must connect states of the same multiplicity—that is, singlet—singlet, triplet-triplet, and so on. The parity selection rule is strictly obeyed for atoms and molecules of high symmetry. In molecules of low symmetry, it tends to break down gradually however,... 

Detection of hydrogen is a particularly important problem for astrochemists because to a first approximation all visible matter is hydrogen. The hydrogen molecule is the most abundant molecule in the Universe but it presents considerable detection problems due to its structure and hence spectroscopy. Hydrogen does not possess a permanent dipole moment and so there is no allowed rotation or vibration spectrum and all electronic spectrum transitions are in the UV and blocked by the atmosphere. The launch of the far-UV telescope will allow the detection of H2 directly but up to now its concentration has been inferred from other measurements. The problem of detecting the H atom, however, has been solved using a transition buried deep in the hyperflne structure of the atom. 



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