Selection rules electric dipole

A very weak peak at 348 mn is the 4 origin. Since the upper state here has two quanta of v, its vibrational syimnetry is A and the vibronic syimnetry is so it is forbidden by electric dipole selection rules. It is actually observed here due to a magnetic dipole transition [21]. By magnetic dipole selection rules the A2- A, electronic transition is allowed for light with its magnetic field polarized in the z direction. It is seen here as having about 1 % of the intensity of the syimnetry-forbidden electric dipole transition made allowed by... 

The electric dipole selection rule for a hannonic oscillator is Av = 1. Because real molecules are not hannonic, transitions with Av > 1 are weakly allowed, with Av = 2 being more allowed than Av = 3 and so on. There are other selection niles for quadnipole and magnetic dipole transitions, but those transitions are six to eight orders of magnitude weaker than electric dipole transitions, and we will therefore not concern ourselves with them. 

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. 

Therefore, we can establish the electric dipole selection rules given in Table 7.8, and then make a proper assignment for the emission peaks of Sm + ions observed in the experimental emission spectmm of Fignre 7.9. 

As an example, consider the electric-dipole selection rules for a particle of charge q in a one-dimensional box. We have... 

Combining these results, we have the hydrogen-atom electric-dipole selection rules ... 

To investigate the spectra of diatomic molecules, we need the selection rules for radiative transitions. We now investigate the electric-dipole selection rules for transitions between vibration-rotation levels belonging to the same 2 electronic state. (Transitions in which the electronic state changes will be considered in Chapter 7.)... 

Recall the selection rule (Section 3.3) that parity changes in an electric-dipole transition. Hence we have the electric-dipole selection rule that forbids a transition between two + or two — rotational levels. This rule is symbolized by... 

The electric-dipole selection rules for pure-rotation transitions will be considered in Section 6.5. Here we will simply give the results. 

We now consider many-electron atoms. We will assume Russell-Saunders coupling, so that an atomic state can be characterized by total electronic orbital and spin angular-momentum quantum numbers L and S, and total electronic angular-momentum quantum numbers J and Mj. (See Section 1.17.) The electric-dipole selection rules for L, J, and Mj can be shown to be (Bethe and Jackiw, p. 224)... 

We now consider the electric-dipole selection rules for radiative transitions between energy levels of the same electronic state of a polyatomic molecule. The electric-dipole transition moment is (4.91), which becomes... 

An interesting development in molecular rotational relaxation has been the microwave double-resonance method176-178. The technique permits the exploration of the fine detail of the processes which occur in collisions of polyatomic molecules, and results for a number of symmetric tops have been reported. For example, Oka has described experiments on NH3 in which inversion doublets for selected J values were pumped by high microwave power. Pumping disturbs the population of the inversion doublet, and also that of other doublets which are populated from the original pair by collision processes. By absorption measurements of other inversion doublets with steady state irradiation, Oka has shown that in NH3/NH3 collisions, transitions which are allowed by the electric dipole selection rules (A/ = 0, 1, + - —) are preferred. Oka s analysis indicates that relaxation is most favourable in collision with molecules having similar J values, which are termed rotational resonances (R-R transfer). For example the process... 

The selection rules are restrictions imposed on the quantum transitions, because of the laws of conservation of angular momentum and parity [59], In the case of IR spectroscopy, within the frame of the harmonic approximation, the applicable rules are the electric dipole selection rules. That is, when the expression in Equation 4.19 has a finite value, the transition is allowed, and when this expression is zero the transition is forbidden. In the Raman case, when one of the integrals given by Equation 4.23 is different from zero, the normal vibration associated is Raman-active. 

The transition probability Rnm 2 is related to selection rules in spectroscopy it is zero for a forbidden transition and non-zero for an allowed transition. By forbidden or allowed we shall mostly be referring to electric dipole selection rules (i.e. to transitions occurring through interaction with the electric vector of the radiation). 

When M is an atom the total change in angular momentum for the process M + hv —> M+ + e must obey the electric dipole selection rule AT = 1 (see Equation 7.21), but the photoelectron can take away any amount of momentum. If, for example, the electron removed is from a d orbital ( = 2) of M it carries away one or three quanta of angular momentum depending on whether A = —1 or +1, respectively. The wave function of a free electron can be described, in general, as a mixture of s, p, d,f,... wave functions but, in this case, the ejected electron has just p and/ character. 

Because two-photon selection rules are different from one-photon (electric dipole) selection rules, two-photon transitions may allow access to states which otherwise could not be reached. We shall consider just one example in detail - a two-photon electronic absorption spectrum. 

Both the alAg — X3I and the b1 it — X3I transitions are extremely weak. The selection rules, discussed in Section 7.2.3, show that both transitions violate the A,S = 0 and the g< 1 >g selection rules. In addition, the a X transition violates the A A = 0, 1 selection rule and the b—Xtransition the + < 1 >— selection rule. Spin-orbit interaction breaks down the AS = 0 selection rule to some extent. Magnetic dipole selection rules, as opposed to the electric dipole selection rules of Section 7.2.3, allow both the a-X and b-X transitions but only weakly. 

Show that the 10.6 pm and 9.6 pm radiation from a C02 laser is due to transitions allowed by electric dipole selection rules. 

STATIC ELECTRIC-DIPOLE SELECTION RULES FOR THE ONE-ELECTRON ATOM... 

---