Selection rules electronic

There are three important selection rules for electronic transitions owing to the properties of the electronic dipole operator, pe- The electronic dipole operator is defined as 

The electric dipole operator conserves total spin, so transitions only occur between states in the same spin manifold. 

The electric dipole operator is antisymmetric with respect to the inversion operator, i, and thus it connects states of opposite inversion symmetry. To see this note that. 

As is the case for vibrational transitions, electronic transitions are mostly of the electric dipole type for which the selection rules are as follows. 

As in atoms, the selection rule breaks down as the nuclear charge increases. For example, triplet singlet transitions are strictly forbidden in H2 but in CO the o I — X]Z+ transition7 is observed weakly. 

6 As for all other types of transitions, the upper state is given first and the lower state second. 

This is relevant only for 2. — 2. transitions so that only Z+ — Z1 and Z — Z transitions are allowed. Note that this selection rule is the opposite of the vibration-rotation selection rule of Equation (6.73). 

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We now turn to electronic selection rules for syimnetrical nonlinear molecules. The procedure here is to examme the structure of a molecule to detennine what synnnetry operations exist which will leave the molecular framework in an equivalent configuration. Then one looks at the various possible point groups to see what group would consist of those particular operations. The character table for that group will then pennit one to classify electronic states by symmetry and to work out the selection rules. Character tables for all relevant groups can be found in many books on spectroscopy or group theory. Ftere we will only pick one very sunple point group called 2 and look at some simple examples to illustrate the method. 

Most stable polyatomic molecules whose absorption intensities are easily studied have filled-shell, totally synuuetric, singlet ground states. For absorption spectra starting from the ground state the electronic selection rules become simple transitions are allowed to excited singlet states having synuuetries the same as one of the coordinate axes, v, y or z. Other transitions should be relatively weak. 

The selection rule for vibronic states is then straightforward. It is obtained by exactly the same procedure as described above for the electronic selection rules. In particular, the lowest vibrational level of the ground electronic state of most stable polyatomic molecules will be totally synnnetric. Transitions originating in that vibronic level must go to an excited state vibronic level whose synnnetry is the same as one of the coordinates, v, y, or z. 

Note that these are the opposite of the electronic selection rules in Equation (7.70). 

In the case of atoms (Section 7.1) a sufficient number of quantum numbers is available for us to be able to express electronic selection rules entirely in terms of these quantum numbers. For diatomic molecules (Section 7.2.3) we require, in addition to the quantum numbers available, one or, for homonuclear diatomics, two symmetry properties (-F, — and g, u) of the electronic wave function to obtain selection rules. 

For the orbital parts of the electronic wave functions of two electronic states the selection rules depend entirely on symmetry properties. [In fact, the electronic selection rules can also be obtained, from symmetry arguments only, for diatomic molecules and atoms, using the (or and Kf point groups, respectively but it is more... 

The term following EL is always less than unity so that an adventitious correction to the laboratory energy occurs. This enhances the precision of the Er measurement. As with electrons, selection rules for ionization and dissociation seem to be relaxed. 

For some direct-gap materials, the quantum electronic selection rules lead to = 0. However, this is only strictly true at / = 0. For 0, it can be assumed, in a first order approximation, that the matrix element involving the top valence and the bottom conduction states is proportional to k that is, Pif k. Within the simplified model of parabolic bands (see Appendix Al), it is obtained that Tuo = Tuog + flp., and therefore Pif k co — cog). Thns, according to Equations (4.31) and (4.32), the absorption coefficient for these transitions (called forbidden direct transitions) has the following spectral dependence ... 

For polyatomic molecules, (7.2) and (7.6) give the wave numbers and transition moment for an electronic transition. Besides the S selection rule (7.7), there are electronic selection rules stating between which electronic symmetry species transitions are allowed these are derived using group theory (Section 9.11). Equation (7.13) applies to polyatomics, except that Pei is now a function of the 3N —6 (or 3Af —5) normal coordinates Qr... 

Molecular electronic selection rules are determined by whether or not the integral n (7-6) vanishes. del belongs to the representation... 

Just as with vibronically allowed transitions, in symmetry groups in which all Cartesian axes are not equivalent (noncubic groups), it is found that, in general, transitions will be allowed only for certain orientations of the electric vector of the incident light. One class of compounds in which this phenomenon has been studied both theoretically and experimentally consists of trischelate compounds such as tris(acetylacetonato)M(III) and tris(oxalato)M(III) complexes. In these complexes the six ligand atoms form an approximately octahedral array but the true molecular symmetry is only Dy Since there is no center of symmetry in these molecules, the pure electronic selection rules might be expected to be dominant. 

The vibronic selection rules are of the same form as the electronic selection rules discussed in Section II, A. What matters is the symmetry species of the integrand... 

Azulene has weak absorption in the visible region (near 7000 A) and more intense band systems in the ultraviolet. The first ultraviolet system, which commences at about 3500 A, has been examined in substitutional solid solution in naphthalene (Sidman and McClure, 1956) and in the vapour state (Hunt and Ross, 1962), and can be observed in fluorescence from the vapour (Hunt and Ross, 1956). Theory predicts that the transition is 1Al<-lAl(C2K), i.e. allowed by the electronic selection rules with polarization parallel to the twofold symmetry axis (see, e.g., Ham, 1960 Mofifitt, 1954 Pariser, 1956b). The vibrational analysis shows that the transition is allowed but does not establish the axis of polarization. The intensity distribution among the vibrational bands indicates a small increase in CC bond distance without change in symmetry. 

If a degenerate state is involved the = is replaced by D. Very often either the same vibration is excited in both states, in which case T(i/j v) = T(i/j") and the selection rule is the same as the electronic selection rule, or no vibration is excited in the upper or lower state, resulting in W ) or Wv) being totally symmetric. 

There are two other fairly common causes of apparent breakdown of the electronic selection rules. First, collisions with other atoms or molecules, or the presence of electric or magnetic fields, may invalidate selection rules based on state descriptions of the unperturbed species. Secondly, although the transition may be forbidden for an electric-dipole interaction, it may be permitted for the (much weaker) magnetic-dipole or electric-quadrupole transitions. 

On the basis of the state correlation diagram depicted in Figure 1, which connects the different stereoisomers of the pentacoordinate fragment [Rh(NH3)4Cl] +, Vanquickenbome etal. infer the main characteristics of the complicated photochemical mechanism in [Rh(NH3)4Cl2]+ and related complexes. This work gave the first evidence that the formulation of electronic selection rules was underlying the photosubstitution mechanism in d and d complexes. In principle, this idea was applicable to any complex with any coordination number. However, at this stage the... 

There are many variants of REMPI. In most REMPI experiments one or more of the photoexcitation steps is a multiphoton transition. The rotation and electronic selection rules and relative intensity factors are quite different for a one-photon... 

A special situation applies to two-photon transitions from initial states since the electronic selection rule is AA = 0, 1, 2, transitions from a + initial state can occur to +, 1n9 and 1Ag final states. For one-color, two-... 

The electronic selection rule for nonzero electrostatic or nuclear kinetic energy coupling matrix elements is quite simple for diatomic molecules only states with identical electronic quantum numbers can perturb each other. For polyatomic molecules, the situation is not always so simple. It is possible that two electronic states will have different electronic quantum numbers in a high-... 

The electronic selection rules for linear molecules are as follows. AA = 0, 1. AS = 0. Again, these are really... 

When spectroscopists speak of electronic selection rules, they generally mean consideration of the integral over only the electronic coordinates for wavefunctions calculated at the equilibrium nuclear configuration of the initial state, Q = Q,... 

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