Some Selection Rules

Transitions between energy levels in organic molecules are subject to certain constraints, referred to as selection rules. 

Spin selection rule An electronic transition takes place with no change in the total electron spin - that is, AS = 0 - hence singlet - triplet transitions are forbidden or very weakly allowed. For example, the S0 — Ti transition in anthracene has a molar absorption coefficient, emax, some 108 times less than that corresponding to the S0 — Si transition. 

The heavy atom effect can show itself as the internal heavy atom effect, where incorporation of a heavy atom in a molecule will enhance S0 — Tx absorption due to spin-orbit coupling. For example, 1-iodonaphthalene has a much stronger S0 — Ti absorption than 1-chloronaphthalene 

The external heavy atom effect shows itself when a heavy atom is incorporated in a solvent molecule. For example, 1-chloronaph-thalene has a much stronger S0 — Ti absorption in iodoethane solution than in ethanol. 

---

The hydrogenolyaia of cyclopropane rings (C—C bond cleavage) has been described on p, 105. In syntheses of complex molecules reductive cleavage of alcohols, epoxides, and enol ethers of 5-keto esters are the most important examples, and some selectivity rules will be given. Primary alcohols are converted into tosylates much faster than secondary alcohols. The tosylate group is substituted by hydrogen upon treatment with LiAlH (W. Zorbach, 1961). Epoxides are also easily opened by LiAlH. The hydride ion attacks the less hindered carbon atom of the epoxide (H.B. Henhest, 1956). The reduction of sterically hindered enol ethers of 9-keto esters with lithium in ammonia leads to the a,/S-unsaturated ester and subsequently to the saturated ester in reasonable yields (R.M. Coates, 1970). Tributyltin hydride reduces halides to hydrocarbons stereoselectively in a free-radical chain reaction (L.W. Menapace, 1964) and reacts only slowly with C 0 and C—C double bonds (W.T. Brady, 1970 H.G. Kuivila, 1968). 

The atomic weight of mercury is high so that some selection rules will not be rigorously obeyed. There is one other prominent transition at 2537 A... 

In the intermediate case Ei < Eq and y T], we observe a photon energy (or frequency) bands either allowed or forbidden for the wave propagation. Therefore, there are some selection rules for the Bragg diffraction of electromagnetic waves on the periodical structure. Here, we see a deep analogy with the Bloch -de Broglie waves in crystals. For this reason we speak of photonic crystals. 

Transition intensities are detennined by the wavefiinctions of the initial and final states as described in the last sections. In many systems there are some pairs of states for which tire transition moment integral vanishes while for other pairs it does not vanish. The temi selection rule refers to a simnnary of the conditions for non-vanishing transition moment integrals—hence observable transitions—or vanishing integrals so no observable transitions. We discuss some of these rules briefly in this section. Again, we concentrate on electric dipole transitions. 

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. 

One of the consequences of this selection rule concerns forbidden electronic transitions. They caimot occur unless accompanied by a change in vibrational quantum number for some antisynnnetric vibration. Forbidden electronic transitions are not observed in diatomic molecules (unless by magnetic dipole or other interactions) because their only vibration is totally synnnetric they have no antisymmetric vibrations to make the transitions allowed. 

The synnnetry selection rules discussed above tell us whether a particular vibronic transition is allowed or forbidden, but they give no mfonnation about the intensity of allowed bands. That is detennined by equation (Bl.1.9) for absorption or (Bl.1.13) for emission. That usually means by the Franck-Condon principle if only the zero-order tenn in equation (B 1.1.7) is needed. So we take note of some general principles for Franck-Condon factors (FCFs). 

The polarization dependence of the photon absorbance in metal surface systems also brings about the so-called surface selection rule, which states that only vibrational modes with dynamic moments having components perpendicular to the surface plane can be detected by RAIRS [22, 23 and 24]. This rule may in some instances limit the usefidness of the reflection tecluiique for adsorbate identification because of the reduction in the number of modes visible in the IR spectra, but more often becomes an advantage thanks to the simplification of the data. Furthenuore, the relative intensities of different vibrational modes can be used to estimate the orientation of the surface moieties. This has been particularly useful in the study of self-... 

Two states /a and /b that are eigenfunctions of a Hamiltonian Hq in the absence of some external perturbation (e.g., electromagnetic field or static electric field or potential due to surrounding ligands) can be "coupled" by the perturbation V only if the symmetries of V and of the two wavefunctions obey a so-called selection rule. In particular, only if the coupling integral (see Appendix D which deals with time independent perturbation theory)... 

Another related issue is the computation of the intensities of the peaks in the spectrum. Peak intensities depend on the probability that a particular wavelength photon will be absorbed or Raman-scattered. These probabilities can be computed from the wave function by computing the transition dipole moments. This gives relative peak intensities since the calculation does not include the density of the substance. Some types of transitions turn out to have a zero probability due to the molecules symmetry or the spin of the electrons. This is where spectroscopic selection rules come from. Ah initio methods are the preferred way of computing intensities. Although intensities can be computed using semiempirical methods, they tend to give rather poor accuracy results for many chemical systems. 

In an E vibrational state there is some splitting of rotational levels, compared with those of Figure 5.6(a), due to Coriolis forces, rather than that found in a If vibrational state, but the main difference in an E — band from an — A band is due to the selection rules... 

In the case of atoms, deriving states from configurations, in the Russell-Saunders approximation (Section 7.1.2.3), simply involved juggling with the available quantum numbers. In diatomic molecules we have seen already that some symmetry properties must be included, in addition to the available quantum numbers, in a discussion of selection rules. 

We conclude our brief tour of one-dimensional CA by mentioning a few special properties of some selected one-dimensional rules. We will have occasion to refer back, more than once, to some of the behaviors discussed here, after the appropriate set of formal tools has been presented in later chapters. 

For forbidden transitions in atoms and molecules this phenomenon may be experimentally observed in spectra induced by collisions. As is known, the selection rules on some transitions may be cancelled during collision. The perturbers are able to induce a dipole moment of transition having the opposite direction in successive collisions due to intercollisional correlation. Owing to this, the induced spectra do involve the gap (Fig. 1.7), the width of the latter being proportional to the gas density [46, 47], Theorists consider intercollisional correlation to be responsible for the above phenomenon [48, 49, 50]. 

The definition of well-posedness and ill-posedness of a scheme is closely connected with the selection rules for norms II j and (-2,)- It niay happen that for some choices of these norms estimate (25) is fulfilled, while... 

Atomic spectra are much simpler than the corresponding molecular spectra, because there are no vibrational and rotational states. Moreover, spectral transitions in absorption or emission are not possible between all the numerous energy levels of an atom, but only according to selection rules. As a result, emission spectra are rather simple, with up to a few hundred lines. For example, absorption and emission spectra for sodium consist of some 40 peaks for elements with several outer electrons, absorption spectra may be much more complex and consist of hundreds of peaks. 

The correct choice of the basis for a calculation will often determine whether the calculation proves to be simple or complex. As with the choice of system boundaries, no all-embracing rules or procedures can be given for the selection of the right basis for any problem. The selection depends on judgement gained by experience. Some guide rules that will help in the choice are ... 

There has also been some work devoted to the preparation of a compound that would show greater selectivity toward activity on the gut and away from activity over the CNS. Diphenoxylate (74) has been used extensively in humans for just this purpose although the drug shows some selectivity, it is far from free of narcotic effects. (The curious will note the compound follows the Beckett rule both in the piperidine and side chain moieties.) Treatment of 74... 

Thus the change in the direction of the spin angular momentum of the electron effectively imparts some singlet character to a triplet state and, conversely, triplet character to a singlet state. This relaxes the spin selection rule since J S St dr is no longer strictly zero. The greater the nuclear charge,... 

---