Absorption selection rule

This spectrum is called a Raman spectrum and corresponds to the vibrational or rotational changes in the molecule. The selection rules for Raman activity are different from those for i.r. activity and the two types of spectroscopy are complementary in the study of molecular structure. Modern Raman spectrometers use lasers for excitation. In the resonance Raman effect excitation at a frequency corresponding to electronic absorption causes great enhancement of the Raman spectrum. 

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 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 transition between levels coupled by the oscillating magnetic field B corresponds to the absorption of the energy required to reorient the electron magnetic moment in a magnetic field. EPR measurements are a study of the transitions between electronic Zeeman levels with A = 1 (the selection rule for EPR). 

The conmron flash-lamp photolysis and often also laser-flash photolysis are based on photochemical processes that are initiated by the absorption of a photon, hv. The intensity of laser pulses can reach GW cm or even TW cm, where multiphoton processes become important. Figure B2.5.13 simnnarizes the different mechanisms of multiphoton excitation [75, 76, 112], The direct multiphoton absorption of mechanism (i) requires an odd number of photons to reach an excited atomic or molecular level in the case of strict electric dipole and parity selection rules [117],... 

Qualitatively, the selection rule for IR absorption for a given mode is that the symmetry of qT ) " must he the same as qT ). Qiianii-talivcly, the transition dipole moment is proportion al to tlie dipole derivative with respect to a given normal mode dp/di. ... 

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

These results provide so-called "selection rules" because they limit the L and M values of the final rotational state, given the L, M values of the initial rotational state. In the figure shown below, the L = L + 1 absorption spectrum of NO at 120 °K is given. The intensities of the various peaks are related to the populations of the lower-energy rotational states which are, in turn, proportional to (2 L + 1) exp(- L (L +1) h /STi IkT). Also included in the intensities are so-called line strength factors that are proportional to the squares of the quantities ... 

The L = L +1 transitions are termed R-branch absorptions and those obeying L = L -1 are called P-branch transitions. Hence, the selection rules... 

Because Raman scattering is also a two-photon process the selection rules for two-photon absorption are the same as for vibrational Raman transitions. For example, for a two-photon electronic transition to be allowed between a lower state j/" and an upper state... 

For a fundamental transition to occur by absorption of infrared dipole radiation, it is necessary that one or more of these integrals (and consequently the intensity) be nonzero. It follows from the selection rule given above that in order that a transition be infrared active p must have the same symmetry properties as at least one of x, y, or z. 

The hyperpolarizability tensor is obtained in a way similar to the case of SHG. However, the selection rules for an SFG resonance at the IR frequency implies that the vibrational mode is both IR and Raman active, as the SF hyperpolarizability tensor elements involve both an IR absorption and a Raman-anti-Stokes cross-section. Conversely, the DFG hyperpolarizability tensor elements involve an IR absorption and a Raman-Stokes cross-section. The hyperpolarizability tensor elements can be written in a rather compact form involving several vibrational excitations as [117] ... 

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. 

In the first case, the difference in intensities Ip — Is is computed. Due to the surface selection rule, what results is a spectrum showing absorption bands of species on the surface. 

In collaboration with E.L. Sibert, we have learned to interpret these Franck-Con-don forbidden, pure torsional band intensities in S,-S0 absorption spectra quantitatively and thus place the key ml+ assignment on firm ground.27 The forbidden bands follow the selection rule Am = 3, so we need a perturbation of the form Vel cos 3a. Working in an adiabatic representation with the S0 and S, electronic states denoted by y0(g a) and /,( a) and the torsional states by m" and m, the electric dipole transition moment is,... 

As seen from (12) and Fig. 6, the peaks in the excitation anisotropy spectrum indicate a small angle between the absorption and emission transition dipoles suggesting allowed 1PA transitions while valleys indicate large angles between these two dipoles, suggesting a forbidden 1PA transition. Due to selection rules for symmetrical cyanine-like dyes, the valleys in the anisotropy spectrum could indicate an allowed 2PA transition as demonstrated in Fig. 6. Thus, an excitation anisotropy spectrum can serve as a useful guide to suggest the positions of the final states in the 2PA spectra. 

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,... 

These selection rules are affected by molecular vibrations, since vibrations distort the symmetry of a molecule in both electronic states. Therefore, an otherwise forbidden transition may be (weakly) allowed. An example is found in the lowest singlet-singlet absorption in benzene at 260 nm. Finally, the Franck-Condon principle restricts the nature of allowed transitions. A large number of calculated Franck-Condon factors are now available for diatomic molecules. 

---