Selection Rules for Radiative Transitions

Three factors influence the probability of absorption or emission of UV-vis radiation. One is based on symmetry considerations and the quantum mechanical formulation of transition moment integrals. If the initial and final 

For a discussion of intersystem crossing, see (a) Turro, N. J. /. Chem. Educ. 1969, 46, 2 (b) McGlynn, S. P. Azumi, T. Kinoshita, M. Molecular Spectroscopy of the Triplet State Prentice Hall Englewood Cliffs, NJ, 1969. 

Although intersystem crossing is usually considered to involve singlet to triplet conversion, reverse intersystem crossing from T2 to Si has been observed in anthracenes Fukumura, H. Kikuchi, K. Koike, K. Kokubun, H.. Photochem. Photohiol. A 1988, 42, 283. 

Bouwman, W. G. Jones, A. C. Phillips, D. Thibodeau, P. Friel, C. Christensen, R. L.. Phys. Chem. 1990, 94, 7429. Both Si — So and S2 — So emissions were observed from tetraenes and pentaenes in the gas phase. 

Electronic transitions are said to be vertical, meaning that absorption and emission of UV-vis radiation occurs with no movement of the nuclei, within the limits of the Bom-Oppenheimer approximation. Since most molecules are in the 0th vibrational level of the ground electronic state, the Franck-Condon term measures the probability of the transition from the 0th vibrational level of the ground state to each vibrational level of the excited state. A transition from the 0th vibrational level of So to the 0th vibrational level of Si is marked 

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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.)... 

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... 

Strahlungsiibergange, Auswahlregeln, selection rules for radiative transition 42. 

These two postulates also explain the existence of spectral terms and the Ritz combination principle. We see from equation (1.7) that the wavenumbers of spectral lines are given by differences of quantities of the form E /hc, These must therefore be the spectral terms. Thus the work of the spectroscopists in deducing the terms from the observed spectra immediately provides one with a table of atomic energy levels. Following this important clarification and the later development of selection rules for radiative transitions, the classification and analysis of atomic and molecular spectra proceeded rapidly. Energy-level tables are now available for the majority of atoms, ions, and simple... 

The selection rules for radiationless transitions are just the opposite of those for radiative transitions. The nuclear kinetic operator is symmetric. The symmetric aromatic molecules normally have symmetrical ground state and antisymmetrical excited state. Therefore, allowed transitions are ... 

The selection rules for radiationless transitions are just the opposite of those for radiative transitions. Allowed transitions are ... 

We now consider radiative transitions foi which both v and J change, but the electronic state does not these transitions give the vibration-rotation spectra of diatomic molecules. The selection rules for these transitions were found in Section 4.4 to be ( 2 states only)... 

The selection rules for radiative processes permit us to evaluate the ease or difficulty with which a particular transition can proceed. The basic rules are as follows ... 

The key observation leading to propensity rules for radiative transitions is that the dipole operator D = rj - - r2 = 2r i.e. the dipole transition involves only the ECM motion. This gives the selection rule At = dbl directly. The linearized ECM dynamics aroimd the saddle point as the motion of an isotropic harmonic oscillator (3) has already explained the quasidegeneracies in the two-electron spectrum. It can also be shown how a linearization of the ECM motion around the saddle leads to the additional selection rule... 

The selection rule (4.138) differs from previously discussed selection rules in that it holds well for nonradiative transitions, as well as for radiative transitions. In deriving (4.138), we made no reference to the operator d, beyond the statement that it did not involve the nuclear spin coordinates. For any time-dependent perturbation that does not involve nuclear spin, the selection rule (4.138) will hold. Thus molecular collisions will not cause nonradiative transitions between symmetric and antisymmetric rotational levels of a homonuclear diatomic molecule. If we somehow start with all the molecules in symmetric levels, the collisions will not populate the antisymmetric levels. 

Radiation is not the only time-dependent perturbation that produces transitions between states. When an atom or molecule comes close to another atom or molecule, it suffers a time-dependent perturbation that can chan its state. Selection rules derived for radiative transitions need not apply to collision processes, since H (t) differs for the two processes. 

The selection rules for a radiative transition between two states of a nucleus are based on the conservation of angular momentum and are... 

These rules are not absolute in the sense of the parity selection rule, since they are based on the assumption of charge independence. Rule (b) in particular is weakened in many cases by Coulomb perturbation which mixes wave functions of different T for a given nuclear state. Other causes of isotopic spin impurity are discussed by MacDonald the experimental evidence for radiative transitions is reviewed by Wilkinson. ... 

The propensity rules are based on the observation that, to the extent that states of given total symmetry are built upon a single MO, transitions between these states are governed by selection rules for transitions between the corresponding MO. In this way the propensity rules arise naturally out of the theory and are not dependent upon empirical deductions. Their simplicity is partly due to the structure of the operators responsible for non-radiative (auto-ionization) a nd radiative decay. 

For C22H2, the nuclear spin of C12 is zero and contributes a factor of 1 to the nuclear statistical weights. The statistical weights are therefore the same as in H2. For the ground vibronic state, the even J levels are s and have nuclear statistical weight 1, corresponding to the one possible ns the odd J levels are a and have nuclear statistical weight 3. The usual selection rule (4.138) holds for collisions as well as radiative transitions, and we have ortho and para acetylene. The two forms have not been separated. 

SELECTION RLILES (Energy Levels). It was found early in the. study of atomic spectra that radiative transitions between certain pairs of energy levels seldom or never occur. A set of rules which are expressed in terms of the differences of the quantum numbers of the two states involved allow a prediction of allowed transitions and forbidden transitions. The conditions for allowed transitions are ... 

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