Selected Singlet-Triplet Transitions

A Jablonski diagram excluding the vibrational manifold of states. 

High temperature limit (equal population of spin sublevels). Planar singlet ground state geometry. 

Potential energy curves for the ground and few lowest triplet states of the N2 molecule. 

Singlet-triplet transition moment curves in N2. All b,c,d, results correspond to valence CAS (CAS-1) calculations. 

The Vegard-Kaplan transitions A3E J - A1E+ have been observed both in emission and in absorption [88], and is the most studied T-S system in N2. Shemansky [86] measured the absorption spectrum, identifying seven vibrational bands (6,0)-(12,0) and extracted from the obtained data an absolute transition moment curve in the interval 1.08-1.4 A. The transition moment curve was found to be quite close to linear in the important interval 1.08-1.2 A. The important feature of the curve is that it changes sign at r = 1.173 A, i.e at the vicinity of re 1.1 A. 

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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 fallacy is that the singlet-triplet transitions are not strictly forbidden. If it were so, the molecule would have been unable to cross from the singlet state. Sx to the triplet state Tr The fact that it did cross implies that there is enough spin-orbit coupling present to break down the singlet triplet selection rule and so this becomes weakly allowed. However, as it is only weakly allowed, the transition Tx—> S0 is slow and may persist even after the illumination has ceased. Thus phosphorescence occurs under the following conditions. 

We notice that singlet-triplet transitions in molecules are forbidden by spin selection rules and the lifetime of triplet states in crystals exceeds by many orders... 

A direct proof of the reversibility of singlet-triplet transition has been deduced from time-resolved studies of the fluorescence observed under a selective excitation of a and X rovibronic states resulting from the perturbation between (u = 0) and (0= 1) vibronic states in CO. In the former case, the fluorescence shows a biexponential decay, while in the latter one it exhibits an initial induction followed by the decay (Fig. 4 see also Fig. 3 bottom). The ratio of rate constants for the s- l and l- s processes (determined by a simple kinetic treatment) is in a good agreement with the expected thermal distribution after a complete equilibration of the ( + / ) system. ... 

The first selection rule is related to all molecules with centers of symmetry and deals with the parity-forbidden transitions. The second rule states that singlet-triplet transitions are forbidden. The third rule applies to forbidden transitions that arise... 

The first selection rule concerns the multiplicity of states Since the components of p are ungerade or odd, the integrand becomes gerade or even only provided the product of the two spin functions is ungerade, i.e., if their multiplicity or the total spin quantum number S does not change, or in other words if AS=0. Thus singlet-triplet transitions are normally forbidden. 

In practice, those selection rules are not strict, and some couplings can make forbidden transitions happen. However, they remain weak, slow, or of low probabiUty. Phosphorescence, for example, is a manifestation of a forbidden singlet triplet transition favored by a spin-orbit coupling, whereas the luminescence of the trivalent lanthanide ions is a manifestation of forbidden f-f transitions favored by the disruption of the spherical (centrosymmetric) symmetry of the free ion once coupled to hgands. 

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,... 

Furthermore, there is a potential surface for each set of excited states for the N nuclei, i.e., for each set of singlets, triplets, etc. (assuming a spin-free Hamiltonian). Transitions from one surface to the next will, instantaneously, still be governed by the Franck-Condon principle and selection rules. Thus, the important question concerning purity of states in an electronic transition can be dismissed. 

Bound electronically excited states of H2 may radiatively decay to lower states subject to the selection rules g u, singlet -H- singlet, triplet -H- triplet. The final state in these transitions may be either a bound or a dissociative state, i.e.,... 

The spin selection rule is a consequence of the fact that the electric dipole and quadrupole moment operators do not operate on spin. Integration over the spin variables then always yields zero if the spin functions of the two states 0 and are different, and an electronic transition is spin allowed only if the multiplicities of the two states involved are identical. As a result, singlet-triplet absorptions are practically inobservable in the absorption spectra of hydrocarbons, or for that matter, other organic compounds without heavy atoms. Singlet-triplet excitations are readily observed in electron energy loss spectroscopy (EELS), which obeys different selection rules (Kuppermann et al., 1979). 

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