Singlet-Triplet Differences

Finally, it should be stressed that the rationalization of singlet-triplet differences based on electron repulsion effects els outlined here is relatively new and not generally accepted. For alternative rationalizations in the case of / ,y-unsaturated ketones, see Refs. 147> 160>. 

Ah initio programs attempt to compute the lowest-energy state of a specified multiplicity. Thus, calculations for different spin states will give the lowest-energy state and a few of the excited states. This is most often done to determine singlet-triplet gaps in organic molecules. 

Table 1. Bond lengths (A) and singlet-triplet energy differences (in kcal/mol) for triplet phosphinidenes ...

Table 2. Singlet-triplet energy differences (A sx) and singlet (BDEj), triplet (BDEx), and composite (BDEsx/xs) bond dissociation energies for phosphinidenes and their W(CO)5 complexes, calculated with BP/TZP...

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,... 

Very often, however, these dyads are not isolated in the solid state and interact with neighboring ones at least along one preferential direction. In this case, we can distinguish two important situations the alternated spin chain and the spin ladder. As shown in Scheme 5, the alternated spin chain is characterized with two different magnetic interactions, noted / and aJ with 0 < a < 1. Note that if a = 0, one recovers the singlet-triplet behavior while if a = 1, we are in the presence of a uniform spin chain. The spin ladder is also characterized by two J values, noted J// and J in the following. 

In connection with Chichibabin s hydrocarbon it is appropriate to mention that there is little or no resonance between states of different multiplicity.4 Thus the singlet-triplet transition represented by the covalent and diradical structures of the hydrocarbon is a true equilibrium and not an example of resonance. 

The first experimental determination of a singlet-triplet energy gap (Mst) for an organic nitrenium ion was made for the 1,3-dimethylbenzotriazolium ion . A powerful ligand, 4,5-bis(diphenylphosphinoyl)-l,2,3-triazole, has been synthesized and found to possess two different modes of chelation <00ACIE3321>. 

Notes ° Eq. 9, M = CR R AH, (H+) = 365.7 kcal/mol. All data refer to 298 K. b Recommended enthalpies of formation from Ref. 134b 2 kcal/mol. cTo AH, (3 CH-CH=CH2) = 93 kcal/mol was added AEst =10 kcal/mol. The calculated singlet-triplet gap of 13.3 kcal/mol (B3LYP/cc-pVTZ) from Ref. 133 was corrected by 3 kcal/mol, which is the difference between the experimental and computed (B3LYP/cc-pVTZ) AEst for methylene. 

The third member, trimethylenemethane (3), had some relevance to our studies on carbenes, since besides methylene and its simply substituted derivatives trimethylenemethane 3 is one of the few molecules having a triplet ground state.22 Also the experience with 3 could be of help in order to deal with the singlet/triplet differentiation in matrix-isolated carbenes. We learned that, if the calculated IR spectra of the singlet and triplet molecule are sufficiently different, it might be possible to determine the multiplicity of the matrix-isolated species by comparison with the experimental IR spectrum. In this context it is also worth mentioning that we were able to measure the matrix IR spectrum of 3, but a special technique (irradiation in halogen-doped xenon matrices) had to be developed in order to achieve a concentration of 3 sufficient for its IR detection.23... 

It is well known that double bonds have a different effect on the singlet-triplet energy separation and thus on the reactivity of the carbene than alkyl groups. The description of the electronic structure of such carbenes is rendered more difficult by the fact that several low-lying electronic states are possible. For... 

On the other hand, there are other series of polyaers having sc-electronic chroaophore such as N-carbazolyl and 1-pyrenyl groups, whose photophysical properties are quite different fron the above polyaers and whose laser cheaistry is studied in detail. A relation aaong interchronophoric interaction, spectral shape and geonetrical structure in the excited singlet, triplet, cationic and anionic... 

Rather loosely, this may be thought of as taking U ao, so that double occupancy of 0) is totally forbidden. Because the wavefunction (11) has different a and /9-spin spatial orbitals, it is not a pure spin state (it will be a mixture of singlet, triplet, quintet, etc.). However, for the problem in hand, this does not seem to be much of a disadvantage. 

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