Excitation singlet/triplet

Avakian, P., Abramson, E. Singlet-triplet excitation spectra in naphthalene and pyrene crystals. J. Chem. Phys. 43, 821 (1965). 

Calculations on the singlet and triplet states of artemisinin were carried out, using several levels of theory, in order to study its singlet-triplet excitations. It was concluded that FIF theory is not sufficient to estimate the adiabatic transition of this endoperoxide and that correlated calculations are required <1998JST87>. 

The promotion gap is determined by two basic excitations. For -electron pairs, the promotion energy is k-fold singlet—triplet excitation of the A—A dimer, while for mixed-valence cases where the number of electrons exceeds the number of centers (e.g., H3 ) and vice versa, the promotion energy is a charge-transfer excitation, (e.g., from Hr to H2 in H i ). Let us now use the promotion gap quantity to pattern the data concerning delocalized species. 

As a first order approximation, the SP-DFT approach connects the spin-potential directly with the singlet-triplet excitation energy. Thus, the gap defined by the highest beta occupied molecular orbital, HOMO, and the... 

Table 2 Spin-potential, e iMC) — eHOMO SaP an< singlet-triplet excitation energy, AE, for Ca, Sr and Ba The confinement radius, Rc, is reported in atomic units and the other quantities in eV...

In the important case of a closed-shell system, the matrix Q of Eqs. 32 to 34 of the spin-restricted TDDFRT can be split into two parts Qs and QT representing the singlet-singlet and singlet-triplet excitations [10, 34]... 

Scheme 6.3 applies these rules by showing the HL structures for two cycloaddition reactions 11R and 11P are the structures for the reactants and products of the Woodward-Hoffmann forbidden 2 + 2 reaction, while 12R and 12P are the structures for the Woodward-Hoffmann allowed Diels—Alder reaction. In both cases, the difference in the HL structure is only the mode of spin coupling, and therefore the promotion energy G will involve only singlet-triplet excitations. In accord, we drew in Fig. 6.5 the corresponding... 

The barriers for a series of radicals have been computed (22), and were found to increase as the R H bond energy D increases the barrier is the largest for R = CF13 and the smallest for R = C(CH3)3. This trend has been interpreted by Pross et al. (23) using the VBSCD model. The promotion gap G that is the origin of the barrier involves the singlet-triplet excitation of the... 

It is seen from Equation 6.Ans.24 that the barrier is positive as long as a>l. When astable cluster. The parameter a is the crucial quantity that determines the transition from a saddle-point species to a stable cluster. From Equation 6.Ans.l8 and the expression for D (see Eq. 6.Ex.2) we can show that a determines the ratio of the singlet—triplet excitation of the bond to its bond energy ... 

Here, grs is a parameter that is quantified either from experimental data, or is calculated by an ab initio method as one-half of the singlet-triplet excitation energy gap of the r—s bond. In terms of the qualitative theory in Chapter 3, grs is therefore identical to the key quantity —2(3 5 - This empirical quantity incorporates the effect of the ionic components of the bond, albeit in an implicit way. (c) The Hamiltonian matrix element between two determinants differing by one spin permutation between orbitals r and s is equal to grs. Only close neighbor grs elements are taken into account all other off-diagonal matrix elements are set to zero. An example of a Hamiltonian matrix is illustrated in Scheme 8.1 for 1,3-butadiene. 

It is not possible to separate the photochemistry of 1,3-cyclohexadiene from that of 1,3,5-hexatriene, its major product, since the latter absorbs radiation in the same region of the spectrum and even more intensely to revert to 1,3-cyclohexadiene. The ir- - w absorption of 1,3,5-hexatriene shows considerable vibrational structure. The radiative lifetimes for the singlet states of both 1,3-cyclohexadiene and 1,3,5-hexatriene can be calculated to be less than 10 sec. The lowest triplet state of trans-1,3,5-hexatriene has been placed at 47 kcal./mole, and a second triplet state may lie at approximately 14 kcal./mole above that. These values were also obtained by direct singlet — triplet excitation. 

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). 

The material, however, is not an uncorrelated semiconductor. This is confirmed by the behaviour of the susceptibility which displays a behaviour characteristic to a singlet-triplet excitation with broad exciton band jFig.. A simple singlet-triplet model with a sharp excitation energy J... 

For branched alkanes, the fragmentation patterns could be very complex [3, 111]. The prompt yield of the -H radicals is always minor the highest yields are of the radicals formed by scission of skeletal C-C bonds next to the branches. For example, in radiolysis of isooctane only 15% of the radicals are of the -H type, the rest bemg tert-butyl and 2-propyl radicals [111]. In radiolysis of 2,3-dimethylbutane, 70% of radicals are 2-propyl and 30% are -H radicals (2,3-dimethyl-2-butyl). It is not known what species dissociate (singlets triplets excited holes excited radicals ) and what controls these fragmentation patterns. 

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