The triplet state

In the triplet state, the excited electron has the same spin orientation (parallel or antiparallel to the external field) as the electron in the original ground-state orbital, so that the state is paramagnetic with total spin S = 5, -I- S2 = 1. Its multiplicity (i.e. the number of quantum mechanically allowed projections of the spin vector 5 on the field B) is then 25 + 1 = 3, with magnetic quantum numbers = 0, 1. 

In general, the anisotropic dipole-dipole interaction between the two unpaired spins in the triplet state (Table 3) gives rise to a very broad EPR spectrum, with in the derivative representation characteristic peaks for directions of B parallel to the principal axes of the dipole-dipole interaction tensor D. For reaction centers the spectrum shows a peculiar distribution of lines that are in emission or in ab- 

II) or close to (bacterial RC) the values found for monomeric triplet states of the chlorophylls in vivo, and why the low-temperature decay rates of the three triplet sublevels are virtually the same in vivo and in vitro. 

The orientation of the transition moment of the long-wavelength absorbance of the primary donor with respect to the dipolar axes of the triplet state can be found from magnetophotoselection EPR or from EPR on oriented or crystalline material [80-85], From EPR on single crystals of Rps. viridis it was found that the triplet X- and y-axes are very close to the pyrrole N-N axes of one of the BChls b making up the primary donor (Refs. 78,79 and J.R. Norris, personal communication). 

---

Because the electron-electron repulsion is less effective in the triplet state, it will nonnally be lower in energy than the corresponding singlet state. 

Typical singlet lifetimes are measured in nanoseconds while triplet lifetimes of organic molecules in rigid solutions are usually measured in milliseconds or even seconds. In liquid media where drfifiision is rapid the triplet states are usually quenched, often by tire nearly iibiqitoiis molecular oxygen. Because of that, phosphorescence is seldom observed in liquid solutions. In the spectroscopy of molecules the tenn fluorescence is now usually used to refer to emission from an excited singlet state and phosphorescence to emission from a triplet state, regardless of the actual lifetimes. 

An individual radical from the RP may encounter a radical from a different RP to fomi what are known as random RPs or F pairs. F pairs which happen to be in the singlet state have a high probability of recombining, so the remaining F pairs will be in the triplet state. Consequently, the initial condition for F pairs is the triplet state in nearly all cases. 

Figure Bl.16.16 shows an example of RTPM in which the radical species is TEMPO (10), a stable nitroxide radical, while the triplet state is produced by photoexcitation of benzophenone (11) [45].

Fessenden R W and Verma N C 1976 Time resolved electron spin resonance spectroscopy. III. Electron spin resonance emission from the hydrated electron. Possible evidence for reaction to the triplet state J. Am. Chem. Soc. 98 243-4... 

The triplet state has two unpaired electrons with the same spin (q) and so the wavefunction state is ... 

Also, the Ms = 1 eomponent of the triplet state having aa orbital oeeupaney ean be written as a single Slater determinant ... 

The advantages of INDO over CNDO involve situations where the spin state and other aspects of electron spin are particularly important. For example, in the diatomic molecule NH, the last two electrons go into a degenerate p-orbital centered solely on the Nitrogen. Two well-defined spectroscopic states, S" and D, result. Since the p-orbital is strictly one-center, CNDO results in these two states having exactly the same energy. The INDO method correctly makes the triplet state lower in energy in association with the exchange interaction included in INDO. 

A principal appHcation for photomedicine is the photodynamic treatment of cancer. Photochemical and clinical aspects of this topic have been reviewed (10,11). Direct irradiation of tumors coupled with adininistration of a sensitizer is used to effect necrosis of the malignancy. In this process, an excited state sensitizer interacts with dissolved in vivo to effect conversion of the oxygen from its triplet ground state to an excited singlet state, which is highly cytotoxic. In principle, excited sensitizers in either the singlet or the triplet state can effect this conversion of molecular oxygen (8). In... 

Photochromism Based on Triplet Formation. Upon absorption of light, many polycycHc aromatic hydrocarbons and their heterocycHc analogues undergo transitions to their triplet state which has an absorption spectmm different from that of the ground state (24). In rigid glasses and some plastics, the triplet state, which may absorb in the visible, has a lifetime of up to 20 seconds. 

The triplet-state energy level of oxytetracycline, the excitation maximum (412 nm), lifetimes of Eu-OxTc (58 p.s) and Eu-OxTc-Cit (158 p.s), were determined. A 25-fold luminescence enhancement at 615 nm occurs upon addition of citrate within a short 5-min incubation time at neutral pH. It s accompanied by a threefold increase of the luminescence decay time. The optimal conditions for determination of OxTc are equal concentrations of Eu(III) and citrate (C = T lO mol-E ), pH 7.2. Eor determination of citrate, the optimal conditions concentrations of Eu(HI) and OxTc are 1 0,5 (Cg = MO Huol-E-i, = 5-10-HuohE-i) at pH 7.2. 

The energy of the triplet state of the sensitizer ( Sens ) must be greater than that of the reactant. If this condition is not met, the energy transfer becomes endothermic and cannot compete with other transformations of Sens. ... 

The transfer of energy must proceed with net conservation of spin. In the usual case, the acceptor molecule is a ground-state singlet, and its reaction with the triplet state of the sensitizer will produce the triplet state of the acceptor. The mechanism for triplet photosensitization is outlined below ... 

Either the singlet or the triplet state may be involved in a photochemical reaction, whereas only singlet species are involved in most thermal processes. This permits the formation of intermediates that are unavailable under thermal conditions. 

The output of the calculation will be the new CASSCF description of the triplet state. We will use this as the starting point for further calculations first, another CAS on the triplet with the target basis set, and then a CAS on the singlet excited state ... 

First, try to draw resonance contributors for both ground state and triplet anthrone. Then display a spin density surface for the triplet state of anthrone. (Note that the spin density surface shows the location of both unpaired electrons, one of which may be in a 7t orbital and one of which may be in a o orbital.) Where are the two unpaired electrons Are they localized or delocalized Given that spin delocalization generally leads to stabilization, would you expect the triplet state of anthrone to be stable ... 

In my discussion of pyridine, I took a combination of these determinants that had the correct singlet spin symmetry (that is, the combination that represented a singlet state). I could equally well have concentrated on the triplet states. In modem Cl calculations, we simply use all the raw Slater determinants. Such single determinants by themselves are not necessarily spin eigenfunctions, but provided we include them all we will get correct spin eigenfunctions on diago-nalization of the Hamiltonian matrix. 

At the dissociation limit the UHF wave function is essentially an equal mixture of a singlet and a triplet state, as discussed in Section 4.4. Removal of the triplet state by projection (PUHF) lowers the energy in the intermediate range, but has no effect when the bond is completely broken, since the singlet and triplet states are degenerate here. 

Optical detection of magnetic resonance (ODMR) was attempted for measurements of the pH effects on the triplet state of purine to investigate the protonation site of purine at low temperatures (78JA7131). The ODMR spectrum did not show the presence of more than one triplet state at liquid helium temperatures. Since the protonated tautomers 1H,9H (3a) and H,1H (3b) have similar bond structures, their triplets should have similar zero-field parameters and are thus not easy to distinguish by ODMR. 

---