State triplet

The perturbations in this case are between a singlet and a triplet state. The perturbation Hamiltonian, H, of the second-order perturbation theory is spin-orbital coupling, which has the effect of mixing singlet and triplet states. 

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

Spectroscopists observed that molecules dissolved in rigid matrices gave both short-lived and long-lived emissions which were called fluorescence and phosphorescence, respectively. In 1944, Lewis and Kasha [25] proposed that molecular phosphorescence came from a triplet state and was long-lived because of the well known spin selection rule AS = 0, i.e. interactions with a light wave or with the surroundings do not readily change the spin of the electrons. 

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. 

Once the excited molecule reaches the S state it can decay by emitting fluorescence or it can undergo a fiirtlier radiationless transition to a triplet state. A radiationless transition between states of different multiplicity is called intersystem crossing. This is a spin-forbidden process. It is not as fast as internal conversion and often has a rate comparable to the radiative rate, so some S molecules fluoresce and otliers produce triplet states. There may also be fiirther internal conversion from to the ground state, though it is not easy to detemiine the extent to which that occurs. Photochemical reactions or energy transfer may also occur from S. ... 

An atom or a molecule with the total spin of the electrons S = 1 is said to be in a triplet state. The multiplicity of such a state is (2.S +1)=3. Triplet systems occur in both excited and ground state molecules, in some compounds containing transition metal ions, in radical pair systems, and in some defects in solids. 

Figure Bl.15.7. Transient EPR. Bottom time-resolved EPR signal of the laser-flash-indueed triplet state of pentaeene in /j-terphenyl. BpO.085 mT. Top initially, the transient magnetization M is aligned along B z. In the presenee of a MW magnetie field B the magnetization preeesses about BJ x (rotating frame representation).

Furrer R, Fujara F, Lange C, Stehlik D, Vieth H and Vollmann W 1980 Transient ESR nutation signals in excited aromatic triplet states Chem. Rhys. Lett. 75 332-9... 

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. 

In the early 1990s, a new spin polarization mechanism was posPilated by Paul and co-workers to explain how polarization can be developed m transient radicals in the presence of excited triplet state molecules (Blattler et al [43], Blattler and Paul [44], Goudsmit et al [45]). While the earliest examples of the radical-triplet pair mechanism (RTPM) mvolved emissive polarizations similar in appearance to triplet mechanism polarizations, cases have since been discovered m which absorptive and multiplet polarizations are also generated by RTPM. 

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].

Closs G L and Czeropski M S 1977 Amendment of the CIDNP phase rules. Radical pairs leading to triplet states J. Am. Chem. Soc. 99 6127-8... 

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... 

Goudsmit G H and Paul H 1993 Time-resolved EPR investigation of triplet state Cgg. Triplet-triplet annihilation, CIDEP, and quenching by nitroxide radicals Chem. Phys. Lett. 208 73-8... 

Liddell P A, Kuciauskas D, Sumida J P, Nash B, Nguyen D, Moore A L, Moore T A and Gust D 1997 Photoinduced charge separation and charge recombination to a triplet state in a carotene-porphyrin-fullerene triad J. Am. Chem. Soc. 119 1400-5... 

Figure C 1.5.10. Nonnalized fluorescence intensity correlation function for a single terrylene molecule in p-terjDhenyl at 2 K. The solid line is tire tlieoretical curve. Regions of deviation from tire long-time value of unity due to photon antibunching (the finite lifetime of tire excited singlet state), Rabi oscillations (absorjDtion-stimulated emission cycles driven by tire laser field) and photon bunching (dark periods caused by intersystem crossing to tire triplet state) are indicated. Reproduced witli pennission from Plakhotnik et al [66], adapted from [118].

The half-electron method can also apply to triplet states. For this calciilatioit. IlyperCheni populates selected molecular orbitals with pairs of half electron s. The final energy is computed by assigning the proper spins. 

Notice lh il Ihc orbiuls nc riol paiied, >.(/i"does n ol liiivc Ihc siimc energy as An unrestricted wave ftinction like this is a natural way of representing system s with unpaired electron s, such as the doublet shown here or a triplet state ... 

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

To understand how the three triplet states have the same energy and why the singlet state has a different energy, and an energy different than the Ms= 0 triplet even though these two states are eomposed of the same two determinants, we proeeed as follows ... 

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