Triplet state spin Hamiltonian

In a previous study at P- and X-band, the temperature dependence of the magnetically coupled spectrum and its analysis based on a triplet-state spin-Hamiltonian were used to propose the range (0.8-100 cm ) for the parameter Jo of the isotropic exchange interaction JoSa Sb, but neither the magnitude of Jo nor its sign could be further specified. ... 

In 1967, Johnson et al. found that the delayed fluorescence of anthracene crystal could be modulated by external magnetic fields below 2 T [11]. The magnitude of the MFEs was dependent on both the field strength and the orientation of its single crystal. These MFEs were successfully interpreted in terms of triplet exciton spin Hamiltonian [12]. The delayed fluorescence is induced from the lowest excited singlet state ( Si) by the annihilation of two lowest triplet excited states ( T ). 

Finally, we consider the spin-orbit coupling term in the Hamiltonian, which acts in a space defined as the direct product of the spin and the geminal space. Within the framework of the simple model, we find that in a perfect biradical the triplet state spin-orbit couples only to the highest-energy singlet state 82-... 

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. 

CIDNP involves the observation of diamagnetic products fonned from chemical reactions which have radical intemiediates. We first define the geminate radical pair (RP) as the two molecules which are bom in a radical reaction with a well defined phase relation (singlet or triplet) between their spins. Because the spin physics of the radical pair are a fiindamental part of any description of the origins of CIDNP, it is instmctive to begin with a discussion of the radical-pair spin Hamiltonian. The Hamiltonian can be used in conjunction with an appropriate basis set to obtain the energetics and populations of the RP spin states. A suitable Hamiltonian for a radical pair consisting of radicals 1 and 2 is shown in equation (B1.16.1) below [12]. 

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. 

The paramagnetism of the triplet state can be observed by electron spin resonance spectroscopy. This is perhaps the most reliable means of determining the existence of a triplet state since the ESR signals can be predicted using the following Hamiltonian operator ... 

We will see that a Hamiltonian term identical in form also arises from spin-orbit coupling, but first we will pause to see the effect of this Hamiltonian on the energy levels and ESR spectrum of a triplet-state molecule. The spin triplet wave functions can be written in the notation S,ms) ... 

Carbenes with triplet ground states are, of course, paramagnetic. Thus they exhibit characteristic epr spectra which can be used to confirm their presence, to provide some data on their structure, and, at least in principle, to reveal AGST in favorable cases. The first epr spectrum of a randomly oriented triplet carbene was observed for DPM (Murray et al., 1962). In subsequent years spectra of many carbenes have been recorded (Table 3). These spectra are commonly interpreted by fitting the results to a spin Hamiltonian H (3), to give the zero field parameters D and E (Stevens, 1952). In the usual... 

The main effect of taking spin-orbit interaction into account will be an admixture of singlet character to triplet states and triplet character to singlet states. The spin-orbit coupling Hamiltonian can to a good approximation be described by an effective one-electron operator Hso ... 

The direct dipole-dipole interaction between electron spins given in Eq. (14) can also contribute to D and E in the spin Hamiltonian. Various estimates of its contribution have shown it to be much smaller than the spin-orbit terms for transition-metal ions. For systems in which the crystal field is greatly distorted, this term can become large, however, and it is found to be the major source of D in the spin Hamiltonian of organic triplet-state molecules, where the spin-orbit terms are small as a result of the small size of the spin-orbit coupling parameter. 

Comparison of the Computed and Observed 253 458 Triplet State Electron Spin Resonance Spin Hamiltonian Parameters for Thymine11... 

If the two 0 ions are coupled, the dimer species formed can be expected to exist either as a ground-state singlet or triplet, depending on its nature. In the alkaline-earth oxides, bulk V° centers have been reported these centers consist of a cation vacancy with two hole centers, one trapped either side of the vacancy. Their spectroscopic behavior is characterized as an axial 5 = 1 center and can be described by the spin Hamiltonian,... 

In the discussion of the hydrogen molecule, it was pointed out that there are two energy levels, Ei corresponding to a symmetrical coordinate wave function (singlet spin function) and En corresponding to an antisymmetrical coordinate wave function (triplet spin functions). If the part of the Hamiltonian labeled H in equation 21 is treated as a perturbation, the energies of the singlet and triplet states are... 

This interaction leads to "fine-structure" splittings in the spectra of atoms and molecules. For atoms and molecules in the S = 1 triplet state, the electron spin-electron spin dipolar interaction leads to the "D and E" fine-structure Hamiltonian. 

Fine-Structure Splittings in ESR Spectra of Triplet States. Consider the hamiltonian H for spin-spin (fine-structure) and Zeeman interactions of two spins Si and S2 a mutual distance r-12 apart, in an external magnetic field H0 ... 

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