INDEX triplet-singlet

Lowercase is used for orbitals and capitals for the total electronic state. Capital S means that the total orbital momentum is S = 0. In Equation 2.59, this follows if all orbitals are s orbitals and also if both orbitals are p orbitals. Capital P means that L = 1, which follows for the orbital combination (s,p) and (p,p). Upper left index in the total state designation is the spin multiplicity 1 for a singlet and 3 for a triplet. Singlet state means that there is a single state where for every a spin orbital there is a p spin orbital. Triplet state appears when there is a possibility for three degenerate states, for which the spins always point in the same direaion. This degeneracy is split in a magnetic field. 

There have been several reviews of mechanisms of photosubstitution in rhodium(III) complexes. Bond indexes for ground and excited states have been discussed in relation to D2h species. " The observation of stereospecificity has been discussed in relation to lifetimes for triplet singlet deactivation and geometric rearrangements. Direct evidence has been presented to support the intermediacy of, and role of rearrangement in, five-coordinate intermediates in ligand field irradiation experiments. Rhodium(III) has been discussed in relation to cobalt(III) and iridium(III), and to ruthenium(II) and ruthenium(III) as well. ... 

A large spin-donicity number is expected when the energy difference is smaller between the triplet and singlet states. Thus, spin-philicity and spin-donicity are also a measure of the energy differences between singlet and triplet states, furthermore, it has been demonstrated the applicability of these reactivity indexes in the prediction of the spin transfer observed in the spin-catalysis phenomenon [21], Equivalent quantities at fixed Ns ([Pg.150]

An overview of the energetics and possible depletion mechanisms of excited electronic states is named a Jablonski diagram. Herein, singlet states are symbolized by So, Si, S2, and so on, and triplets by T0, Ti, T2, and so on, where the index labels their energetic order and should not be confused with tensor components. A typical Jablonski diagram for an organic molecule is shown in Figure 19. 

The result follows from spin orthogonality. It is perfectly clear from experiments on atoms and molecules (Zeeman effect) that singlet-triplet and other apparently spin-forbidden transitions do occur, so we are led to assume that the spin and orbital motions of an electron are not uncoupled. In the above example, the transition moment will never vanish identically if the state with spin-orbit coupling operator ffjo- Assume that the state with index n and spin function a-j can interact with another state, say tn, with spin perturbation theory, the corrected state xi l is given by... 

The arrows represent the spin state, and the index 1 and 2 on the arrows represent electron 1 and 2, respectively. The subscript shows the wave function is symmetric and this excited state is called singlet state (S = 0), while the subscript + shows the wave function is antisymmetric and this excited state is called triplet state (S = 1). 

The simplest truncation of the eigenvalue equation (2) for the excitation energies is to ignore all coupling between poles, except that between a singlet-triplet pair. This is equivalent to setting (gl/nxcl ) to zero, for q q. (We have dropped the spin-index on these contributions, since we deal only with closed shell systems). Then the eigenvalue problem reduces to a simple 2x2 problem, with solutions... 

In the radical pair system studied, however, the classical hyperfine field D interacting with each radical spin which is responsible for singlet-triplet mixing is composed of the contributions of the various nuclei (with index i) n = E (Aj-Ij). Ij is the nuclear spin of the... 

Thus, in case of a closed-shell system the delocalization index between two domains equals the difference between the singlet-coupled and 1/3 of the triplet-coupled pairs formed between the domains (so-called effective pairon population" ). However, such straightforward relationship is not valid for open-shell systems. 

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