Triplet spin state

For the triplet spin states it is only necessary to consider one of the three possible spin wave functions and we will take the J wave function. Since... 

Electron-electron repulsion integrals, 28 Electrons bonding, 14, 18-19 electron-electron repulsion, 8 inner-shell core, 4 ionization energy of, 10 localization of, 16 polarization of, 75 Schroedinger equation for, 2 triplet spin states, 15-16 valence, core-valence separation, 4 wave functions of, 4,15-16 Electrostatic fields, of proteins, 122 Electrostatic interactions, 13, 87 in enzymatic reactions, 209-211,225-228 in lysozyme, 158-161,167-169 in metalloenzymes, 200-207 in proteins ... 

A), in which the donation bond is supplemented by back donation from Cvid into the tt orbital of the olefin. This implies that chromium formally gets oxidized to Cr(IV), adopting a triplet spin state. 

The reaction of BA with isopropyl alcohol is particularly revealing. Direct irradiation of DABA in neat isopropyl alcohol gives the ether (17%) expected from the reaction of the singlet carbene, and the radical coupling products characteristic of the triplet spin state (21). The ratio of the yields of radical-derived products to ether depends inversely on the concentration of isopropyl alcohol in a benzene solution. This behavior is particularly meaningful when compared with that of FL, XA and DPM. For these... 

In the experiment done under conditions of inefficient spin-lattice relaxation the triplet spin states originally produced are retained during internal conversion and vibrational relaxation. Important conclusions about the routes of intersystem crossing can thus be obtained from a study of the population of the triplet sublevels, the so-called "spin alignment . 

The nodal planes used qualitatively to discuss cis/trans isomerization clearly appear in the ELF profiles. For AA and BB at the crossing point, the picture reveals the numerical artifact of the adiabatic calculations. At the respective attractors, AA and BB show the expected nodal plane distribution. The method is not capable to distinguish between singlet and triplet spin-state ELF. This issue was discussed during the meeting. The reader may find appropriate discussions in this volume. 

Fig. 26. General reaction scheme for dye sensitized hole injection in organic crystals. The scheme shows the excitation of the adsorbed dye ( ... ) in the first row at the left hand side. Through electron transfer the "reduced dye-hole pair" (2D. . , 2C+) is generated with its singlet and triplet spin state (2. row). The dissociated "reduced dye-hole pair is shown in the third row, and finally the hole contributing to the injection current in the fourth row. The regeneration of the dye molecules can be seen on the left hand side of the third row and the generation of sensitized delayed crystal fluorescence in the first row on the right hand side. Details are explained in Section IV 4 of the text...

These complexes are paramagnetic and posses a singlet-triplet spin state equilibrium in solid and solution phases30, Pignolet, L. H., Patterson, G. S., Weiher, J. F., Holm, R. H. Inorg. Chem. 13, 1263 (19741... 

Both singlet and triplet spin states were considered for the eight coordination modes depicted in Figure 1. Results from B3LYP and PWP potentials show the... 

Rebmann, A., Zhou, J., Schuler, P., Rieker, A.J. and Stegmann, H.B. (1997) Synthesis of two novel para-extended bisaroxyls and characterization of their triplet spin states. Journal of the Chemical Society. Perkin Transactions, 2, 1615-7. 

Fig. 3 Schematic molecular orbital diagram for singlet and triplet spin states of a metal complex, showing doubly-occupied (ligand-based, for example) molecular orbitals a and b, and a degenerate pair of metal orbitals, 1 and 2...

The first combination is symmetric, and the second is antisymmetric with respect to permutation. In the ground state of the helium atom both electrons occupy the same spatial orbital (Is), so that they must have the antisymmetric spin function for the total wave function to be antisymmetric they therefore form a singlet spin state. In order to find a helium atom with a triplet spin state (so-called spins parallel), the spatial part of the wave function must be antisymmetric with respect to interchange. 

The triplet spin state is associated with the antisymmetric spatial function ... 

Clarke (326) has studied the optical electron spin polarization in triplet anthracene and has observed ESR emission at 1.5°K which was attributed to a non-Boltzman distribution over the triplet spin levels at low temperature. The dynamics of optical spin polarization in triplet naphthalene at 1.6°K was also reported by Sixl and Schwoerer (327a) and van der Waals et al. (327b). have used a general method to study dynamics of populating and depopulating triplet spin levels by microwave-induced delayed phosphorescence. These experiments enable measurements of the lifetimes of each triplet spin state and thus can provide important information about intramolecular decay processes and intermolecular triplet energy transfer. 

Use of the Heisenberg spin Hamiltonian (equation 1) to represent the energy difference of the singlet and triplet spin states is easily demonstrated. Two spins, Sj and Sj, can be added to produce a maximum spin of 5 max = Sj + Sj, and lower values - 1, max - 2 down to a minimum of Si - Sj. When the two spins are both one-half, the two possible values for the total spin are 5 tot = 1 and 5 tot = 0, the spin triplet and singlet, respectively. To evaluate the energies of these states from equation f, it is necessary to know the value of Si Sj for the two states. This can be found by evaluating the vector sum of the spins and employing the basic quantum rule... 

In the encounter RP, the ratio of singlet and triplet spin state populations is 1 3 as shown by reaction (9-12c). The MIE arises almost completely from the T-S conversion of tripler RP. Thus, the recombination probability of peroxy radicals with terminal atoms is higher than that of radicals with terminal 0 or 0 atoms. In the case of polypropylene, the a value of 1.060 0.005 was obtained for O, but 1.015 0.010 for 0. This result certified that (MIE) a(CIE) for reaction (9-12). 

In this section we shall detail the analytical derivation of the absorption spectrum for a magnetic species in a triplet spin state tumbling in a viscous disordered liquid. This an ytical structure consists of the sum of product of continued fractions. The standard Mori structure of Eq. (2.19) is recovered in the absence of orienting potentials. 

Figure 6. Absorption lineshape for a molecule in a triplet spin state dissolved in a disordered liquid. t>o 0. Frequency sweeps from Uy — - (i -I- 6) to oy = (i -t- 8). — 10 t)...

Figure 11. Absorption lineshape for a molecule in a triplet spin state subjected to an orienting potential. Ug = 0. D — 10 t. The frequency sweep ranges from u,- — (i) -f S) to ay...

These are collectively designated as the triplet spin state, there being three possible orientations for a total spin angular momentum of 1. 

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