Matrix zero-field splitting

For axial symmetry (i.e., / = 0) this is a diagonal matrix with only two eigenvalues D and -D and a zero-field splitting AE = D —D = 2D as we have previously noted in... 

The arylcarbenes are also bent, the angle being about 150—155° for phenyl-and diphenylcarbenes 63,64) jj g zero-field splitting parameters were shown to be appreciably dependent on the host matrix used >. However diphenylcarbene prepared from different precursors proved to be identical and is believed to be the triplet species of diphenylcarbene. 

Table 4. Calculated spin-orbit matrix elements (using Eq. (3)), calculated (using Eq. (2)) and observed Zero Field Splittings...

The Influence of the Host Matrix on EPR Line WidthB and Zero-field Splitting Parameters for Diphenylmethylene0... 

Only spatially degenerate states exhibit a first-order zero-field splitting. This condition restricts the phenomenon to atoms, diatomics, and highly symmetric polyatomic molecules. For a comparison with experiment, computed matrix elements of one or the other microscopic spin-orbit Hamiltonian have to be equated with those of a phenomenological operator. One has to be aware of the fact, however, that experimentally determined parameters are effective ones and may contain second-order contributions. Second-order SOC may be large, particularly in heavy element compounds. As discussed in the next section, it is not always distinguishable from first-order effects. 

As a most remarkable difference, the total zero-field splitting AE(ZFS) = AE is more than one order of magnitude larger for the Ir(III) than for the Pt(II) compound. Further, the decay time rm is significantly shorter. Moreover, the AE(ZFS) values and individual emission decay times are found to exhibit distinct site- and matrix-dependences for Ir(4,6-dFppy)2(acac), while these parameters are much less affected for Pt(4,6-dFppy)(acac). 

Certainly, a deeper understanding of these temperature and matrix dependent processes of sir in the lowest triplet state of Pd(2-thpy)2 requires further investigations. On the other hand, a detailed study of the processes of spin-lattice relaxation that govern the decay behavior of Pt(2-thpy)2 has recently been carried out. In this compound, the three triplet sublevels are spectrally well resolvable due to the larger zero-field splittings and thus the corresponding decay processes are more easily accessible than in Pd(2-thpy)2. (See Sects. 4.2.6 to 4.2.9 and the Refs. [24,60,62,64,65].)... 

ESR e3q>eriments, after several trials, were successful in detecting ScCO in an argon matrix at 4 K (52). The ground state was found to be as predicted by theory, with the zero-field splitting parameter d >1 cm". Hyperfine interaction with the Sc... 

We have used two spectroscopic methods to investigate the triplet state of localized diradicals. On the one hand, matrix electron paramagnetic resonance (EPR) spectroscopy was employed, which affords the zero-field splitting (zfs) parameters D and E and gives valuable information on the electronic structure [5-7]. On the other hand, time-resolved transient... 

Triplet methylnitrene can be produced by sensitized photolysis in the condensed phase or in a gas-phase corona discharge. " Barash et al. and Wasserman reported a value of the zero-field splitting parameter D/hc of 1.595 cm" for matrix isolated triplet CHgN. This earlier experiment is questionable, and a revised value ( D/hc = 1.720 cm" ) was obtained for CH3N using gas-phase spectroscopy. The triplet-triplet absorption spectrum " of 14 and its emission spectrum " " are well known. The 0-0 transition in the absorption spectrum of 14 was found to occur at 316.9 nm in an Ng matrix and at 314.3 nm in the gas phase, similar to the spectrum of the parent NH (336 nm). ... 

The advantage of this high-temperature expansion is that we need not determine the individual energy levels but can use the theorem of the invariance of the trace of a matrix. For example, to find the value of e2 we square the Hamiltonian and pick out only the diagonal terms. On summing these terms over all possible values, many of the sums cancel. For example, the zero-field splitting Hamiltonian of the form... 

With the help of the angular momentum matrices (Appendix 2) it is easy to construct the zero-field splitting Hamiltonian matrix for the given value of S (Table 8.21). 

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