ENDOR transition probability

The quantity Gm contains contributions from the hyperfine tensor A and the nuclear Zeeman term i n- A quadrupole energy term Pm contributes when I > Vi. By applying 2nd order corrections frequencies can be obtained with better accuracy when the condition Gm Pm does not strictly apply. Equation (3.33) for the ENDOR transition probability first given by Toriyama et al. [45b] applies for species with small g anisotopy. 

The direction of the radiofrequency field (RE) is specified by the unit vector r. An exhaustive analysis of ENDOR transition probabilities including cases with anisotropic g and with circularly polarised RE fields has been presented by Schweiger and Gunthard [45c]. 

For the evaluation of energy levels, ENDOR frequencies and nuclear transition probabilities from the spin Hamiltonian (3.1), we apply the generalized operator transform method, published by Schweiger et al.55, which is only based on the assumptions 3fEZ > and 2fhfs s> 3 Q. No restrictions are made on the relative magnitudes of 3 hfs and... 

Nuclear transition probabilities are also influenced by the quadrupole interaction, e.g. for 2 hfs — 2 q transitions with Ami > 1 may be induced. Nitrogen ENDOR spectra with Ami = 2 transitions have been observed in several metal complexes with small 14N hf couplings59,70,715. 

The two techniques, ENDOR and ESE envelope modulation, supplement each other. ESE envelope modulation seems to be more sensitive in detecting nuclear transitions at very low frequencies but is limited in the frequency range by yeB , where ye denotes the gyromagnetic ratio of the electron and Bj the microwave pulse amplitude. ENDOR, whose sensitivity increases with frequency, suffers on the other hand from the small transition probability at low frequencies. 

The 14N hf and quadrupole parameters observed in Co(acacen) by Rudin et al.59 are the first magnetic data reported on equatorial nitrogen ligand nuclei in a low-spin Co(II) complex. Only two of the four predicted AmN = 1 ENDOR transitions (3.9) were observed for each nitrogen nucleus. A numerical calculation of the transition probabilities shows that the corresponding transitions in the other ms-state are at least ten times less intense (hyperfine enhancement). 

D4H covering symmetry. The symmetry of the A/N4 unit of Cu(TPP) and Ag(TPP) diluted into (H20)Zn(TPP) was found to be essentially 041, . When Bo is directed along the molecular x or y axis (between the M-N bonds), all four nitrogens are equivalent. For these field orientations. Brown and Hoffinan observed a broad N-ENDOR pattern with only partially resolved structure. An analytical calculation of the ENDOR frequencies and transition probabilities for these Bq field orientations is straightforward, but very tedious To get a better insight into the complexity of the ENDOR spectrum for Bo oriented along a molecular axis a numerical diagonalization of the fuU Hamiltonian matrix (four 1 = 1 nuclei) with Bq normal to the porphyrin plane has been performed. In Fig. 10 the calculated transition fi-equencies and intensities for this particular Bq field orientation are compared with the observed spectrum. 

ENDOR and FT ESEEM spectra differ mainly in the intensities of the lines, which in ESEEM are given by a factor related to the ESR transition probabilities. A necessary prerequisite for modulations in the time domain spectrum is that the allowed Ami = 0 and forbidden Ami = 1 hyperfine lines have appreciable intensities in ESR. The zero ESEEM amplitude thus predicted with the field along the principal axes of the hyperfine coupling tensor is of relevance for the analysis of powder spectra. Analytical expressions describing the modulations have been obtained for nuclear spins I = V2 and / = 1 [54, 57] by quantum mechanical treatments that take into account the mixing of nuclear states under those conditions. Formulae are reproduced in Appendix A3.4. 

Fig. 3.28 Experimental top) and simulated powder ENDOR spectrum due to CO2 ion radicals formed by X-irradiation of a polycrystalline lithium formate sample at room temperature. The experimental spectrum was obtained by saturating the central ESR resonance line. The simulated spectra represent the components due to the hyperflne couplings of Li at four different positions in the vicinity of the CO2 ion. The sum spectrum is obtained by addition of the components. The low frequency branches of the transitions are weak or not observable in experimental and theoretical spectra probably due to different hyperflne enhancement effects for = Vi and -Vi. The figure is reproduced from [K. Komaguchi et al. Spectrochimica Acta Part A 66,754 (2007)] with permission from Elsevier...

A/Mj = 0, whereas the nuclear spin transition operator connects states with Tx = and Airij 0. Pure electron spin and nuclear spin transitions can then be observed, as in ordinary high-field (hf) experiments. The probability of the former is considerably higher than that of the latter owing to differences in the magnitudes of the respective moments. However, as in zf experiments on doublet states (e.g., H atom), the mixing of the basis functions by off-diagonal hyperfine terms allows the observation in zf of simultaneous electron-nuclear transitions (i.e., Tx and Anij 0) and contributes additional oscillator strength to the pure nuclear spin transitions. The electron spin transition operator can be the major source of intensity in zf ENDOR experiments (Harris and Buckley, 1976). 

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