Nuclear transition frequencies

The analysis of ESEEM data usually involves simulation of the ESEEM spectrum from a spin Hamiltonian that models the nuclear transition frequencies. Therefore it is important that ESEEM spectra accurately report on the... 

The dipole-dipole interaction between an electron spin S= l2 with g=g and a proton has a magnitude of 79 MHz at a distance of 1 A. It scales with distance as r and is proportional to the product of the electron and nuclear g factors. Only in exceptional cases are splittings due to this interaction resolved in EPR spectra. Usually. ENDOR or ESEEM techniques are applied that measure nuclear transition frequencies with a sensitivity roughly comparable to an EPR experiment. " The resolution of the measurements is determined by the static NMR line width, which is typically up to 100 kHz for protons in solids and less for other nuclei. This indicates that distances up to 8 A between an electron spin and a proton can be measured. The precision of the distance measurement is not usually limited by the precision of the frequency measurement but rather by the spatial distribution of the unpaired electron. For a paramagnetic center with known structure, the latter contribution can be estimated by quantum-chemical computations of the hyperfine coupling and can thus be corrected. 

The pulsed EPR technique of Electron Spin Echo Envelope Modulation (ESEEM) is used to measure the nuclear transition frequencies of paramagnetic nuclei magnetically coupled to unpaired electron spins. We have employed this technique to study the Mn center of the Photosystem II oxygen-evolving complex. ESEEM measurements were performed on the multiline Mn EPR signal associated with the S2 state of the Kok cycle. 

The pulse EPR methods discussed here for measuring nuclear transition frequencies can be classified into two categories. The first involves using electron nuclear double resonance (ENDOR) techniques where flie signal arises from the excitation of EPR and NMR transitions by microwave (m.w.) and radiofrequency (r.f) irradiation, respectively. In the second class of experiments, based on flic electron spin echo envelope modulation (ESEEM) effect, flic nuclear transition frequencies are indirectly measured by the creation and detection of electron or nuclear coherences using only m.w. pulses. No r.f irradiation is required. ENDOR and ESEEM spectra often give complementary information. ENDOR experiments are especially suited for measuring nuclear frequencies above approximately 5 MHz, and are often most sensitive when the hyperfine interaction in not very anisotropic. Conversely, anisotropic interactions are required for an ESEEM effect, and the technique can easily measure low nuclear frequencies. 

Apart from ESEEM methods, electron nuclear double resonance (ENDOR) spectroscopy is the other well-estabhshed technique for measuring nuclear transition frequencies of paramagnetic compounds. We start with a brief discussion of the two standard pulse schemes, Davies and Mims ENDOR, before moving onto 2D sequences aimed at resolution improvement. 

Effect of Weak cfi on Nuclear Transition Frequencies and Appearance of ENDOR Spectra [39]... 

In some cases, it may be beneficial to use ELDOR-detected NMR [20] instead of ENDOR to obtain the larger nuclear transitions. This technique bears similarities with the above-mentioned ENDOR techniques, but instead of using an RF pulse, a microwave pulse with variable microwave frequency is used to affect the electron populations. The nuclear transition frequencies follow from monitoring the polarization changes as a function of the difference between the two microwave frequencies. 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

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... 

In a spin system, each nuclear spin precesses around its individual effective static field Beff = B0 + Be(ms), (Sect. 3.3). Since the resonance frequency of a nuclear transition is proportional to B=ff, ENDOR lines for different types of nuclei may be observed in the same frequency range. 

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 hfs and quadrupole tensors of one of the nitrogen ligands have been determined with ENDOR by Calvo et al.63). The 14N-ENDOR transition frequencies observed between 11 and 23 MHz were found to depend significantly on the nuclear quantum number mCu of the EPR observer line. These shifts are due to Cu-N crossterms (Sect. 3.2) and amount to more than 1 MHz for certain orientations of B0. ENDOR resonances of... 

The principle of the ENDOR method is illustrated in Fig. 1. It refers to the most simple spin system with an electron spin S = 1/2 and a nuclear spin I = 1/2 for which an isotropic hf interaction, aiso, is considered. In a steady state ENDOR experiment4, an EPR transition (A, D), called the observer, is partly saturated by microwave radiation of amplitude B while a driving rf field of amplitude B2, called the pump, induces nuclear transitions. At frequencies vj and v2, the rf field tends to equalize the populations within the ms-states. This alters the degree of saturation of the observer so that, in the display of the EPR signal height versus the radio frequency, two ENDOR lines at transition frequencies vj = aiso/2 - vn (A, B) and v2 = ais0/2 + v (C, D) will be observed (v = / NgnBo denotes the nuclear Zeeman frequency for a static field B0). 

We wanted to extend this approach to include dynamical effects on line shapes. As discussed earlier, for this approach one needs a trajectory co t) for the transition frequency for a single chromophore. One could extract a water cluster around the HOD molecule at every time step in an MD simulation and then perform an ab initio calculation, but this would entail millions of such calculations, which is not feasible. Within the Born Oppenheimer approximation the OH stretch potential is a functional of the nuclear coordinates of all the bath atoms, as is the OH transition frequency. Of course we do not know the functional. Suppose that the transition frequency is (approximately) a function of a one or more collective coordinates of these nuclear positions. A priori we do not know which collective coordinates to choose, or what the function is. We explored several such possibilities, and one collective coordinate that worked reasonably well was simply the electric field from all the bath atoms (assuming the point charges as assigned in the simulation potential) on the H atom of the HOD molecule, in the direction of the OH bond. 

Except for coi (transition frequencies of the nuclear spin Hamiltonian) all values are temperature-dependent. From the previous subsection the behaviour of a>s is known. From the anomalous contribution to the birefringence which is proportional to (Sp ) we get the information concerning Ai. If we assume that the damping of the soft mode is non-critical (which is generally accepted), Eq. 10 describes a transition from an under-damped mode to an over-damped one as Tc is approached from either side. 

ENDOR spectroscopy has proven to be a valuable technique to provide information on both free and protein bound flavin radicals. Since flavin radical ESR spectra can be partially saturated at moderate microwave power, ENDOR spectra may be observed as nuclear spin transitions by detection of changes in the partially saturated ESR signal as a function of nuclear radio frequency. The resonance condition for nuclei (when I = Vz) is described by the following equation ... 

Use of (1.244) shows that the allowed ESR transitions are between levels 1 and 3 and between levels 2 and 4. The electron s spin flips, while the nuclear spin remains unchanged. The transition frequencies are... 

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