Nuclear frequency spectra

Nuclear Frequency Spectra of Spin Systems with S = Vi and Arbitrary I... 

Figure 1. Typical nuclear frequency spectra for an 5 = Vi spin system with one nuclear spin ...

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

The correlation patterns are more complex if the nuclear quadrupole, the hyperfine, and the nuclear Zeeman interactions are of the same order of magnitude. This situation is often encountered in X-band HYSCORE spectra of weakly coupled nitrogen nuclei in transition metal complexes. A special case, where the spectrum is considerably simplified, is the so-called exact cancellation condition, where Xs 2 coi. Under this condition, the nuclear frequencies within one of the two ms manifolds correspond to the nuclear quadrupole resonance (NQR) frequencies coq = 2Kt], co = K(3 - t]), and cu+ = K 3 + rj) [43], which are orientation independent. Consequently, correlation peaks involving these frequeneies appear as narrow features in the nuclear frequency spectrum. 

There are many specific ways to generate equally spaced tags but they are all based on the same principle of manipulating the rf pulses to generate equally spaced bands of rf radiation in the frequency domain. It is well known that under ordinary conditions, meaning normal levels of nuclear spin excitation, the frequency spectrum of the rf excitation pulse(s) is approximately the Fourier transform of the pulses in the time domain. Thus, a single slice can be generated in the... 

Fig. 3. (a) Partially resolved nuclear hyperfine structure in the p.SR spectrum for Mu in GaAs in an applied field of 0.3 T. The structure occurs in the line corresponding to 0 = 90° and Ms = —1/2. (b) Theoretical frequency spectrum obtained by exact diagonalization of the spin Hamiltonian using the nuclear hyperfine and electric quadrupole parameters in Table I for the nearest-neighbor Ga and As on the Mu symmetry axis. Both Ga isotopes, 69Ga and 71Ga, were taken into account. From Kiefl et al. (1987). 

It is also possible to Fourier transform the echo envelope modulation to obtain a frequency spectrum showing the various nuclear hyperfine frequencies. In practice there are some experimental difficulties and the intensities of the Fourier transformed spectrum which are related to the number of Interacting nuclei are not well defined. However, the frequency spectrum does help to Identify frequency components associated with specific nuclei and the presence of weak isotropic hyperfine interactions. In the... 

Lastly, Gill found that the ring proton frequency in the nuclear magnetic spectrum of aminothiadiazole is shifted upheld by -1-0.53t versus the unsubstituted compound. The NH3+ group in 98, however. 

Successful first-principles molecular dynamics simulations in the Car-Paxrinello framework requires low temperature for the annealed electronic parameters while maintaining approximate energy conservation of the nuclear motion, all without resorting to unduly small time steps. The most desirable situation is a finite gap between the frequency spectrum of the nuclear coordinates, as measured, say, by the velocity-velocity autocorrelation function. 

For a given value of B, the energies of Am/ = 1 transitions between the nuclear sublevels of a given electronic spin state are much lower than those between the electronic spin components. Information on the amplitude of the wave function of the electron whose spin is responsible for the ESR spectrum at different lattice sites in the vicinity of the centre was obtained by Feher [17] by monitoring the ESR spectrum as a function of the frequencies in the nuclear frequency range, and this technique was called electron nuclear double resonance (ENDOR). Improvements in the sensitivity of ESR can be obtained using optical or electrical detection methods [47]. 

Obviously, the details in the time-profile, 7, and the frequency spectrum, Fp, of the incident X-pulse, depend on the experimental setup. However, if the duration of the pulse is either sufficiently short or sufficiently long compared to the time scale of the nuclear dynamics, 7 may be replaced by either a delta function or a constant on the nuclear time scale. Likewise, if the width of Fp can be neglected (known as the static approximation ), we can obtain simplified expressions for the differential scattering signal. However, as pointed out earlier, the frequency widths of X-ray pulses obtained from, e.g., synchrotron radiation are typically on the order of percent of the carrier frequency. Hence, in order to simulate the finer details of the experimental signal, the actual frequency distribution of the incident X-ray pulse must be taken into account [29],... 

Fig. 4. Radio frequency spectrum of H2 in the vicinity of the proton resonance frequency [4] in first clearly observed multiple line spectra with coherent radiation. The resonance frequencies are primarily determined by the interaction of the proton magnetic moment with the external magnetic field, but the states of different mj and mj are displaced relative to each other by the different values of the nuclear spin-spin and spin rotational interaction energies [4].

When we studied the radio-frequency spectrum of D2 we hit another surprise [5]. The separation of the spectral lines in D2 were greater than in H2 even though the nuclear spin-spin interaction and the nuclear spin molecular rotation interaction should be much less. We found a similar anomaly for HD. We finally interpreted this as due the deuterium nucleus having a quadrupole moment (being ellipsoidal in shape) which gave rise to a spin dependent electrical interaction. The existence of the quadrupole moment, in turn, implied the existence of a new elementary particle force called a tensor force. In this way, magnetic resonance made a fundamental contribution to particle physics. 

One of the most interesting and important results of the study was to show how the molecular constants change as the vibrational quantum number v increases. This behaviour is presented in table 8.10. The electron spin-spin and rotational constant values came, initially, from the analysis of the optical electronic spectrum [47], although the values of the spin spin constants for different vibrational levels were refined by the analysis of the radio frequency spectrum. The nuclear hyperfine parameters are obtained solely from the magnetic resonance experiments. We will discuss the significance of these constants in the following subsection. 

ENDOR lines are thus separated by the hyperfine coupling a, and the spectrum is centered at the nuclear frequency as in Fig. 2.1(a). The same result is obtained by quantum mechanics using the equation given in Fig. 2.2, where a denotes the hfc in energy units. In the opposite case with a > 2vh a spectrum like that in Fig. 2.1(b) appears. 

In a three-pulse ESEEM experiment the time T between the second and the third pulse is increased while the time x between the first and second pulse is kept constant. In contrast to the two-pulse ESEEM experiment, the three-pulse ESEEM spectra do not contain sum and difference frequencies as illustrated schematically in Fig. 2.21 for an S = Vi species with anisotropic hyperfine coupling due to a proton. Both spectra contain lines with nuclear frequencies and v expected for = /2. The combination lines at v v seen as satellites in the two-pulse spectrum do not appear in the corresponding 3-pulse spectrum. On the other hand lines can escape detection in the 3-pulse spectrum for certain values of the time x between the first and second pulse at so called blind spots. It is therefore customary to record several 3-pulse specfra with different values of x. 

The asymmetry of the ESR spectrum in Fig. 3.13 arises because of the different values for the nuclear frequencies vi and v i, while vh is approximately equal to the nuclear frequency, or ca. 14 MHz. The hyperfine sphtting in frequency units... 

Powder ENDOR lines are usually broadened by the anisotropy of the hyperfine couplings. The parameters of well resolved spectra can be extracted by a visual analysis analogous to that applied in ESR. The principle is indicated in Fig. 3.25 for an 5 = V2 species with anisotropic H hyperfine structure, where the hyperfine coupling tensor of axial symmetry is analysed under the assumption that 0 < A < Aj. < 2 vh- The lines for electronic quantum numbers ms = V2 and -Vi, centered at the nuclear frequency vh 14.4 MHz at X-band, are separated by distances equal to the principal values of the hyperfine coupling tensor as indicated in the figure. Absorption-like peaks separated by A in the 1st derivative spectrum occur due to the step-wise increase of the amplitude in the absorption spectrum, like in powder ESR spectra (Section 3.4.1). The difference in amplitude commonly observed between the ms = /2 branches is caused by the hyperfine enhancement effect on the ENDOR intensities first explained by Whiffen [45a]. The effect of hyperfine enhancement is apparent in Figs. 3.25 and 3.26. 

Whereas the paramagnetic shift of the nuclear magnetic resonance frequency for a given applied field is related to the strength of the local hyperfine field at the nuclear site, induced by the electronic moments, the nuclear spin-lattice relaxation rate yields information about the low-frequency spectrum of thermally induced spin fluctuations. The influence of pair-correlation effects on the NMR relaxation in paramagnets was analysed experimentally and theoretically by... 

The translational motions and spin dynamics of conduction electrons in metals produce fluctuating local magnetic hyperfine fields. These couple to the nuclear magnetic moments, inducing transitions between nuclear spin levels and causing nuclear spin relaxation. The translational motions of electrons occur on a very rapid time scale in metals (<10 s), so the frequency spectrum of hyperfine field fluctuations is spread over a wide range of w-values. Only a small fraction of the spectral intensity falls at the relatively low nuclear resonance frequency (ojq 10 s ). Nevertheless, the interaction is so strong that this process is usually the dominant mode of relaxation for nuclei in metallic systems, either solid or liquid. 

Electron spin echo modulation spectroscopy (Norris et al., 1980 Dikanov Tsvetkov, 1992) is sometimes called FT-ENDOR because the echo modulation time series yields a frequency spectrum that corresponds to transitions among nuclear sublevel (Rowan et al., 1965). The ESEEM technique is often said to be complementary to ENDOR (Tsvetkov Dikanov, 1987) beeause ESEEM tends to yield well-resolved spectra in the low-frequency range (<4 MHz) of the nuclear hyperfine spectrum, where cw-ENDOR is often problematie. The eonverse is likewise true ESEEM tends to be problematic at recording hyperfine frequencies above 10 MHz. 

Relaxation effects in Mossbauer spectroscopy are of a different nature from those in NMR. The term relaxation effects or relaxation spectra in nuclear gamma resonance spectroscopy refers to averaging effects that occur in the hyperfine spectrum when the hyperfine interactions fluctuate at a rate more rapid than the nuclear frequency characteristic of the hyperfine interaction itself. This situation is a consequence of the rapid relaxation of the host ion among its energy levels, and the relaxation time for such effects is characteristic of the ion and not of the nuclear spins. The relaxation processes involved also affect electron spin resonance spectra, and their discussion is best considered in that context (see sections 3.3. and 3.4.). In the following subsections the principal interactions which contribute to the nuclear spin relaxation times in NMR experiments are briefly considered, and the connections between these and the parameters characterizing the steady-state spectrum are outlined. 

---