Pake-pattern

Four-pulse DEER measurements were performed on a dimer of copper-substituted azurin molecules with a Cu(II)-Cu(II) distance of 26 A.27 Experiments were performed at 10 K with pulse lengths of 16 ns for ji/2 and 32 ns for p pulses and a 75 MHz difference between the frequencies of the pump and observe pulses. Analysis of the dipolar frequencies required consideration of orientation selection in both the pump and observe pulses because only a subset of the Pake pattern is represented in the Fourier transform of the experimental data. For this sample the orientation of the interspin vector relative to the g matrices of the two centres was known from high-field EPR. Dipolar modulation could not be detected for a second dimer with a copper-copper distance of 14.6 A.27... 

If the molecular tumbling rate is slow enough that larger electron-electron dipolar couplings are not motionally averaged, Fourier deconvolution can be used to analyze dipolar interactions in fluid solution.18 Distances in doubly spin-labelled rhodopsin were measured by Fourier deconvolution of CW line-shape changes in room temperature solution.78 The broadening function was modelled as the sum of Pake patterns from a distribution of distances. As a reference point for the distance measurements one label was attached at the cytoplasmic termination of transmembrane helix 1. The second label was attached near the cytoplasmic termination of transmembrane helix 7 or in the short helix 8. The distances and conformational flexibility in the dark state are... 

Instead of Fourier transforming the time traces, they are commonly analyzed with the program DeerAnalysis2008 from Jeschke et al. (2006), which is based on Tikhonov regularization and the assumption that the full Pake pattern is excited. 

In this case, the frequencies of the Pake pattern are shifted by J and the frequency of the edge (0y) and peak (0/) of the Pake pattern do not behave like2 l (Fig. 16.8) what they do if J is zero (Fig. 16.2C). However, if the full Pake pattern is observed both contributions can be disentangled and quantified. From the frequencies at which the peaks and edges of the Pake pattern appear, the dipolar coupling constant vdd and J can be calculated using Eqs. (16.8) and (16.9) derived from Eqs. (16.7) and (16.3) (Milov etal, 1998) ... 

Figure 16.8 Pake pattern of a biradical with dipolar and exchange coupling. The edges and peaks do not behave like 1 2 (taken from Margraf ft al., 2009).

One-dimensional quadrupole echo NMR lineshape analysis of powder samples is particularly informative when fast, discrete jumps occur between sites of well-defined geometry as, for example, in a phenyl group undergoing two-site exchange. In this case, the characteristic Pake-pattern is transformed into an axially asymmetric lineshape with an apparent asymmetry parameter r] 9 0 (see Equation (6.2.3)) [1-8]. The asymmetric lineshapes, shown on the left in Fig. 6.2.2, can be derived by considering how the individual components of the principal EFG tensor become averaged by the discrete jumps. Within the molecular frame, and in units of as defined by Equation (6.2.2), the static axially symmetric tensor consists of the components = 1, = — 1/2, and V y = — 112. This traceless tensor satisfies the... 

First, in an evolution period ti the system evolves with its initial frequency distribution, which corresponds to the simple Pake-pattern. Subsequently, the spin state is stored throughout a mixing time t, , during which... 

Figure 21.18 compares experimental H solid echo NMR spectra and the simulated H FID-NMR spectra of the RU-D2 complex trans-[Ru(D2)Cl(dppe)2[PFg (Ru-D2). At temperatures below 10 K the singularities of a satellite Pake pattern are visible as a splitting of the spectra at 60 kHz. This satellite Pake pattern is the... 

At temperatures above 23 K the NMR line corresponds to a typical NMR quadrupolar Pake pattern with an asymmetry oitj = 0.2. The satellite pattern has completely disappeared. The width of the line decreases slowly with increasing temperature, which is an indication of a weakening of the T/ -bond between the metal and dihydrogen. 

The temperature dependence of the Pake pattern can be used to deduce that the bound dihydrogen ligand undergoes a torsional or hindered rotation motion around an axis perpendicular to the metal-dihydrogen axis. The bound hydrogen is characterized as a rigid planar rotator. In some cases, the potential surface for this rotation can be characterized by these measurements. 

FIGURE 5.3 Measurement of dipolar couplings (Pake patterns) in solid-state H NMR spectra of H2 complexes. (Reprinted with permission from Ref. 123. Copyright 1990 Elsevier.)... 

In connection with these studies we have recently measured the solid state DQCC of a carbyne species W(=CMes)(dmpe)2D (Mes = mesityl) and a nitrosyl compound [16] W(CO)(NO)(PMe3)3D. It came to a surprise that in both cases only at lower temperatures the expected double modal Pake curve could be noticed. At room temperature, just a residual Pake pattern could be observed, while otherwise a strong singlet resonance developed for the nucleus of the above complexes. This can only be interpreted in terms of deuteride mobility in the solid state. Even though the mechanism for this process is not clear yet at the present time, this experiment points to the general propensity for deuteridic, or hydridic cleavage of hydridic L M-D(H) bonds. 

Dipolar interaction can lead to an EPR line broadening (Fig. 6). The spectrum of the interacting spins can be treated as the convolution of the non-interacting powder pattern spectrum with a dipolar broadening function which is known as Pake pattern in randomly oriented samples. 

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