ALBERT

Notes: Static and dynamic properties related to the internal configurational motions have been calculated for the alkyl chains of phospholipid molecules in a membrane environment in the liquid crystal phase. The calculations have been performed for the chain 1 of 1,2-dipalmitoyl 3-sn-phosphatidylcholine (DPPC), a typical constituent of phospholipid membranes. Under the assumption of fixed bond lengths and bond angles, the internal dynamics of the chain is described in terms of 15 dihedral angles. The time evolution of the angular variables is assumed to be diffusional in character, and a master equation for transitions among the stable conformers is constructed from the energetics and hydrodynamics of the chain. This method is an extension to the time domain of the rotational isomeric state (RIS) approximation, which has been widely used to compute static properties of the chains. After calculation of the suitable correlation functions, effective rate constants relevant for spectroscopic and kinetic observables have been computed, and the results have been compared with those obtained by recent Brownian dynamics (BD) calculations. The position dependence of the rate constants along the chain has been examined with special reference to understanding the effects resulting from cooperativity in the conformational transitions. The overall spinning and tumbling of the chain has also been described by a diffusive model. The calculated spectral densities for the composite motional process have been used to rationalize the behavior of the relaxation times T1, T2, and T1ρ measured in deuterium nuclear magnetic resonance (NMR) experiments.

Notes: Electron spin–echo (ESE) and two-dimensional electron–electron double resonance (2D ELDOR) experiments have been performed as a function of director orientation and temperature in the smectic A phase of the liquid crystal S2 for the spin–probe PD-tempone(2×10−3 M). Over the entire temperature range studied (288–323 K) we observe significant 2D ELDOR cross peaks only for ΔMI =±1 indicative of 14N spin–relaxation and negligible Heisenberg exchange. From the angular dependent 14N spin–relaxation rates we obtain the dipolar spectral densities at the hyperfine (hf) frequency, whereas from a combination of ESE and 2D ELDOR we obtain the dipolar and Zeeman-dipolar spectral densities at zero frequency. The angular dependent spectral densities were successfully decomposed into their basic components in accordance with theory. The angular dependent spectral densities at the hf frequency are not predicted by a model of anisotropic rotational diffusion in a nematic orienting potential, but are consistent with predictions of a model due to Moro and Nordio of solute rototranslational diffusion in a McMillan-type potential. The angular dependence also indicates that order director fluctuations in the smectic phase are suppressed at frequencies on the order of 10 MHz. An additional contribution to solute reorientation due to cooperative hydrocarbon chain fluctuations is suggested to account for the behavior of the observed spectral densities at zero frequency. An evaluation of the relevance of several other dynamical models to this experimental work is also presented.

Notes: We describe our pulsed two-dimensional Fourier transform ESR experiment and demonstrate its applicabilty for the double resonance of motionally narrowed nitroxides. Multiple pulse irradiation of the entire nitroxide spectrum enables the correlation of two precessional periods, allowing observation of cross correlations between hyperfine lines introduced by magnetization transfer in the case of a three-pulse experiment (2D ELDOR), or coherence transfer in the case of a two-pulse experiment (COSY). Cross correlations are revealed by the presence of cross peaks which connect the autocorrelation lines appearing along the diagonal ω1=ω2. The amplitudes of these cross peaks are determined by the rates of magnetization transfer in the 2D ELDOR experiment. The density operator theory for the experiment is outlined and applied to the determination of Heisenberg exchange (HE) rates in 2,2,6,6-tetramethyl-4-piperidone-N-oxyl-d15 (PD-tempone) dissolved in toluene-d8. The quantitative accuracy of this experiment is established by comparison with the HE rate measured from the dependence of the spin echo T2 on nitroxide concentration.

Notes: New Fourier transform ESR techniques, which permit rapid data acquisition of ESR spectra, now allow one to perform a variety of two-dimensional ESR experiments. Two prototype experiments on a fast motional nitroxide spectrum are described. The first is based upon detection of the Han echo and may be used for discriminating the homogeneous broadening of an inhomogeneous spectrum (and/or the echo envelope modulation). The second is based upon detection of the FID after the three-pulse Jeener–Ernst sequence, and it leads to cross peaks due to Heisenberg spin exhange among the hyperfine lines.

Notes: The complex symmetric Lanczos algorithm (LA) has proven to be a very efficient means of calculating magnetic resonance line shapes and spectral densities associated with Fokker–Planck forms. However, the relative importance of the various components of the basis set in an accurate representation of the spectrum and the proper number of recursive steps are not easily assessed in practice using the Lanczos algorithm. A systematic and objective procedure for the determination of optimal basis sets and number of recursive steps is developed using a generalization of the conjugate gradient method (CGM) appropriate for the type of complex symmetric matrices occuring in these problems. The relative importance of the individual basis vectors is determined by using the CGM to obtain the "solution vector'' from the set of algebraic equations defining the spectrum. This is done at several values of the sweep variable (e.g., the frequency or the magnetic field). The maximum (over these values of sweep variable) for each component of the solution vector is taken to be a measure of the overall importance of the corresponding basisvector in the complete spectrum. Using this method signficant basis set truncation is conveniently possible. The number of recursive steps needed for an accurate representation of the spectrum is easily obtained by monitoring the residual in the approximate solution vector at the center of the spectrum and by recognizing the close relationship between the LA and the CGM. It is this relationship that enables construction of the Lanczos tridiagonal matrix with the CGM which can either be used to calculate the cw ESR spectrum directly or else the eigenvalues. The information obtained from the CGM can be used to "turbocharge'' the LA by taking advantage of the nearly optimal basis set and number of recursive steps. Significant savings in computation time are possible, and relative savings are greatest for the most difficult problems. This is illustrated with a variety of examples of slow-motional cw ESR spectra and of the new two-dimensional electron-spin-echo technique. In keeping with the greater sensitivity of the latter technique to motional dynamics, it is consistently found to require significantly larger optimal basis sets and number of recursive steps for an accurate representation. One of the most challenging problems for both types of spectroscopy is the case of macroscopically oriented samples where the macroscopic director is tilted at an angle relative to the applied static magnetic field, since this removes much of the symmetry in the problem. This case is found to yield to very significant truncation of basis sets, and a new symmetry-based decoupling of certain basis vectors was found in this study for the particular example of a 90° tilt angle.