Research Interests

Method Development in Solid-State NMR and Application to Biomolecules

Heteronuclear spin decoupling in solid-state NMR

Spin decoupling in solids is a complicated process since several time-dependent processes on different time scales are involved. Firstly, there is the averaging by the radio-frequency field which leads to a partial averaging of the heteronuclear dipolar coupling. Secondly, the strong coupling among the abundant spins leads to spin diffusion resulting in an exchange-type narrowing of the residual line width. Thirdly, often magic-angle sample spinning (MAS) is used which introduces an additional time dependence of all anisotropic quantities and leads also to partial or full averaging.
We have propose a simple model to describe heteronuclear spin decoupling in solid-state NMR under MAS. It is based on a coherent description of two heteronuclear dipolar-coupled spins (I and S) and an incoherent description of the interaction of the I-spin with a large number of other I-spins. The abundant and strongly coupled I-spins are irradiated. The selected I-spin is coupled by a spin-diffusion type superoperator to the I-spin bath, and this coupling is described by a single spin-diffusion rate constant. Such a model allows us to simulate efficiently the behavior of a spin system under heteronuclear decoupling in the case of CW irradiation as well as in the case of phase-modulated sequences such as TPPM.
We have recently introduced a simple heteronuclear decoupling scheme for spin-1/2 nuclei under magic-angle sample spinning (MAS). The sequence, called XiX, consists of windowless rf irradiation with a repeat of two pulses of equal width, phase-shifted by 180°. In contrast to other pulsed decoupling schemes, the XiX scheme is found to be, within certain limits, insensitive to the flip angle of the individual pulses but only sensitive to the pulse width in units of the rotor period. It is therefore easier to implement and optimize than previously used sequences. The new sequence can lead to a significant improvement in decoupling over published sequences, in particular at high MAS frequencies.
Our current research goals in the area of heteronuclear spin decoupling under MAS are to improve the theoretical understanding of decoupling which will, hopefully, also lead to further improvements in decoupling. In addition we are also looking at alternative ways to achieve decoupling at high MAS frequencies.

fast Magic-Angle Spinning

In collaboration with Dr. Ago Samoson from National Institute of Chemical Physics and Biophysics in Tallinn, Estonia we are trying to develop solid-state NMR methods which work at the highest MAS frequencies currently achievable. The group of Dr. Samoson built an MAS spinning system which allows us to reach MAS frequencies of up to 50 kHz reliably. The system uses 2mm MAS rotors with a volume of about 11ul.
We have investigated the possibility of a low-power rf-irradiation approach to heteronuclear spin decoupling in solid-state NMR under high-frequency magic-angle sample spinning. Decoupling is achieved by applying an rf-field with an amplitude corresponding to a precession frequency much lower than the spinning frequency. This leads to a reversal of the averaging processes compared to normal high-power continuos-wave decoupling. Such an approach becomes increasingly interesting with increasing MAS spinning frequency. In rigid solids, low-power decoupling becomes competitive above about 40 kHz MAS frequency.
Currently, we are trying to improve the CW low-power decoupling at high MAS frequencies by using multiple-pulse sequences.

Dipolar recoupling under fast MAS by adiabatic methods

Fast rotation of the sample around the magic angle (MAS) in combination with strong decoupling significantly improves the 13C spectral resolution of uniformly enriched samples. Because high resolution is a prerequisite for structural investigations of large biological molecules with solid-state NMR techniques, we are interested in the development of methods which can be used under high-speed spinning. High-speed MAS offers many advantages for solid-state NMR experiments. The most important point is the increase in resolution of otherwise unresolved spectral lines containing many resonances. However, the high MAS speeds which are possible today ( ~50 kHz ) also average out very efficiently interactions which contain valuable spatial information. Recoupling of one of these interactions, the dipolar interaction, is the main focus of one of our research interests. The method we employ uses amplitude-modulated rf fields for adiabatic polarisation transfer between dipolar-coupled spins. This method has the advantage that it is efficient while at the same time being tolerant to experimental parameters. The method is applied as a spin pair filter which is able to select spin pairs and reject isolated spins and it is applied as a mixing sequence in homonuclear 2D correlation spectroscopy.

Application to Biomolecules

We are currently investigating methods to assign peptides and small proteins at high MAS frequencies. Spinning at MAS frequencies above 25 kHz has the advantage that one avoids all rotational-resonance recoupling conditions which might lead to undesired broadening of resonances. In addition, spinning at higher MAS frequencies leads to narrower lines due to an improved averaging of the homonuclear dipolar couplings among the carbon atoms. It requires, however, cooling of the sample to compensate for the heating due to the fast sample rotation. Fast MAS allows us to use efficient polarization-transfer methods (DREAM, APHH). We are also investigating methods to obtain structural constraints under these conditions.

Fundamental Research in Physical Chemistry Using Solid-State NMR

Echo phenomena in solid-state NMR

Echo phenomena have found very important applications in NMR and magnetic-resonance imaging. Understanding the details of different types of echoes has been going for many years.
We have recently investigated the question of echo formation in cross polarization. Cross-polarization at the Hartmann-Hahn condition in solid-state NMR is often described in terms of thermodynamics. In this model, spin temperatures characterizing the canonical density operator are assigned to the Zeeman reservoirs of the two spins and the cross-polarization process brings about a state of equilibrium of the two reservoirs with a common temperature. In such a model, cross-polarization from an initially polarized spin species (I spins) to another spin species (S spins) is inherently an irreversible process accompanied by an increase in the entropy of the system. However, a cross-polarization echo can be generated whereby the polarization transferred to the S spins returns to the I spins restoring the initial density operator. A thermodynamic description should therefore be applied with care even in samples where the build-up and the decay of the magnetization can be well approximated by multi-exponential processes. Such cross-polarization echoes are formed by the consecutive application of two pulse trains that produce effective Hamiltonians differing in sign. The "time reversal" of cross polarization is consistent with both the increase of the Zeeman entropy during the approach to equilibrium and with the constraint of unitary quantum evolution.
We intend to investigate the behavior of homonuclear strongly dipolar-coupled spin systems. In a first step we plan to build a single-channel high-field probe which allows us to use rf-field strength of more than 500 kHz. Such high fields open the possibility to investigate the source of the decay in the so-called "magic echoes" and "polarization echoes" . We plan to clarify whether the decay of these echoes is due to an incomplete truncation of the Hamiltonian by the rf field or due to dissipative processes which destroy multi-spin terms in the density operator. In the context of very high rf fields it is also important to re-evaluate the influence of phase transients and to develop better ways of avoiding and compensating them.

Comments to Matthias Ernst (
last changed 09 July 2002