Rotational echo double resonance in
IS
N
spin networks: Deconvolution
of multiple dipole–dipole couplings
Oskar Liivak
a)
Department of Physics, Cornell University, Ithaca, New York 14853
David B. Zax
Department of Chemistry and Chemical Biology, Baker Laboratory, and Cornell Center for Materials
Research, Cornell University, Ithaca, New York 14853
͑Received 8 January 2001; accepted 18 April 2001͒
In a recent paper we have demonstrated how a simple modification to the standard rotational echo
double resonance pulse sequence, where the flip angle of the pulse applied to the S spin is varied,
can be used to separate the measurement of the magnitude of I –S dipole–dipole couplings from that
of their relative orientation. An equivalent result can be achieved via phase modulation which labels
and differentiates between different evolving coherences in the density matrix based on the number
of S spins participating—exactly as is done in multiple quantum spectroscopy. As phase modulation
can be effected on modern instruments with much higher precision, in this paper we explore the
experimental implementation of this method in the IS
2
spin system glycine–
13
C
2
–
15
N, and discuss
generalizations of this technique to larger spin systems. © 2001 American Institute of Physics.
͓DOI: 10.1063/1.1378040͔
I. INTRODUCTION
One approach to the derivation of structural information
in disordered materials relies on the sensitivity of solid state
nuclear magnetic resonance ͑NMR͒ to the dipole–dipole
couplings between nuclear spins, which depend directly on
internuclear distances. Successful exploitation of these cou-
plings in structural studies, however, remains somewhat in-
efficient. Evolution under the anisotropic, multispin dipole–
dipole Hamiltonian as would characterize abundant spins
depends not only upon the set of internuclear distances but
also the local geometry. While the combination of distances
and orientation angles provides a powerful tool for structure
determination, difficulties in unambiguously deconvolving
distances from angular factors largely limits application of
rotational echo double resonance ͑REDOR͒ type methods to
measurements of a single heteronuclear coupling at a time.
Alternatively, ⌰-REDOR
1
has been shown to deconvolve
multiple couplings using small flip-angle pulses—with the
drawback that much of the available magnetization is left
unused. Thus, extended structural studies via REDOR may
require compounds labeled at multiple sites in a pairwise
fashion. It would be preferable, instead, to measure many
couplings in a single experiment.
2
The need for more effi-
cient methods of measuring multiple distances becomes even
more important as REDOR studies attempt to measure
longer distances—as the number of potentially interacting
couplings increases rapidly as the targeted volume increases,
and these interactions substantially complicate the analysis
of experimentally obtained REDOR dephasing curves.
3
Recently we have suggested an experiment which allows
for a simplified analysis of REDOR data appropriate to the
derivation of dipole–dipole couplings from dipolar-dephased
REDOR spectra in IS
2
spin networks. We begin by present-
ing the modified REDOR pulse sequence we apply to mul-
tiple spin systems, and present an analysis of the new fea-
tures not previously discussed. We continue with
experimental results derived from triply labeled glycine, and
with a discussion of common experimental errors which
complicate the analysis of these REDOR experiments, and
which demonstrate the increased robustness of this modified
version. Finally, we close with a discussion of the generali-
zation of these experiments to arbitrarily large spin networks.
II. PULSE SEQUENCE ANALYSIS
REDOR pulse sequences are shown in Fig. 1, including
a modified version of what we proposed in our recent work.
4
A general analysis applicable to such sequences was de-
scribed in detail in that same paper, and we rely heavily on
those previous results. A characteristic of all REDOR-like
sequences is the application of a sequence of pulses to the I
spins designed to produce an effective Hamiltonian which
includes only a scaled version of the heteronuclear dipolar
Hamiltonian, H
¯
ϰ
͚
j
D,j
I
z
S
z,j
. The two spin species, I and
S, are decoupled from one another by the action of magic
angle sample spinning which accompanies any high-
resolution solid state technique. The dipole–dipole couplings
can be selectively reintroduced by the application of the
REDOR pulse sequences illustrated, where in both cases we
apply a train of
pulses to the S spins every half-rotor
period, except that no pulse is applied at the exact middle of
the sequence. This sequence of pulses generates in each half
of the dipolar evolution period an average Hamiltonian of the
desired form.
a͒
Current address: IBM Almaden Research Center, 650 Harry Road, San
Jose, CA 95120.
JOURNAL OF CHEMICAL PHYSICS VOLUME 115, NUMBER 1 1 JULY 2001
4020021-9606/2001/115(1)/402/8/$18.00 © 2001 American Institute of Physics