Chapter
2
Multiple-Quantum Magic-Angle Spinning NMR of Half-Integer Quadrupolar Nuclei 1
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Ales Medek, Laura Marinelli, and Lucio Frydman
Department of Chemistry (M/C 111), University of Illinois at Chicago, 845 West Taylor Street, Chicago, IL 60607-7061
The present report reviews some of the principles and practical details involved in multiple-quantum magic-angle spinning (MQMAS) NMR, a technique that we have recently introduced for the acquisition of high-resolution solid phase spectra from half-integer quadrupolar spins. The way in which MQMAS achieves the simultaneous averaging of all solid state spin anisotropies is discussed and placed in perspective with respect to previous procedures involving spatial averaging. The new chemical information that in a high resolution format can become available using MQMAS is described and illustrated, as are a number of experimental hints useful for its practical implementation. Challenges currently faced by the MQMAS procedure are discussed and potential solutions to these problems presented.
The NMR of Half-Integer Quadrupolar Spins Quadrupolar nuclei with half-integer spin numbers (S = 3/2, 5/2, 7/2, 9/2) constitute the single largest group of magnetically active nuclides in the Periodic Table (Figure 1) (1). The elements associated with these isotopes play fundamental roles in a variety of technologically important materials including ceramics, glasses, catalysts and semi-conductors, as well as in numerous bioorganic processes and biological structures. The inconvenience and sometimes even impossibility of characterizing the structure and dynamics of many of these systems using conventional liquid phase spectroscopy has stimulated a continued interest in the development of methods that will allow their study in the solid phase. Particularly promising appears the study of these mostly inorganic structures by way of nuclear magnetic resonance (NMR) (2-4), a method which has already proven decisive in the study of organic and bioorganic systems using spin-1/2 probes (5). An important difference that from the NMR point of view arises between the spectroscopy of half-integer quadrupoles and that of spin-1/2 nuclei, is that the former interact not only with the external magnetic field but also with local electric field gradients (6). The resulting quadrupolar interaction can give origin to considerably large coupling constants (e qQ/h) capable of reaching into the hundreds or even thousands of MHz; in such extreme cases quadrupole and Larmor frequencies become comparable and the 2
136
©1998 American Chemical Society In Solid-State NMR Spectroscopy of Inorganic Materials; Fitzgerald, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
137 observation of signals form powdered samples may actually become easier to achieve under zero-field operation (6,7). The scenario that we will be considering here is one where although large, the e qQ/h coupling constant is still small compared to the Larmor frequency νχ,. It is then possible to describe the effects introduced by the quadrupolar couplings on a spin energy spectrum using a perturbative approach like the one illustrated in Figure 2 for a spin-3/2. As shown in this hierarchical diagram quadrupole effects are to first order proportional to the square of the ζ angular momentum of the S spin (m = 3/2, 1/2,...), thus shifting the satellite +3/2+l/2 and -3/2Ί/2 transitions but leaving unaffected the central -l/2*->+l/2 spectral line. Since these first order effects Αι(Θ,φ) are proportional to e qQ/h and anisotropic, they will complicate or even preclude the detection in powdered solids of all single-quantum transitions other than the central one. For small enough values of e qQ/h this remaining -1/2+1/2 transition will be essentially devoid from quadrupolar broadening, and high-resolution solid state NMR spectra can simply be recorded by its observation (8,9). This situation does occasionally arise when dealing with chemical sites possessing a sufficiently high degree of local symmetry; in a majority of cases, however, quadrupolar effects will not be sufficiently small to allow this first-order description of the events to be appropriate. In these cases the e qQ/h (θ. ψ)). +
(1)
Each of these terms possesses a characteristic behavior upon sample reorientation. 8^ is an orientation independent contribution of quadrupolar origin that behaves very similarly to the isotropic chemical shift v \ δ^(θ,φ) is a second-rank anisotropic frequency term that transforms in the same manner as shielding or dipolar anisotropics; is a new fourth-rank anisotropy that arises due to the fact that we are dealing with the square of the quadrupolar interaction. Notice that in spite of their different angular dependence all these terms will affect an NMR spectrum in direct proportion to the quadrupole coupling squared, and inversely proportional to the strength of the applied field B . cs
0
In Solid-State NMR Spectroscopy of Inorganic Materials; Fitzgerald, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
138
He
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H
Half-Integer Quadrupolar Spins Β iSpin-1/2 iNo Spin Al Si
c
Li Be
1 Na Mg 1
GSο P
S
F
m
Cl
AT
Κ Ca Sc Tl V Or Mn Fe Co m Cu Zn Ga Ge As Se Br Kr Mo Tc R» Rh Pd Ag Cd In Su Sb Te 1 Xe
Rb Sr Y
Cs Ba La Hf Ta W Re o$
Ir Pt Au
Tl Pb Bt Po At Rn
Fr Ra Ac Ce Fr m Pm Sm Eu Gd n> By Ho £r Tm Yb Lu Np Pu Am Cm Bk Cf Es Fm Md No Lr
Th Pa υ
Figure 1. Periodic Table of the Elements indicating the nature of the most abundant NMR-active isotopes.
c
S
z
„ Zeeman
Quadrupolar (first-order)
Quadrupolar (second-order)
m=3/2 VL
VL+Διίθ,φ)
m=l/2
m=-l/2
VL+A2@,(p)
m=-3/2
Figure 2. Perturbative description of the effects introduced by Zeeman and quadrupolar interactions on the energy levels of a spin-3/2.
In Solid-State NMR Spectroscopy of Inorganic Materials; Fitzgerald, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
139
Although the presence of an isotropic quadrupolar shift opens up the attractive possibility of distinguishing chemical sites according to the symmetry of their ground-state electronic environments, δί > and δί > will usually broaden the 2
4
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central transition signals arising from Δ2(Θ,φ) and thus prevent the resolution or analysis of inequivalent sites. The resolution of these quadrupolar spectra can be improved by rapid spinning of the powdered sample at an angle β with respect to the external magnetic field (5). Under the effect of this process each term in equation 1 will transform differently, leading in the fast-spinning regime to an average time evolution given by (13,14) Φ(Μ=(νl(vj 2
4
4
+ v2\c[ Hm1)\/0 Hl/2),
v) 2
(18)
This linear manipulation of the 2D spectrum exploits the fact that anisotropic quadrupolar contributions along the two frequency axes are proportional to one another (equations 14 and 15), in order to remove the broadening from one of the spectral axes and yield a purely isotropic-anisotropic correlation spectrum (Figure 5). A convenient way of carrying out such shearing of the data without resorting to interpolations is by implementing it in the mixed time-frequency domain (tj,v ) using a time-proportional phase correction (19,20). It should be kept in mind, however, that this shearing may complicate the referencing of the resulting peaks, particularly if an external reference placed at a frequency other than the transmitter carrier is employed. Besides their high resolution, an interesting feature of the 2D NMR spectra resulting from this procedure is that the centers of mass characterizing resonances along the two spectral axes are different. These centers of mass are solely determined by isotropic chemical and quadrupolar shift contributions, and their non-coincident values are a reflection of the different strengths with which these shifts influence the evolution of multiple- and single-quantum coherences. The weighting coefficients (α^,α* ) that define the isotropic chemical and quadrupolar contributions to peaks in sheared MQMAS NMR spectra can be calculated from equations 9 and 11, and they are summarized for different S and mj numbers in Table I. These coefficients allow one to discriminate the relative contributions of 2
In Solid-State NMR Spectroscopy of Inorganic Materials; Fitzgerald, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
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143
βΟ
60
Figure 3. Orientation dependence of Legèndre polynomials {Ρ i(cosβ)} 1=2,4 on the spinning angle /?, indicating the positions of their non-coincident roots (β = 54.7°: magic angle).
2lNmS0
4
kHz
(S=3/2)
0
KS5Mn0 (S=5/2) 4
2.5
kHz
-2.5
Figure 4. MAS and MQMAS experiments onS = 3/2, S = 5/2 samples. Top: 2D triple-Vsingle-quantum MAS data sets showing the ridges of anisotropy-free data, and their comparison with the expected t\/t2 ratios. Center: MAS powder NMR spectra originated by second-order quadrupole effects. Bottom: Isotropic spectra afforded by the MQMAS experiment. All data were acquired at 4.7 Τ using a home-built spectrometer and probe while doing MAS at ca. 7 kHz; asterisks indicate spinning sidebands.
In Solid-State NMR Spectroscopy of Inorganic Materials; Fitzgerald, J.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.
144 Vcs and \r ' by a simple center of mass calculation of a peak's position in the 2D NMR spectra; it is worth noting that until now similar model-free determination of these parameters required measurements at two or more magnetic field strengths (9,21).
Table I. Coefficients ( a , a ) ( α£ , a ) determining a peak's center of mass cs
q
t
5
q
( Vj), ( v ) in a sheared MQMAS spectrum in terms of isotropic chemical and quadrupolar shifts. *^ 2 Spin Transition cs «1 4 cs 5 -mj+mj 3/2 1 3 -3/2
