Simulation of SPAM MQMAS
NMR for a spin I = 5/2.
Contributor: R. Hajjar

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Soft Pulse Added Mixing MQMAS

AIM: We provide Mathematica-5 notebooks and SIMPSON1.1.1 Tcl scripts to optimize the amplitude of the echo and that of the antiecho in SPAM MQMAS NMR applied to half-integer quadrupole spin according to the phase (X or -X) of the third or soft pulse.

Z. Gan and H.-T. Kwak [Enhancing MQMAS sensitivity using signals from multiple coherence transfer pathways, J. Magn. Reson. 168, 346-351 (2004)] present the SPAM approach to enhance the MQMAS NMR sensitivity of half-integer quadrupole spins using three coherence transfer pathways for the echo and for the antiecho signals.

Z-filtered MQMAS sequence and SPAM echo transfer pathways for a spin I = 5/2

Fig. 1: SPAM echo transfer pathways for a spin I = 5/2 system.

Z-filtered MQMAS sequence and SPAM antiecho transfer pathways for a spin I = 5/2

Fig. 2: SPAM antiecho transfer pathways for a spin I = 5/2 system.

Method: We simulate the echo and the antiecho amplitudes of a spin I = 5/2 with increasing second-pulse duration in a powder rotating at the magic angle, using Mathematica-5 notebooks and SIMPSON1.1.1 Tcl scripts. The six coherence transfer pathways are simulated with phases X and -X for the third or soft pulse.

The parameters for these simulations are:

(A) Mathematica-5 notebook

(1) Preliminary

Coherence transfer
pathway
X, X, X
sequence
notebook
X, X, -X
sequence
notebook
0Q->3Q->1Q->-1Q spam_P2
(pdf)
spam_P2
(pdf)
0Q->3Q->0Q->-1Q spam_P2
(pdf)
spam_P2
(pdf)
0Q->3Q->-1Q->-1Q spam_P2
(pdf)
spam_P2
(pdf)
0Q->-3Q->1Q->-1Q spam_P2
(pdf)
spam_P2
(pdf)
0Q->-3Q->0Q->-1Q spam_P2
(pdf)
spam_P2
(pdf)
0Q->-3Q->-1Q->-1Q spam_P2
(pdf)
spam_P2
(pdf)
  1. Download the twelve Mathematica-5 notebooks, that for MAS NMR utilities QUADRUPOLE_1_0.nb (the corresponding PDF file), and the crystal file rep100_simp.
  2. Save these files into the software Mathematica-5 folder. Forbidden the Operating System of your computer to include extra file extension to rep100_simp by providing the file name with double quotes such as "rep100_simp".
  3. Open QUADRUPOLE_1_0.nb file with Mathematica-5.
  4. Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start the notebook. (Some warning messages appear but they have no consequences on the results.) A file called QUADRUPOLE is created in Mathematica-5 folder.

(2) Simulation

  1. Open a simulation file such as spam_P2_3Q1Qxxx.nb with Mathematica-5.
  2. Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start simulation. (Some warning messages precede the simulation.) After the simulation a data file, called spam_P2_3Q1Qxxx, is created in Mathematica-5 folder. MS Excel can open this data file for graphic representation.

(B) SIMPSON1.1.1 Tcl script

(1) Preliminary

Coherence transfer
pathway
X, X, X
sequence
Tcl script
X, X, -X
sequence
Tcl script
0Q->3Q->1Q->-1Q spam_p2 spam_p2
0Q->3Q->0Q->-1Q spam_p2 spam_p2
0Q->3Q->-1Q->-1Q spam_p2 spam_p2
0Q->-3Q->1Q->-1Q spam_p2 spam_p2
0Q->-3Q->0Q->-1Q spam_p2 spam_p2
0Q->-3Q->-1Q->-1Q spam_p2 spam_p2

Download and save these twelve files into the software SIMPSON1.1.1 folder.

(2) Simulation

Run a SIMPSON1.1.1 Tcl script file such as spam_p2_3Q1Qxxx.in in a DOS window. The simulated signal amplitudes are saved in the file called spam_p2_3Q1Qxxx.fid in SIMPSON1.1.1 folder. MS Excel also can open this data file for graphic representation.

(C) Result

Figures 3 and 4 represent the twelve simulated data. Notebooks and Tcl scripts provide the same data.

Aluminum SPAM 3Q-echo amplitudes

Fig. 3: 27Al SPAM 3Q-echo amplitudes obtained with X, X, X pulse sequence (left-hand side) and with X, X, -X pulse sequence (right-hand side) versus the second-pulse duration for the three coherence 0transfer pathways.
0Q curve for coherence transfer pathway 0Q->3Q->0Q->-1Q;
±1Q curve for coherence transfer pathway 0Q->3Q->±1Q->-1Q.

Aluminum SPAM -3Q-antiecho amplitudes

Fig. 4: 27Al SPAM -3Q-antiecho amplitudes obtained with X, X, X pulse sequence (left-hand side) and with X, X, -X pulse sequence (right-hand side) versus the second-pulse duration for the three coherence transfer pathways.
0Q curve for coherence transfer pathway 0Q->-3Q->0Q->-1Q;
±1Q curve for coherence transfer pathway 0Q->-3Q->±1Q->-1Q.

For a given pulse sequence (X, X, X or X, X, -X), the 0Q curve describing the echo amplitude and that describing the antiecho amplitude have the same sign. In contrast, the ±1Q curves describing the echo amplitude and those describing the antiecho amplitude have opposite signs

Alternating the phase of the third or soft pulse

For a given phase (-X or X) of the third or soft pulse

(D) Conclusions

  1. The highest sensitivity enhancement in SPAM 3QMAS sequence is obtained with an X phase for the third or soft pulse.
  2. On the other hand, the highest sensitivity enhancement in SPAM -3QMAS sequence is obtained with a -X phase for the third or soft pulse.
  3. Therefore, when the echo signal and that of the antiecho are acquired separately, the echo amplitude and the antiecho amplitude have opposite signs.

These results are in agreement with those of J.-P. Amoureux and coworkers, [Increasing the sensitivity of 2D high-resolution NMR methods applied to quadrupolar nuclei, J. Magn. Reson. 172, 268-278 (2005)].

We provide notebooks and SIMPSON1.1.1 Tcl scripts for these two cases. They allow us to optimize the echo amplitude and that of the antiecho using each of the three pulses:

SPAM Notebook SIMPSON1.1.1
Tcl script
3QMAS P1_3Qxxx.nb (pdf) p1_3Qxxx.in
P2_3Qxxx.nb (pdf) p2_3Qxxx.in
P3_3Qxxx.nb (pdf) p3_3Qxxx.in
-3QMAS P1_-3Qxx-x.nb (pdf) p1_-3Qxx-x.in
P2_-3Qxx-x.nb (pdf) p2_-3Qxx-x.in
P3_-3Qxx-x.nb (pdf) p3_-3Qxx-x.in

We also provide notebooks and SIMPSON1.1.1 Tcl scripts as above files, but all the coherences belonging to the same MQ coherence transfer pathway are considered:

SPAM Notebook SIMPSON1.1.1
Tcl script
3QMAS P1_3QxxxS.nb (pdf) p1_3QxxxS.in
P2_3QxxxS.nb (pdf) p2_3QxxxS.in
P3_3QxxxS.nb (pdf) p3_3QxxxS.in
-3QMAS P1_-3Qxx-xS.nb (pdf) p1_-3Qxx-xS.in
P2_-3Qxx-xS.nb (pdf) p2_-3Qxx-xS.in
P3_-3Qxx-xS.nb (pdf) p3_-3Qxx-xS.in

Nicolas Malicki and coworkers [Multiplex MQMAS NMR of quadrupolar nuclei, Solid State Nucl. Magn. Reson. 28, 13-21 (2005)] present the Multiplex SPAM approach which reduces the experimental time considerably.

Solid-state NMR bibliography for:

Aluminum-27
Antimony-121/123
Arsenic-75
Barium-135/137
Beryllium-9
Bismuth-209
Boron-11
Bromine-79/81
Calcium-43
Cesium-133
Chlorine-35/37
Chromium-53
Cobalt-59
Copper-63/65
Deuterium-2
Gallium-69/71
Germanium-73
Gold-197
Hafnium-177/179
Indium-113/115
Iodine-127
Iridium-191/193
Krypton-83
Lanthanum-139
Lithium-7
Magnesium-25
Manganese-55
Mercury-201
Molybdenum-95/97
Neon-21
Nickel-61
Niobium-93
Nitrogen-14
Osmium-189
Oxygen-17
Palladium-105
Potassium-39/41
Rhenium-185/187
Rubidium-85/87
Ruthenium-99/101
Scandium-45
Sodium-23
Strontium-87
Sulfur-33
Tantalum-181
Titanium-47/49
Vanadium-51
Xenon-131
Zinc-67
Zirconium-91
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