Simulation of SQ and MQ coherence line intensities of a crystal.
Contributor: R. Hajjar

Home and Applets > Quadrupole Interaction > One-Pulse MAS > New Version for Rotating Crystal

One pulse applied to MAS crystal

AIM: We provide a new Mathematica-5 notebook to simulate single-quantum and multiple-quantum coherence line intensities for MQMAS NMR applied to half-integer quadrupole spin in a crystal.

Method: We simulate single-quantum and multiple-quantum coherence line intensities of a spin I = 3/2 with increasing pulse duration in a crystal rotating at the magic angle.

The parameters for these simulations are:

(A) Mathematica-5 notebook: oneCrystalMAS.nb

Get["QUADRUPOLE"];
(*------------- Nucleus ----------*)
quadrupoleSpin = 1.5;
larmorFrequencyMhz = 105.8731007;

(*----- Quadrupole interaction ----*)
quadrupoleOrder = 2; QCCMHz = 8; η = -1;

(*--- Rotor Euler angles in PAS ---*)
αPR = 30; βPR = 30; γPR = 30;

(*----------- Parameters ----------*)
startOperator = 0.4*Iz;
ωRFkHz = 100;
spinRatekHz = 15;
powderFile = "rep100_simp";
numberOfGammaAngles = 1;
t1 = 20;
Δt = 1;
np = t1/Δt;

(*--------- Pulse sequence ---------*)
detectelt = {{3, 2}};

fsimulation := (
  acq0;
  For [p = 1, p <= np, p++, {
    pulse[Δt, ωRFkHz];
    acq[p];
  }];
);

(*---Execute, plot, and save simulation
  in "oneCrystalMAS" file--------------*)
run;
tabgraph["oneCrystalMAS"];
    

(1) Preliminary

  1. Download Mathematica-5 notebook oneCrystalMAS.nb (the corresponding PDF file), that for MAS NMR utilities QUADRUPOLE_1_0.nb (the corresponding PDF file), and the crystal file rep100_simp.
  2. Save these three files into 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 new file called QUADRUPOLE is created in Mathematica-5 folder.

(2) Simulation

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

(B) Result

The simulated line intensities are gathered in the following table.

t
(μs)
oneCrystalMAS.nb
New version
crystal_MAS.nb
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0              
0.1909263462
0.1179498378
-0.1095760968
-0.1748410673
0.05933795078
0.349769756
0.3342515848
-0.2783335973
-0.4104664941
-0.04702774168
0.4073285563
0.3241038495
-0.1948624526
-0.4306262691
-0.05748909539
0.4018103486
0.3128637066
-0.1999188914
-0.4520927211
-0.01315623676
0              
0.1909263462
0.1179498378
-0.1095760968
-0.1748410673
0.05933795078
0.349769756
0.3342515848
-0.2783335973
-0.4104664941
-0.04702774168
0.4073285563
0.3241038495
-0.1948624526
-0.4306262691
-0.05748909539
0.4018103486
0.3128637066
-0.1999188914
-0.4520927211
-0.01315623676

(C) Conclusion

The two notebooks provide identical line intensities.

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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