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:

• Observed line intensity: central transition
• Nucleus: 23Na
• Spin: 3/2
• 23Na Larmor frequency: 105.8731007 MHz
• Proton Larmor frequency: 400 MHz
• Amplitude of the radio-frequency pulse: 100 kHz
• Initial pulse duration: 0
• Final pulse duration: 20 μs
• Pulse duration increment: 1 μs
• Rotor spinning speed: 15 kHz
• Quadrupole interaction: first and second orders
• Quadrupole coupling constant: 8 MHz
• Asymmetry parameter: -1
• Crystal file: rep100_simp
• αPR: 30
• βPR: 30
• γPR: 30
• Number of summation steps of the Euler angle γ of the rotor: 1

### (A) Mathematica-5 notebook: oneCrystalMAS.nb

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

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:

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