## One pulse applied to MAS powder

**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 powder.

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

The parameters for these simulations are:

- Observed line intensity: central transition
- Nucleus:
^{23}Na - Spin: 3/2
^{23}Na 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**and**-15 kHz** - Quadrupole interaction: first and second orders
- Quadrupole coupling constant: 8 MHz
- Asymmetry parameter: -1
- Crystal file: rep100_simp
- Number of summation steps of the Euler angle γ of the rotor: 3

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

Get["QUADRUPOLE"]; (*------------- Nucleus ----------*) quadrupoleSpin = 1.5; larmorFrequencyMhz = 105.8731007; (*----- Quadrupole interaction ----*) quadrupoleOrder = 2; QCCMHz = 8; η = -1; (*--- Rotor Euler angles in PAS ---*) α_{PR}= 30; β_{PR}= 80; γ_{PR}= 120; (*----------- Parameters ----------*) startOperator = 0.4*Iz; ωRFkHz = 100; spinRatekHz = 15; powderFile = "rep100_simp"; numberOfGammaAngles = 3; 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 "onePowderMAS" file--------------*) run; tabgraph["onePowderMAS"];

#### (1) Preliminary

- Download Mathematica-5 notebook onePowderMAS.nb (the corresponding PDF file), that for MAS NMR utilities QUADRUPOLE_1_0.nb (the corresponding PDF file), and the crystal file rep100_simp.
- 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".
- Open QUADRUPOLE_1_0.nb file with Mathematica-5.
- 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

- Open onePowderMAS.nb file with Mathematica-5.
- 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 onePowderMAS is created in Mathematica-5 folder. MS Excel can open this data file for graphic representation.

### (B) Result

The simulated line intensities for two opposite rotor spinning speeds are gathered in the following table.

t (μs) |
Rotor spinning speed: 15 kHz |
Rotor spinning speed: -15 kHz |
---|---|---|

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 |
0 0.1966516113 0.1407515005 -0.07013333075 -0.1418308959 0.004308044472 0.1484301615 0.09519135239 -0.06704005251 -0.1129497492 0.01198907045 0.124670265 0.07777468433 -0.04395928328 -0.07373481123 0.01932615899 0.08592484193 0.03816589776 -0.04505499021 -0.04325721476 0.03423029552 |
0 0.1966516113 0.1405010943 -0.07193143925 -0.1464688148 0.008288630193 0.1550069159 0.08993224876 -0.08208032528 -0.121105739 0.02564040147 0.1439525973 0.07957656183 -0.06646607056 -0.08892222642 0.02320356206 0.10851410743 0.05282811978 -0.05239192631 -0.05929601348 0.02762217095 |

### (C) Conclusion

Powder averaging using crystal file (or powderFile) for line intensity simulation provides different results for two opposite rotor spinning speeds. However this discrepancy disappears when the asymmetry parameter is zero, or when one of the two angles α and β is zero in the crystal file (or powderFile).