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
• α_PR: 30
• β_PR: 30
• γ_PR: 30
• Number of summation steps of the Euler angle γ of the rotor: 1

(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.

(C) Conclusion

The two notebooks provide identical line intensities.