One-pulse line intensity
for a spin I = 3/2 in MAS powder with rep100 file.
Contributor: R. Hajjar




Home and Applets > Quadrupole Interaction > One-Pulse MAS > Rotating Powder with Rep100 File

One-pulse line intensity for MAS powder, Part 2

AIM: With a same crystal file for powder simulation, we show that Mathematica-5 notebook and SIMPSON1.1.1 Tcl script generate identical results.

Equipment: Mathematica-5 (or MathReader for reading the notebook if you do not have Mathematica-5) and SIMPSON1.1.1.

Method: We simulate the central-line intensities of a spin I = 3/2 for pulse duration t increasing from 0 to 20 s by steps of 1 s in a powder rotating at the magic angle, using Mathematica-5 notebook and SIMPSON1.1.1 Tcl script. The crystal files rep100 and rep100_simp are used for the summation of the Euler angles α and β.

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
  • Strength of the radio-frequency pulse: 100 kHz
  • Initial pulse duration: 0
  • Final pulse duration: 20 s
  • Pulse duration increment: 1 s
  • Number of pulse duration increment: 20
  • Rotor spinning speed: 15 kHz
  • Quadrupole interaction: first- and second-orders
  • Quadrupole coupling constant: 8 MHz
  • Asymmetry parameter: -1 or 1
  • Crystal file: rep100
  • Number maxγ of summation steps of the Euler angle γ of the rotor: 3

(A) Mathematica-5 notebook

  1. Download the Mathematica-5 notebook called powder_MAS_rep.nb or the notebook as PDF file powder_MAS_rep.pdf (53 Kb) and the crystal file rep100_simp.
  2. Save these files into the software Mathematica-5 folder.
  3. Open this file with Mathematica-5 and change the value of the asymmetry parameter.
  4. Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start simulation.
  5. A file called powderMASrep.m is created in Mathematica-5 folder. MS Excel can open this data file.

(B) SIMPSON1.1.1 Tcl script

  1. Select and paste the following green lines in MS Bloc-notes.
  2. Save this file as "onepowderMAS.in" into the software SIMPSON folder.
  3. Modify the value of the asymmetry parameter and save modification.
  4. Run this SIMPSON Tcl script file in a DOS window.
  5. The simulated line intensities are saved in the file called onepowderMAS.fid in SIMPSON folder.

SIMPSON Tcl script

# onepowderMAS.in
# Spin-3/2 central-line intensity calculation
# for a powder rotating at the magic angle,
# submitted to the first- and the second-order
# quadrupole interactions.

spinsys {
  channels 23Na
  nuclei   23Na
  quadrupole 1 2 8e6 1 0 0 0
}



par {
  proton_frequency 400e6
  spin_rate        15000
  variable tsw     1
  sw               1.0e6/tsw
  np               21
  crystal_file     rep100
  gamma_angles     3
  start_operator   0.4*I1z
  verbose          1101
  variable rf      100000
}

proc pulseq {} {
  global par
  maxdt $par(tsw)

  matrix set detect elements {{2 3}}


  acq

  for {set i 1} {$i < $par(np)} {incr i} {
    pulse $par(tsw) $par(rf) x
    acq -y
  }
}

proc main {} {
  global par

  fsave [fsimpson] $par(name).fid

  puts "Larmor frequency (Hz) of 23Na: "
  puts [resfreq 23Na $par(proton_frequency)]
}

Comment

File name.
Description.






Spin I = 3/2.
1st- and 2nd-order
quadrupole
interactions,
qcc = 8 MHz,
eta = 1.


MAS powder.
1 s pulse increment.

20 pulse increments.
Powder simulation.
Number of gamma.
0.4 for normalization.

100 kHz RF pulse.




1 μs pulse increment.

Central transition,
fictitious spin-1/2
convention.
No pulse, no signal.


Variable x-pulse.
Receiver phase -y.



(C) Result

The simulated line intensities are gathered in the following table.

t
(μs)
Mathematica-5
powder_MAS_rep.nb
SIMPSON1.1.1 Tcl script
onepowderMAS.in
  η = 1 η = -1 η = 1 η = -1
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0              
0.1963519484
0.139885498
-0.07450714233
-0.1511577544
0.006769210342
0.1593556203
0.1029767836
-0.0742168327
-0.1230433622
0.01279076315
0.137397243
0.07944278327
-0.05992684336
-0.08156846799
0.02760405068
0.1019645589
0.04178107761
-0.05554552193
-0.05549098729
0.02988776444
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              
0.196651611
0.140751501
-0.0701333307
-0.141830896
0.00430804447
0.148430161
0.0951913524
-0.0670400525
-0.112949749
0.0119890704
0.124670265
0.0777746843
-0.0439592833
-0.0737348112
0.019326159
0.0859248419
0.0381658978
-0.0450549902
-0.0432572148
0.0342302955
0              
0.196351948
0.139885498
-0.0745071423
-0.151157754
0.00676921034
0.15935562
0.102976784
-0.0742168327
-0.123043362
0.0127907631
0.137397243
0.0794427833
-0.0599268434
-0.081568468
0.0276040507
0.101964559
0.0417810776
-0.0555455219
-0.0554909873
0.0298877644


(D) Conclusions

  1. With a crystal file for simulating powder, both Mathematica-5 notebook and SIMPSON1.1.1 Tcl script provide differents results for opposite values of the asymmetry parameter.
  2. Mathematica-5 notebook, which uses the convention η = (VXX - VYY)/VZZ, and SIMPSON Tcl script, which uses the opposite convention, generate the same results if we choose the same convention for the asymmetry parameter.
 

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