One-pulse line intensity for MAS crystal, Part 1

AIM: We show that SIMPSON1.1.0 Tcl script with a negative value of the asymmetry parameter η generates wrong results. However, SIMPSON1.1.1 Tcl script provides us with right results.

Equipment: Mathematica-5 (or MathReader for reading the notebook if you do not have Mathematica-5), SIMPSON1.1.0, and SIMPSON1.1.1.

Definition: The NMR line intensity, which depends on the various interactions involved during the RF pulses, is proportional to the amplitude of the first sampled point of a free-induction decay or the integrated area of the corresponding spectrum.

Method: We simulate the central-line intensities of a spin I = 3/2 for pulse duration t increasing from 0 to 20 µs by steps of 1 µs in a crystal rotating at the magic angle, using Mathematica-5 notebook and SIMPSON Tcl script.

The parameters for these simulations are:

• Observed line intensity: central transition (中心躍遷)
• 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 µs
• Pulse duration increment: 1 µs
• Number of pulse duration increment: 20
• Rotor spinning speed (轉子的轉速): 15 kHz
• Quadrupole interaction: first and second orders
• Quadrupole coupling constant: 8 MHz
• Asymmetry parameter: -1 or 1
• Euler angle α of the rotor in the PAS of the EFG tensor: 30°
• Euler angle β of the rotor in the PAS of the EFG tensor: 30°
• Euler angle γ of the rotor in the PAS of the EFG tensor: 30°

(A) Mathematica-5 notebook

1. Download the Mathematica-5 notebook called crystal_MAS.nb or the notebook as PDF file crystal_MAS.pdf (51 Kb)
2. Save this file 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 crystalMAS.m is created in Mathematica-5 folder. MS Excel can open this file.

(B) SIMPSON Tcl script

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

# onextalMAS.in
# Spin-3/2 central-line intensity calculation
# for a crystal 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 30 30 30 
}







par {
  proton_frequency 400e6
  spin_rate        15000
  variable tsw     1
  sw               1.0e6/tsw
  np               21
  crystal_file     alpha0beta0
  gamma_angles     1
  start_operator   0.2*I1z
  detect_operator  I1c
  verbose          1101
  variable rf      100000
}

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

  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)]
}
        

File name.
Description.






Spin I = 3/2.

1st- and 2nd-order
quadrupole
interactions,
qcc = 8 MHz,
eta = 1,
αPC = 30°,
βPC = 30°,
γPC = 30°.



MAS crystal.

1 µs pulse increment.
20 pulse increments.


0.2 for normalization.
Central-transition.

100 kHz RF pulse.




1 µs pulse increment.

No pulse, no signal.


Variable x-pulse.
Receiver phase -y.
        

(C) Result

The simulated line intensities are gathered in the following table.

(D) Conclusions

1. Mathematica-5 notebook cystal_MAS.nb, which uses the convention η = (V_XX - V_YY)/V_ZZ, and SIMPSON Tcl script, which uses the opposite convention η = (V_YY - V_XX)/V_ZZ, generate the same results if we choose the same convention for the asymmetry parameter.
2. SIMPSON1.1.0 Tcl script with a negative value of η generates wrong results.