Mathematica versus SIMPSON: one-pulse NMR for MAS powder

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 μs by steps of 1 μs 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 μs
Pulse duration increment: 1 μs
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

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.
Save these files into the software Mathematica-5 folder.
Open this file with Mathematica-5 and change the value of the asymmetry parameter.
Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start simulation.
A file called powderMASrep.m is created in Mathematica-5 folder. MS Excel can open this data file.

(B) SIMPSON1.1.1 Tcl script

Select and paste the following green lines in MS Bloc-notes.
Save this file as "onepowderMAS.in" into the software SIMPSON folder.
Modify the value of the asymmetry parameter and save modification.
Run this SIMPSON Tcl script file in a DOS window.
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 μs 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

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.
Mathematica-5 notebook, which uses the convention η = (V_XX - V_YY)/V_ZZ, and SIMPSON Tcl script, which uses the opposite convention, generate the same results if we choose the same convention for the asymmetry parameter.

Definition

One-pulse MAS

MQ-MAS

Reference