We can extract the strength of the RF field and the quadrupole coupling constant involved in the simulated VFF composite-pulse nutation data (the first-pulse length is variable whereas the other two are constant) using SIMPSON version 1.1.1, a general simulation program for solid-state NMR spectroscopy provided by M. Bak, J. T. Rasmussen, and N. C. Nielsen, J. Magn. Reson. 147, 296-330 (2000).

Due to different conventions for the definition of the asymmetry parameter used in SIMPSON and the Java applets, these two approaches provide different simulations. Fortunately, as proposed by Klaus Eichele, if we add 90° to alpha, the first Euler angle in SIMPSON TCL scripts, these two approaches give identical results.

# compositevffxtalfit.in
# Fitting spin-3/2 central-line intensity
# for a static crystal.
# With alpha0beta0 crystal_file and
# whatever the asymmetry parameter,
# qcc = 1 MHz gives a line splitting of 500 kHz
# and a quadrupole coupling omegaQ of 250 kHz.

spinsys {
  channels 23Na
  nuclei   23Na
  quadrupole 1 1 1 1 90 0 0
}



par {
  proton_frequency 400e6
  spin_rate        0
  variable tsw     0.5
  sw               1.0e6/tsw
  np               41
  crystal_file     alpha0beta0
  gamma_angles     1
  start_operator   0.2*I1z
  detect_operator  I1
#verbose          1101
  variable rf      0
  variable p1      0
  variable p2      5
  variable p3      5
}

proc pulseq {} {
  global par
  acq

  for {set i 1} {$i < $par(np)} {incr i} {

    pulse $par(tsw) $par(rf) $par(ph1)

    store 1

    pulse $par(p2) $par(rf) $par(ph2)

    pulse $par(p3) $par(rf) $par(ph3)


    acq $par(ph31)

    Reset


    prop 1
  }
}

proc minuit {} {
  global par mn g i
  set i [expr $i+1]

  #make some nice output
  puts "$i. call to minuit ----------------"
  puts -nonewline "qcc = $mn(qcc)"
  puts -nonewline "  "
  puts -nonewline "rffield = $mn(rffield)"

  #simulate curve
  foreach p {{-x x  x -y}\
            {-x x -x  y}\
            { x x -x -y}\
            { x x  x  y}} {
    set par(ph1)   [lindex $p 0]
    set par(ph2)   [lindex $p 1]
    set par(ph3)   [lindex $p 2]
    set par(ph31)  [lindex $p 3]

    set par(rf)  $mn(rffield)
    set h [fsimpson [list \
    [list quadrupole_1_aniso  $mn(qcc)]]]

    if [info exists f] {
      fadd $f $h
      funload $h
    } else {
      set f $h
    }
  }

  fsave $f $par(name).fid
  set rms [frms $f $g -re ]
  puts " => rms = $rms"
  return $rms
  funload $f
}

proc main {} {
  global par mn g i
  set g [fload "compositevffxtal.fid"]
  set i 0

  #setup start paramaters to fit with minuit
  #mnpar name       val  step   [min      max]
  mnpar  qcc     1.10e6   50    0.80e6  1.20e6
  mnpar rffield   95000   50    90000   120000

  #tell minuit the strategy (mnminimize, mnscan, mnfix)

  mnminimize
  puts ""
  puts ""
  puts "Best Fit Parameters"
  puts "--------------------------------------"
  puts "qcc: $mn(qcc)"
  puts "rffield: $mn(rffield)"
}
        

File name.
Description.








Spin I = 3/2.
1st-order
quadrupole
interaction,
qcc = 1 Hz,
eta = 1.


Static crystal.
0.5 µs pulse increment.

40 pulse increments.


0.2 for normalization.
Central-transition.

RF pulse.
1st-pulse length.
2nd-pulse length.
3th-pulse length.




No pulse, no signal.



1st (variable) pulse
with ph1 phase.
Save propagator.

2nd-pulse
with ph2 phase.
3th-pulse
with ph3 phase.

Receiver phase ph31.

Reset propagator to
initial value.

Recall the propagator
at the end of
the 1st pulse.










































Filename of data to
fit-simpson-composite



Initial values for qcc,
for rffield.
        

SIMPSON uses gyromagnetic ratios provided by IUPAC for the determination of the Larmor frequency of a nucleus. For example:

²³Na Larmor frequency = Proton Larmor frequency * ²³Na gyromagnetic ratio / Proton gyromagnetic ratio;

400 MHz * 7.0808493 / 26.7522128 = 105.8731007 MHz.

SIMPSON input file: Hahn-echo pulse program with phase cycling by Laura Gasque, Michiel A. Verhoeven, Sylvain Bernès, Fabiola Barrios, Jaap G. Haasnoot, and Jan Reedijk, The added value of solid-state Pb NMR spectroscopy to understand the 3D structures of Pb amino acid complexes, Eur. J. Inorg. Chem. 2008 (supporting information).