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.
*******SIMPSON fitting procedure*******# 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)" } |
****Comment****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).