## One-pulse NMR line intensity simulation for a spin I = 3/2 in MAS crystal. Contributor: R. Hajjar

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## 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.

## SIMPSON Tcl script

# 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)]
}

## Comment

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.

t
(μs)
Mathematica-5
crystal_MAS.nb
SIMPSON1.1.1 Tcl script
onextalMAS.in
SIMPSON1.1.0 Tcl script
onextalMAS.in
η = 1 η = -1 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
0.1908436366
0.1177854316
-0.1181422712
-0.1905155811
0.001057244221
0.1907815382
0.1133924352
-0.1248704872
-0.1859337477
0.02289503175
0.1977216871
0.07441321387
-0.1621577611
-0.1474539514
0.1001725545
0.1828394272
0.2477641061
0.01321514969
-0.1920845034
-0.1248137891
0
0.1909263462
0.1179498378
-0.1095760968
-0.1748410673
0.05933795078
0.349769756
0.3342515848
-0.2783335973
-0.4104664941
-0.04702774168
0.4073285563
0.3241038495
-0.1948624526
-0.4306262691
-0.05748909539
0.4018103486
0.3128637066
-0.1999188914
-0.4520927211
-0.01315623676
0
0.190926346
0.117949838
-0.109576097
-0.174841067
0.0593379508
0.349769756
0.334251585
-0.278333597
-0.410466494
-0.0470277417
0.407328556
0.32410385
-0.194862453
-0.430626269
-0.0574890954
0.401810349
0.312863707
-0.199918891
-0.452092721
-0.0131562368
0
0.190843637
0.117785432
-0.118142271
-0.190515581
0.00105724422
0.190781538
0.113392435
-0.124870487
-0.185933748
0.0228950317
0.197721687
0.0744132139
-0.162157761
-0.147453951
0.100172554
0.182839427
0.247764106
0.0132151497
-0.192084503
-0.124813789
0
0.190926346
0.117949838
-0.109576097
-0.174841067
0.0593379508
0.349769756
0.334251585
-0.278333597
-0.410466494
-0.0470277417
0.407328556
0.32410385
-0.194862453
-0.430626269
-0.0574890954
0.401810349
0.312863707
-0.199918891
-0.452092721
-0.0131562368
0
0.188972561
0.116081908
-0.11688695
-0.188263998
0.00261906922
0.189059486
0.117694207
-0.115041902
-0.18870292
-0.00390478132
0.18494291
0.127804355
-0.0722959819
0.0219328185
0.457229299
0.050283905
-0.349208801
-0.30430997
0.180687224
0.410775791

### (D) Conclusions

1. Mathematica-5 notebook cystal_MAS.nb, which uses the convention η = (VXX - VYY)/VZZ, and SIMPSON Tcl script, which uses the opposite convention η = (VYY - VXX)/VZZ, 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.

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[Contact me] - Last updated December 16, 2012
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