## One-pulse line intensity for a spin I = 3/2 in MAS powder with rep100 file. Contributor: R. Hajjar

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## 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

1. 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.
2. Save these files 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 powderMASrep.m is created in Mathematica-5 folder. MS Excel can open this data file.

### (B) SIMPSON1.1.1 Tcl script

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

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
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.

### (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

1. 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.
2. Mathematica-5 notebook, which uses the convention η = (VXX - VYY)/VZZ, and SIMPSON Tcl script, which uses the opposite convention, generate the same results if we choose the same convention for the asymmetry parameter.

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