One-pulse line intensity
for a spin I = 3/2 in MAS powder with classic8 file.
Contributor: R. Hajjar

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## One-pulse line intensity for MAS powder, Part 3

AIM: We show that with a crystal file for powder simulation whose summation steps on the Euler angle α are a 4-fold number, Mathematica-5 notebook and SIMPSON1.1.1 Tcl script generate identical results whatever the convention of the asymmetry parameter.

Equipment, method, and parameters are identical to those involved in one-pulse line intensity for MAS powder, Part 2. Only the crystal files are different: classic8 instead of rep100 in SIMPSON Tcl script or rep100_simp in Mathematica-5 notebook.

classic8
(crystal file for
powder_MAS_rep.nb
in Mathematica-5)
classic8.cry
(crystal file for
onepowderMAS.in
in SIMPSON1.1.1 Tcl)
0   60  0.125
0   120 0.125
90  60  0.125
90  120 0.125
180 60  0.125
180 120 0.125
270 60  0.125
270 120 0.125
8
0   60  0.125
0   120 0.125
90  60  0.125
90  120 0.125
180 60  0.125
180 120 0.125
270 60  0.125
270 120 0.125

The summation steps are 4 for α, that is, α = 0°, 90°, 180°, and 270°.

The summation steps are 3 for β, that is, β = 0°, 60°, 120°, and 180°. Since sin β = 0 for β = 0° and 180°, only β = 60° and 120°are considered in the crystal files.

Since the probabilities are equal (sin 60° = sin 120°), they are rescaled to 0.125 so that their summation is equal to 1.

If the probability summation is not equal to 1, SIMPSON automatically rescales all the probabilities so that the probability summation is equal to 1.

### (A) Mathematica-5 notebook

1. Select the eight lines of data in the left-side column of the above table and paste them into MS Bloc-notes.
2. Save the file as "classic8" in Mathematica-5 folder.
3. Open the file powder_MAS_rep.nb with Mathematica-5 and change the name of the crystal file with classic8 and 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 the nine lines of data in the right-side column of the above table and paste them into MS Bloc-notes.
2. Save this file as "classic8.cry" into SIMPSON folder.
3. Open the file onepowderMAS.in with MS Bloc-notes. Or create it as described in one-pulse line intensity for MAS powder, Part 2.
4. Modify the name of crystal file and the value of the asymmetry parameter. Then save modifications.
5. Run this SIMPSON Tcl script file in a DOS window.
6. The simulated line intensities are saved in the file called onepowderMAS.fid in SIMPSON folder.

### (C) Result

The simulated line intensities are gathered in the following table. The four columns of line intensities are identical.

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
0.1925985564
0.1293907806
-0.1077674015
-0.1879416054
0.02128334292
0.2154930249
0.1291226131
-0.1060680258
-0.1474266216
0.02349693465
0.1589359388
0.08642667024
-0.08869034668
-0.1293824039
0.003600270058
0.1470723902
0.09131621753
-0.07532814639
-0.110829948
0.04113410356
0
0.1925985564
0.1293907806
-0.1077674015
-0.1879416054
0.02128334292
0.2154930249
0.1291226131
-0.1060680258
-0.1474266216
0.02349693465
0.1589359388
0.08642667024
-0.08869034668
-0.1293824039
0.003600270058
0.1470723902
0.09131621753
-0.07532814639
-0.110829948
0.04113410356
0
0.192598556
0.129390781
-0.107767401
-0.187941605
0.0212833429
0.215493025
0.129122613
-0.106068026
-0.147426622
0.0234969346
0.158935939
0.0864266702
-0.0886903467
-0.129382404
0.00360027005
0.14707239
0.0913162175
-0.0753281464
-0.110829948
0.0411341036
0
0.192598556
0.129390781
-0.107767401
-0.187941605
0.0212833429
0.215493025
0.129122613
-0.106068026
-0.147426622
0.0234969346
0.158935939
0.0864266702
-0.0886903467
-0.129382404
0.00360027005
0.14707239
0.0913162175
-0.0753281464
-0.110829948
0.0411341036

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