SIMPSON simulation with cogwheel phase cycling parameters

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## SIMPSON simulation for cogwheel phase cycling parameters

We provide three SIMPSON1.1.1 Tcl scripts simulating the antiecho amplitude of sodium nucleus versus the duration of the first pulse. The results agree with an accuracy of 10-8.

### 1. Simulation

For the three-pulse split-t1 MQMAS sequence, previous XSLT search results show that the winding numbers are:

${w}_{A}$ = -14, ${w}_{B}$ = -11, ${w}_{C}$ = -10, and ${w}_{\mathrm{Rec}}$ = 0.

There are two ways to denote the cogwheel phase cycling: Cog23(-14, -11, -10, 0) or Cog23(0, 3, 4, 14).

We compare three SIMPSON1.1.1 Tcl scripts, two with these cogwheel phase cycling parameters, the other with the traditional coherence filtering method. The other NMR parameters are defined in these scripts, where the antiecho amplitude in the coherence filtering method has been normalized to the number N (= 23) of phase cycling:

### 2. Result

1st-pulse
duration (μs)
Cog23(-14, -11, -10, 0) Cog23(0, 3, 4, 14) Coherence filtering
0000
0.25-2.05588265e-05-2.05584676e-05-2.05583862e-05
0.50-0.000619528565-0.000619528229-0.000619528094
0.75-0.00425033403-0.00425033373-0.00425033355
1.00-0.015561427-0.0155614268-0.0155614266
1.25-0.0398291138-0.0398291135-0.0398291133
1.50-0.0806927982-0.080692798-0.0806927977
1.75-0.138941008-0.138941008-0.138941007
2.00-0.213223134-0.213223133-0.213223133
2.25-0.301964835-0.301964834-0.301964834
2.50-0.404752632-0.404752632-0.404752632
2.75-0.521872148-0.521872148-0.521872147
3.00-0.652226709-0.652226709-0.652226709
3.25-0.791301451-0.791301451-0.791301451
3.50-0.931003982-0.931003981-0.931003981
3.75-1.06193022-1.06193022-1.06193022
4.00-1.17683433-1.17683433-1.17683433

Due to the value of N = 23, the anti-echo amplitudes of the three simulations agree with an accuracy of 10-8 only.

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