## 40-phase cycling of the second and the third pulses in 3-pulse z-filter ±5Q-MAS of I = 5/2

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## Z-filter 5Q-MAS with 40-phase cycling

Two approaches:
(1) filtering the coherences,
(2) explicit phase cycling the pulses and the receiver,
are used for the simulation of echo and antiecho amplitude in ±5Q-MAS of spin I = 5/2 system. The sequence consists of two strong amplitude pulses followed by a weak amplitude pulse.

#### (1) 40-phase cycling the second and the third pulses

φ1 = 0° 0° 36° 72° 108° 144° 180° 216° 252° 288° 324° {0°}X10  {90°}X10  {180°}X10  {270°}X10 {0° 180°}X5   {90° 270°}X5    {180° 0°}X5   {270° 90°}X5

This 40-phase cycling selects the three families of coherence transfer pathways:

1. 0Q -> -1Q -> +4Q -> -1Q,
2. 0Q -> +1Q -> -4Q -> -1Q,
3. 0Q -> ±5Q -> +0Q -> -1Q (the desired coherence transfer pathways),

as shown in the following figure. Family a is yellow pathway, family b is brown pathway, and family c is red pathways:

#### (2) Simulation

We provide SIMPSON2 Tcl scripts for simulating the echo and antiecho amplitude versus a pulse duration:
(1) filtering the coherences (a Tcl script is associated with each family),
(2) 40-phase cycling the pulses and the receiver.

Duration Filtering 40-phase cycling
1st-pulse
a + b + c: total-p1
al-p2p3-cycl-p1
2nd-pulse
a + b + c: total-p2
al-p2p3-cycl-p2
3rd-pulse
a + b + c: total-p3
al-p2p3-cycl-p3

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