## Z-filtered MQMAS

**AIM:** We provide Mathematica-5 notebooks and
SIMPSON1.1.1 Tcl scripts to optimize the echo and antiecho amplitudes
for z-filtered MQMAS NMR experiment applied to half-integer
quadrupole spin.

**J.-P. Amoureux** and coworkers [**Z
filtering in MQ MAS NMR**, *J. Magn. Reson. A*
**123**, 116-118 (1996)] present the
z-filter approach
which allows the symmetrization of both echo and antiecho
transfer pathways, generating a 2D pure absorption MQMAS spectrum.

Fig. 1: Z-filtered MQMAS pulse sequence and coherence transfer
pathways for 3Q echo and -3Q antiecho of a spin I = 5/2 system.

0Q -> 3Q -> 0Q -> -1Q is the 3Q echo transfer pathway.

0Q -> -3Q -> 0Q -> -1Q is the -3Q antiecho transfer pathway.

**The echo amplitude and the antiecho amplitude have the same sign**.

**Method:** We simulate the echo and the antiecho
amplitudes of a spin I = 5/2 with increasing second-pulse duration
in a powder rotating at the magic angle, using Mathematica-5 notebooks
and SIMPSON1.1.1 Tcl scripts.

The parameters for these simulations are:

- Nucleus:
^{27}Al - Spin: 5/2
^{27}Al Larmor frequency: 208.61889974 MHz- Proton Larmor frequency: 800 MHz
- Only 3Q and -3Q coherences belonging to the second diagonal of the density matrix are taken into account for the simulation
- Amplitude of the strong radio-frequency pulse: 90 kHz
- Amplitude of the weak radio-frequency pulse: 9.3 kHz
- First-pulse duration: 4 µs
- Initial duration of the second pulse: 0
- Final duration of the second pulse: 4 µs
- Pulse duration increment: 0.25 µs
- Number of the second-pulse duration increment: 17
- Third-pulse duration: 9 µs
- Rotor spinning speed: 5 kHz
- Quadrupole interaction: first and second orders
- Quadrupole coupling constant: 5 MHz
- Asymmetry parameter: -1 for notebook and 1 for Tcl script
- Crystal file: rep100_simp for notebook and rep100.cry for Tcl script
- Number of summation steps of the Euler angle γ of the rotor: 10

### (A) Mathematica-5 notebook

#### (1) Preliminary

Optimization with |
Notebook |
---|---|

strong pulse p1 | zfilter_P1.nb (pdf) |

strong pulse p2 | zfilter_P2.nb (pdf) |

soft pulse p3 | zfilter_P3.nb (pdf) |

- Download Mathematica-5 notebook zfilter_P2.nb, that for MAS NMR utilities QUADRUPOLE_1_0.nb (the corresponding PDF file), and the crystal file rep100_simp.
- Save these three files into the software Mathematica-5 folder. Forbidden the Operating System of your computer to include extra file extension to rep100_simp by providing the file name with double quotes such as "rep100_simp".
- Open QUADRUPOLE_1_0.nb file with Mathematica-5.
- Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start the notebook. (Some warning messages appear but they have no consequences on the results.) A new file called QUADRUPOLE is created in Mathematica-5 folder.

#### (2) Simulation

- Open zfilter_P2.nb file with Mathematica-5.
- Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start simulation. (Some warning messages precede the simulation.) At the end a data file called zfilter_P2 is created in Mathematica-5 folder. MS Excel can open this data file for graphic representation.

### (B) SIMPSON1.1.1 Tcl script

#### (1) Preliminary

Optimization with | SIMPSON1.1.1 |
---|---|

strong pulse p1 | zfilter_p1.in |

strong pulse p2 | zfilter_p2.in |

soft pulse p3 | zfilter_p3.in |

Download and save zfilter_p2.in file into the software SIMPSON1.1.1 folder.

#### (2) Simulation

- Run zfilter_p2.in in a DOS window.
- The simulated signal amplitudes are saved in the file called zfilter_p2.fid in SIMPSON1.1.1 folder. MS Excel also can open this data file for graphic representation.

### (C) Result

Figure 2 represents the simulated data. Notebook and Tcl script provide the same curve.

Fig. 2: ^{27}Al z-filtered 3Q echo and -3Q antiecho amplitudes
versus the second-pulse duration.

We also provide notebooks and SIMPSON1.1.1 Tcl scripts where all the coherences belonging to the same MQ coherence transfer pathway are considered:

Optimization with |
Notebook | SIMPSON 1.1.1 |
---|---|---|

strong pulse p1 | zfilter_P1S.nb, (pdf) |
zfilter_p1S.in |

strong pulse p2 | zfilter_P2S.nb, (pdf) |
zfilter_p2S.in |

soft pulse p3 | zfilter_P3S.nb, (pdf) |
zfilter_p3S.in |

These files allow us to compare simulated data with those obtained with SPAM MQMAS approach.

**Nicolas Malicki** and coworkers [**Multiplex
MQMAS NMR of quadrupolar nuclei**, *Solid State Nucl. Magn.
Reson.* **28**, 13-21 (2005)] present the
Multiplex z-filter approach which reduces the experimental time
considerably.

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