## Soft Pulse Added Mixing MQMAS

**AIM:** We provide Mathematica-5 notebooks and SIMPSON1.1.1 Tcl
scripts to optimize the amplitude of the echo and that of the antiecho in
SPAM MQMAS NMR applied to half-integer quadrupole spin according to
the phase (X or -X) of the third or soft pulse.

**Z. Gan** and **H.-T. Kwak**
[**Enhancing MQMAS sensitivity using signals from multiple
coherence transfer pathways**, *J. Magn. Reson.*
**168**, 346-351 (2004)] present the
SPAM approach to enhance the MQMAS NMR sensitivity of half-integer
quadrupole spins using three coherence transfer pathways for
the echo and for the antiecho signals.

Fig. 1: SPAM echo transfer pathways for a spin I = 5/2 system.

Fig. 2: SPAM antiecho transfer pathways for a spin I = 5/2 system.

**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 six coherence transfer pathways
are simulated with phases X and -X for the third or soft pulse.

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

Coherence transfer pathway |
X, X, X sequence notebook |
X, X, -X sequence notebook |
---|---|---|

0Q->3Q->1Q->-1Q | spam_P2 (pdf) |
spam_P2 (pdf) |

0Q->3Q->0Q->-1Q | spam_P2 (pdf) |
spam_P2 (pdf) |

0Q->3Q->-1Q->-1Q | spam_P2 (pdf) |
spam_P2 (pdf) |

0Q->-3Q->1Q->-1Q | spam_P2 (pdf) |
spam_P2 (pdf) |

0Q->-3Q->0Q->-1Q | spam_P2 (pdf) |
spam_P2 (pdf) |

0Q->-3Q->-1Q->-1Q | spam_P2 (pdf) |
spam_P2 (pdf) |

- Download the twelve Mathematica-5 notebooks, that for MAS NMR utilities QUADRUPOLE_1_0.nb (the corresponding PDF file), and the crystal file rep100_simp.
- Save these 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 file called QUADRUPOLE is created in Mathematica-5 folder.

#### (2) Simulation

- Open a simulation file such as spam_P2_3Q1Qxxx.nb with Mathematica-5.
- Press "Ctrl-A" to select the notebook, then press "Shift-enter" to start simulation. (Some warning messages precede the simulation.) After the simulation a data file, called spam_P2_3Q1Qxxx, is created in Mathematica-5 folder. MS Excel can open this data file for graphic representation.

### (B) SIMPSON1.1.1 Tcl script

#### (1) Preliminary

Coherence transfer pathway |
X, X, X sequence Tcl script |
X, X, -X sequence Tcl script |
---|---|---|

0Q->3Q->1Q->-1Q | spam_p2 | spam_p2 |

0Q->3Q->0Q->-1Q | spam_p2 | spam_p2 |

0Q->3Q->-1Q->-1Q | spam_p2 | spam_p2 |

0Q->-3Q->1Q->-1Q | spam_p2 | spam_p2 |

0Q->-3Q->0Q->-1Q | spam_p2 | spam_p2 |

0Q->-3Q->-1Q->-1Q | spam_p2 | spam_p2 |

Download and save these twelve files into the software SIMPSON1.1.1 folder.

#### (2) Simulation

Run a SIMPSON1.1.1 Tcl script file such as spam_p2_3Q1Qxxx.in in a DOS window. The simulated signal amplitudes are saved in the file called spam_p2_3Q1Qxxx.fid in SIMPSON1.1.1 folder. MS Excel also can open this data file for graphic representation.

### (C) Result

Figures 3 and 4 represent the twelve simulated data. Notebooks and Tcl scripts provide the same data.

Fig. 3: ^{27}Al SPAM 3Q-echo amplitudes obtained
with X, X, X pulse sequence (left-hand side) and with X, X, -X pulse sequence
(right-hand side) versus the second-pulse duration for the three coherence
0transfer pathways.

0Q curve for coherence transfer pathway
0Q->3Q->0Q->-1Q;

±1Q curve for coherence transfer pathway 0Q->3Q->±1Q->-1Q.

Fig. 4: ^{27}Al SPAM -3Q-antiecho amplitudes obtained
with X, X, X pulse sequence (left-hand side) and with X, X, -X pulse sequence
(right-hand side) versus the second-pulse duration for the three coherence
transfer pathways.

0Q curve for coherence transfer pathway
0Q->-3Q->0Q->-1Q;

±1Q curve for coherence transfer pathway
0Q->-3Q->±1Q->-1Q.

For a given pulse sequence (X, X, X or X, X, -X), the 0Q curve describing
the echo amplitude and that describing the antiecho amplitude have
**the same sign**. In contrast, the ±1Q curves describing
the echo amplitude and those describing the antiecho amplitude have
**opposite signs**

Alternating the phase of the third or soft pulse

- changes the sign of the echo amplitude and that of the antiecho associated with 0Q->3Q->0Q->-1Q and 0Q->-3Q->0Q->-1Q coherence transfer pathways;
- but does not change the sign of the echo amplitudes and those of the antiecho associated with 0Q->3Q->±1Q->-1Q and 0Q->-3Q->±1Q->-1Q coherence transfer pathways.

For a given phase (-X or X) of the third or soft pulse

- the echo and the antiecho associated with 0Q->3Q->0Q->-1Q and 0Q->-3Q->0Q->-1Q coherence transfer pathways have the same amplitude;
- but the echo and the antiecho associated with 0Q->3Q->±1Q->-1Q and 0Q->-3Q->±1Q->-1Q coherence transfer pathways have almost opposite amplitudes.

### (D) Conclusions

- The highest sensitivity enhancement in SPAM 3QMAS sequence is obtained with an X phase for the third or soft pulse.
- On the other hand, the highest sensitivity enhancement in SPAM -3QMAS sequence is obtained with a -X phase for the third or soft pulse.
- Therefore, when the echo signal and that of the antiecho are acquired
separately,
**the echo amplitude and the antiecho amplitude have opposite signs**.

These results are in agreement with those of **J.-P. Amoureux**
and coworkers, [**Increasing the sensitivity of 2D high-resolution
NMR methods applied to quadrupolar nuclei**, *J. Magn. Reson.*
**172**, 268-278 (2005)].

We provide notebooks and SIMPSON1.1.1 Tcl scripts for these two cases. They allow us to optimize the echo amplitude and that of the antiecho using each of the three pulses:

SPAM | Notebook | SIMPSON1.1.1 Tcl script |
---|---|---|

3QMAS | P1_3Qxxx.nb (pdf) | p1_3Qxxx.in |

P2_3Qxxx.nb (pdf) | p2_3Qxxx.in | |

P3_3Qxxx.nb (pdf) | p3_3Qxxx.in | |

-3QMAS | P1_-3Qxx-x.nb (pdf) | p1_-3Qxx-x.in |

P2_-3Qxx-x.nb (pdf) | p2_-3Qxx-x.in | |

P3_-3Qxx-x.nb (pdf) | p3_-3Qxx-x.in |

We also provide notebooks and SIMPSON1.1.1 Tcl scripts as above files, but all the coherences belonging to the same MQ coherence transfer pathway are considered:

SPAM | Notebook | SIMPSON1.1.1 Tcl script |
---|---|---|

3QMAS | P1_3QxxxS.nb (pdf) | p1_3QxxxS.in |

P2_3QxxxS.nb (pdf) | p2_3QxxxS.in | |

P3_3QxxxS.nb (pdf) | p3_3QxxxS.in | |

-3QMAS | P1_-3Qxx-xS.nb (pdf) | p1_-3Qxx-xS.in |

P2_-3Qxx-xS.nb (pdf) | p2_-3Qxx-xS.in | |

P3_-3Qxx-xS.nb (pdf) | p3_-3Qxx-xS.in |

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