SIMPSON

Numerical simulations in solid-state NMR using SIMPSON

A collection of annotated SIMPSON input files (.in) for common solid-state NMR pulse sequences — homo- and heteronuclear recoupling, decoupling, cross-polarisation, quadrupolar excitation, TEDOR, RESPDOR, DIPSHIFT, and third-spin-assisted recoupling (TSAR). Each script reproduces or closely follows simulations from the literature, with the reference given alongside it.

Disclaimer: these files are teaching/starting-point scripts, not a validated package. Modify them freely, but please follow the official SIMPSON courses/tutorials for the underlying theory, and open an issue if you spot an error — no guarantee is made that any given script works as intended out of the box.

If you use these scripts, please cite the repository — see Citing this repository.

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Table of contents

• Requirements & running a simulation
• Repository structure
• Index of simulations
• Homonuclear recoupling
• Heteronuclear recoupling
  • RESPDOR
  • TEDOR
  • DIPSHIFT
• Heteronuclear decoupling
• Quadrupolar NMR
• Third-spin-assisted recoupling (TSAR)
• Cross polarisation
• Homonuclear decoupling
• Key SIMPSON references
• Citing this repository
• Contributing
• License

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Requirements & running a simulation

You need a working install of SIMPSON (the Tcl-scriptable spin-dynamics simulation package from Aarhus/Vosegaard & Nielsen). Installation instructions and binaries are on the INANO website linked above.

Once SIMPSON is installed and on your PATH, run any script from its own directory, e.g.:

cd homonuclear_recoupling
simpson S3_CC.in

Some scripts (e.g. S3_CC.in, SR26_CC.in) prompt interactively for a recoupling time in ms. Others (e.g. hetdec.in, mq_excitation.in) loop over several sequences or parameter values automatically and write one output file per case. Outputs are plain-text .txt/.fid files (real/imaginary columns) that you can plot with your tool of choice (e.g. xreim, Python, Origin).

allseq_HH_modular.in additionally requires recoupling.tcl to be present in the same directory — it holds the actual pulse-sequence definitions and is sourced at runtime.

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Repository structure

simpson/
├── homonuclear_recoupling/      S3, bracketed-S3, SR26, POST-C7, R-sequences, BABA, SWf-BABA
├── heteronuclear_recoupling/    DIPSHIFT
├── respdor/                     R-RESPDOR, S-RESPDOR
├── tedor/                       TEDOR, zf-TEDOR (with/without phase cycling)
├── heteronuclear_decoupling/    CW, rCW, TPPM, SWf-TPPM, SPINAL-64, XiX
├── quadrupoles/                 MQ excitation, quad-MAS detection, low-power CT-selective CP, quad x dipole SIMPSON v6
├── tsar/                        PAR, PAIN-CP, broadband PAR grid simulations
├── cross_polarisation/          Square-pulse CP, ramped CP
└── homonuclear_decoupling/      wPMLG, wLG-N (FSLG/LG4/LG6), subsampled LG4

Index of simulations

Category	File	What it simulates	Key reference
Homonuclear recoupling	allseq_HH_modular.in + recoupling.tcl	DQ buildup vs. mixing time; select S3, [S3], SR26, POST-C7, R-sequences, BABA, SWf-BABA interactively	—
Homonuclear recoupling	S3_CC.in	S3 DQ buildup with reusable propagators (fumaric acid)	Teymoori et al., J. Magn. Reson. 261 (2015) 205–220
Homonuclear recoupling	SR26_CC.in	SR26 DQ buildup with reusable propagators	Teymoori et al., J. Magn. Reson. 261 (2015) 205–220
Homonuclear recoupling	brS3_CC.in	Bracketed-S3 DQ buildup (faster build-up vs. plain S3)	Teymoori et al., J. Magn. Reson. 261 (2015) 205–220
Homonuclear recoupling	c14_3spin_relayed_transfer.in	Leakage/relayed transfer in a 3-spin system	Brinkmann, Edén & Levitt, J. Chem. Phys. 112 (2000) 8539–54
Homonuclear recoupling	refocused_inadequate.in	Transfer efficiency of refocused INADEQUATE	Nakai & Mcdowell, J. Magn. Reson. 104 (1993) 146; Cadars et al., J. Phys. Chem. B 110 (2006) 16982
Homonuclear recoupling	S3SR26_SiSi_varydist.in	2D grid: transfer efficiency vs. distance and recoupling time	—
Heteronuclear recoupling	dipshift.in	Constant-time DIPSHIFT dephasing/rephasing curve	Jain, Rajalakshmi, Agarwal, Madhu & Mote, J. Magn. Reson. 308 (2019) 106563
Heteronuclear recoupling	dipshift_finitepulse.in	DIPSHIFT with finite pulses (keeps the curve symmetric)	same as above
RESPDOR	r-respdor.in	R-RESPDOR dephasing	Gan, Chem. Commun. 2006, 4712–4714
RESPDOR	s-respdor.in	S-RESPDOR dephasing	Lu, Lafon, Trébosc & Amoureux, J. Magn. Reson. 215 (2012) 34–49
TEDOR	tedor.in	Conventional TEDOR	Jaroniec, Filip & Griffin, JACS 124 (2002) 10728–10742
TEDOR	zftedor.in	Z-filtered out-and-back TEDOR	same as above
TEDOR	zftedor_filter.in	zf-TEDOR without phase cycling	same as above
Heteronuclear decoupling	hetdec.in	CW, rCW, TPPM, SWf-TPPM, SPINAL-64, XiX decoupling on a CH₂ spin system	—
Quadrupolar NMR	mq_excitation.in	MQ excitation efficiency vs. pulse length, RF, spin rate, Cq	—
Quadrupolar NMR	quadmas.in	Quadrupolar central-transition excitation/detection in frequency space	—
Quadrupolar NMR	quadcpmas_detect.in	Low-power central-transition-selective CP	—
Quadrupolar NMR	quad_x_dipole.in	Quadrupolar x Dipolar coupling and their effect	--
TSAR	par_grid.in	PAR third-spin-assisted recoupling map (L-alanine, from xyz coords)	Lewandowski et al., JACS 131 (2009) 5769–5776; De Paëpe et al., J. Chem. Phys. 129 (2008) 245101; Paul et al., Annu. Rep. NMR Spectrosc. 85 (2015) 93–142
TSAR	pain_grid.in	PAIN-CP third-spin-assisted recoupling map	same as above
TSAR	pspar_grid.in	Broadbanded PAR variant (900 MHz, 60 kHz MAS)	Giffard et al., PCCP 14 (2012) 7246–55
Cross polarisation	cpmas.in	Square-pulse CP buildup, CH₂–CO-type system	—
Cross polarisation	rampcp.in	Ramped CP	—
Homonuclear decoupling	wpmlg.in	Windowed PMLG (wPMLGmmbar, wPMLGppbar)	Leskes et al., J. Chem. Phys. 125 (2006) 124506 and 128 (2008) 052309
Homonuclear decoupling	wlg4.in	Subsampled LG4, 55° phase offset	Halse et al., Isr. J. Chem. 54 (2014) 136–46
Homonuclear decoupling	wLG-N.in	General FSLG/LG-N family (N=1 → FSLG, N=2 → LG4, N=3 → LG6, …)	Halse et al. (2014); Paul et al., J. Magn. Reson. 197 (2009) 14–19

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Homonuclear recoupling

The main file allseq_HH_modular.in 📜 calculates the DQ magnetisation buildup as a function of the recoupling sequence's mixing time. It asks the user for the recoupling sequence to use, which is then pulled from recoupling.tcl.

Implemented sequences:

1. S3
2. [S3] — bracketed S3
3. SR26
4. POST-C7
5. R-sequence: flexible N, n, and ν
6. BABA
7. SWf-BABA

S3_CC.in 📜 and SR26_CC.in 📜 simulate polarisation buildup using reusable propagators to speed up the calculation. The spin system and parameters are those of formic acid, reproducing simulations reported in the literature.

brS3_CC.in 📜 simulates DQ buildup in the same spin system but with bracketed S3, as reported in Teymoori et al., J. Magn. Reson. 261 (2015) 205–220. The scaling and faster buildup of the bracketed version relative to plain S3 is shown in S3vsbrS3_scaling.png.

c14_3spin_relayed_transfer.in 📜 simulates how much leakage/transfer occurs when a third spin is involved, reproducing the polarisation-transfer profile from Brinkmann, Edén & Levitt, J. Chem. Phys. 112, no. 19 (2000): 8539–54.

refocused_inadequate.in 📜 helps simulate the transfer efficiency for the sequence given in:

1. Nakai, T., and C. A. Mcdowell. J. Magn. Reson. 104 (1993) 146.
2. Cadars et al. J. Phys. Chem. B 110 (2006) 16982.

It does not include relaxation, but this can be added afterwards as Lorentzian broadening during plotting.

S3SR26_SiSi_varydist.in 📜 runs a grid simulation with distance on one axis and recoupling time on the other; the resulting contour gives the polarisation-transfer efficiency.

Heteronuclear recoupling

RESPDOR

Two variants of RESPDOR are included:

1. R-RESPDOR: Gan, Z. Chem. Commun. 2006, No. 45, 4712–4714.
2. S-RESPDOR: Lu, X.; Lafon, O.; Trébosc, J.; Amoureux, J.-P. J. Magn. Reson. 2012, 215, 34–49.

TEDOR

Two variants of TEDOR are included. tedor.in 📜 is conventional TEDOR. zftedor.in 📜 is a variant of out-and-back TEDOR proposed by Christopher Jaroniec:

Jaroniec, C. P.; Filip, C.; Griffin, R. G. 3D TEDOR NMR Experiments for the Simultaneous Measurement of Multiple Carbon–Nitrogen Distances in Uniformly ¹³C, ¹⁵N-Labeled Solids. Journal of the American Chemical Society 2002, 124 (36), 10728–10742. https://doi.org/10.1021/ja026385y.

zftedor_filter.in 📜 is the same sequence with the phase cycling of zftedor.in removed.

DIPSHIFT

DIPSHIFT is a REDOR variant with a constant-time experiment that monitors dephasing and rephasing within one rotor period. dipshift.in 📜 is based on:

Jain, Mukul G., G. Rajalakshmi, Vipin Agarwal, P. K. Madhu, and Kaustubh R. Mote. "On the Direct Relation between REDOR and DIPSHIFT Experiments in Solid-State NMR." Journal of Magnetic Resonance 308 (November 2019): 106563. https://doi.org/10.1016/j.jmr.2019.07.050.

dipshift_finitepulse.in 📜 uses finite pulses and can help keep the DIPSHIFT curve symmetric.

Heteronuclear decoupling

hetdec.in 📜 simulates various heteronuclear decoupling sequences on a CH₂ spin system: CW, rCW, TPPM, SWf-TPPM, SPINAL-64, and XiX. These are starting points — feel free to improve on them; optimisation of decoupling sequences is a topic of its own.

To run just one sequence instead of the full list, edit the loop in main {}:

foreach dectype [list cw tppm swftppm spinal64 xix rcw]

to, e.g.:

foreach dectype [list tppm]

Quadrupolar NMR

mq_excitation.in 📜 simulates MQ excitation efficiency as a function of pulse length; you can vary RF power, spinning frequency, and Cq to see how efficiency changes.

quadmas.in 📜 performs quadrupolar central-transition excitation and detection in the frequency domain.

quadcpmas_detect.in 📜 performs low-power central-transition-selective cross-polarisation. Compare its spectrum against direct excitation if needed.

quad_x_dipole.in: 📜 an example of how spectrum of a nuclei is affected when there is both quadrupolar and dipolar coupling.

Third-spin-assisted recoupling (TSAR)

par_grid.in 📜 and pain_grid.in 📜 simulate third-spin-assisted recoupling maps, as reported in:

• Lewandowski, J. R. et al. Journal of the American Chemical Society 2009, 131 (16), 5769–5776. https://doi.org/10.1021/ja806578y.
• De Paëpe, G. et al. Journal of Chemical Physics 2008, 129 (24), 245101. https://doi.org/10.1063/1.3036928.
• Paul, S. et al. Annual Reports on NMR Spectroscopy; 2015; Vol. 85, pp 93–142. https://doi.org/10.1016/bs.arnmr.2014.12.003.

These files use acq_block and block diagonalisation to speed up the simulation. The spin system is derived from the xyz coordinates of L-alanine.

pspar_grid.in 📜 simulates a broadbanded PAR variant, for a 900 MHz (¹H Larmor frequency) field and 60 kHz MAS. Reference:

• Giffard, Mathilde et al. Physical Chemistry Chemical Physics 14, no. 20 (May 2012): 7246–55. https://doi.org/10.1039/c2cp40406k.

Cross polarisation

cpmas.in 📜 simulates polarisation buildup for a CH₂–CO-type system using square RF pulses.

rampcp.in 📜 simulates cross polarisation using a ramp.

Homonuclear decoupling

wpmlg.in 📜 simulates windowed PMLG decoupling (wPMLGmmbar and wPMLGppbar). See:

• Leskes, Michal, et al. "Proton Line Narrowing in Solid-State Nuclear Magnetic Resonance: New Insights from Windowed Phase-Modulated Lee-Goldburg Sequence." JCP 125 (2006) 124506. https://doi.org/10.1063/1.2352737.
• Leskes, Michal et al. "Supercycled Homonuclear Dipolar Decoupling in Solid-State NMR: Toward Cleaner ¹H Spectrum and Higher Spinning Rates." JCP 128 (2008) 052309. https://doi.org/10.1063/1.2834730.

wlg4.in simulates subsampled LG4-type decoupling; with a 55° added phase, its scaling factor is similar to wPMLG. See:

• Halse, Meghan E., et al. "High-Resolution ¹H Solid-State NMR Spectroscopy Using Windowed LG4 Homonuclear Dipolar Decoupling." Israel Journal of Chemistry 54, no. 1–2 (2014): 136–46. https://doi.org/10.1002/ijch.201300101.

wLG-N.in 📜 simulates FSLG- or LG4-type decoupling generally: N = 1 gives FSLG, N = 2 gives LG4, N = 3 gives LG6, and so on. See:

• Halse, Meghan E., et al. (2014), as above.
• Paul, S., et al. "Supercycled Homonuclear Dipolar Decoupling Sequences in Solid-State NMR." Journal of Magnetic Resonance 197, no. 1 (2009): 14–19. https://doi.org/10.1016/j.jmr.2008.11.011.

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Key SIMPSON references

1. Bak, Mads, Jimmy T. Rasmussen, and Niels Chr Nielsen. "SIMPSON: A General Simulation Program for Solid-State NMR Spectroscopy." Journal of Magnetic Resonance 147, no. 2 (December 2000): 296–330. https://doi.org/10.1006/jmre.2000.2179.
2. Juhl, Dennis W., Zdeněk Tošner, and Thomas Vosegaard. "Versatile NMR Simulations Using SIMPSON." In Annual Reports on NMR Spectroscopy, 100:1–59. Elsevier, 2020. https://doi.org/10.1016/bs.arnmr.2019.12.001.
3. Tošner, Zdeněk, Rasmus Andersen, Baltzar Stevensson, Mattias Edén, Niels Chr Nielsen, and Thomas Vosegaard. "Computer-Intensive Simulation of Solid-State NMR Experiments Using SIMPSON." Journal of Magnetic Resonance 246 (September 2014): 79–93. https://doi.org/10.1016/j.jmr.2014.07.002.
4. Vosegaard, Thomas, Anders Malmendal, and Niels C Nielsen. "The Flexibility of SIMPSON and SIMMOL for Numerical Simulations in Solid- and Liquid-State NMR Spectroscopy." Monatshefte für Chemie / Chemical Monthly 133, no. 12 (1 December 2002): 1555–74. https://doi.org/10.1007/s00706-002-0519-2.
5. Goodwin, David L., José P. Carvalho, Anders B. Nielsen, et al. “Extending Numerical Simulations in SIMPSON: Electron Paramagnetic Resonance, Dynamic Nuclear Polarisation, Propagator Splitting, Pulse Transients, and Quadrupolar Cross Terms.” Journal of Magnetic Resonance Open 27 (June 2026): 100218. https://doi.org/10.1016/j.jmro.2026.100218.

Citing this repository

If you use these scripts in research or teaching, please cite this repository (see CITATION.cff):

Contributing

Suggestions, corrections, and additional sequences are welcome — please open an issue or pull request. This project follows the Contributor Covenant Code of Conduct.

License

Released under the MIT License.