Optimal Design of Offset-Specific Radio Frequency Pulses for Solution and Solid-State NMR Using a Genetic Algorithm

  • Manu Veliparambil Subrahmanian
  • Aurelio James Dregni
  • Gianluigi VegliaEmail author
Reference work entry


In this chapter, we describe the necessary steps to optimize the design of radiofrequency pulses for solution and solid-state NMR spectroscopy using a genetic algorithm (GA). We show that GA-optimized pulses significantly improve both sensitivity and resolution of NMR experiments, eliminating experimental imperfections. Additionally, we demonstrate the use of GA optimization to design band-selective pulses and manipulate individual spin systems with significantly different chemical shifts such as carbonyl and aliphatic carbon nuclei. These new offset-specific pulses (OSP) are of general use and can perform various operations on nuclei based on their chemical shift offsets. Replacing multiple band selective pulses with a single OSP can dramatically reduce pulsing time and power in classical NMR pulse sequences, increasing the sensitivity in multidimensional experiments.


Genetic algorithm optimization NMR pulse design Composite pulses RF inhomogeneity Broad-band pulses 


  1. 1.
    Ernst RR, Bodenhausen G, Wokaun A. Principles of nuclear magnetic resonance in one and two dimensions. Oxford Oxfordshire/New York: Clarendon Press/Oxford University Press; 1987.Google Scholar
  2. 2.
    Levitt MH. Spin dynamics: basics of nuclear magnetic resonance. Chichester/New York: John Wiley & Sons; 2001.Google Scholar
  3. 3.
    Abragam A. The principles of nuclear magnetism. Oxford: Clarendon Press; 1961.Google Scholar
  4. 4.
    Cavanagh J, Fairbrother WJ, Palmer AG, Rance M, Skelton NJ. Protein NMR spectroscopy: principles and practice. 2nd ed. New York: Elsevier Acadamic Press; 2007. p. 1–888.CrossRefGoogle Scholar
  5. 5.
    Berger S, Braun S. 200 and more NMR experiments: a practical course. Weinheim: Wiley-Vch; 2004.Google Scholar
  6. 6.
    Levitt MH, Freeman R, Frenkiel T. Broadband heteronuclear decoupling. J Magn Reson. 1982;47:328–30.Google Scholar
  7. 7.
    Shaka AJ. Composite pulses for ultra-broadband spin inversion. Chem Phys Lett. 1985;120:201–5.CrossRefGoogle Scholar
  8. 8.
    Levitt MH, Freeman R. Composite pulse decoupling. J Magn Reson. 1981;43:502–7.Google Scholar
  9. 9.
    Tannus A, Garwood M. Adiabatic pulses. NMR Biomed. 1997;10:423–34.CrossRefGoogle Scholar
  10. 10.
    Garwood M, DelaBarre L. The return of the frequency sweep: designing adiabatic pulses for contemporary NMR. J Magn Reson. 2001;153:155–77.CrossRefGoogle Scholar
  11. 11.
    Levitt MH. Composite pulses. Prog Nucl Magn Reson Spectrosc. 1986;18:61–122.CrossRefGoogle Scholar
  12. 12.
    Levitt MH, Freeman R. NMR population-inversion using a composite pulse. J Magn Reson. 1979;33:473–6.Google Scholar
  13. 13.
    Freeman R, Kempsell SP, Levitt MH. Radiofrequency pulse sequences which compensate their own imperfections. J Magn Reson. 1980;38:453–79.Google Scholar
  14. 14.
    Counsell C, Levitt MH, Ernst RR. Analytical theory of composite pulses. J Magn Reson. 1985;63:133–41.Google Scholar
  15. 15.
    Levitt MH, Freeman R. Compensation for pulse imperfections in NMR spin-echo experiments. J Magn Reson. 1981;43:65–80.Google Scholar
  16. 16.
    Levitt MH. Symmetrical composite pulse sequences for NMR population-inversion. 1. Compensation of radiofrequency field inhomogeneity. J Magn Reson. 1982;48:234–64.Google Scholar
  17. 17.
    Levitt MH. Symmetrical composite pulse sequences for NMR population-inversion. 2. Compensation of resonance offset. J Magn Reson. 1982;50:95–110.Google Scholar
  18. 18.
    Shaka AJ, Freeman R. Composite pulses with dual compensation. J Magn Reson. 1983;55:487–93.Google Scholar
  19. 19.
    Yang XJ, Zhi ZL, Huang XB, Gao BH, Lu LD, Wang X. Dual-compensating composite inversion pulses for NMR. Spectrosc Lett. 1998;31:1665–76.CrossRefGoogle Scholar
  20. 20.
    Odedra S, Thrippleton MJ, Wimperis S. Dual-compensated antisymmetric composite refocusing pulses for NMR. J Magn Reson. 2012;225:81–92.CrossRefGoogle Scholar
  21. 21.
    Kocher SS, Heydenreich T, Zhang Y, Reddy GN, Caldarelli S, Yuan H, Glaser SJ. Time-optimal excitation of maximum quantum coherence: physical limits and pulse sequences. J Chem Phys. 2016;144:164103.CrossRefGoogle Scholar
  22. 22.
    Khaneja N, Reiss T, Kehlet C, Schulte-Herbruggen T, Glaser SJ. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J Magn Reson. 2005;172:296–305.CrossRefGoogle Scholar
  23. 23.
    Li JS, Ruths J, Yu TY, Arthanari H, Wagner G. Optimal pulse design in quantum control: a unified computational method. Proc Natl Acad Sci U S A. 2011;108:1879–84.CrossRefGoogle Scholar
  24. 24.
    Skinner TE, Reiss TO, Luy B, Khaneja N, Glaser SJ. Application of optimal control theory to the design of broadband excitation pulses for high-resolution NMR. J Magn Reson. 2003;163:8–15.CrossRefGoogle Scholar
  25. 25.
    Fortunato EM, Pravia MA, Boulant N, Teklemariam G, Havel TF, Cory DG. Design of strongly modulating pulses to implement precise effective Hamiltonians for quantum information processing. J Chem Phys. 2002;116:7599–606.CrossRefGoogle Scholar
  26. 26.
    Manu VS, Kumar A. Singlet-state creation and universal quantum computation in NMR using a genetic algorithm. Phys Rev A. 2012;86:022324.CrossRefGoogle Scholar
  27. 27.
    Manu VS, Kumar A. Quantum simulation using fidelity-profile optimization. Phys Rev A. 2014;89:052331.CrossRefGoogle Scholar
  28. 28.
    Manu VS, Veglia G. Genetic algorithm optimized triply compensated pulses in NMR spectroscopy. J Magn Reson. 2015;260:136–43.CrossRefGoogle Scholar
  29. 29.
    Manu VS, Veglia G. Optimization of identity operation in NMR spectroscopy via genetic algorithm: application to the TEDOR experiment. J Magn Reson. 2016;273:40–6.CrossRefGoogle Scholar
  30. 30.
    Morris GM, Goodsell DS, Halliday RS, Huey R, Hart WE, Belew RK, Olson AJ. Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function. J Comput Chem. 1998;19:1639–62.CrossRefGoogle Scholar
  31. 31.
    Holland JH. Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. Ann Arbor: University of Michigan Press; 1975.Google Scholar
  32. 32.
    Whitley D. A genetic algorithm tutorial. Stat Comput. 1994;4:65–85.CrossRefGoogle Scholar
  33. 33.
    Forrest S. Genetic algorithms: principles of natural selection applied to computation. Science. 1993;261:872–8.CrossRefGoogle Scholar
  34. 34.
    Goldberg DE. Genetic algorithms in search, optimization, and machine learning. Reading: Addison-Wesley; 1989.Google Scholar
  35. 35.
    Schwefel H-P. Evolution and optimum seeking. New York: Wiley; 1995.Google Scholar
  36. 36.
    Manu VS, Kumar A. Fast and accurate quantification using Genetic Algorithm optimized H-1-C-13 refocused constant-time INEPT. J Magn Reson. 2013;234:106–11.CrossRefGoogle Scholar
  37. 37.
    Pang Y, Shen GX. Improving excitation and inversion accuracy by optimized RF pulse using genetic algorithm. J Magn Reson. 2007;186:86–93.CrossRefGoogle Scholar
  38. 38.
    Freeman R, Wu XL. Design of magnetic-resonance experiments by genetic evolution. J Magn Reson. 1987;75:184–9.Google Scholar
  39. 39.
    Grimminck DLAG, Vasa SK, Meerts WL, Kentgens APM, Brinkmann A. EASY-GOING DUMBO on-spectrometer optimisation of phase modulated homonuclear decoupling sequences in solid-state NMR. Cheml Phys Lett. 2011;509:186–91.CrossRefGoogle Scholar
  40. 40.
    Herbst C, Herbst J, Leppert J, Ohlenschlager O, Gorlach M, Ramachandran R. Numerical design of RN (n) (nu) symmetry-based RF pulse schemes for recoupling and decoupling of nuclear spin interactions at high MAS frequencies. J Biomol NMR. 2009;44:235–44.CrossRefGoogle Scholar
  41. 41.
    Bechmann M, Clark J, Sebald A. Genetic algorithms and solid state NMR pulse sequences. J Magn Reson. 2013;228:66–75.CrossRefGoogle Scholar
  42. 42.
    Zeidler D, Frey S, Kompa KL, Motzkus M. Evolutionary algorithms and their application to optimal control studies. Phys Rev A. 2001;64, art. no. 023420.Google Scholar
  43. 43.

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Manu Veliparambil Subrahmanian
    • 1
  • Aurelio James Dregni
    • 1
  • Gianluigi Veglia
    • 1
    • 2
    Email author
  1. 1.Department of Biochemistry, Molecular Biology and BiophysicsUniversity of MinnesotaMinneapolisUSA
  2. 2.Department of ChemistryUniversity of MinnesotaMinneapolisUSA

Personalised recommendations