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Plane-Wave Based Low-Scaling Electronic Structure Methods for Molecules

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Linear-Scaling Techniques in Computational Chemistry and Physics

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 13))

Abstract

This paper reviews the use of plane-wave based methods to decrease the scaling of the most time-consuming part in molecular electronic structure calculations, the Coulomb interaction. The separability of the inverse distance operator allows the efficient calculation of the Coulomb potential in momentum space. Using the Fast Fourier Transform, this can be converted to the real space in essentially linearly scaling time. Plane wave expansions are periodic, and are better suited for infinite periodic systems than for molecules. Nevertheless, they can be successfully applied to molecules, and lead to large performance gains. The open problems in the field are discussed.

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References

  1. Greengard L, Rokhlin V (1985) J Comp Phys 60:187

    Article  Google Scholar 

  2. White CA, Johnson BG, Gill PMW, Head-Gordon M (1994) Chem Phys Lett 230:8

    Google Scholar 

  3. Payne MC, Teter MP, Allan DC, Arias TA, Joannopoulos JD (1992) Rev Mod Phys 64:1045

    Article  CAS  Google Scholar 

  4. Car R, Parrinello M (1985) Phys Rev Lett 55:22

    Article  Google Scholar 

  5. Segall MD, Lindan PJD, Probert MJ, Pickard CJ, Hasnip PJ, Clark SJ, Payne MC (2002) J Phys Condens Matter 14:2727

    Google Scholar 

  6. See: http://cms.mpi.univie.ac.at/vasp/

  7. Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Dal Corso A, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM (2009) J Phys Condens Matter 21:395502 See also: http://www.quantum-espresso.org

    Google Scholar 

  8. Singh DJ (1994) Plane waves, pseudopotentials and the LAPW method. Kluger, Norwell, MA

    Google Scholar 

  9. Blöchl PE (1994) Phys Rev B 59:1758

    Google Scholar 

  10. Vanderbilt D (1990) Phys Rev B 41:7892

    Article  Google Scholar 

  11. Kresse G, Joubert J (1999) Phys Rev B 59:1758

    Article  CAS  Google Scholar 

  12. Lippert G, Hutter J, Parrinello M (1997) Mol Phys 92:477

    CAS  Google Scholar 

  13. VandeVondele J, Krack M, Mohamed F, Chassaing T, Hutter J (2005) Comp Phys Comm 167:103

    Article  CAS  Google Scholar 

  14. Lippert G, Hutter J, Parrinello M (1999) Theor Chem Acc 103:124

    Article  CAS  Google Scholar 

  15. Krack M, Parrinello M (2000) Phys Chem Chem Phys 2:2105

    Article  CAS  Google Scholar 

  16. Hutter J (2003) J Chem Phys 118:3928

    Article  CAS  Google Scholar 

  17. Iannuzzi M, Chassaing T, Wallman T, Hutter J (2005) Chimia 59:499

    Article  CAS  Google Scholar 

  18. VandeVondele J, Iannuzzi M, Hutter J (2006) Lect Notes Phys 703:287

    Article  CAS  Google Scholar 

  19. Guidon M, Schiffman F, Hutter J, VandeVondele J (2008) J Chem Phys 128:214104

    Article  Google Scholar 

  20. Parallel Quantum Solutions, LLC, Fayetteville, AR, USA. See: http://www.pqs-chem.com

  21. Baker J, Wolinski K, Malagoli M, Kinghorn DR, Wolinski P, Magyarfalvi G, Saebo S, Janowski T, Pulay P (2009) J Comput Chem 30:317

    Article  CAS  Google Scholar 

  22. Füsti-Molnár L, Pulay P (2002) J Chem Phys 116:7795

    Article  Google Scholar 

  23. Füsti-Molnár L, Pulay P (2002) J Chem Phys 117:7827

    Article  Google Scholar 

  24. Füsti-Molnár L, Pulay P (2003) J Mol Struct (THEOCHEM) 666:25

    Article  Google Scholar 

  25. Füsti-Molnár L (2003) J Chem Phys 119:11080

    Article  Google Scholar 

  26. Baker J, Füsti-Molnár L, Pulay P (2004) J Phys Chem A 108:3040

    Article  CAS  Google Scholar 

  27. Baker J, Wolinski K, Pulay P (2007) J Comput Chem 28:2581

    Article  CAS  Google Scholar 

  28. Kong J, White CA, Krylov AI et al. (2000) J Comput Chem 21:1532

    Article  CAS  Google Scholar 

  29. Füsti-Molnár L, Kong J (2005) J Chem Phys 122:074108

    Article  Google Scholar 

  30. Kong J, Brown ST, Füsti-Molnár L (2006) J Chem Phys 124:094109

    Article  Google Scholar 

  31. Kong J, Brown ST, Füsti-Molnár L (2006) J Chem Phys 124:219904

    Article  Google Scholar 

  32. Brown ST, Füsti-Molnár L, Kong J (2006) Chem Phys Lett 418:490

    Article  CAS  Google Scholar 

  33. Kohn W (1995) Int J Quant Chem 56:229

    Article  CAS  Google Scholar 

  34. Schwegler E, Challacombe M (1996) J Chem Phys 105:2726

    Article  CAS  Google Scholar 

  35. Burant JC, Scuseria GE, Frisch M (1996) J Chem Phys 105:8969

    Article  CAS  Google Scholar 

  36. Schwegler E, Challacombe M, Head-Gordon M (1997) J Chem Phys 106:9708

    Article  CAS  Google Scholar 

  37. Ochsenfeld C, White CA, Head-Gordon M (1998) J Chem Phys 109:1663

    Article  CAS  Google Scholar 

  38. Heyd J, Scuseria GE, Ernzerhof M (2003) J Chem Phys 118:8207

    Article  CAS  Google Scholar 

  39. Harris F (1975) In: Electronic structure of polymers and molecular crystals. Plenum Press, New York, NY, p 453

    Google Scholar 

  40. Barnett RN, Landman U (1993) Phys Rev B 48:2081

    Article  CAS  Google Scholar 

  41. DeLeeuw SW, Perram JW, Smit ER (1980) Proc Roy Soc Lond A 373:27

    Article  CAS  Google Scholar 

  42. Hockney RW In: Alder B, Fernbach S, Rothenberg M (1970) Methods in computational physics, Academic, New York, NY 9:136

    Google Scholar 

  43. Hockney RW, Eastwood JW (1988) Computer simulation using particle, Adam Hilger, London

    Book  Google Scholar 

  44. Pollock EL, Glosli J (1996) Comp Phys Comm 95:93

    Article  CAS  Google Scholar 

  45. Bylaska EJ, Valiev M, Kawai R, Weare JH (2002) Comp Phys Comm 143:11

    Article  CAS  Google Scholar 

  46. Martyna GJ, Tuckerman ME (1999) J Chem Phys 110:2810

    Article  CAS  Google Scholar 

  47. Mináry P, Moorone JA, Yarne DA, Tuckerman ME, Martyna GJ (2004) J Chem Phys 121:11949

    Article  Google Scholar 

  48. Vanderbilt D (1994) Phys Rev B 50:17953

    Article  Google Scholar 

  49. Blöchl PE (1990) Phys Rev B 41:5414

    Article  Google Scholar 

  50. Blöchl PE, Parrinello M (1992) Phys Rev B 45:9413

    Article  Google Scholar 

  51. Stewart JJP, Császár P, Pulay P (1982) J Comp Chem 3:556

    Article  Google Scholar 

  52. VandeVondele J, Hutter J (2003) J Chem Phys 118:4365

    Article  CAS  Google Scholar 

Download references

Acknowledgments

This work was supported by the National Science Foundation under grant number CHE-0911541 and by the Mildred B. Cooper Chair at the University of Arkansas. Acquisition of the Star of Arkansas supercomputer was supported in part by the National Science Foundation under award number MRI-0722625.

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Authors and Affiliations

  1. Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, AR, 72701, USA

    Peter Pulay

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  1. Peter Pulay
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Correspondence to Peter Pulay .

Editor information

Editors and Affiliations

  1. Inst. Physical & Theoretical Chemistry, Wroclaw University of Technology, Wyb. Wyspianskiego 27, Warszawa, 50-370, Poland

    Robert Zalesny

  2. Institute of Organic &, Pharmaceutical Chemistry, National Hellenic Research Foundation, Vas. Constantinou Ave. 48, Athens, 116 35, Greece

    Manthos G. Papadopoulos

  3. Dept. Chemistry, University of Saskatchewan, Saskatoon, S7N 0W0, Saskatchewan, Canada

    Paul G. Mezey

  4. Jackson State University, J. R. Lynch St. 1325, Jackson, 39217, Mississippi, USA

    Jerzy Leszczynski

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Pulay, P. (2011). Plane-Wave Based Low-Scaling Electronic Structure Methods for Molecules. In: Zalesny, R., Papadopoulos, M., Mezey, P., Leszczynski, J. (eds) Linear-Scaling Techniques in Computational Chemistry and Physics. Challenges and Advances in Computational Chemistry and Physics, vol 13. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2853-2_1

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