How Can One Locate the Global Energy Minimum for Hydrogen-Bonded Clusters?

Chapter
First Online:

Abstract

An important problem in many areas of chemistry and physics is finding the global energy minimum on a potential energy surface. The difficulty stems from the exponential increase in the number of local minima with the size of the system. An efficient algorithm to find the global minima of water clusters is described and tested. It works well for clusters containing up to about 55 water molecules. A generalization to other hydrogen-bonded clusters is outlined. Applications of this algorithm to water clusters and methanol clusters have already been reported in the literature.

Keywords

Hydrogen-bonded clusters TIP4P model Bernal-Fowler model Basin hopping Topology optimization (H2O)26 cluster Water cluster 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

The Natural Sciences and Engineering Research Council of Canada (NSERC) supported this work. SK is grateful to the University of New Brunswick for the award of a Frank J. and Norah Toole Graduate Scholarship.

References

  1. 1.
    Johnston RL (2002) Atomic and molecular clusters. CRC Press, Boca RatonCrossRefGoogle Scholar
  2. 2.
    Scheiner S (1997) Hydrogen bonding: a theoretical perspective. Oxford, New YorkGoogle Scholar
  3. 3.
    Stone AJ (1996) The theory of intermolecular forces. Oxford, New YorkGoogle Scholar
  4. 4.
    Thakkar AJ (2001) In: Moore J, Spencer N (eds) Encyclopedia of chemical physics and physical chemistry, vol I. Fundamentals, chap. A1.5, pp 161–186. Institute of Physics Publishing, BristolGoogle Scholar
  5. 5.
    Keutsch FN, Saykally RJ (2001) Proc Nat Acad Sci USA 98:10533CrossRefGoogle Scholar
  6. 6.
    Keutsch FN, Cruzan JD, Saykally RJ (2003) Chem Rev 103:2533CrossRefGoogle Scholar
  7. 7.
    Buch V, Bauerecker S, Devlin JP, Buck U, Kazimirski JK (2004) Int Rev Phys Chem 23:375CrossRefGoogle Scholar
  8. 8.
    Prell JS, Williams ER (2009) J Am Chem Soc 131:4110CrossRefGoogle Scholar
  9. 9.
    Hamashima T, Mizuse K, Fujii A (2011) J Phys Chem A 115:620CrossRefGoogle Scholar
  10. 10.
    Sliter R, Gish M, Vilesov AF (2011) J Phys Chem A 115:9682CrossRefGoogle Scholar
  11. 11.
    Nilsson A, Pettersson LGM (2011) Chem Phys 389:1CrossRefGoogle Scholar
  12. 12.
    Ceponkus J, Uvdal P, Nelander B (2012) J Phys Chem A 116:4842CrossRefGoogle Scholar
  13. 13.
    Pérez C, Muckle MT, Zaleski DP, Seifert NA, Temelso B, Shields GC, Kisiel Z, Pate BH (2012) Science 336:897CrossRefGoogle Scholar
  14. 14.
    Pradzynski CC, Forck RM, Zeuch T, Slavíček P, Buck U (2012) Science 337:1529CrossRefGoogle Scholar
  15. 15.
    Saykally RJ, Wales DJ (2012) Science 336:814CrossRefGoogle Scholar
  16. 16.
    Richardson JO, Wales DJ, Althorpe SC, McLaughlin RP, Viant MR, Shih O, Saykally RJ (2013) J Phys Chem A 117:6960CrossRefGoogle Scholar
  17. 17.
    Bulusu S, Yoo S, Aprà E, Xantheas S, Zeng XC (2006) J Phys Chem A 110:11781CrossRefGoogle Scholar
  18. 18.
    Lenz A, Ojamäe L (2010) J Mol Struct (Theochem) 944:163CrossRefGoogle Scholar
  19. 19.
    Loboda O, Goncharuk V (2010) Chem Phys Lett 484:144CrossRefGoogle Scholar
  20. 20.
    Yoo S, Aprà E, Zeng XC, Xantheas SS (2010) J Phys Chem Lett 1:3122CrossRefGoogle Scholar
  21. 21.
    Shanker S, Bandyopadhyay P (2011) J Phys Chem A 115:11866CrossRefGoogle Scholar
  22. 22.
    Góra U, Podeszwa R, Cencek W, Szalewicz K (2011) J Chem Phys 135:224102CrossRefGoogle Scholar
  23. 23.
    Temelso B, Archer KA, Shields GC (2011) J Phys Chem A 115:12034CrossRefGoogle Scholar
  24. 24.
    Ramírez F, Hadad CZ, Guerra D, David J, Restrepo A (2011) Chem Phys Lett 507:229CrossRefGoogle Scholar
  25. 25.
    Liu X, Lu WC, Wang CZ, Ho KM (2011) Chem Phys Lett 508:270CrossRefGoogle Scholar
  26. 26.
    Bates DM, Tschumper GS (2011) J Chem Theory Comput 7:2753CrossRefGoogle Scholar
  27. 27.
    Pruitt SR, Addicoat MA, Collins MA, Gordon MS (2012) Phys Chem Chem Phys 14:7752CrossRefGoogle Scholar
  28. 28.
    Wang Y, Babin V, Bowman JM, Paesani F (2012) J Am Chem Soc 134:11116CrossRefGoogle Scholar
  29. 29.
    Gillan MJ, Manby FR, Towler MD, Alfè D (2012) J Chem Phys 136:244105CrossRefGoogle Scholar
  30. 30.
    Miliordos E, Apra E, Xantheas SS (2013) J Chem Phys 139:114302CrossRefGoogle Scholar
  31. 31.
    Iwata S, Bandyopadhyay P, Xantheas SS (2013) J Phys Chem A 117:6641CrossRefGoogle Scholar
  32. 32.
    Weinhold F (1998) J Chem Phys 109:373CrossRefGoogle Scholar
  33. 33.
    Chaplin MF (2000) Biophys Chem 83:211CrossRefGoogle Scholar
  34. 34.
    Ludwig RW (2007) ChemPhysChem 8:938CrossRefGoogle Scholar
  35. 35.
    Bukowski R, Szalewicz K, Groenenboom GC, van der Avoird A (2007) Science 315:1249CrossRefGoogle Scholar
  36. 36.
    Lenz A, Ojamäe L (2009) J Chem Phys 131:134302CrossRefGoogle Scholar
  37. 37.
    Wales DJ (2003) Energy landscapes. Cambridge University Press, New YorkGoogle Scholar
  38. 38.
    Kazachenko S, Thakkar AJ (2009) AIP Conf Proc 1108:90CrossRefGoogle Scholar
  39. 39.
    Kazachenko S, Thakkar AJ (2009) Chem Phys Lett 476:120CrossRefGoogle Scholar
  40. 40.
    Kazachenko S, Thakkar AJ (2010) Mol Phys 108:2187CrossRefGoogle Scholar
  41. 41.
    Kazachenko S, Thakkar AJ (2013) J Chem Phys 138:194302CrossRefGoogle Scholar
  42. 42.
    Kazachenko S (2013) Global energy optimization of hydrogen-bonded clusters. PhD thesis, University of New Brunswick, Fredericton, CanadaGoogle Scholar
  43. 43.
    Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML (1983) J Chem Phys 79:926CrossRefGoogle Scholar
  44. 44.
    Bernal JD, Fowler RH (1933) J Chem Phys 1:515CrossRefGoogle Scholar
  45. 45.
    Tsai CJ, Jordan KD (1993) J Phys Chem 97:5208CrossRefGoogle Scholar
  46. 46.
    Wales DJ, Hodges MP (1998) Chem Phys Lett 286:65CrossRefGoogle Scholar
  47. 47.
    Hartke B (2000) Z Phys Chem 214:1251CrossRefGoogle Scholar
  48. 48.
    Kabrede H, Hentschke R (2003) J Phys Chem B 107:3914CrossRefGoogle Scholar
  49. 49.
    Kazimirski JK, Buch V (2003) J Phys Chem A 107:9762CrossRefGoogle Scholar
  50. 50.
    Kabrede H (2006) Chem Phys Lett 430:336CrossRefGoogle Scholar
  51. 51.
    Takeuchi H (2008) J Chem Inf Model 48:2226CrossRefGoogle Scholar
  52. 52.
    Goedecker S (2004) J Chem Phys 120:9911CrossRefGoogle Scholar
  53. 53.
    Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Science 220:671CrossRefGoogle Scholar
  54. 54.
    Černý V (1985) J Optim Theory Appl 45:41CrossRefGoogle Scholar
  55. 55.
    Salomon P, Sibani P, Frost R (2002) Facts, conjectures and improvements for simulated annealing. SIAM, PhiladelphiaCrossRefGoogle Scholar
  56. 56.
    Li Z, Scheraga HA (1987) Proc Natl Acad Sci USA 84:6611CrossRefGoogle Scholar
  57. 57.
    Wales DJ, Doye JPK (1997) J Phys Chem A 101:5111CrossRefGoogle Scholar
  58. 58.
    Doye JPK, Wales DJ (1998) Phys Rev Lett 80:1357CrossRefGoogle Scholar
  59. 59.
    Doye JPK, Wales DJ, Miller MA (1998) J Chem Phys 109:8143CrossRefGoogle Scholar
  60. 60.
    Fraser AS (1959) Biometrics 15:158Google Scholar
  61. 61.
    Booker LB, Goldberg DE, Holland JH (1989) Artif Intell 40:235CrossRefGoogle Scholar
  62. 62.
    Goldberg D (1989) Genetic algorithms in search, optimization, and machine learning. Addison-Wesley, New YorkGoogle Scholar
  63. 63.
    Wales DJ, Scheraga HA (1999) Science 285:1368CrossRefGoogle Scholar
  64. 64.
    Nocedal J (1980) Math Comp 35:773CrossRefGoogle Scholar
  65. 65.
    Liu DC, Nocedal J (1989) Math Prog 45:503CrossRefGoogle Scholar
  66. 66.
    Davidon WC (1975) Math Prog 9:1CrossRefGoogle Scholar
  67. 67.
    Kazachenko S, Bulusu S, Thakkar AJ (2013) J Chem Phys 138:224303CrossRefGoogle Scholar
  68. 68.
    Franzblau DS (1991) Phys Rev B 44:4925CrossRefGoogle Scholar
  69. 69.
    McDonald S, Ojamäe L, Singer SJ (1998) J Phys Chem A 102:2824CrossRefGoogle Scholar
  70. 70.
    Kuo JL, Ciobanu CV, Ojamäe L, Shavitt I, Singer SJ (2003) J Chem Phys 118:3583CrossRefGoogle Scholar
  71. 71.
    Lenz A, Ojamäe L (2005) Phys Chem Chem Phys 7:1905CrossRefGoogle Scholar
  72. 72.
    Anick DJ (2003) J Chem Phys 119:12442CrossRefGoogle Scholar
  73. 73.
    Belair SD, Francisco JS (2003) Phys Rev A 67:063206CrossRefGoogle Scholar
  74. 74.
    Shi Q, Kais S, Francisco JS (2005) J Phys Chem A 109:12036CrossRefGoogle Scholar
  75. 75.
    Khan A (2008) J Mol Struct (Theochem) 850:144CrossRefGoogle Scholar
  76. 76.
    Tissandier MD, Singer SJ, Coe JV (2000) J Phys Chem A 104:752CrossRefGoogle Scholar
  77. 77.
    Vukičević D, Grubeša T, Graovac A (2005) Chem Phys Lett 416:212CrossRefGoogle Scholar
  78. 78.
    Anick DJ (2002) J Mol Struct (Theochem) 587:87CrossRefGoogle Scholar
  79. 79.
    Anick DJ (2002) J Mol Struct (Theochem) 587:97CrossRefGoogle Scholar
  80. 80.
    Suitte BP, Belair SD, Francisco JS (2005) Phys Rev A 71:043204CrossRefGoogle Scholar
  81. 81.
    Anick DJ (2010) J Chem Phys 132:164311CrossRefGoogle Scholar
  82. 82.
    Miyake T, Aida M (2002) Chem Phys Lett 363:106CrossRefGoogle Scholar
  83. 83.
    Vukičević D, Graovac A (2008) Croat Chem Acta 81:347Google Scholar
  84. 84.
    Bandow B, Hartke B (2006) J Phys Chem A 110:5809CrossRefGoogle Scholar
  85. 85.
    Schönborn SE, Goedecker S, Roy S, Oganov AR (2009) J Chem Phys 130:144108CrossRefGoogle Scholar
  86. 86.
    Cheng L, Feng Y, Yang J, Yang J (2009) J Chem Phys 130:214112CrossRefGoogle Scholar
  87. 87.
    Cheng L, Cai W, Shao X (2005) Chem Phys Lett 404:182CrossRefGoogle Scholar
  88. 88.
    Molinero V, Moore EB (2009) J Phys Chem B 113:4008CrossRefGoogle Scholar
  89. 89.
    Stillinger FH, Weber TA (1985) Phys Rev B 31:5262CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of New BrunswickFrederictonCanada
  2. 2.Department of ChemistryQueen’s UniversityKingstonCanada

Personalised recommendations