Real-World Predictions from Ab Initio Molecular Dynamics Simulations

  • Barbara Kirchner
  • Philipp J. di Dio
  • Jürg Hutter
Chapter
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 307)

Abstract

In this review we present the techniques of ab initio molecular dynamics simulation improved to its current stage where the analysis of existing processes and the prediction of further chemical features and real-world processes are feasible. For this reason we describe the relevant developments in ab initio molecular dynamics leading to this stage. Among them, parallel implementations, different basis set functions, density functionals, and van der Waals corrections are reported. The chemical features accessible through AIMD are discussed. These are IR, NMR, as well as EXAFS spectra, sampling methods like metadynamics and others, Wannier functions, dipole moments of molecules in condensed phase, and many other properties. Electrochemical reactions investigated by ab initio molecular dynamics methods in solution, on surfaces as well as complex interfaces, are also presented.

Keywords

Ab initio molecular dynamics simulations Always stable predictor-corrector algorithm Associated liquids Basis set Born–Oppenheimer molecular dynamics simulations Car–Parrinello molecular dynamics simulations Catalysis Collective variable Discrete variable representation Dispersion Effective core potential Enhanced sampling Fictitious mass First-principles molecular dynamics simulations Free energy surface Hartree–Fock exchange Ionic liquids Linear scaling Metadynamics Nudged elastic band Numerically tabulated atom-centered orbitals Plane waves Pseudopotential Rare event Relativistic electronic structure Retention potential Self consistent field SHAKE algorithm Solvent effect String method van der Waals interaction Wannier orbitals Water Wavelets 

Abbreviations

AIMD

Ab initio molecular dynamics; molecular dynamics with electronic structure calculations on the fly

ASPC

Always stable predictor–corrector algorithm

BOMD

Born–Oppenheimer molecular dynamics; molecular dynamics with electronic structure calculations on the fly, diagonalization in each step

CPMD

Car–Parrinello molecular dynamics; molecular dynamics with electronic structure calculations on the fly, orthogonalization in each step otherwise the coefficients of the wavefunction are propagated like the nuclear positions

CV

Collective variables

DFT

Density functional theory; static quantum chemical method using functionals of the electronic density to account for electron correlation

DVR

Discrete variable representation

ECP

Effective core potential also called pseudopotential

FBR

Finite basis representation

FES

Free energy surface

FFT

Fast Fourier transformation

GGA

Generalized gradient approximation (GGA) functional, a functional that depends on density and its gradient

HF

Hartree–Fock, static quantum chemical method

IR

Infrared red

loc

Local functional depending only on r

MD

Molecular dynamics, simulation method

MEP

Minimum energy path

MFEP

Minimum free energy path

MLWC

Maximally localized Wannier centers

MLWO

Maximally localized Wannier orbitals

MTD

Metadynamics, method to calculate rare events

NAO

Numerically tabulated atom-centered orbitals

NEMD

Non-equilibrium molecular dynamics

nl

Non-local, functional depending not only on r but also on r′

NPT

NPT ensemble: isothermal-isobaric ensemble; constant particle (N), pressure (P), and temperature (T) simulation

PBC

Periodic boundary conditions

QM/MM

Hybrid quantum-mechanical/molecular-mechanical calculations

RPA

Random phase approximation

SCF

Self consistent field

vdW

van der Waals, dispersion forces; usually not well-described in DFT

References

  1. 1.
    Ehrenfest P (1927) Z Phys A 45:455–457Google Scholar
  2. 2.
    Dirac PAM (1930) Proc Camb Phil Soc 26:376–385Google Scholar
  3. 3.
    Marx D, Hutter J (2009) Ab initio molecular dynamics: basic theory and advanced methods. Cambridge University Press, CambridgeGoogle Scholar
  4. 4.
    Car R, Parrinello M (1985) Phys Rev Lett 55:2471–2474Google Scholar
  5. 5.
    Andersen HC (1980) J Chem Phys 72:2384–2393Google Scholar
  6. 6.
    Parrinello M, Rahman A (1980) Phys Rev Lett 45:1196–1199Google Scholar
  7. 7.
    Niklasson AMN, Tymczak CJ, Challacombe M (2006) Phys Rev Lett 97:123001Google Scholar
  8. 8.
    Niklasson AMN (2008) Phys Rev Lett 100:123004Google Scholar
  9. 9.
    Tuckerman ME (2010) Statistical mechanics: theory and molecular simulations. Oxford University Press, OxfordGoogle Scholar
  10. 10.
    Allen MP, Tildesley DJ (1987) Computer simulation of liquids. Oxford University Press, OxfordGoogle Scholar
  11. 11.
    Frenkel D, Smit B (2002) Understanding molecular simulation – from algorithms to applications, 2nd edn. Academic, San DiegoGoogle Scholar
  12. 12.
    Huber H, Dyson AJ, Kirchner B (1999) Chem Soc Rev 28:121–133Google Scholar
  13. 13.
    Szabo A, Ostlund NS (1996) Modern quantum chemistry: introduction to advanced electronic structure theory. Dover Publications, Inc., Mineola, New YorkGoogle Scholar
  14. 14.
    McQuarrie DA, Simon JD (1997) Physical chemistry: a molecular approach. University Science Books, Saulalito, CaliforniaGoogle Scholar
  15. 15.
    Ryckaert J-P, Ciccotti G, Berendsen HJC (1977) J Comput Phys 23:327–341Google Scholar
  16. 16.
    Tangney P (2006) J Chem Phys 124:044111Google Scholar
  17. 17.
    Kolafa J (2004) J Comput Chem 25:335–342Google Scholar
  18. 18.
    Niklasson AMN, Steneteg P, Odell A, Bock N, Challacombe M, Tymczak CJ, Holmstroem E, Zheng G, Weber V (2009) J Chem Phys 130:214109Google Scholar
  19. 19.
    Odell A, Delin A, Johansson B, Bock N, Challacombe M, Niklasson AMN (2009) J Chem Phys 131:244106Google Scholar
  20. 20.
    Steneteg P, Abrikosov IA, Weber V, Niklasson AMN (2010) Phys Rev B 82:075110Google Scholar
  21. 21.
    Brommer KD, Larson BE, Needels M, Joannopoulos JD (1993) Comput Phys 7:350–362Google Scholar
  22. 22.
    Marx D Hutter J (2009) Ab initio molecular dynamics: basic theory and advanced methods. In: Modern methods and algorithms of quantum chemistry. p 301Google Scholar
  23. 23.
    Gygi F (2006) J Phys Conf Ser 46:268–277Google Scholar
  24. 24.
    Hutter J, Curioni A (2005) Parallel Comput 31:1–17Google Scholar
  25. 25.
    Hutter J, Curioni A (2005) Chem Phys Chem 6:1788–1793Google Scholar
  26. 26.
    Giannozzo P, Cavazzoni C (2009) Il Nuovo Cimento 32:49–52Google Scholar
  27. 27.
    VandeVondele J, Krack M, Mohamed F, Parrinello M, Chassaing T, Hutter J (2005) Comput Phys Commun 167:103–128Google Scholar
  28. 28.
    Haynes PD, Skylaris C-K, Mostofi AA, Payne MC (2006) Phys Status Solidi B 243:2489–2499Google Scholar
  29. 29.
    Resch M, Bönisch T, Tiyyagura S, Furui T, Seo Y, Bez W (eds) (2007) High performance computing on vector systems 2006. Springer, BerlinGoogle Scholar
  30. 30.
    Thar J, Reckien W, Kirchner B (2007) Top Curr Chem 268:133–171Google Scholar
  31. 31.
    Fattebert J-L, Gygi F (2006) Phys Rev B 73:115124Google Scholar
  32. 32.
    Bowler DR, Choudhury R, Gillan MJ, Miyazaki T (2006) Phys Status Solidi B 243:989–1000Google Scholar
  33. 33.
    Lee H-S, Tuckerman ME (2006) J Phys Chem A 110:5549–5560Google Scholar
  34. 34.
    Hine NDM, Haynes PD, Mostofi AA, Skylaris C-K, Payne M (2009) Comput Phys Commun 180:1041–1053Google Scholar
  35. 35.
    Genovese L et al (2008) J Chem Phys 129:014109Google Scholar
  36. 36.
    Lippert G, Hutter J, Parrinello M (1997) Mol Phys 92:477–488Google Scholar
  37. 37.
    Artacho E et al (2008) J Phys Condens Matter 20:064208Google Scholar
  38. 38.
    Blum V, Gehrke R, Hanke F, Havu P, Havu V, Ren X, Reuter K, Scheffler M (2009) Comput Phys Commun 180:2175–2196Google Scholar
  39. 39.
    Gaigeot M-P, Vuilleumier R, Sprik M, Borgis D (2005) J Chem Theory Comput 1:772–789Google Scholar
  40. 40.
    Cohen AJ, Mori-Sánchez P, Yang W (2008) Science 321:792–794Google Scholar
  41. 41.
    Heyd J, Scuseria GE, Ernerhof M (2003) J Chem Phys 118:8207–8215Google Scholar
  42. 42.
    Zhao Y, Truhlar DG (2008) Acc Chem Res 41:157–167Google Scholar
  43. 43.
    Spencer J, Alavi A (2008) Phys Rev B 77:193110Google Scholar
  44. 44.
    Guidon M, Hutter J, VandeVondele J (2009) J Chem Theory Comput 5:3010–3021Google Scholar
  45. 45.
    Guidon M, Schiffmann F, Hutter J, VandeVondele J (2008) J Chem Phys 128:214104Google Scholar
  46. 46.
    Paier J, Janesko BG, Henderson TM, Scuseria GE, Grüneis A, Kresse G (2010) J Chem Phys 132:094103Google Scholar
  47. 47.
    Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2004) Phys Rev Lett 92:246401Google Scholar
  48. 48.
    Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2005) Phys Rev Lett 95:109902(E)Google Scholar
  49. 49.
    Langreth DC, Dion M, Rydberg H, Schröder E, Hyldgaard P, Lundqvist BI (2005) Int J Quant Chem 101:599–610Google Scholar
  50. 50.
    Langreth DC et al (2009) J Phys Condens Matter 21:084203Google Scholar
  51. 51.
    Lee K, Murray ED, Kong L, Lundqvist BI, Langreth DC (2010) Phys Rev B 82:081101Google Scholar
  52. 52.
    von Lilienfeld OA, Tavernelli I, Röthlisberger U, Sebastiani D (2004) Phys Rev Lett 93:153004Google Scholar
  53. 53.
    Tapavicza E, Lin I-C, von Lilienfeld OA, Tavernelli I, Coutinho-Neto M, Röthlisberger U (2007) J Chem Theory Comput 3:1673–1679Google Scholar
  54. 54.
    Grimme S (2004) J Comput Chem 25:1463–1473Google Scholar
  55. 55.
    Grimme S (2006) J Comput Chem 27:1787–1799Google Scholar
  56. 56.
    Grimme S, Antony J, Ehrlich S, Krieg H (2010) J Chem Phys 132:154104Google Scholar
  57. 57.
    Thar J, Kirchner B (2009) J Chem Phys 130:124103Google Scholar
  58. 58.
    Kühne TD, Krack M, Mohamed FR, Parrinello M (2007) Phys Rev Lett 98:066401Google Scholar
  59. 59.
    Dai J, Yuan J (2009) Europhys Lett 88:20001Google Scholar
  60. 60.
    Kühne TD, Krack M, Parrinello M (2009) J Chem Theory Comput 5:235–241Google Scholar
  61. 61.
    Klimeš J, Bowler DR, Michaelides A (2010) J Phys Condens Matter 22:074203Google Scholar
  62. 62.
    Maragliano L, Fischer A, Vanden-Eijnden E, Ciccotti G (2006) J Chem Phys 125:024106Google Scholar
  63. 63.
    Ren W, Vanden-Eijnden E (2002) Phys Rev B 66:52301Google Scholar
  64. 64.
    Mills G, Jónsson H, Schenter GK (1995) Surf Sci 324:305–337Google Scholar
  65. 65.
    Laio A, Parrinello M (2002) Proc Natl Acad Sci USA 99:12562–12566Google Scholar
  66. 66.
    Iannuzzi M, Laio A, Parrinello M (2003) Phys Rev Lett 90:238302Google Scholar
  67. 67.
    Martonňák R, Laio A, Bernasconi M, Ceriani C, Raiteri P, Zipoli F, Parrinello M (2005) Z Kristallogr 220:489–498Google Scholar
  68. 68.
    Ensing B, Laio A, Parrinello M, Klein MI (2005) J Phys Chem B 109:6676–6687Google Scholar
  69. 69.
    Laio A, Rodriguez-Fortea A, Gervasio FL, Ceccarelli M, Parrinello M (2005) J Phys Chem B 109:6714–6721Google Scholar
  70. 70.
    Ensing B, Vivo MD, Liu Z, Moore P, Klein ML (2006) Acc Chem Res 39:73–81Google Scholar
  71. 71.
    Cucinotta CS, Ruini A, Catellani A, Stirling A (2006) Chem Phys Chem 7:1229–1234Google Scholar
  72. 72.
    Iftimie R, Tuckerman ME (2005) J Chem Phys 122:214508Google Scholar
  73. 73.
    Kaupp M, Bühl M, Malkin VG (eds) (2004) Calculation of NMR and EPR parameters – theory and application. Wiley-VCH Verlag GmbH & Co. KGaA, WeinheimGoogle Scholar
  74. 74.
    Sebastiani D, Parrinello M (2001) J Phys Chem A 105:1951–1958Google Scholar
  75. 75.
    Ochsenfeld C, Kussmann J, Koziol F (2004) Angew Chem Int Ed 43:4485–4489Google Scholar
  76. 76.
    Weber V, Iannuzzi M, Giani S, Hutter J, Declerck R, Waroquier M (2009) J Chem Phys 131:014106Google Scholar
  77. 77.
    Cavalleri M, Odelius M, Nilsson A, Petterson LGM (2004) J Chem Phys 121:10065–10075Google Scholar
  78. 78.
    Cavalleri M, Odelius M, Nordlund D, Nilsson A, Petterson LGM (2005) Phys Chem Chem Phys 7:2854–2858Google Scholar
  79. 79.
    Odelius M, Cavalleri M, Nilsson A, Pettersson LGM (2006) Phys Rev B 73:024205Google Scholar
  80. 80.
    Iannuzzi M, Hutter J (2007) Phys Chem Chem Phys 9:1599–1610Google Scholar
  81. 81.
    Iannuzzi M (2008) J Chem Phys 128:204506Google Scholar
  82. 82.
    Leetmaa M, Ljungberg M, Lyubartsev A, Nilsson A, Pettersson L (2010) J Electron Spectrosc Rel Phenom 177:135–157Google Scholar
  83. 83.
    Wannier GH (1937) Phys Rev 52:191–197Google Scholar
  84. 84.
    Savin A, Nesper R, Wengert S, Fässler TF (1997) Angew Chem Int Ed 36:1809–1832Google Scholar
  85. 85.
    Fukui K (1981) Acc Chem Res 14:363–368Google Scholar
  86. 86.
    Silvestrelli PL, Marzari N, Vanderbilt D, Parrinello M (1998) Solid State Commun 107:7–11Google Scholar
  87. 87.
    Fitzhenry P, Bilek MMM, Mariks NA, Cooper NC, McKenzie DR (2003) J Phys Condens Matter 15:165–173Google Scholar
  88. 88.
    Bühl M, Chaumont A, Schurhammer R, Wipff G (2005) J Phys Chem B 109:18591–18599Google Scholar
  89. 89.
    Kirchner B, Seitsonen AP (2007) Inorg Chem 46:2751–2754Google Scholar
  90. 90.
    Kirchner B, Sebastiani D (2004) J Phys Chem A 108:11728–11732Google Scholar
  91. 91.
    di Dio PJ, Kirchner B (2011) Stereo-electronic effects from ab initio molecular dynamics simulations. Top Curr Chem. Springer (accepted)Google Scholar
  92. 92.
    Silvestrelli PL, Parrinello M (1999) Phys Rev Lett 82:3308–3311Google Scholar
  93. 93.
    Silvestrelli PL, Parrinello M (1999) J Chem Phys 111:3572–3580Google Scholar
  94. 94.
    Kuo I-FW, Mundy CJ (2004) Science 303:658–660Google Scholar
  95. 95.
    McGrath MJ, Siepmann JI, Kuo I-FW, Mundy CJ, VandeVondele J, Hutter J, Mohamed F, Krack M (2006) J Phys Chem A 110:640–646Google Scholar
  96. 96.
    Handgraaf J-W, van Erp TS, Meijer EJ (2003) Chem Phys Lett 367:617–624Google Scholar
  97. 97.
    Whitfield TW, Crain J, Martyna GJ (2006) J Chem Phys 124:094503Google Scholar
  98. 98.
    Laasonen K, Sprik M, Parrinello M, Car R (1993) J Chem Phys 99:9080–9089Google Scholar
  99. 99.
    Fois ES, Sprik M, Parrinello M (1994) Chem Phys Lett 223:411–415Google Scholar
  100. 100.
    Sprik M, Hutter J, Parrinello M (1996) J Chem Phys 105:1142–1152Google Scholar
  101. 101.
    Silvestrelli PL, Bernasconi M, Parrinello M (1997) Chem Phys Lett 277:478–482Google Scholar
  102. 102.
    Asthagiri D, Pratt LR, Kress JD (2003) Phys Rev E 68:041505Google Scholar
  103. 103.
    Sharma M, Wu Y, Car R (2003) Int J Quant Chem 95:821–829Google Scholar
  104. 104.
    VandeVondele J, Mohamed F, Krack M, Hutter J, Sprik M, Parrinello M (2005) J Chem Phys 122:014515Google Scholar
  105. 105.
    Lee H-S, Tuckerman ME (2006) J Chem Phys 125:154507Google Scholar
  106. 106.
    Schmidt J, VandeVondele J, Kuo I-FW, Sebastiani D, Siepmann JI, Hutter J, Mundy CJ (2009) J Phys Chem B 113:11959–11964Google Scholar
  107. 107.
    Lin I-C, Seitsonen AP, Coutinho-Neto MD, Tavernelli I, Röthlisberger U (2009) J Phys Chem B 113:1127–1131Google Scholar
  108. 108.
    Rogers RD, Seddon KR (2003) Science 302:792–793Google Scholar
  109. 109.
    Kirchner B (2009) In: Kirchner B (ed) Ionic liquids. Top Curr Chem, vol 290. Springer, Berlin, pp xi–xiiiGoogle Scholar
  110. 110.
    Kirchner B (2009) In: Kirchner B (ed) Ionic liquids. Top Curr Chem, vol 290. Springer, Berlin, pp 213–262Google Scholar
  111. 111.
    Wasserscheid P, Welton T (eds) (2003) Ionic liquids in synthesis. Wiley-VCH, WeinheimGoogle Scholar
  112. 112.
    Rogers RD, Seddon KR (eds) (2005) Ionic liquids III A: fundamentals, progress, challenges, and opportunities. ACS Symposium Series, vol 901. American Chemical Society, Washington, DCGoogle Scholar
  113. 113.
    Del Pópolo MG, Lynden-Bell RM, Kohanoff J (2005) J Phys Chem B 109:5895–5902Google Scholar
  114. 114.
    Bhargava B, Balasubramanian S (2006) Chem Phys Lett 417:486–491Google Scholar
  115. 115.
    Bhargava BL, Balasubramanian S (2007) J Phys Chem B 111:4477–4487Google Scholar
  116. 116.
    Bhargava BL, Balasubramanian S (2008) J Phys Chem B 112:7566–7573Google Scholar
  117. 117.
    Thar J, Brehm M, Seitsonen AP, Kirchner B (2009) J Phys Chem B 113:15129–15132Google Scholar
  118. 118.
    Zahn S, Thar J, Kirchner B (2010) J Chem Phys 132:124506Google Scholar
  119. 119.
    Zahn S, Kirchner B (2008) J Phys Chem A 112:8430–8435Google Scholar
  120. 120.
    Izgorodina EI, Bernard UL, MacFarlane DR (2009) J Phys Chem A 113:7064–7072Google Scholar
  121. 121.
    Diraison M, Martyna GJ, Tuckerman ME (1999) J Chem Phys 111:1096–1103Google Scholar
  122. 122.
    Tsuchida E (2004) J Chem Phys 121:4740–4746Google Scholar
  123. 123.
    Röthlisberger U, Parrinello M (1997) J Chem Phys 106:4658–4694Google Scholar
  124. 124.
    Galli G, Hood RQ, Hazi AU, Gygi F (2000) Phys Rev B 61:909–912Google Scholar
  125. 125.
    Bonev SA, Militzer B, Galli G (2004) Phys Rev B 69:014101Google Scholar
  126. 126.
    Galli G, Martin RM, Car R, Parrinello M (1990) Phys Rev B 42:7470–7482Google Scholar
  127. 127.
    Marks NA, McKenzie DR, Pailthorpe BA, Bernasconi M, Parrinello M (1996) Phys Rev B 54:9703–9714Google Scholar
  128. 128.
    Silvestrelli PL, Parrinello M (1998) J Appl Phys 83:2478–2485Google Scholar
  129. 129.
    McCulloch DG, McKenzie DR, Goringe CM (2000) Phys Rev B 61:2349–2355Google Scholar
  130. 130.
    Wang X, Scandolo S, Car R (2005) Phys Rev Lett 95:185701Google Scholar
  131. 131.
    Kirchner B, Seitsonen AP, Hutter J (2006) J Phys Chem B 110:11475–11480Google Scholar
  132. 132.
    Senda Y, Shimojo F, Hoshino K (2002) J Phys Condens Matter 14:3715–3723Google Scholar
  133. 133.
    Anta JA, Madden PA (1999) J Phys Condens Matter 11:6099–6111Google Scholar
  134. 134.
    Foley M, Smargiassi E, Madden PA (1994) J Phys Condens Matter 6:5231–5241Google Scholar
  135. 135.
    Ji M, Gong XG (2004) J Phys Condens Matter 16:2507–2514Google Scholar
  136. 136.
    Štich I, Car R, Parrinello M (1991) Phys Rev B 44:4262–4274Google Scholar
  137. 137.
    Sugino O, Car R (1995) Phys Rev Lett 74:1823–1826Google Scholar
  138. 138.
    Senda Y, Shimojo F, Hoshino K (1999) J Phys Condens Matter 11:5387–5398Google Scholar
  139. 139.
    Gu T, Qin J, Xu C, Bian X (2004) Phys Rev B 70:144204Google Scholar
  140. 140.
    Jakse N, Pasturel A (2004) J Chem Phys 120:6124–6127Google Scholar
  141. 141.
    Pasquarello A, Laasonen K, Car R, Lee C, Vanderbilt D (1992) Phys Rev Lett 69:1982–1985Google Scholar
  142. 142.
    Godlevsky VV, Derby JJ, Chelikowsky JR (1998) Phys Rev Lett 81:4959–4962Google Scholar
  143. 143.
    Kresse G, Hafner J (1994) Phys Rev B 49:14251–14269Google Scholar
  144. 144.
    Kulkarni RV, Aulbur WG, Stroud D (1997) Phys Rev B 55:6896–6903Google Scholar
  145. 145.
    Chai J-D, Stroud D, Hafner J, Kresse G (2003) Phys Rev B 67:104205Google Scholar
  146. 146.
    Shimojo F, Munejiri S, Hoshino K, Zempo Y (2000) J Phys Condens Matter 12:6161–6172Google Scholar
  147. 147.
    Shimojo F, Hoshino K, Watabe M, Zempo Y (1998) J Phys Condens Matter 10:1199–1210Google Scholar
  148. 148.
    Jakse N, Pasturel A (2003) Phys Rev Lett 91:195501Google Scholar
  149. 149.
    de Wijs GA, Pastore G, Selloni A, van der Lugt W (1994) Europhys Lett 27:667–672Google Scholar
  150. 150.
    Kresse G, Hafner J (1997) Phys Rev B 55:7539–7548Google Scholar
  151. 151.
    Kresse G (1995) J Non-Cryst Solids 193:222–229Google Scholar
  152. 152.
    Laasonen K, Klein ML (1994) J Am Chem Soc 116:11620–11621Google Scholar
  153. 153.
    Kirchner B (2007) Chem Phys Chem 8:41–43Google Scholar
  154. 154.
    Marx D (2006) Chem Phys Chem 7:1848–1870Google Scholar
  155. 155.
    Marsalek O, Uhlig F, Frigato T, Schmidt B, Jungwirth P (2010) Phys Rev Lett 105:043002Google Scholar
  156. 156.
    Marsalek O, Uhlig F, Jungwirth P (2010) J Phys Chem C 114:20489–20495Google Scholar
  157. 157.
    Marsalek O, Frigato T, VandeVondele J, Bradforth SE, Schmidt B, Schtte C, Jungwirth P (2010) J Phys Chem B 114:915–920Google Scholar
  158. 158.
    Frigato T, VandeVondele J, Schmidt B, Schtte C, Jungwirth P (2008) J Phys Chem A 112:6125–6133Google Scholar
  159. 159.
    Kirchner B, Hutter J (2004) J Chem Phys 121:5133–5142Google Scholar
  160. 160.
    Kirchner B, Reiher M (2002) J Am Chem Soc 124:6206–6215Google Scholar
  161. 161.
    Gaigeot M-P, Sprik M (2003) J Phys Chem B 107:10344–10358Google Scholar
  162. 162.
    van Erp TS, Meijer EJ (2003) J Chem Phys 118:8831–8840Google Scholar
  163. 163.
    Kirchner B, Hutter J, Kuo I-FW, Mundy CJ (2004) Int J Mod Phys B 18:1951–1962Google Scholar
  164. 164.
    Thar J, Zahn S, Kirchner B (2008) J Phys Chem B 112:1456–1464Google Scholar
  165. 165.
    Tuckerman M, Laasonen K, Sprik M, Parrinello M (1995) J Chem Phys 103:150–161Google Scholar
  166. 166.
    Yarne DA, Tuckerman ME, Klein ML (2000) Chem Phys 258:163–169Google Scholar
  167. 167.
    Kuo I-F, Tobias DJ (2001) J Phys Chem B 105:5827–5832Google Scholar
  168. 168.
    Tobias DJ, Jungwirth P, Parrinello M (2001) J Chem Phys 114:7036–7044Google Scholar
  169. 169.
    Raugei S, Klein ML (2002) J Chem Phys 116:196–202Google Scholar
  170. 170.
    Leung K, Rempe SB (2004) J Am Chem Soc 126:344–351Google Scholar
  171. 171.
    Heuft JM, Meijer EJ (2005) J Chem Phys 122:094501Google Scholar
  172. 172.
    Heuft JM, Meijer EJ (2005) J Chem Phys 123:094506Google Scholar
  173. 173.
    Marx D, Sprik M, Parrinello M (1997) Chem Phys Lett 273:360–366Google Scholar
  174. 174.
    Ramaniah LM, Bernasconi M, Parrinello M (1999) J Chem Phys 111:1587–1591Google Scholar
  175. 175.
    Lyubartsev AP, Laasonen K, Laaksonen A (2001) J Chem Phys 114:3120–3126Google Scholar
  176. 176.
    Lightstone FC, Schwegler E, Hood RQ, Gygi F, Galli G (2001) Chem Phys Lett 343:549–555Google Scholar
  177. 177.
    Bakó I, Hutter J, Pálinkás G (2002) J Chem Phys 117:9838–9843Google Scholar
  178. 178.
    Lightstone FC, Schwegler E, Allesch M, Gygi F, Galli G (2005) Chem Phys Chem 6:1745–1749Google Scholar
  179. 179.
    Ikeda T, Hirata M, Kimura T (2005) J Chem Phys 122:024510Google Scholar
  180. 180.
    Amira S, Spångberg D, Hermansson K (2006) J Chem Phys 124:104501Google Scholar
  181. 181.
    Sa R, Zhu W, Shen J, Gong Z, Cheng J, Chen K, Jiang H (2006) J Phys Chem B 110:5094–5098Google Scholar
  182. 182.
    Moret M-E, Tavernelli I, Chergui M, Rothlisberger U (2010) Chem Eur J 16:5889–5894Google Scholar
  183. 183.
    Todorova T, Hünenberger PH, Hutter J (2008) J Chem Theory Comput 4:779–789Google Scholar
  184. 184.
    Mallik BS, Siepmann JI (2010) J Phys Chem B 114:12577–12584Google Scholar
  185. 185.
    Spickermann C, Thar J, Lehmann SBC, Zahn S, Hunger J, Buchner R, Hunt PA, Welton T, Kirchner B (2008) J Chem Phys 129:104505Google Scholar
  186. 186.
    Raugei S, Cardini G, Schettino V (1999) J Chem Phys 111:10887–10894Google Scholar
  187. 187.
    Raugei S, Cardini G, Schettino V (2001) J Chem Phys 114:4089–4098Google Scholar
  188. 188.
    Pagliai M, Raugei S, Cardini G, Schettino V (2001) Phys Chem Chem Phys 3:4870–4873Google Scholar
  189. 189.
    Pagliai M, Raugei S, Cardini G, Schettino V (2003) J Mol Struct (Theochem) 630:141–149Google Scholar
  190. 190.
    Mugnai M, Cardini G, Schettino V (2003) J Chem Phys 118:2767–2774Google Scholar
  191. 191.
    Ammal SC, Yamataka H, Aida M, Dupuis M (2003) Science 299:1555–1557Google Scholar
  192. 192.
    Yang S-Y, Fleurat-Lessard P, Hristov I, Ziegler T (2004) J Phys Chem A 108:9461–9468Google Scholar
  193. 193.
    Reiher M, Kirchner B, Hutter J, Sellmann D, Hess BA (2004) Chem Eur J 10:4443–4453Google Scholar
  194. 194.
    Kirchner B, Reiher M, Hille A, Hutter J, Hess BA (2005) Chem Eur J 11:574–583Google Scholar
  195. 195.
    Schenk S, Kirchner B, Reiher M (2009) Chem Eur J 15:5073–5082Google Scholar
  196. 196.
    Urakawa A, Iannuzzi M, Hutter J, Baiker A (2007) Chem Eur J 13:6828–6840Google Scholar
  197. 197.
    Michel C, Laio A, Mohammad F, Krack M, Parrinello M, Milet A (2007) Organometallics 26:1241–1249Google Scholar
  198. 198.
    Michel C, Milet A (2008) J Mol Struct (Theochem) 852:54–61Google Scholar
  199. 199.
    Izvekov S, Mazzolo A, VanOpdorp K, Voth GA (2001) J Chem Phys 114:3248–3257Google Scholar
  200. 200.
    Izvekov S, Voth GA (2001) J Chem Phys 115:7196–7206Google Scholar
  201. 201.
    Sugino O, Hamada I, Otani M, Morikawa Y, Ikeshoji T, Okamoto Y (2007) Surf Sci 601:5237–5240Google Scholar
  202. 202.
    Otani M, Hamada I, Sugino O, Morikawa Y, Okamoto Y, Ikeshoji T (2008) Phys Chem Chem Phys 10:3609–3612Google Scholar
  203. 203.
    Blumberger J, Tateyama Y, Sprik M (2005) Comput Phys Commun 169:256–261Google Scholar
  204. 204.
    VandeVondele J, Ayala R, Sulpizi M, Sprik M (2007) J Electroanal Chem 607:113–120Google Scholar
  205. 205.
    VandeVondele J, Sulpizi M, Sprik M (2007) Chimia 61:155–158Google Scholar
  206. 206.
    Lynden-Bell R (2007) Electrochem Commun 9:1857–1861Google Scholar
  207. 207.
    Moens J, Seidel R, Geerlings P, Faubel M, Winter B, Blumberger J (2010) J Phys Chem B 114:9173–9182Google Scholar
  208. 208.
    Tateyama Y, Blumberger J, Sprik M, Tavernelli I (2005) J Chem Phys 122:234505Google Scholar
  209. 209.
    Blumberger J, Bernasconi L, Tavernelli I, Vuilleumier R, Sprik M (2004) J Am Chem Soc 126:3928–3938Google Scholar
  210. 210.
    Blumberger J, Sprik M (2004) J Phys Chem B 180:6529–6535Google Scholar
  211. 211.
    Blumberger J (2008) J Am Chem Soc 130:16065–16068Google Scholar
  212. 212.
    Blumberger J, Sprik M (2005) J Phys Chem B 109:6793–6804Google Scholar
  213. 213.
    Blumberger J, Sprik M (2006) Theor Chem Acc 115:113–126Google Scholar
  214. 214.
    Seidel R, Faubel M, Winter B, Blumberger J (2009) J Am Chem Soc 131:16127–16137Google Scholar
  215. 215.
    Oberhofer H, Blumberger J (2009) J Chem Phys 131:064101Google Scholar
  216. 216.
    Ayala R, Sprik M (2006) J Chem Theory Comput 2:1403–1415Google Scholar
  217. 217.
    Tateyama Y, Blumberger J, Ohno T, Sprik M (2007) J Chem Phys 126:204506Google Scholar
  218. 218.
    Blumberger J, Tavernelli I, Klein ML, Sprik M (2006) J Chem Phys 124:064507Google Scholar
  219. 219.
    VandeVondele J, Lynden-Bell R, Meijer EJ, Sprik M (2006) J Phys Chem B 110:3614–3623Google Scholar
  220. 220.
    Cheng J, Sulpizi M, Sprik M (2009) J Chem Phys 131:154504Google Scholar
  221. 221.
    Sulpizi M, Raugei S, VandeVondele J, Carloni P, Sprik M (2007) J Phys Chem B 111:3969–3976Google Scholar
  222. 222.
    Santana JA, Mateo JJ, Ishikawa Y (2010) J Phys Chem C 114:4995–5002Google Scholar
  223. 223.
    Skúlason E, Tripkovic V, Björketun ME, Gudmundsdóttir S, Karlberg G, Rossmeisl J, Bligaard T, Jónsson H, Nørskov JK (2010) J Phys Chem C 114:18182–18197Google Scholar
  224. 224.
    Wang Y, Balbuena PB (2004) J Phys Chem B 108:4376–4384Google Scholar
  225. 225.
    Okamoto Y (2008) Appl Surf Sci 255:3434–3441Google Scholar
  226. 226.
    Hirunsit P, Balbuena PB (2009) Surf Sci 603:3239–3248Google Scholar
  227. 227.
    Ford DC, Nilekar AU, Xu Y, Mavrikakis M (2010) Surf Sci 604:1565–1575Google Scholar
  228. 228.
    Santana JA, Ishikawa Y (2010) Electrochim Acta 56:945–952Google Scholar
  229. 229.
    Schiffmann F, VandeVondele J, Hutter J, Urakawa A, Wirz R, Baiker A (2010) Proc Natl Acad Sci USA 107:4830–4833Google Scholar
  230. 230.
    Schiffmann F, Hutter J, VandeVondele J (2008) J Phys Condens Matter 20:064206Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Barbara Kirchner
    • 1
  • Philipp J. di Dio
    • 1
  • Jürg Hutter
    • 2
  1. 1.Wilhelm-Ostwald Institute of Physical and Theoretical ChemistryUniversity of LeipzigLeipzigGermany
  2. 2.Physical Chemistry InstituteUniversity of ZürichZürichSwitzerland

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