Theoretical Chemistry Accounts

, Volume 115, Issue 2–3, pp 113–126 | Cite as

Quantum versus classical electron transfer energy as reaction coordinate for the aqueous Ru2+/Ru3+ redox reaction

Regular Article

Abstract

Applying density functional theory (DFT)-based molecular dynamics simulation methods we investigate the effect of explicit treatment of electronic structure on the solvation free energy of aqueous Ru2+ and Ru3+.Our approach is based on the Marcus theory of redox half reactions, focussing on the vertical energy gap for reduction or oxidation of a single aqua ion. We compare the fluctuations of the quantum and classical energy gap along the same equilibrium ab initio molecular dynamics trajectory for each oxidation state. The classical gap is evaluated using a standard point charge model for the charge distribution of the solvent molecules (water). The quantum gap is computed from the full DFT electronic ground state energies of reduced and oxidized species, thereby accounting for the delocalization of the electron in the donor orbital and reorganization of the electron cloud after electron transfer (ET). The fluctuations of the quantum ET energy are well approximated by gaussian statistics giving rise to parabolic free energy profiles. The curvature is found to be independent of the oxidation state in agreement with the linear response assumption underlying Marcus theory. By contrast, the diabatic free energy curves evaluated using the classical gap as order parameter, while also quadratic, are asymmetric reflecting the difference in oxidation state. The response of these two order parameters is further analysed by a comparison of the spectral density of the fluctuations and the corresponding reorganization free energies.

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References

  1. Marcus RA. (1956). J Chem Phys. 24:966CrossRefGoogle Scholar
  2. Marcus RA. (1960). Discuss Faraday Soc. 29:21CrossRefGoogle Scholar
  3. Marcus RA. (1965). J Chem Phys. 43:679CrossRefGoogle Scholar
  4. Marcus RA. (1993). Rev Mod Phys. 65:599CrossRefGoogle Scholar
  5. Jortner J., Bixon M. (eds). (1999). Electron transfer – from isolated molecules to biomolecules. Adv Chem Phys. 106:107Google Scholar
  6. Barzykin AV., Frantsukov PA., Seki K., Tachiya M. (2002). Adv Chem Phys. 123:511CrossRefGoogle Scholar
  7. Warshel A. (1982). J Phys Chem. 86:2218CrossRefGoogle Scholar
  8. Hwang JK., Warshel A. (1987). J Am Chem Soc. 109:715CrossRefGoogle Scholar
  9. King G., Warshel A. (1990). J Chem Phys. 93:8682Google Scholar
  10. Kuharski RA., Bader JS., Chandler D., Sprik M., Klein ML., Impey RW. (1988). J Chem Phys. 89:3248CrossRefGoogle Scholar
  11. Carter EA., Hynes JT (1989) J Phys Chem. 93:2184CrossRefGoogle Scholar
  12. Rose DA., Benjamin I. (1994) J Chem Phys. 100:3545CrossRefGoogle Scholar
  13. Rose DA., Benjamin I (1995). Chem Phys Lett. 234:209CrossRefGoogle Scholar
  14. Yelle RB., Ichiye Y. (1997). J Phys Chem B. 101:4127CrossRefGoogle Scholar
  15. Straus JB., Voth GA. (1993). J Phys Chem. 97:7388CrossRefGoogle Scholar
  16. Straus JB., Calhoun A., Voth GA. (1995). J Chem Phys. 102:529CrossRefGoogle Scholar
  17. Calhoun A., Voth GA. (1996). J Phys Chem. 100:10746CrossRefGoogle Scholar
  18. Calhoun A., Voth GA. (1998). J Phys Chem B. 102:8563CrossRefGoogle Scholar
  19. Calhoun A., Koper MTM., Voth GA. (1999). J Phys Chem B. 103:3442CrossRefGoogle Scholar
  20. Calhoun A., Koper MTM., Voth GA. (1999). Chem Phys Lett. 305:94CrossRefGoogle Scholar
  21. Small DW., Matyushov DV., Voth GA. (2003). J Am Chem Soc. 125:7470PubMedCrossRefGoogle Scholar
  22. Ando K., Kato S. (1991). J Chem Phys. 95:5966CrossRefGoogle Scholar
  23. Ando K. (1997). J Chem Phys. 106:116CrossRefGoogle Scholar
  24. Ando K. (2001). J Chem Phys. 114:9040CrossRefGoogle Scholar
  25. Ando K. (2001). J Chem Phys. 114:9470CrossRefGoogle Scholar
  26. Hartnig C., Koper MTM. (2001). J Chem Phys. 115:8540CrossRefGoogle Scholar
  27. Hartnig C., Koper TM. (2003). J Am Chem Soc.125:9840PubMedCrossRefGoogle Scholar
  28. Kakitani T., Mataga N. (1985). J Phys Chem. 89:8CrossRefGoogle Scholar
  29. Kakitani T., Mataga N. (1985). Chem Phys. 93:381CrossRefGoogle Scholar
  30. Tachiya M. (1989). J Phys Chem. 93:7050CrossRefGoogle Scholar
  31. Matyushov DV., Voth GA. (2000). J Chem Phys. 113:5413CrossRefGoogle Scholar
  32. Bard AJ., Faulkner LR. (eds). (2001). Electrochemical Methods. 2nd ed. Wiley, LondonGoogle Scholar
  33. Blumberger J., Bernasconi L., Tavernelli I., Vuilleumier R., Sprik M. (2004). J Am Chem Soc. 126:3928CrossRefPubMedGoogle Scholar
  34. Blumberger J., Sprik M. (2004). J Phys Chem B. 108(21):6529CrossRefGoogle Scholar
  35. Blumberger J., Sprik M. (2005). J Phys Chem B. 109:6793CrossRefGoogle Scholar
  36. Tateyama Y., Blumberger J., Sprik M., Tavernelli I. (2005). J Chem Phys. 122:234505PubMedCrossRefGoogle Scholar
  37. Wasserman E., Rustad JR., Xantheas SS. (1997). J Phys Chem. 106:9769CrossRefGoogle Scholar
  38. Ikeda I., Hirata M., Kimura T. (2003). J Chem Phys. 119:12386CrossRefGoogle Scholar
  39. Spångberg D., Hermansson K. (2004). J Phys Chem. 120:4829CrossRefGoogle Scholar
  40. Amira S., Spångberg D., Zelin V., Probst M., Hermansson K. (2005). J Phys Chem B. 109:14235CrossRefGoogle Scholar
  41. Martinez JM., Pappalardo RR., Sánchez Marcos E. (1998). J Chem Phys.109:1445CrossRefGoogle Scholar
  42. Zwanzig RW. (1954). J Chem Phys. 22:1420CrossRefGoogle Scholar
  43. Tavernelli I., Vuilleumier R., Sprik M. (2002). Phys Rev Lett. 88:213002CrossRefPubMedGoogle Scholar
  44. Hummer G., Pratt LR., Garcia AE. (1998). J Phys Chem A. 102:7885CrossRefGoogle Scholar
  45. Brunschwig BS., Creutz C., McCartney DH., Sham TK., Sutin N. (1982). Faraday Discuss Chem Soc. 74:113CrossRefGoogle Scholar
  46. Böttcher W., Brown GM., Sutin N. (1979). Inorg Chem. 18:1447CrossRefGoogle Scholar
  47. Bernhard P., Burgi H-B., Hauser J., Lehmann H., Ludi A. (1982). Inorg Chem. 21:3936CrossRefGoogle Scholar
  48. Bernhard P., Ludi A. (1984). Inorg Chem. 23:870CrossRefGoogle Scholar
  49. Sprik M., Hutter J., Parrinello M. (1996). J Chem Phys. 105:1142CrossRefGoogle Scholar
  50. Vuilleumier R., Sprik M. (2001). J Chem Phys. 115:3454CrossRefGoogle Scholar
  51. Car R., Parrinello M. (1985). Phys Rev Lett. 55:2471CrossRefPubMedGoogle Scholar
  52. Hutter J., Ballone P., Bernasconi M, Focher P, Fois E, Goedecker St, Marx D, Parrinello M, Tuckerman M (1998) CPMD version 3.3, MPI fur Festkárperforschung and the IBM Zurich Research LaboratoryGoogle Scholar
  53. Hockney RW. (1970). Methods Comput Phys. 9:136Google Scholar
  54. Troullier N., Martins. (1991). J Phys Rev B. 43:1993CrossRefGoogle Scholar
  55. Becke AD. (1988). Phys Rev A. 38:3098CrossRefPubMedGoogle Scholar
  56. Lee C., Yang W., Parr R. (1988). Phys Rev B. 37:785CrossRefGoogle Scholar
  57. Ohtaki H., Radnai T. (1993). Chem Rev. 93:1157CrossRefGoogle Scholar
  58. Martinez JM., Pappalardo RR., SanchezMarcos E. (1997). J Phys Chem A. 101:4444CrossRefGoogle Scholar
  59. Jarzecki AA., Anbar AD., Spiro TG. (2004). J Phys Chem A. 108:2726CrossRefGoogle Scholar
  60. Karlstrom G. (1988). J Phys Chem. 92:1318CrossRefGoogle Scholar
  61. Bertran J., Ruiz-Lopez MF., Rinaldi D., Rivail JL. (1992). Theor Chim Acta. 84:181CrossRefGoogle Scholar
  62. Martinez JM., Pappalardo RR., SanchezMarcos E., Mennucci B., Tomasi J. (2002). J Phys Chem B. 106:1118CrossRefGoogle Scholar
  63. Akesson R., Pettersson LGM., Sanstrom M., Wahlgren U. (1994). J Am Chem Soc. 116:8691CrossRefGoogle Scholar
  64. Rosso KM., Rustad JR., Gibbs GV. (2002). J Phys Chem A. 106:8133CrossRefGoogle Scholar
  65. ADF2002.03, SCM, http://www.scm.com.(2002). Theoretical Chemistry, Vrije Universiteit, Amsterdam, The NetherlandsGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of CambridgeCambridgeUnited Kingdom

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