Advertisement

Theoretical Chemistry Accounts

, Volume 116, Issue 1–3, pp 206–218 | Cite as

Quantized Hamilton Dynamics

  • Oleg V. Prezhdo
Regular Article

Abstract

The paper describes the quantized Hamilton dynamics (QHD) approach that extends classical Hamiltonian dynamics and captures quantum effects, such as zero point energy, tunneling, decoherence, branching, and state-specific dynamics. The approximations are made by closures of the hierarchy of Heisenberg equations for quantum observables with the higher order observables decomposed into products of the lower order ones. The technique is applied to the vibrational energy exchange in a water molecule, the tunneling escape from a metastable state, the double-slit interference, the population transfer, dephasing and vibrational coherence transfer in a two-level system coupled to a phonon, and the scattering of a light particle off a surface phonon, where QHD is coupled to quantum mechanics in the Schrödinger representation. Generation of thermal ensembles in the extended space of QHD variables is discussed. QHD reduces to classical mechanics at the first order, closely resembles classical mechanics at the higher orders, and requires little computational effort, providing an efficient tool for treatment of the quantum effects in large systems.

Keywords

Semiclassical dynamics Closure Heisenberg representation Extended phase space Gaussians 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Zewail AH (1996). J Phys Chem 100:12701CrossRefGoogle Scholar
  2. Butler LJ (1998). Annu Rev Phys Chem 49:125CrossRefPubMedGoogle Scholar
  3. Truhlar DG, Garrett BC, Klippenstein SJ (1996). J Phys Chem 100:12771CrossRefGoogle Scholar
  4. Jonsson H (2000). Annu Rev Phys Chem 51:623CrossRefPubMedGoogle Scholar
  5. Bolhuis PG, Chandler D, Dellago C, Geissler PL (2002). Annu Rev Phys Chem 53:291CrossRefPubMedGoogle Scholar
  6. Fleming GR (1986). Annu Rev Phys Chem 37:81CrossRefGoogle Scholar
  7. Xie XS, Trautman JK (1998). Annu Rev Phys Chem 49:441CrossRefPubMedGoogle Scholar
  8. Makri N (1999). Annu Rev Phys Chem 50:167CrossRefPubMedGoogle Scholar
  9. Meyer HD, Worth GA (2003). Theor Chem Acc 108:251CrossRefGoogle Scholar
  10. Warshel A (2003). Annu Rev Biophys Biomol Struct 32:425CrossRefPubMedGoogle Scholar
  11. Redondo A, LeSar R (2004). Annu Rev Mat Res 34:279CrossRefGoogle Scholar
  12. Schwartz BJ, Rossky PJ (1994). J Chem Phys 101:6917CrossRefGoogle Scholar
  13. Schwartz BJ, Rossky PJ (1994). Phys Rev Lett 72:3282CrossRefPubMedGoogle Scholar
  14. Prezhdo OV, Rossky PJ (1996). J Phys Chem 100:17094CrossRefGoogle Scholar
  15. Schwartz BJ, Bittner ER, Prezhdo OV, Rossky PJ (1996). J Chem Phys 104:5942CrossRefGoogle Scholar
  16. Prezhdo OV, Rossky PJ (1997). J Chem Phys 107:5863CrossRefGoogle Scholar
  17. Mosyak AA, Prezhdo OV, Rossky PJ (1998). J Chem Phys 109:6390CrossRefGoogle Scholar
  18. Mosyak AA, Prezhdo OV, Rossky PJ (1999). J Mol Struct 485-486:545CrossRefGoogle Scholar
  19. Tully JC (2000). Ann Rev Phys Chem 51:153CrossRefGoogle Scholar
  20. Tully JC, Gomez M, Head-Gordon M (1993). J Vac Sci Tech A – Vac Surf Films 11:1914CrossRefGoogle Scholar
  21. Head-Gordon M, Tully JC (1995). J Chem Phys 103:10137CrossRefGoogle Scholar
  22. Miller WH (2001). J Phys Chem A 105:2942CrossRefGoogle Scholar
  23. Miller WH, Zhao Y, Ceotto M, Yang S (2003). J Chem Phys 119:1329CrossRefGoogle Scholar
  24. Yamamoto T, Miller WH (2005). J Chem Phys 122:044106CrossRefGoogle Scholar
  25. Ceotto M, Miller WH (2004). J Chem Phys 120:6356CrossRefPubMedGoogle Scholar
  26. Zhao Y, Yamamoto T, Miller WH (2004). J Chem Phys 120:3100CrossRefPubMedGoogle Scholar
  27. Guallar V, Gherman BF, Miller WH, Lippard SJ, Friesner RA (2002). J Am Chem Soc 124:3377CrossRefPubMedGoogle Scholar
  28. Fiete GA, Heller EJ (2003). Rev Mod Phys 75:933CrossRefGoogle Scholar
  29. Vanicek J, Heller EJ (2003). Phys Rev E 67:016211CrossRefGoogle Scholar
  30. Batista VS, Brumer P (2002). Phys Rev Lett 89:143201CrossRefPubMedGoogle Scholar
  31. Shapiro EA, Kalinski M, Eberly JH (1998). Opt Expr 3:124CrossRefGoogle Scholar
  32. Guian CS, Wyatt RE (2000). J Chem Phys 112:3580CrossRefGoogle Scholar
  33. Yu N, Coker DF (2004). Mol Phys 102:1031CrossRefGoogle Scholar
  34. Cina JA, Kilin DS, Humble TS (2003). J Chem Phys 118:46CrossRefGoogle Scholar
  35. Blinov NV, Roy PN, Voth GA (2001). J Chem Phys 115:4484CrossRefGoogle Scholar
  36. Hone TD, Voth GA (2004). J Chem Phys 121:6412CrossRefPubMedGoogle Scholar
  37. Cui Q, Elstner M, Karplus M (2002). J Phys Chem B 106:2721CrossRefGoogle Scholar
  38. Gao JL, Truhlar DG (2002). Ann Rev Phys Chem 53:467CrossRefGoogle Scholar
  39. Soudackov A, Hatcher E, Hammes-Schiffer S (2005). J Chem Phys 122:014505CrossRefGoogle Scholar
  40. Bittner ER, Karabunarliev S (2003). Int J Quant Chem 95:521CrossRefGoogle Scholar
  41. Karabunarliev S, Bittner ER (2003). Phys Rev Lett 90:057402CrossRefPubMedGoogle Scholar
  42. Stier W, Prezhdo OV (2002). J Phys Chem B 106:8047CrossRefGoogle Scholar
  43. Stier W, Prezhdo OV (2003). Isr J Chem 42:213CrossRefGoogle Scholar
  44. Stier W, Prezhdo OV (2003). J Mol Struct (Theochem). 630:33CrossRefGoogle Scholar
  45. Stier W, Duncan WR, Prezhdo OV (2003). SPIE Proc 5223:132CrossRefGoogle Scholar
  46. Stier W, Duncan WR, Prezhdo OV (2004). Adv Mat 16:240CrossRefGoogle Scholar
  47. Duncan WR, Prezhdo OV (2005). J Phys Chem B 109:365CrossRefGoogle Scholar
  48. Duncan WR, Stier WM, Prezhdo OV (2005). J Am Chem Soc 127:7941CrossRefPubMedGoogle Scholar
  49. Duncan WR, Prezhdo OV (2005) J Phys Chem B(in press)Google Scholar
  50. Craig CF, Duncan WR, Prezhdo OV (2005). Phys Rev Lett 95:163001CrossRefPubMedGoogle Scholar
  51. Sun X, Miller WH (1997). J Chem Phys 106:6346CrossRefGoogle Scholar
  52. Herman MF, Kluk E (1984). Chem Phys 91:27CrossRefGoogle Scholar
  53. Billing GD (2002). Phys Chem Chem Phys 4:2865CrossRefGoogle Scholar
  54. Ben-Nun M, Martinez TJ (1998). J Chem Phys 108:7244CrossRefGoogle Scholar
  55. Ben-Nun M, Martinez TJ (2000). J Chem Phys 112:6113CrossRefGoogle Scholar
  56. Kay KG (1992). Phys Rev A 46:1213CrossRefPubMedGoogle Scholar
  57. Donoso A, Martens CC (2001). Phys Rev Lett 87:223202CrossRefPubMedGoogle Scholar
  58. Prezhdo OV, Kisil VV (1997). Phys Rev A 56:162CrossRefGoogle Scholar
  59. Kapral R, Ciccotti G (1999). J Chem Phys 110:8919CrossRefGoogle Scholar
  60. Sergi A, Kapral R (2003). J Chem Phys 119:12776CrossRefGoogle Scholar
  61. Sergi A, Kernan DM, Ciccotti G, Kapral R (2003). Theor Chem Acc 110:49Google Scholar
  62. Prezhdo OV, Brooksby C (2001). Phys Rev Lett 86:3215CrossRefPubMedGoogle Scholar
  63. Lopreore CL, Wyatt RE (1999). Phys Rev Lett 82:5190CrossRefGoogle Scholar
  64. Bittner ER, Wyatt RE (2000). J Chem Phys 113:8888CrossRefGoogle Scholar
  65. Wyatt RW, Lopreore CL, Parlant G (2001). J Chem Phys 114:5113CrossRefGoogle Scholar
  66. Burghardt I, Moller KB, Parlant G, Cederbaum LS, Bittner ER (2004). Int J Quant Chem 100:1153CrossRefGoogle Scholar
  67. Babyuk D, Wyatt RE (2004). Chem Phys Lett 400:145CrossRefGoogle Scholar
  68. Burghardt I(2005). J Chem Phys 122:094103CrossRefPubMedGoogle Scholar
  69. Halliwell JJ (1998). Phys Rev D 57:2337CrossRefGoogle Scholar
  70. Prezhdo OV (2000). Phys Rev Lett 85:4413CrossRefPubMedGoogle Scholar
  71. Gelman D, Kosloff R (2003). Chem Phys Lett 381:129CrossRefGoogle Scholar
  72. Prezhdo OV (1999). J Chem Phys 111:8366CrossRefGoogle Scholar
  73. Tully JC (1990). J Chem Phys 93:1061CrossRefGoogle Scholar
  74. Hammes-Schiffer S, Tully JC (1994). J Chem Phys 101:4657CrossRefGoogle Scholar
  75. Bittner ER, Rossky PJ (1995). J Chem Phys 103:8130CrossRefGoogle Scholar
  76. Prezhdo OV, Rossky PJ (1998). Phys Rev Lett 81:5294CrossRefGoogle Scholar
  77. Hack MD, Truhlar DG (2001). J Chem Phys 114:9305CrossRefGoogle Scholar
  78. Sholl DS, Tully JC (1998). J Chem Phys 109:7702CrossRefGoogle Scholar
  79. Webster FA, Rossky PJ, Friesner RA (1991). Comp Phys Comm 63:494CrossRefGoogle Scholar
  80. Prezhdo OV, Rossky PJ (1997). J Chem Phys 107:825CrossRefGoogle Scholar
  81. Prezhdo OV, Pereverzev YV (2000). J Chem Phys 113:6557CrossRefGoogle Scholar
  82. Brooksby C, Prezhdo OV (2001). Chem Phys Lett 346:463CrossRefGoogle Scholar
  83. Prezhdo OV, Pereverzev YV (2002). J Chem Phys 116:4450CrossRefGoogle Scholar
  84. Pahl E, Prezhdo OV (2002). J Chem Phys 116:8704CrossRefGoogle Scholar
  85. Prezhdo OV (2002). J Chem Phys 117:2995CrossRefGoogle Scholar
  86. Brooksby C, Prezhdo OV (2003). Chem Phys Lett 378:533CrossRefGoogle Scholar
  87. Prezhdo OV, Brooksby C (2003). Adv Topic in Theor Chem Phys 12:339Google Scholar
  88. Kilin D, Pereverzev YV, Prezhdo OV (2004). J Chem Phys 120:11209CrossRefPubMedGoogle Scholar
  89. Heatwole E, Prezhdo OV (2004). J Chem Phys 121:10967CrossRefPubMedGoogle Scholar
  90. Heatwole E, Prezhdo OV (2005). J Chem Phys 122:234109CrossRefPubMedGoogle Scholar
  91. Kilin D, Prezhdo OV, Brooksby C (2003). J. Mol. Struct. (Theochem) 630:45CrossRefGoogle Scholar
  92. Wick GC (1950). Phys Rev 80:268CrossRefGoogle Scholar
  93. Wilson S (1984) Electronic correlation in molecules. Oxford University Press, Oxford, EnglandGoogle Scholar
  94. Piecuch P, Kowalski K, Pimienta ISO, Fan P-D, Lodriguito M, McGuire MJ, Kucharski SA, Kus T, Musial M (2004). Theor Chem Acc 112:349CrossRefGoogle Scholar
  95. Bogoliubov NN (1965) The dynamic theory in statistical physics. Hindustan, DelhiGoogle Scholar
  96. Kawasaki K (1970). Ann Phys 61:1CrossRefGoogle Scholar
  97. Liboff RL (1990) Kinetic theory: classical, quantum and relativistic descriptions. Prentice Hall, Englewood Cliffs, NJGoogle Scholar
  98. Heller EJ (1996). J Chem Phys 64:63CrossRefGoogle Scholar
  99. Heller EJ (1981). J Chem Phys 75:2923CrossRefGoogle Scholar
  100. Sawada S-I, Metiu H (1986). J Chem Phys 84:227CrossRefGoogle Scholar
  101. Coalson RD, Karplus M (1990). J Chem Phys 93:3919CrossRefGoogle Scholar
  102. Buch V (2002). J Chem Phys 117:4738CrossRefGoogle Scholar
  103. Ando K (2003). Chem Phys Lett 376:532CrossRefGoogle Scholar
  104. Toukan K, Rahman A (1985). Phys Rev B 31:2643CrossRefGoogle Scholar
  105. Anderson J, Ullo JJ, Yip S (1987). J Chem Phys 87:1726CrossRefGoogle Scholar
  106. Gelabert R, Geminez X, Thoss M, Wang H, Miller WH (2001). J Chem Phys 114:2572CrossRefGoogle Scholar
  107. Stromquist J, Gao S (1996). J Chem Phys 106:5751CrossRefGoogle Scholar
  108. Guo Y, Thompson DL, Sewell TD (1996). J Chem Phys 104:576CrossRefGoogle Scholar
  109. Jaynes ET, Cummings FW (1963). Proc IEEE 51:89CrossRefGoogle Scholar
  110. Khalil M, Demirdoven N, Tokmakoff A (2004). J Chem Phys 121:362CrossRefPubMedGoogle Scholar
  111. Gruebele M (2004). J Phys - Cond Mat 16:R1057CrossRefGoogle Scholar
  112. Cina JA, Fleming GR (2004). J Phys Chem A 108:11196CrossRefGoogle Scholar
  113. Scheurer C, Mukamel S (2002). J Chem Phys 116:6803CrossRefGoogle Scholar
  114. Corbin N, Singer K (1982). Mol Phys 46:671Google Scholar
  115. Singer K, Smith W (1986). Mol Phys 57:761Google Scholar
  116. McQuarrie DA (1976) Statistical Mechanics. Harper & Row, New YorkGoogle Scholar
  117. Gardiner CW, Zoller P (2000) Quantum noise : a handbook of Markovian and non-Markovian quantum stochastic methods with applications to quantum optics. Springer Berlin Heidelberg, New YorkGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Department of ChemistryUniversity of WashingtonSeattleUSA

Personalised recommendations