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Thermodynamic Dual Descriptor

Marco FRANCO-PÉREZ ,  José L. GÁZQUEZ ,  W. AYERS Paul ,  Alberto VELA

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Citation:  FRANCO-PÉREZ Marco, GÁZQUEZ José L., AYERS Paul W., VELA Alberto. Thermodynamic Dual Descriptor[J]. Acta Physico-Chimica Sinica, 2018, 34(6): 683-391. doi: 10.3866/PKU.WHXB201801031 shu

Thermodynamic Dual Descriptor

  • 1.

    Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México, 09340, México

  • 2.

    Department of Chemistry, McMaster University, Hamilton, Ontario, L8S 4M1, Canada

  • 3.

    Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, Ciudad de México, 07360, México

    • 通讯作者: FRANCO-PÉREZMarco, qimfranco@hotmail.com
  • 基金项目:

    PWA thanks NSERC for support from the Canada Research Chairs, Compute Canada, and an NSERC Discovery Grant. MFP thanks Universidad Autónoma Metropolitana-Iztapalapa for a Visiting Professor Invitation. JLG and AV thank Conacyt for Grants 237045 and 128369, respectively

摘要: A new definition of the dual descriptor, namely, the thermodynamic dual descriptor, is developed within the grand canonical potential formalism. This new definition is formulated to describe the same physical phenomenon as the original definition proposed by Morell, Grand, and Toro-Labbé (J. Phys. Chem. A 2005, 109, 205), which is characterized by a second-order response of the electron density towards an electron flux. To formulate the new definition, we performed two successive partial derivatives of the average electron density, one with respect to the average number of electrons, and the other with respect to the chemical potential of the electron reservoir. When the derivative is expressed in terms of the three-state ensemble model, in the regime of low temperatures up to temperatures of chemical interest, one finds that the thermodynamic dual descriptor can be expressed as ∆fT(r) = (β/2)C[f+(r)-f-(r)], where β = 1/kBT, C is a global quantity that depends on the temperature and global electronic properties of the molecule (the first ionization potential and the electron affinity), C = 1 for systems with zero fractional charge, and C = Cω > 0 (albeit very close to zero) for systems with nonzero fractional charge, , and f+(r) and f-(r) are the nucleophilic and electrophilic Fukui functions, respectively. The quantity within the square brackets is the original definition of the dual descriptor. As the local terms (the ones containing regioselectivity information) are equal to those of the dual descriptor, ∆fT(r) has the same regioselectivity information, multiplied by the global quantity (β/2)C. This implies that the regioselectivity information contained in the original dual descriptor is preserved at all temperatures different from zero, and for any value of C > 0. One of the most important features of this new definition is that it avoids the undesired Dirac delta behavior observed when the second order partial derivative of the average density is taken with respect to the average number of electrons, using the exact density dependence of the average number of electrons.

English

    1. [1]

      Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford UP: New York, NY, USA, 1989. http://www.oalib.com/references/13102733

    2. [2]

      Chermette, H. J. Comp. Chem. 1999, 20, 129. doi: 10.1002/(SICI)1096-987X(19990115)20:1 < 129::AID-JCC13 > 3.0.CO; 2-A

    3. [3]

      Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. Rev. 2003, 103, 1793. doi: 10.1021/cr990029p

    4. [4]

      Gázquez, J. L. J. Mex. Chem. Soc. 2008, 52, 3.

    5. [5]

      Chattaraj, P. K. Chemical Reactivity Theory: A Density Functional View; CRC Press: Boca Raton, FL, USA, 2009.

    6. [6]

      Liu, S. B. Acta Phys. -Chim. Sin. 2009, 25, 590. doi: 10.3866/PKU.WHXB20090332

    7. [7]

      Johnson, P. A.; Bartolotti, L.; Ayers, P. W.; Fievez, T.; Geerlings, P. Charge Density and Chemical Reactions: A Unified View from Conceptual DFT. In Modern Charge-Density Analysis; Gatti, C., Macchi, P., Eds.; Springer: Dordrecht, The Netherlands, 2012; pp. 715–764.

    8. [8]

      Parr, R. G.; Donnelly, R. A.; Levy, M.; Palke, W. E. J. Chem. Phys. 1978, 68, 3801. doi: 10.1063/1.436185

    9. [9]

      Mulliken, R. S. J. Chem. Phys. 1934, 2, 782. doi: 10.1063/1.1749394

    10. [10]

      Iczkowski, R.; Margrave, J. L. J. Am. Chem. Soc. 1961, 83, 3547. doi: 10.1021/ja01478a001

    11. [11]

      Pearson, R. G. J. Am. Chem. Soc. 1963, 85, 3533. doi: 10.1021/ja00905a001

    12. [12]

      Pearson, R. G. Science 1966, 151, 172. doi: 10.1126/science.151.3707.172

    13. [13]

      Parr, R. G.; Pearson, R. G. J. Am. Chem. Soc. 1983, 105, 7512. doi: 10.1021/ja00364a005

    14. [14]

      Pearson, R. G. J. Chem. Educ. 1987, 64, 561. doi: 10.1021/ed064p561

    15. [15]

      Pearson, R. G. Inorg. Chim. Acta 1995, 240, 93. doi: 10.1016/0020-1693(95)04648-8

    16. [16]

      Pearson, R. G., Chemical Hardness: Applications from Molecules to Solids; Wiley-VCH: Oxford, UK, 1997.

    17. [17]

      Parr, R. G.; Yang, W. T. J. Am. Chem. Soc. 1984, 106, 4049. doi: 10.1021/ja00326a036

    18. [18]

      Yang, W. T.; Parr, R. G.; Pucci, R. J. Chem. Phys. 1984, 81, 2862. doi: 10.1063/1.447964

    19. [19]

      Ayers, P. W.; Levy, M. Theor. Chem. Acc. 2000, 103, 353. doi: 10.1007/s002149900093

    20. [20]

      Morell, C.; Grand, A.; Toro-Labbe, A. J. Phys. Chem. A 2005, 109, 205. doi: 10.1021/jp046577a

    21. [21]

      Morell, C.; Grand, A.; Toro-Labbe, A. Chem. Phys. Lett. 2006, 425, 342. doi: 10.1016/j.cplett.2006.05.003

    22. [22]

      Cardenas, C.; Echegaray, E.; Chakraborty, D.; Anderson, J. S. M.; Ayers, P. W. J. Chem. Phys. 2009, 130, 244105. doi: 10.1063/1.3151599

    23. [23]

      De Proft, F.; Ayers, P. W.; Fias, S.; Geerlings, P. J. Chem. Phys. 2006, 125, 214101. doi: 10.1063/1.2387953

    24. [24]

      Ayers, P. W.; Morell, C.; De Proft, F.; Geerlings, P. Chem. Eur. J. 2007, 13, 8240. doi: 10.1002/chem.200700365

    25. [25]

      De Proft, F.; Chattaraj, P. K.; Ayers, P. W.; Torrent-Sucarrat, M.; Elango, M.; Subramanian, V.; Giri, S.; Geerlings, P. J. Chem. Theory Comput. 2008, 4, 595. doi: 10.1021/ct700289p

    26. [26]

      Morell, C.; Ayers, P. W.; Grand, A.; Gutierrez-Oliva, S.; Toro-Labbe, A. Phys. Chem. Chem. Phys. 2008, 10, 7239. doi: 10.1039/b810343g

    27. [27]

      Chamorro, E.; Pérez, P.; Duque, M.; De Proft, F.; Geerlings, P. J. Chem. Phys. 2008, 129, 064117. doi: 10.1063/1.2965594

    28. [28]

      Cárdenas, C.; Rabi, N.; Ayers, P. W.; Morell, C.; Jaramillo, P.; Fuentealba, P. J. Phys. Chem. A 2009, 113, 8660. doi: 10.1021/jp902792n

    29. [29]

      Araya, J. I. M. Chem. Phys. Lett. 2011, 506, 104. doi: 10.1016/j.cplett.2011.02.051

    30. [30]

      Morell, C.; Ayers, P. W.; Grand, A.; Chermette, H. Phys. Chem. Chem. Phys. 2011, 13, 9601. doi: 10.1039/c0cp02083d

    31. [31]

      Geerlings, P.; Ayers, P. W.; Toro-Labbe, A.; Chattaraj, P. K.; De Proft, F. Accounts Chem. Res. 2012, 45, 683. doi: 10.1021/ar200192t

    32. [32]

      Tognetti, V.; Morell, C.; Ayers, P. W.; Joubert, L.; Chermette, H. Phys. Chem. Chem. Phys. 2013, 15, 14465. doi: 10.1039/c3cp51169c

    33. [33]

      Morell, C.; Gázquez, J. L.; Vela, A.; Guegan, F.; Chermette, H. Phys. Chem. Chem. Phys. 2014, 16, 26832. doi: 10.1039/c4cp03167a

    34. [34]

      Guegan, F.; Mignon, P.; Tognetti, V.; Joubert, L.; Morell, C. Phys. Chem. Chem. Phys. 2014, 16, 15558. doi: 10.1039/c4cp01613k

    35. [35]

      Tognetti, V.; Morell, C.; Joubert, L. J. Comp. Chem. 2015, 36, 649. doi: 10.1002/jcc.23840

    36. [36]

      De Proft, F.; Forquet, V.; Ourri, B.; Chermette, H.; Geerlings, P.; Morell, C. Phys. Chem. Chem. Phys. 2015, 17, 9359. doi: 10.1039/c4cp05454g

    37. [37]

      Guegan, F.; Tognetti, V.; Joubert, L.; Chermette, H.; Luneau, D.; Morell, C. Phys. Chem. Chem. Phys. 2016, 18, 982. doi: 10.1039/c5cp04982b

    38. [38]

      Perdew, J. P.; Parr, R. G.; Levy, M.; Balduz, J. L. Phys. Rev. Lett. 1982, 49, 1691. doi: 10.1103/PhysRevLett.49.1691

    39. [39]

      Zhang, Y. K.; Yang, W. T. Theor. Chem. Acc. 2000, 103, 346. doi: 10.1007/s002149900021

    40. [40]

      Yang, W. T.; Zhang, Y. K.; Ayers, P. W. Phys. Rev. Lett. 2000, 84, 5172. doi: 10.1103/PhysRevLett.84.5172

    41. [41]

      Ayers, P. W. J. Math. Chem. 2008, 43, 285. doi: 10.1007/s10910-006-9195-5

    42. [42]

      Miranda-Quintana, R. A.; Ayers, P. W. J. Chem. Phys. 2016, 144, 244112. doi: 10.1063/1.4953557

    43. [43]

      Heidar Zadeh, F.; Miranda-Quintana, R. A.; Verstraelen, T.; Bultinck, P.; Ayers, P. W. J. Chem. Theory Comput. 2016, 12, 5777. doi: 10.1021/acs.jctc.6b00494

    44. [44]

      Ayers, P. W.; Morell, C.; De Proft, F.; Geerlings, P. Chem. Eur. J. 2007, 13 8240. doi: 10.1002/chem.200700365

    45. [45]

      Polanco-Ramírez, C. A.; Franco-Pérez, M.; Carmona-Espíndola, J.; Gázquez, J. L.; Ayers, P. W. Phys. Chem. Chem. Phys. 2017, 19, 12355. doi: 10.1039/c7cp00691h

    46. [46]

      Kaplan, T. A. J. Statist. Phys. 2006, 122, 1237. doi: 10.1007/s10955-005-8067-x

    47. [47]

      Ayers, P. W. Theor. Chem. Acc. 2007, 118, 371. doi: 10.1007/s00214-007-0277-7

    48. [48]

      Franco-Pérez, M.; Ayers, P. W.; Gázquez, J. L.; Vela, A. J. Chem. Phys. 2015, 143, 244117. doi: 10.1063/1.4938422

    49. [49]

      Franco-Pérez, M.; Gázquez, J. L.; Ayers, P. W.; Vela, A. J. Chem. Phys. 2015, 143, 154103. doi: 10.1063/1.4932539

    50. [50]

      Franco-Pérez, M.; Gázquez, J. L.; Vela, A. J. Chem. Phys. 2015, 143, 024112. doi: 10.1063/1.4923260

    51. [51]

      Malek, A.; Balawender, R. J. Chem. Phys. 2015, 142, 054104. doi: 10.1063/1.4906555

    52. [52]

      Franco-Pérez, M.; Ayers, P. W.; Gázquez, J. L. Theor. Chem. Acc. 2016, 135, 199. doi: 10.1007/s00214-016-1961-2

    53. [53]

      Miranda-Quintana, R. A.; Ayers, P. W. Phys. Chem. Chem. Phys. 2016, 18, 15070. doi: 10.1039/c6cp00939e

    54. [54]

      Franco-Pérez, M.; Ayers, P. W.; Gázquez, J. L.; Vela, A. Phys. Chem. Chem. Phys. 2017, 19, 13687. doi: 10.1039/c7cp00692f

    55. [55]

      Franco-Pérez, M.; Ayers, P. W.; Gázquez, J. L.; Vela, A. J. Chem. Phys. 2017, 147, 094105. doi: 10.1063/1.4999761

    56. [56]

      Franco-Pérez, M.; Gázquez, J. L.; Ayers, P. W.; Vela, A. J. Chem. Phys. 2017, 147, 074113. doi: 10.1063/1.4998701

    57. [57]

      Franco-Pérez, M.; Heidar-Zadeh, F.; Ayers, P. W.; Gázquez, J. L.; Vela, A. Phys. Chem. Chem. Phys. 2017, 19, 11588. doi: 10.1039/c7cp00224f

    58. [58]

      Franco-Pérez, M.; Polanco-Ramirez, C. A.; Ayers, P. W.; Gázquez, J. L.; Vela, A. Phys. Chem. Chem. Phys. 2017, 19, 16095. doi: 10.1039/c7cp02613g

    59. [59]

      Miranda-Quintana, R. A. J. Chem. Phys. 2017, 146, 214113. doi: 10.1063/1.4984611

    60. [60]

      Miranda-Quintana, R. A.; Chattaraj, P. K.; Ayers, P. W. J. Chem. Phys. 2017, 147, 124103. doi: 10.1063/1.4996443

    61. [61]

      Miranda-Quintana, R. A.; Kim, T. D.; Cardenas, C.; Ayers, P. W. Theor. Chem. Acc. 2017, 136, 135. doi: 10.1007/s00214-017-2167-y

    62. [62]

      Mermin, N. D. Phys. Rev. 1965, 137, A1441. doi: 10.1103/PhysRev.137.A1441

    63. [63]

      Kohn, W.; Vashishta, P. Theory of the Inhomogeneous Electron Gas; March, N. H., Ed.; Plenum: New York, NY, USA, 1983; p. 124.

    64. [64]

      Parr, R. G.; Chattaraj, P. K. J. Am. Chem. Soc. 1991, 113, 1854. doi: 10.1021/ja00005a072

    65. [65]

      Chattaraj, P. K.; Cedillo, A.; Parr, R. G. Chem. Phys. 1996, 204, 429. doi: 10.1016/0301-0104(95)00276-6

    66. [66]

      Chandler, D. Introduction to Modern Statistical Mechanics; Oxford University Press: New York, NY, USA, 1987; p. 288.

    67. [67]

      Landau, L. D.; Lifshitz, E. M. Statistical Physics; Pergamon Press: Elmsford, NY, USA, 1959.

    68. [68]

      Franco-Pérez, M.; Gázquez, J. L.; Ayers, P.; Vela, A. J. Chem. Theory Comput. 2017, doi: 10.1021/acs.jctc.7b00940

    69. [69]

      Yang, W. T.; Parr, R. G. Proc. Nat. Acad. Sci. 1985, 82, 6723. doi: 10.1073/pnas.82.20.6723

    70. [70]

      Berkowitz, M.; Parr, R. G. J. Chem. Phys. 1988, 88, 2554. doi: 10.1063/1.454034

    71. [71]

      Ayers, P. W.; Parr, R. G. J. Am. Chem. Soc. 2001, 123, 2007. doi: 10.1021/ja002966g

    72. [72]

      Sablon, N.; De Proft, F.; Ayers, P. W.; Geerlings, P. J. Chem. Theory Comput. 2010, 6, 3671. doi: 10.1021/ct1004577

    73. [73]

      Sablon, N.; De Proft, F.; Geerlings, P. J. Phys. Chem. Lett. 2010, 1, 1228. doi: 10.1021/jz1002132

    74. [74]

      Geerlings, P.; Fias, S.; Boisdenghien, Z.; De Proft, F. Chem. Soc. Rev. 2014, 43, 4989. doi: 10.1039/c3cs60456j

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  • 发布日期:  2018-06-15
  • 收稿日期:  2017-11-16
  • 接受日期:  2017-12-27
  • 修回日期:  2017-12-27
  • 网络出版日期:  2018-06-03
通讯作者: 陈斌, bchen63@163.com
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