Thermodynamic Dual Descriptor

doi:10.3866/PKU.WHXB201801031

摘要/Abstract

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 ∆f_T(r) = (β/2)C[f⁺(r)-f^-(r)], where β = 1/k_BT, 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 = C_ω > 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, ∆f_T(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.

关键词: Dual descriptor, Chemical stability, Finite temperature chemical reactivity theory, Fractional average number of electrons, Amphiphilicity

Abstract:

Key words: Dual descriptor, Chemical stability, Finite temperature chemical reactivity theory, Fractional average number of electrons, Amphiphilicity

FRANCO-PÉREZ Marco,GÁZQUEZ José L.,AYERS Paul W.,VELA Alberto. Thermodynamic Dual Descriptor[J]. 物理化学学报, 2018, 34(6), 683-391. doi: 10.3866/PKU.WHXB201801031

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

链接本文: https://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201801031

https://www.whxb.pku.edu.cn/CN/Y2018/V34/I6/683

参考文献

1	Parr R. G. ; Yang W. Density-Functional Theory of Atoms and Molecules; Oxford UP: New York, NY, USA 1989.
2	Chermette H. J. Comp. Chem. 1999, 20, 129.
3	Geerlings P. ; De Proft F. ; Langenaeker W. Chem. Rev. 2003, 103, 1793.
4	Gázquez J. L. J. Mex. Chem. Soc. 2008, 52, 3.
5	Chattaraj P. K. Chemical Reactivity Theory: A Density Functional View; CRC Press: Boca Raton, FL, USA 2009.
6	Liu S. B. Acta Phys. -Chim. Sin. 2009, 25, 590.
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	Parr R. G. ; Donnelly R. A. ; Levy M. ; Palke W. E. J. Chem. Phys. 1978, 68, 3801.
9	Mulliken R. S. J. Chem. Phys. 1934, 2, 782.
10	Iczkowski R. ; Margrave J. L. J. Am. Chem. Soc. 1961, 83, 3547.
11	Pearson R. G. J. Am. Chem. Soc. 1963, 85, 3533.
12	Pearson R. G. Science 1966, 151, 172.
13	Parr R. G. ; Pearson R. G. J. Am. Chem. Soc. 1983, 105, 7512.
14	Pearson R. G. J. Chem. Educ. 1987, 64, 561.
15	Pearson R. G. Inorg. Chim. Acta 1995, 240, 93.
16	Pearson R. G. Chemical Hardness: Applications from Molecules to Solids; Wiley-VCH: Oxford, UK 1997.
17	Parr R. G. ; Yang W. T. J. Am. Chem. Soc. 1984, 106, 4049.
18	Yang W. T. ; Parr R. G. ; Pucci R. J. Chem. Phys. 1984, 81, 2862.
19	Ayers P. W. ; Levy M. Theor. Chem. Acc. 2000, 103, 353.
20	Morell C. ; Grand A. ; Toro-Labbe A. J. Phys. Chem. A 2005, 109, 205.
21	Morell C. ; Grand A. ; Toro-Labbe A. Chem. Phys. Lett. 2006, 425, 342.
22	Cardenas C. ; Echegaray E. ; Chakraborty D. ; Anderson J. S. M. ; Ayers P. W. J. Chem. Phys. 2009, 130, 244105.
23	De Proft F. ; Ayers P. W. ; Fias S. ; Geerlings P. J. Chem. Phys. 2006, 125, 214101.
24	Ayers P. W. ; Morell C. ; De Proft F. ; Geerlings P. Chem. Eur. J. 2007, 13, 8240.
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.
26	Morell C. ; Ayers P. W. ; Grand A. ; Gutierrez-Oliva S. ; Toro-Labbe A. Phys. Chem. Chem. Phys. 2008, 10, 7239.
27	Chamorro E. ; Pérez P. ; Duque M. ; De Proft F. ; Geerlings P. J. Chem. Phys. 2008, 129, 064117.
28	Cárdenas C. ; Rabi N. ; Ayers P. W. ; Morell C. ; Jaramillo P. ; Fuentealba P. J. Phys. Chem. A 2009, 113, 8660.
29	Araya J. I. M. Chem. Phys. Lett. 2011, 506, 104.
30	Morell C. ; Ayers P. W. ; Grand A. ; Chermette H. Phys. Chem. Chem. Phys. 2011, 13, 9601.
31	Geerlings P. ; Ayers P. W. ; Toro-Labbe A. ; Chattaraj P. K. ; De Proft F. Accounts Chem. Res. 2012, 45, 683.
32	Tognetti V. ; Morell C. ; Ayers P. W. ; Joubert L. ; Chermette H. Phys. Chem. Chem. Phys. 2013, 15, 14465.
33	Morell C. ; Gázquez J. L. ; Vela A. ; Guegan F. ; Chermette H. Phys. Chem. Chem. Phys. 2014, 16, 26832.
34	Guegan F. ; Mignon P. ; Tognetti V. ; Joubert L. ; Morell C. Phys. Chem. Chem. Phys. 2014, 16, 15558.
35	Tognetti V. ; Morell C. ; Joubert L. J. Comp. Chem. 2015, 36, 649.
36	De Proft F. ; Forquet V. ; Ourri B. ; Chermette H. ; Geerlings P. ; Morell C. Phys. Chem. Chem. Phys. 2015, 17, 9359.
37	Guegan F. ; Tognetti V. ; Joubert L. ; Chermette H. ; Luneau D. ; Morell C. Phys. Chem. Chem. Phys. 2016, 18, 982.
38	Perdew J. P. ; Parr R. G. ; Levy M. ; Balduz J. L. Phys. Rev. Lett. 1982, 49, 1691.
39	Zhang Y. K. ; Yang W. T. Theor. Chem. Acc. 2000, 103, 346.
40	Yang W. T. ; Zhang Y. K. ; Ayers P. W. Phys. Rev. Lett. 2000, 84, 5172.
41	Ayers P. W. J. Math. Chem. 2008, 43, 285.
42	Miranda-Quintana R. A. ; Ayers P. W. J. Chem. Phys. 2016, 144, 244112.
43	Heidar Zadeh F. ; Miranda-Quintana R. A. ; Verstraelen T. ; Bultinck P. ; Ayers P. W. J. Chem. Theory Comput. 2016, 12, 5777.
44	Ayers P. W. ; Morell C. ; De Proft F. ; Geerlings P. Chem. Eur. J. 2007, 13, 8240.
45	Polanco-Ramírez C. A. ; Franco-Pérez M. ; Carmona-Espíndola J. ; Gázquez J. L. ; Ayers P. W. Phys. Chem. Chem. Phys. 2017, 19, 12355.
46	Kaplan T. A. J. Statist. Phys. 2006, 122, 1237.
47	Ayers P. W. Theor. Chem. Acc. 2007, 118, 371.
48	Franco-Pérez M. ; Ayers P. W. ; Gázquez J. L. ; Vela A. J. Chem. Phys. 2015, 143, 244117.
49	Franco-Pérez M. ; Gázquez J. L. ; Ayers P. W. ; Vela A. J. Chem. Phys. 2015, 143, 154103.
50	Franco-Pérez M. ; Gázquez J. L. ; Vela A. J. Chem. Phys. 2015, 143, 024112.
51	Malek A. ; Balawender R. J. Chem. Phys. 2015, 142, 054104.
52	Franco-Pérez M. ; Ayers P. W. ; Gázquez J. L. Theor. Chem. Acc. 2016, 135, 199.
53	Miranda-Quintana R. A. ; Ayers P. W. Phys. Chem. Chem. Phys. 2016, 18, 15070.
54	Franco-Pérez M. ; Ayers P. W. ; Gázquez J. L. ; Vela A. Phys. Chem. Chem. Phys. 2017, 19, 13687.
55	Franco-Pérez M. ; Ayers P. W. ; Gázquez J. L. ; Vela A. J. Chem. Phys. 2017, 147, 094105.
56	Franco-Pérez M. ; Gázquez J. L. ; Ayers P. W. ; Vela A. J. Chem. Phys. 2017, 147, 074113.
57	Franco-Pérez M. ; Heidar-Zadeh F. ; Ayers P. W. ; Gázquez J. L. ; Vela A. Phys. Chem. Chem. Phys. 2017, 19, 11588.
58	Franco-Pérez M. ; Polanco-Ramirez C. A. ; Ayers P. W. ; Gázquez J. L. ; Vela A. Phys. Chem. Chem. Phys. 2017, 19, 16095.
59	Miranda-Quintana R. A. J. Chem. Phys. 2017, 146, 214113.
60	Miranda-Quintana R. A. ; Chattaraj P. K. ; Ayers P. W. J. Chem. Phys. 2017, 147, 124103.
61	Miranda-Quintana R. A. ; Kim T. D. ; Cardenas C. ; Ayers P. W. Theor. Chem. Acc. 2017, 136, 135.
62	Mermin N. D. Phys. Rev. 1965, 137, A1441.
63	Kohn W. ; Vashishta P. Theory of the Inhomogeneous Electron Gas; March N. H..., Ed.; Plenum: New York, NY, USA 1983, p. 124.
64	Parr R. G. ; Chattaraj P. K. J. Am. Chem. Soc. 1991, 113, 1854.
65	Chattaraj P. K. ; Cedillo A. ; Parr R. G. Chem. Phys. 1996, 204, 429.
66	Chandler D. Introduction to Modern Statistical Mechanics; Oxford University Press: New York, NY, USA 1987, p. 288.
67	Landau L. D. ; Lifshitz E. M. Statistical Physics; Pergamon Press: Elmsford, NY, USA 1959.
68	Franco-Pérez M. ; Gázquez J. L. ; Ayers P. ; Vela A. J. Chem. Theory Comput. 2017.
69	Yang W. T. ; Parr R. G. Proc. Nat. Acad. Sci. 1985, 82, 6723.
70	Berkowitz M. ; Parr R. G. J. Chem. Phys. 1988, 88, 2554.
71	Ayers P. W. ; Parr R. G. J. Am. Chem. Soc. 2001, 123, 2007.
72	Sablon N. ; De Proft F. ; Ayers P. W. ; Geerlings P. J. Chem. Theory Comput. 2010, 6, 3671.
73	Sablon N. ; De Proft F. ; Geerlings P. J. Phys. Chem. Lett. 2010, 1, 1228.
74	Geerlings P. ; Fias S. ; Boisdenghien Z. ; De Proft F. Chem. Soc. Rev. 2014, 43, 4989.