密度泛函活性理论中的信息论方法

doi:10.3866/PKU.WHXB201510302

摘要/Abstract

摘要：

密度泛函活性理论(DFRT)运用简单的密度泛函探讨和定量化分子的反应活性，是近来发展起来的一个关于分子活性理论的新方法。在新近的文献中，这样的简单密度泛函的例子包括香农熵，费舍尔信息以及其它来自信息论中的密度泛函。本文综述了DFRT信息论方法的原理，包括物理信息极小原理、最小信息增益原理和信息守恒原理。总结了DFRT信息论方法在电子密度、形态密度和分子中的原子三种表述下的理论框架。此外，还介绍了运用信息论方法在定量描述空间位阻效应、亲电性、亲核性和区域选择性中的突出应用，以及对亲电芳香取代反应的邻对间位取代效应的起源和本质提供的一个全新诠释。最后简要地展望了该领域的几个可能的未来发展方向。

关键词: 香农熵, 费舍尔信息, 密度泛函理论反应, 立体效应, 亲电性, 亲核性, 区域选择性, 邻对间位取代效应

Abstract:

Density functional reactivity theory (DFRT) is a recent endeavor to appreciate and quantify molecular reactivity with simple density functionals. Examples of such density functionals recently investigated in the literature included Shannon entropy, Fisher information, and other quantities from information theory. This review presents an overview on the principles of the information-theoretic approach in DFRT, including the extreme physical information principle, minimum information gain principle, and information conservation principle. Three representations of this approach with electron density, shape function, and atoms-in-molecules are also summarized. Moreover, their applications in quantifying steric effect, electrophilicity, nucleophilicity, and regioselectivity are highlighted, so are the recent results in a completely new understanding about the nature and origin of ortho/para and meta group directing phenomena in electrophilic aromatic substitution reactions. A brief outlook of a few possible future developments is discussed at the end.

Key words: Shannon entropy, Fisher information, Density functional reactivity theory, Steric effect, Electrophilicity, Nucleophilicity, Regioselectivity, Ortho/para and meta group directing effect

刘述斌. 密度泛函活性理论中的信息论方法[J]. 物理化学学报, 2016, 32(1), 98-118. doi: 10.3866/PKU.WHXB201510302

Shu-Bin LIU. Information-Theoretic Approach in Density Functional Reactivity Theory[J]. Acta Phys. -Chim. Sin. 2016, 32(1), 98-118. doi: 10.3866/PKU.WHXB201510302

链接本文: https://www.whxb.pku.edu.cn/CN/10.3866/PKU.WHXB201510302

https://www.whxb.pku.edu.cn/CN/Y2016/V32/I1/98

参考文献

1	Parr R. G. ; Yang W. Density-Functional Theory of Atoms and Molecules. In International Series of Monographs on Chemistry; Clarendon Press: Oxford, England 1989.
2	Levy M. ; Ouyang H. Phys. Rev. A 1988, 38, 625.
3	Herring C. ; Chopra M. Phys. Rev. A 1988, 37, 311.
4	Liu S. B. ; Ayers P. W. Phys. Rev. A 2004, 70, 022501.
5	Geerlings P. ; DeProft F. ; Langenaeker W. Chem. Rev. 2003, 103, 1793.
6	Chattaraj P. K. ; Sarkar U. ; Roy D. R. Chem. Rev. 2006, 106, 2065.
7	Liu S. B. Acta Phys. -Chim. Sin. 2009, 25, 590.
7	刘述斌. 物理化学学报, 2009, 25, 590.
8	Fukui K. Accounts Chem. Res. 1971, 4, 57.
9	Hoffmann R. ; Woodward R. B. J. Am. Chem. Soc. 1965, 87, 2046.
10	Geerlings P. ; Ayers P. W. ; Toro-LabbéA. ; Chattaraj P. K. ; De Proft F. Accounts Chem. Res. 2012, 45, 683.
11	Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, England, 1990.
12	Johnson E. R. ; Keinan S. ; Mori-SÁnchez P. ; Contreras-García J. ; Cohen A. J. ; Yang W. J. Am. Chem. Soc 2010, 132, 6498.
13	Nalewajski R. F. ; Parr R. G. Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 8879.
14	Hirshfeld F. Theor. Chim. Acc. 1977, 44, 129.
15	Liu S. B. J. Chem. Phys. 2007, 126, 244103.
16	Liu S. B. ; Rong C. Y. ; Lu T. J. Phys. Chem. A 2014, 118, 3698.
17	Zhou X. Y. ; Rong C. Y. ; Lu T. ; Liu S. B. Acta Phys. -Chim. Sin. 2014, 30, 2055.
17	周夏禹; 荣春英; 卢天; 刘述斌. 物理化学学报, 2014, 30, 2055.
18	Liu S. B. J. Chem. Phys. 2014, 141, 194109.
19	Rong C. Y. ; Lu T. ; Ayers P. W. ; Chattaraj P. K. ; Liu S. B. Phys. Chem. Chem. Phys. 2015, 17, 4977.
20	Liu S. B. J. Phys. Chem. A 2015, 119, 3107.
21	Wu W. J. ; Wu Z. M. ; Rong C. Y. ; Lu T. ; Huang Y. ; Liu S. B. J. Phys. Chem. A 2015, 119, 8216.
22	Wu W. Z. ; Rong C. Y. ; Lu T. ; Ayers P. W. ; Liu S. B. Phys. Chem. Chem. Phys. 2015, 17, 27052.
23	Nagy Á. Int. J. Quantum Chem. 2015, 115, 1392.
24	Nagy Á. Europhys. Lett. 2015, 109, 60002.
25	Nagy Á ; Romera E. Chem. Phys. Lett. 2014, 597, 139.
26	Nagy Á Int. J. Quantum Chem. 2014, 114, 24812.
27	Nagy Á ; Romera E. Chem. Phys. Lett. 2010, 490, 242.
28	Nagy Á ; Romera E. Int. J. Quantum Chem. 2009, 109, 2490.
29	Parr R. G. ; Yang W. J. Am. Chem. Soc. 1984, 106, 4049.
30	Morell C. ; Grand A. ; Toro-Labbé A. J. Phys. Chem. A 2005, 109, 205.
31	Liu S. B. ; Pedersen L. G. J. Phys. Chem. A 2009, 113, 3648.
32	Liu S. B. ; Schauer C. K. ; Pedersen L. G. J. Chem. Phys. 2009, 131, 164107.
33	Burger S. K. ; Liu S. B. ; Ayers P. W. J. Phys. Chem. A 2011, 115, 1293.
34	Huang Y. ; Liu L. ; Liu W. ; Liu S. G. ; Liu S. B. J. Phys. Chem. A 2011, 115, 14697.
35	Huang Y. ; Liu L. ; Liu S. B. Chem. Phys. Lett. 2012, 527, 73.
36	Liu S. B. ; Ess D. H. ; Schauer C. K. J. Phys. Chem. A 2011, 115, 4738.
37	Kumar N. ; Liu S. B. ; Kozlowski P. M. J. Phys. Chem. Lett. 2012, 3, 1035.
38	Pan S. ; Sola M. ; Chattaraj P. K. J. Phys. Chem. A 2013, 117, 1843.
39	Chattaraj P. K. ; Giri S. ; Duley S. J. Phys. Chem. A 2012, 116, 790.
40	von Szentpaly L. J. Phys. Chem. A 2011, 115, 8528.
41	von Szentpaly L. J. Phys. Chem. A 2013, 117, 200.
42	von Szentpaly L. J. Phys. Chem. A 2015, 119, 1715.
43	Nalewajski R. F. ; Parr R. G. J. Phys. Chem. A 2001, 105, 7391.
44	Parr R. G. ; Ayers P. W. ; Nalewajski R. F. J. Phys. Chem. A 2005, 109, 3957.
45	Ayers P. W. Theor. Chem. Acc. 2006, 115, 370.
46	Tsirelson V. G. ; Stash A. I. ; Liu S. B. J. Chem. Phys. 2010, 133, 114110.
47	Liu S. B. J. Chem. Phys. 2007, 126, 191107.
48	Esquivel R. O. ; Liu S. B. ; Angulo J. C. ; Dehesa J. S. ; Antolín J. ; Molina-Espíritu M. J. Phys. Chem. A 2011, 115, 4406.
49	Liu S. B. ; Govind N. J. Phys. Chem. A 2008, 112, 6690.
50	Liu S. B. ; Govind N. ; Pedersen L. G. J. Chem. Phys. 2008, 129, 094104.
51	Liu S. B. ; Hu H. ; Pedersen L. G. J. Phys. Chem. A 2010, 114, 5913.
52	Ess D. H. ; Liu S. B. ; De Proft F. J. Phys. Chem. A 2010, 114, 12952.
53	Huang Y. ; Zhong A. G. ; Yang Q. ; Liu S. B. J. Chem. Phys. 2011, 134, 084103.
54	Zhao D. B. ; Rong C. Y. ; Jenkins S. ; Kirk S. R. ; Yin D. L. ; Liu S. B. Acta Phys. -Chim. Sin. 2013, 29, 43.
54	赵东波; 荣春英; 苏曼; 苏文; 尹笃林; 刘述斌. 物理化学学报, 2013, 29, 43.
55	Tsirelson V. G. ; Stash A. I. ; Karasiev V. V. ; Liu S. B. Comp. Theor. Chem. 2013, 1006, 92.
56	Torrent-Sucarrat M. ; Liu S. B. ; De Proft F. J. Phys. Chem. A 2009, 113, 3698.
57	Liu S. B. J. Phys. Chem. A 2013, 117, 962.
58	Liu S. B. ; Schauer C. K. J. Chem. Phys. 2015, 142, 054107.
59	Shannon C. E. Bell Syst. Tech. J. 1948, 27, 379.
60	Sears S. B. ; Parr R. G. ; Dinur U. Isr. J. Chem. 1980, 19, 165.
61	Sears S. B. ; Gadre S. R. J. Chem. Phys. 1981, 75, 4626.
62	Romera E. ; Sanchez-Moreno P. ; Dehesa J. S. Chem. Phys. Lett. 2005, 414, 468.
63	Fisher R. A. Proc. Cambridge Philos. Soc. 1925, 22, 700.
64	Ghosh S. K. ; Berkowitz M. ; Parr R. G. Proc. Natl. Acad. Sci. U. S. A. 1984, 81, 8028.
65	Liu, S. B.; Rong, C. Y.; Wu, Z. M.; Lu, T. Acta Phys. -Chim. Sin. 2015, 31, 2057.
65	刘述斌,荣春英,吴泽民,卢天. 2015, 31, 2057. doi: 10.3866/PKU.WHXB201509183
66	ényiA.. Probability Theory; North-Holland: Amsterdam, 1970.
67	Tsallis C. J. Stat. Phys. 1988, 52, 479.
68	Onicescu O. C. R. Acad. Sci. Paris A 1966, 263, 25.
69	Kullback S. ; Leibler R. A. Ann. Math. Stat. 1951, 22, 79.
70	Parr R. G. ; Bartolotti L. J. J. Phys. Chem. 1983, 87, 2810.
71	De Proft F. ; Ayers P. W. ; Sen K. D. ; Geerlings P. J. Chem. Phys. 2004, 120, 9969.
72	Ayers P. W. Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 1959.
73	Rong C. Y. ; Lu T. ; Liu S. B. J. Chem. Phys. 2014, 140, 024109.
74	Rong C. Y. ; Lu T. ; Chattaraj P. K. ; Liu S. B. Indian J. Chem. Sect. A 2014, 53, 970.
75	Becke A. D. J. Chem. Phys. 1988, 88, 2547.
76	Lu T. ; Chen F. J. Comput. Chem. 2012, 33, 580.
77	von Weizsäcker C. F. Z. Phys. 1935, 96, 431.
78	March N. H. Phys. Lett. A 1986, 113, 476.
79	Holas A. ; March N. H. Phys. Rev. A 1991, 44, 5521.
80	Nagy Á J. Chem. Phys. 2003, 119, 9401.
81	Flores J. A. ; Keller J. Phys. Rev. A 1992, 45, 6259.
82	Levy M. ; Perdew J. P. Phys. Rev. A 1985, 32, 2010.
83	Liu S. B. ; Parr R. G. Phys. Rev. A 1996, 53, 2211.
84	Liu S. B. Phys. Rev. A 1996, 54, 1328.
85	Borgoo A. ; Teale A. M. ; Tozer D. J. Phys. Chem. Chem. Phys. 2015, 16, 14578.
86	Borgoo A. ; Tozer D. J. J. Chem. Theory Comput. 2013, 9, 2250.
87	Weisskopf V. F. Science 1975, 187, 605.
88	Badenhoop J. K. ; Weinhold F. J. Chem. Phys. 1997, 107, 5406.
89	Swain C. G. ; Scott C. B. J. Am. Chem. Soc. 1953, 75, 141.
90	Ritchie C. D. Accounts Chem. Res. 1972, 5, 348.
91	Mayr H. ; Patz M. Angew. Chem. Int. Edit. 1994, 33, 938.
92	Mayr H. ; Bug T. ; Gotta M. F. ; Hering N. ; Irrgang B. ; Janker B. ; Kempf B. ; Loos R. ; Ofial A. R. ; Remennikov G. ; Schimmel H. J. Am. Chem. Soc. 2001, 123, 9500.
93	Lucius R. ; Loos R. ; Mayr H. Angew. Chem. Int. Edit. 2002, 41, 91.
94	Mayr H. ; Kempf B. ; Ofial A. R. Accounts Chem. Res. 2003, 36, 66.
95	Crum Brown A. ; Gibson J. J. Chem. Soc. Trans. 1892, 61, 367.
96	Solomons T. W. G. ; Fryhle C. B. ; Snydeer S. A. Organic Chemistry; Wiley: New York, USA 2013.
97	Wade, L. G., Jr. Organic Chemistry; Prentice-Hall: New Jersey, USA, 2003.

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