Citation: LIU Shu-Bin. Information-Theoretic Approach in Density Functional Reactivity Theory[J]. Acta Physico-Chimica Sinica, ;2016, 32(1): 98-118. doi: 10.3866/PKU.WHXB201510302 shu

Information-Theoretic Approach in Density Functional Reactivity Theory

LIU Shu-Bin ^,

1.
Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, USA

Corresponding author: LIU Shu-Bin,
Received Date: 2 October 2015
Available Online: 29 October 2015

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.
- Shannon entropy,
- Fisher information,
- Density functional reactivity theory,
- Steric effect,
- Electrophilicity,
- Nucleophilicity,
- Regioselectivity,
- Ortho/para and meta group directing effect
1. [1]
  (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. [2]
  (2) Levy, M.; Ouyang, H. Phys. Rev. A 1988, 38, 625. doi: 10.1103/PhysRevA.38.625
3. [3]
  (3) Herring, C.; Chopra, M. Phys. Rev. A 1988, 37, 311.
4. [4]
  (4) Liu, S. B.; Ayers, P. W. Phys. Rev. A 2004, 70, 022501. doi: 10.1103/PhysRevA.70.022501
5. [5]
  (5) Geerlings, P.; DeProft, F.; Langenaeker, W. Chem. Rev. 2003, 103, 1793. doi: 10.1021/cr990029p
6. [6]
  (6) Chattaraj, P. K.; Sarkar, U.; Roy, D. R. Chem. Rev. 2006, 106, 2065. doi: 10.1021/cr040109f
7. [7]
  (7) Liu, S. B. Acta Phys. -Chim. Sin. 2009, 25, 590. [刘述斌. 物理化学学报, 2009, 25, 590.] doi: 10.3866/PKU.WHXB20090332
8. [8]
  (8) Fukui, K. Accounts Chem. Res. 1971, 4, 57. doi: 10.1021/ar50038a003
9. [9]
  (9) Hoffmann, R.; Woodward, R. B. J. Am. Chem. Soc. 1965, 87, 2046. doi: 10.1021/ja01087a034
10. [10]
  (10) Geerlings, P.; Ayers, P. W.; Toro-Labbé, A.; Chattaraj, P. K.; De Proft, F. Accounts Chem. Res. 2012, 45, 683. doi: 10.1021/ar200192t
11. [11]
  (11) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, England, 1990.
12. [12]
  (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. [13]
  (13) Nalewajski, R. F.; Parr, R. G. Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 8879. doi: 10.1073/pnas.97.16.8879
14. [14]
  (14) Hirshfeld, F. Theor. Chim. Acc. 1977, 44, 129. doi: 10.1007/BF00549096
15. [15]
  (15) Liu, S. B. J. Chem. Phys. 2007, 126, 244103. doi: 10.1063/1.2747247
16. [16]
  (16) Liu, S. B.; Rong, C. Y.; Lu, T. J. Phys. Chem. A 2014, 118, 3698. doi: 10.1021/jp5032702
17. [17]
  (17) Zhou, X. Y.; Rong, C. Y.; Lu, T.; Liu, S. B. Acta Phys. -Chim. Sin. 2014, 30, 2055. [周夏禹, 荣春英, 卢天, 刘述斌. 物理化学学报, 2014, 30, 2055.] doi: 10.3866/PKU.WHXB201409193
18. [18]
  (18) Liu, S. B. J. Chem. Phys. 2014, 141, 194109. doi: 10.1063/1.4901898
19. [19]
  (19) Rong, C. Y.; Lu, T.; Ayers, P. W.; Chattaraj, P. K.; Liu, S. B. Phys. Chem. Chem. Phys. 2015, 17, 4977; Phys. Chem. Chem. Phys. 2015, 17, 11110.
20. [20]
  (20) Liu, S. B. J. Phys. Chem. A 2015, 119, 3107. doi: 10.1021/acs.jpca.5b00443
21. [21]
  (21) Wu, W. J.; Wu, Z. M., Rong, C. Y.; Lu, T.; Huang, Y.; Liu, S. B. J. Phys. Chem. A 2015, 119, 8216. doi: 10.1021/acs.jpca.5b04309
22. [22]
  (22) Wu, W. Z.; Rong, C. Y.; Lu, T.; Ayers, P. W.; Liu, S. B. Phys. Chem. Chem. Phys. 2015,17, 27052. doi: 10.1039/C5CP04442A
23. [23]
  (23) Nagy, Á. Int. J. Quantum Chem. 2015, 115, 1392. doi: 10.1002/qua.v115.19
24. [24]
  (24) Nagy, Á. Europhys. Lett. 2015, 109, 60002. doi: 10.1209/0295-5075/109/60002
25. [25]
  (25) Nagy, Á.; Romera, E. Chem. Phys. Lett. 2014, 597, 139. doi: 10.1016/j.cplett.2014.02.032
26. [26]
  (26) Nagy, Á. Int. J. Quantum Chem. 2014, 114, 24812.
27. [27]
  (27) Nagy, Á.; Romera, E. Chem. Phys. Lett. 2010, 490, 242. doi: 10.1016/j.cplett.2010.03.057
28. [28]
  (28) Nagy, Á.; Romera, E. Int. J. Quantum Chem. 2009, 109, 2490. doi: 10.1002/qua.v109:11
29. [29]
  (29) Parr, R. G.; Yang, W. J. Am. Chem. Soc. 1984, 106, 4049. doi: 10.1021/ja00326a036
30. [30]
  (30) Morell, C.; Grand, A.; Toro-Labbé, A. J. Phys. Chem. A 2005, 109, 205. doi: 10.1021/jp046577a
31. [31]
  (31) Liu, S. B.; Pedersen, L. G. J. Phys. Chem. A 2009, 113, 3648. doi: 10.1021/jp811250r
32. [32]
  (32) Liu, S. B.; Schauer, C. K.; Pedersen, L. G. J. Chem. Phys. 2009, 131, 164107. doi: 10.1063/1.3251124
33. [33]
  (33) Burger, S. K.; Liu, S. B.; Ayers, P. W. J. Phys. Chem. A 2011, 115, 1293. doi: 10.1021/jp111148q
34. [34]
  (34) Huang, Y.; Liu, L.; Liu, W.; Liu, S. G.; Liu, S. B. J. Phys. Chem. A 2011, 115, 14697. doi: 10.1021/jp209540p
35. [35]
  (35) Huang, Y.; Liu, L.; Liu, S. B. Chem. Phys. Lett. 2012, 527, 73. doi: 10.1016/j.cplett.2012.01.014
36. [36]
  (36) Liu, S. B.; Ess, D. H.; Schauer, C. K. J. Phys. Chem. A 2011, 115, 4738. doi: 10.1021/jp112319d
37. [37]
  (37) Kumar, N.; Liu, S. B.; Kozlowski, P. M. J. Phys. Chem. Lett. 2012, 3, 1035.
38. [38]
  (38) Pan, S.; Sola, M.; Chattaraj, P. K. J. Phys. Chem. A 2013, 117, 1843. doi: 10.1021/jp312750n
39. [39]
  (39) Chattaraj, P. K.; Giri, S.; Duley, S. J. Phys. Chem. A 2012, 116, 790. doi: 10.1021/jp208541x
40. [40]
  (40) von Szentpaly, L. J. Phys. Chem. A 2011, 115, 8528.
41. [41]
  (41) von Szentpaly, L. J. Phys. Chem. A 2013, 117, 200. doi: 10.1021/jp3103386
42. [42]
  (42) von Szentpaly, L. J. Phys. Chem. A 2015, 119, 1715. doi: 10.1021/jp5084345
43. [43]
  (43) Nalewajski, R. F.; Parr, R. G. J. Phys. Chem. A 2001, 105, 7391. doi: 10.1021/jp004414q
44. [44]
  (44) Parr, R. G.; Ayers, P. W.; Nalewajski, R. F. J. Phys. Chem. A 2005, 109, 3957. doi: 10.1021/jp0404596
45. [45]
  (45) Ayers, P. W. Theor. Chem. Acc. 2006, 115, 370. doi: 10.1007/s00214-006-0121-5
46. [46]
  (46) Tsirelson, V. G.; Stash, A. I.; Liu, S. B. J. Chem. Phys. 2010, 133, 114110. doi: 10.1063/1.3492377
47. [47]
  (47) Liu, S. B. J. Chem. Phys. 2007, 126, 191107. doi: 10.1063/1.2741244
48. [48]
  (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. doi: 10.1021/jp1095272
49. [49]
  (49) Liu, S. B.; Govind, N. J. Phys. Chem. A 2008, 112, 6690. doi: 10.1021/jp800376a
50. [50]
  (50) Liu, S. B.; Govind, N.; Pedersen, L. G. J. Chem. Phys. 2008, 129, 094104. doi: 10.1063/1.2976767
51. [51]
  (51) Liu, S. B.; Hu, H.; Pedersen, L. G. J. Phys. Chem. A 2010, 114, 5913. doi: 10.1021/jp101329f
52. [52]
  (52) Ess, D. H.; Liu, S. B.; De Proft, F. J. Phys. Chem. A 2010, 114, 12952. doi: 10.1021/jp108577g
53. [53]
  (53) Huang, Y.; Zhong, A. G.; Yang, Q.; Liu, S. B. J. Chem. Phys. 2011, 134, 084103. doi: 10.1063/1.3555760
54. [54]
  (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. [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.] doi: 10.3866/PKU.WHXB201211121
55. [55]
  (55) Tsirelson, V. G.; Stash, A. I.; Karasiev, V. V.; Liu, S. B. Comp. Theor. Chem. 2013, 1006, 92. doi: 10.1016/j.comptc.2012.11.015
56. [56]
  (56) Torrent-Sucarrat, M.; Liu, S. B.; De Proft, F. J. Phys. Chem. A 2009, 113, 3698. doi: 10.1021/jp8096583
57. [57]
  (57) Liu, S. B. J. Phys. Chem. A 2013, 117, 962. doi: 10.1021/jp312521z
58. [58]
  (58) Liu, S. B.; Schauer, C. K. J. Chem. Phys. 2015, 142, 054107. doi: 10.1063/1.4907365
59. [59]
  (59) Shannon, C. E. Bell Syst. Tech. J. 1948, 27, 379. doi: 10.1002/bltj.1948.27.issue-3
60. [60]
  (60) Sears, S. B.; Parr, R. G.; Dinur, U. Isr. J. Chem. 1980, 19, 165. doi: 10.1002/ijch.v19:1-4
61. [61]
  (61) Sears, S. B.; Gadre, S. R. J. Chem. Phys. 1981, 75, 4626. doi: 10.1063/1.442578
62. [62]
  (62) Romera, E.; Sanchez-Moreno, P.; Dehesa, J. S. Chem. Phys. Lett. 2005, 414, 468. doi: 10.1016/j.cplett.2005.08.032
63. [63]
  (63) Fisher, R. A. Proc. Cambridge Philos. Soc. 1925, 22, 700. doi: 10.1017/S0305004100009580
64. [64]
  (64) Ghosh, S. K. ; Berkowitz, M.; Parr, R. G. Proc. Natl. Acad. Sci. U. S. A. 1984, 81, 8028. doi: 10.1073/pnas.81.24.8028
65. [65]
  (65) Liu, S. B.; Rong, C. Y.; Wu, Z. M.; Lu, T. Acta Phys. -Chim. Sin. 2015, 31, 2057. [刘述斌, 荣春英, 吴泽民, 卢天. 2015, 31, 2057.] doi: 10.3866/PKU.WHXB201509183
66. [66]
  (66) Rényi, A. Probability Theory; North-Holland: Amsterdam, 1970.
67. [67]
  (67) Tsallis, C. J. Stat. Phys. 1988, 52, 479. doi: 10.1007/BF01016429
68. [68]
  (68) Onicescu, O. C. R. Acad. Sci. Paris A 1966, 263, 25.
69. [69]
  (69) Kullback, S.; Leibler, R. A. Ann. Math. Stat. 1951, 22, 79.
70. [70]
  (70) Parr, R. G.; Bartolotti, L. J. J. Phys. Chem. 1983, 87, 2810. doi: 10.1021/j100238a023
71. [71]
  (71) De Proft, F.; Ayers, P. W.; Sen, K. D.; Geerlings, P. J. Chem. Phys. 2004, 120, 9969. doi: 10.1063/1.1729856
72. [72]
  (72) Ayers, P. W. Proc. Natl. Acad. Sci. U. S. A. 2000, 97, 1959. doi: 10.1073/pnas.040539297
73. [73]
  (73) Rong, C. Y.; Lu, T.; Liu, S. B. J. Chem. Phys. 2014, 140, 024109. doi: 10.1063/1.4860969
74. [74]
  (74) Rong, C. Y.; Lu, T.; Chattaraj, P. K.; Liu, S. B. Indian J. Chem. Sect. A 2014, 53, 970.
75. [75]
  (75) Becke, A. D. J. Chem. Phys. 1988, 88, 2547. doi: 10.1063/1.454033
76. [76]
  (76) Lu, T.; Chen, F. J. Comput. Chem. 2012, 33, 580. doi: 10.1002/jcc.v33.5
77. [77]
  (77) von Weizsäcker, C. F. Z. Phys. 1935, 96, 431. doi: 10.1007/BF01337700
78. [78]
  (78) March, N. H. Phys. Lett. A 1986, 113, 476. doi: 10.1016/0375-9601(86)90123-4
79. [79]
  (79) Holas, A.; March, N. H. Phys. Rev. A 1991, 44, 5521. doi: 10.1103/PhysRevA.44.5521
80. [80]
  (80) Nagy, Á. J. Chem. Phys. 2003, 119, 9401. doi: 10.1063/1.1615765
81. [81]
  (81) Flores, J. A.; Keller, J. Phys. Rev. A 1992, 45, 6259. doi: 10.1103/PhysRevA.45.6259
82. [82]
  (82) Levy, M.; Perdew, J. P. Phys. Rev. A 1985, 32, 2010. doi: 10.1103/PhysRevA.32.2010
83. [83]
  (83) Liu, S. B.; Parr, R. G. Phys. Rev. A 1996, 53, 2211. doi: 10.1103/PhysRevA.53.2211
84. [84]
  (84) Liu, S. B. Phys. Rev. A 1996, 54, 1328. doi: 10.1103/PhysRevA.54.1328
85. [85]
  (85) Borgoo, A.; Teale, A. M.; Tozer, D. J. Phys. Chem. Chem. Phys. 2015, 16, 14578.
86. [86]
  (86) Borgoo, A.; Tozer, D. J. J. Chem. Theory Comput. 2013, 9, 2250. doi: 10.1021/ct400129d
87. [87]
  (87) Weisskopf, V. F. Science 1975, 187, 605. doi: 10.1126/science.187.4177.605
88. [88]
  (88) Badenhoop, J. K.; Weinhold, F. J. Chem. Phys. 1997, 107, 5406. doi: 10.1063/1.474248
89. [89]
  (89) Swain, C. G.; Scott, C. B. J. Am. Chem. Soc. 1953, 75, 141. doi: 10.1021/ja01097a041
90. [90]
  (90) Ritchie, C. D. Accounts Chem. Res. 1972, 5, 348. doi: 10.1021/ar50058a005
91. [91]
  (91) Mayr, H.; Patz, M. Angew. Chem. Int. Edit. 1994, 33, 938.
92. [92]
  (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. doi: 10.1021/ja010890y
93. [93]
  (93) Lucius, R.; Loos, R.; Mayr, H. Angew. Chem. Int. Edit. 2002, 41, 91. doi: 10.1002/1521-3773(20020104)41:1<>1.0.CO;2-5
94. [94]
  (94) Mayr, H.; Kempf, B.; Ofial, A. R. Accounts Chem. Res. 2003, 36, 66. doi: 10.1021/ar020094c
95. [95]
  (95) Crum Brown, A.; Gibson, J. J. Chem. Soc. Trans. 1892, 61, 367. doi: 10.1039/ct8926100367
96. [96]
  (96) Solomons, T. W. G.; Fryhle, C. B.; Snydeer, S. A. Organic Chemistry; Wiley: New York, USA, 2013.
97. [97]
  (97) Wade, L. G., Jr. Organic Chemistry; Prentice-Hall: New Jersey, USA, 2003.
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