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1 [1] [2] [3] [4] [5, 6] log(k /k ) or log(k /K ) = "(# r$# R ) k/k K/K "# R $ # %# [7] [8] 9 [9] - 5 -
2 [1] log(k /k ) or log(k /K ) = "(# r $ $ %# R r %# R ) $ "# R % # $ $# [6] r "# R.6 1. [11] [12] [13] [14] N N 3 [15, 16] p-o
3 N Table 1. pka values for anilinium ions and dimethylanilinium ions in aqueous solution at 25 C. a Substituent Anilinium Dimethylanilinium Substituent Anilinium Dimethylanilinium ions ions ions ions p-c m-c p-oc m-oc b p-pho b m-pho b p-sc m-sc b --- b p-co 2 Et m-co 2 Et p-c 3 CO m-c 3 CO p-f b m-f b p-c 6 5 CO m-c 6 5 CO b p-cl m-cl b p-br m-br p-n=nph b m-n=nph --- b --- b p-cf m-cf p-con b m-con b --- b p-co 2 C m-co 2 C b --- b p-so 2 N m-so 2 N b m-cn p-co m-co --- b 3.76 p-so 2 C b m-so 2 C b --- b --- b m-no a) Apparent pka values at ionic strength of.38. Experimental errors were within.5pka unit for all ions. Ref. [15]. b) No data available
4 5. N 2!pKa O, 25 C p-cf 3 m-cf 3 m-br m-co 2 Et m-co p-br p-cl p-s m- p- p-o p-co p-coph m-no 2 p-so 2 N 2 p-co m-cn p-co 2 Et p-co 2!pKa N 3 2 O, 25 C slope meta = 1.19 R =.9996 slope all = 1.19 R = Fig. 1.!pKa's of Dimethylanilinium ions against those of anilinium ions. Gaussian3 [17] Pentium4 E (3) N N 3 N 3 N E E (3) E E (N (N 2 ) 3 ) E (N 3 ) E (N 2 ) - 8 -
5 E (3) = E (N 2 ) E (N 3 ) E (N 3 ) E (N 2 ) B3LYP/6-311G(2d,p) [18].8929 [19] N N N 3 N 3 N 9 -fixed 9 -fixed N N 2 N 2 N N N N 2 N 2 9 -fixed 9 -fixed E E (3) E (6) G (aq.,exptl) E (3), E (5), E (6), E (7) [9] E (3) G (aq.,exptl) R= kcal mol
6 Table 2. Energy changes (ΔE x ) a of reactions 3, 5, 6, and 7 calculated at the B3LYP/6-311G(2d,p) ZPE b. Substituent reaction (para substituents) N N O OC C C i-c t-c F Cl CO 2 C SOC CF CN SO 2 C C 3 CO C 6 5 CO CO NO (meta substituents) N N O OC C C i-c t-c F Cl CO 2 C SOC CF CN SO 2 C C 3 CO C 6 5 CO CO NO a) In unit of kcal mol -1. b) Scaled
7 Table 3. Results of linear regression analysis for ΔE x against ΔG x (aq.,exptl.). Reaction Substituents b a b R N (3) meta all (6) meta all a) ΔE x s are calculated energy differences in gas phase. Least squares method was applied for -ΔE x = a ΔG x (aq.,exptl.)b. R is correlation coefficient. b) Number of substituents included in the analyses. Table 4. Results of linear regression analysis for ΔE x against σ. Reaction Substituents b ρ c R N (3) meta all (5) meta all (6) meta all (7) meta all a) ΔE x s are calculated energy differences in gas phase. Least squares method was applied for -ΔE x = ρ σ c. R is correlation coefficient. b) Number of substituents included in the analyses. E (3) m-no 2 m- 2 N 2kcal mol -1 R= kcal mol -1 E (5) R= kcal mol
8 N 3 N N N !E x (3) / kcal mol -1 slope meta = 4.32 R =.8967 slope all = 2.83 R =.876 p-cf 3 p-so 2 C 3 p-co p-c 3 CO p-c 6 5 CO p-co 2 C kcal mol -1 N 3 N !G x (aq., exptl.) / kcal mol -1 Fig. 2. Calculated -!E x (3) in gas phase vs. experimental -!G x (aq.) in aqueous phase. 2 N N 3 N N N 3 1 -!E x (3) / kcal mol -1 " meta = 16. R =.9955 " all = 17.9 R =.9868 p-co 2 C 3 p-c 6 5 CO p-so 2 C 3 p-cf 3 p-co p-c 3 CO 2.81 kcal mol -1 N 3-1 # (theoretical) Fig. 3. The # plot of -!E x (3)
9 2 N N 3 9 -fixed N 9 -fixed 1 -!E x (5) / kcal mol -1 " meta = 15.2 R =.9949 " all = 15.6 R =.9956 p-so 2 C 3 p-cf 3 p-co p-c 3 CO p-co 2 C 3 p-c 6 5 CO.7 kcal mol -1 N 3-1 # (theoretical) Fig. 4. The # plot of -!E x (5). E (6) G (aq.,exptl) R= kcal mol -1 E (6) m-no 2 m- 2 N 2kcal mol -1 R= kcal mol -1 E (7) R= kcal mol
10 N 2 N N N !G x (aq., exptl.) / kcal mol -1 Fig. 5. Calculated -!E x (6) in gas phase vs. experimental -!G x (aq.) in aqueous phase. N 2 N N 2 1 -!E x (6) / kcal mol -1 -!E x (6) / kcal mol -1 slope meta = 3.59 R =.9792 slope all = 2.4 R =.8986 " meta = 15. R =.9961 " all = 17. R =.9841 p-cf 3 N 2 p-co 2 C 3 p-c 6 5 CO p-co p-c 3 CO p-c 6 5 CO p-co 2 C 3 N p-so 2 C 3 p-cf 3 p-co p-c 3 CO 6.58 kcal mol -1 N N kcal mol -1 N 2-1 # (theoretical) Fig. 6. The # plot of -!E x (6)
11 2 N 2 N N 9 -fixed 9 -fixed 1 -#E x (7) / kcal mol -1! meta = 13.7 R =.9954! all = 14. R =.9961 p-so 2 C 3 p-cf 3 p-co p-c 3 CO p-co 2 C 3 p-c 6 5 CO.9 kcal mol -1 N 2-1 " (theoretical) Fig. 7. The " plot of -#E x (7). p- 2 N 25 kcal mol R=.9994 [15,16] N 3 [14]
12 2 N 2 N N N !E x (6) / kcal mol -1 p-so 2 C 3 p-cf 3 p-co p-c 3 CO p-co 2 C 3 p-c 6 5 CO -!E x (3) / kcal mol -1 slope meta =.942 R meta =.9998 slope all =.954 R all = kcal mol N 3 N N N 3 Fig. 8. Calculated -!E x (6) vs. -!E x (3)
13 B3LYP/6-311G(2d,p) ZPE [14] [1] Shorter, J. "Correlation Analysis in Chemistry," eds. by Chapman, N. B.; Shorter, J. Plenum Press, New York 1978, [2] ammett, L. P. Physical Organic Chemistry, McGraw-ill Book Co. Inc., New York, N. Y., 194, Chapter VII. [3] Yukawa, Y.; Tsuno, Y.; Sawada, M. Bull. Chem. Soc. Jpn. 1966, 39, [4] Brown,. C.; Okamoto, Y. J. Am. Chem. Soc. 1957, 79, [5] Yukawa, Y.; Tsuno, Y. Bull. Chem. Soc. Jpn. 1959, 32, [6] Tsuno, Y.; Fujio, M. Chem. Soc. Rev. 1996, 25, [7] ehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab initio Molecular Orbital Theory, Wiley: New York [8] (a) Nakata, K.; Fujio, M.; Saeki, Y.; Mishima, M.; Tsuno, Y.; Nishimoto, K. J. Phys. Org. Chem. 1996, 9, (b) Nakata, K.; Fujio, M.; Saeki, Y.; Mishima, M.; Tsuno, Y.; Nishimoto, K. J. Phys. Org. Chem. 1996, 9, (c) Nakata, K.; Fujio, M.; Mishima, M.; Tsuno, Y.; Nishimoto, K. J. Phys. Org. Chem. 1998, 11, [9] Nakata, K.; Fujio, M.; Nishimoto, K.; Tsuno, Y. J. Phys. Org. Chem. 23, 16,
14 [1] Mishima, M.; Usui, S.; Inoue,.; Fujio, M.; Tsuno, Y. Nippon Kagaku Kaishi 1989; [11] (A) 57 [12] Fujio, M.; McIver, R. T., Jr.; Taft, R. W. J. Am. Chem. Soc. 1981, 13, [13] Vol. 1, pp.2-28 (24) [14] Vol. 3, pp.7-41 (26) [15] (B) 54 [16] (a) Bolton, P. D.; all, F. M. Aust. J. Chem., 1967; 2, (b) Bolton, P. D.; all, J. Chem. Soc.(B), 1969; 259. (c) Biggs, A. I.; Robinson R. A. J. Chem. Soc., 1961; 388. (d) Robinson, R. A.; Biggs A. I. Aust. J. Chem., 1957; 1, 128. (e) Fickling, M. M.; Fisher, A. J. Am. Chem. Soc., 1959; 81, (f) Roberts; J. D. J. Am. Chem. Soc., 195; 72, 48. (g) Bryson; A. J. Am. Chem. Soc., 196; 82, (h) Vandenbelt; J. M. Anal. Chem., 1954; 25, 726. (i) Sheppard; W. A. J. Am. Chem. Soc., 1962; 84, 372. (j) Bordwell; F. G., Cooper; G. D. J. Am. Chem. Soc., 1952; 74, 158. (k) Greenbaum; S. B. J. Am. Chem. Soc., 1955; 77, (l) Klotz; I. M., Gruen; D. M. J. Am. Chem. Soc., 1954; 67, 844. (m) Bascombe; K. N., Bell; R. P. J. Chem. Soc., 1959; 196. [17] Frisch, M. J.; Trucks, G. W.; Schlegel,. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S., Tomasi, J.; Barone, V.; nnucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji,.; ada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; asegawa, J.; Ishida, M.; Nakajima, T.; onda, Y.; Kitao, O.; Nakai,.; Klene, M.; Li,.; Knox, J. E.; ratchian,. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 3, Revision C.2; Gaussian, Inc.,: Wallingford CT, 24. [18] Becke, A. D. Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 1993, 98, [19] (a) Pople, J. A.; Krishnan, R.; Schlegel,. B.; DeFrees, D.; Binkley, J. S.; Frisch, M. J.; Whiteside, R. F.; out, R. F.; ehre, W. J. Int. J. Quantum Chem., Symp. 1981, 15, 269. (b) Pople, J. A.; Scott, A. P.; Wong, M. W.; Radom, L. Israel J. Chem. 1993, 33,
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