Comparison of Quantum Chemical Parameters and Hammett Constants in Correlating pK a Values of Substituted Anilines Kevin C. Gross and Paul G. Seybold* Department of Chemistry, Wright State University, Dayton, Ohio 45435 Zenaida Peralta-Inga, Jane S. Murray, † and Peter Politzer ‡ Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 paul.seybold@wright.edu Received March 5, 2001 Historically, Hammett constants have been extremely effective in describing the influence of substituents on chemical reactivity and other physical and chemical properties, whereas variables derived from quantum chemical calculations have generally been less effective. Taking the experimental pK a s of substituted anilines as a representative physicochemical property, five ab initio quantum chemical indices are compared for effectiveness as one-parameter regression descriptors for pK a . All of the tested descriptors performed well for a set of 19 mono-, 13 di-, and 4 trisubstituted anilines, and two performed somewhat better than the traditional Hammett σ constants. Among the calculated quantities, the best representation of the aniline pK a s is produced by the minimum average local ionization energy on the molecular surface. Introduction Since their introduction in the 1930s, 1,2 Hammett constants (σ) have been the workhorse of organic chem- ists in relating the nature of substituents to their effects on chemical reactivity and other properties. These con- stants remain today an excellent guide in structure- property and structure-activity studies. In a recent review Hansch et al. observed: “Hammett constants have been astonishingly successful in correlating almost every kind of organic reaction in all sorts of solvents. Eventu- ally one assumes that quantum chemical calculations will replace them, but this is not possible at present.” 3 Indeed, σ constants have found use in predicting many types of chemical phenomena, including pK a s, reaction rates, and proton NMR shifts; 4-7 any reaction series exhibiting a linear free-energy relationship can be ex- pected to correlate with σ constants. 2,6,8,9 However, de- spite their unusual success and far-reaching applicability, Hammett constants are empirical parameters and cannot be expected to work in all situations. For example, σ constants will fail to correlate reaction rates in situations where the substituent change results in a shift of the transition state position. 9 In cases such as this, a quantum chemical approach may be more desirable. 5,10,11 Our earlier work with substituted anilines demonstrated that certain quantum chemical parameters, namely the natural charge on the amino nitrogen atom Q n , 12 the minimum electrostatic potential V min , 13 and the minimum local ionization energy on the molecular surface I h S,min , 13 correlate well with the Hammett σ values. Accordingly, in the context of the comment by Hansch et al., we wished to test whether these and other computed quantities might now be comparable in effectiveness to Hammett constants. The amino moiety is one of the most fundamental functional groups in organic chemistry, and its pK a is an important and extensively studied property. (The pK a refers to the conjugate acid, but it is used as a measure of the amine’s basicity as pK a + pK b ) pK w , where K w is the ionization constant of water.) The amino group K a can vary over several orders of magnitude (ammonia, pK a ) 9.26; aniline, pK a ) 4.63) depending on its molecular environment. Variations in pK a are crucial to the action of enzymes 14 and important for RNA activity in protein synthesis. 15 While it is qualitatively understood how changes in the amino group’s environment affect its alkaline nature, the ability to predict this property quantitatively in a wide variety of chemical systems is still actively pursued in our 12,13 and other research groups. 14,16-19 * To whom correspondence should be addressed. † E-mail: jsmurray@uno.edu. ‡ E-mail: ppolitze@uno.edu. (1) Hammett, L. P. J. Am. Chem. Soc. 1937, 59, 96-103. (2) Hammett, L. P. Trans. Faraday Soc. 1938, 34, 156-165. (3) Hansch, C.; Hoekman, D.; Gao, H. Chem. Rev. 1996, 96, 1045- 1075. (4) Exner, O. Correlation Analysis of Chemical Data; Plenum Press: New York, 1988. (5) Schu ¨u ¨ rmann, G. Sci. Total Environ. 1991, 221-235. (6) Shorter, J. Correlation Analysis in Organic Chemistry: An Introduction to Linear Free-Energy Relationships; Clarendon Press: Oxford, 1973. (7) Shorter, J. Correlation Analysis of Organic Reactivity, with Particular Reference to Multiple Regression; Research Studies Press: New York, 1982. (8) Jaffe ´, H. H. Chem. Rev. 1953, 53, 191-261. (9) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry, 3rd ed.; Harper Collins: New York, 1987. (10) Ertl, P. Quant. Struct.-Act. Relat. 1997, 16, 377-382. (11) Sullivan, J. J.; Jones, A. D.; Tanji, K. K. J. Chem. Inf. Comput. Sci. 2000, 40, 1113-1127. (12) Gross, K. C.; Seybold, P. G. Int. J. Quantum Chem. 2000, 80, 1107-1115. (13) Haeberlein, M.; Murray, J. S.; Brinck, T.; Politzer, P. Can. J. Chem. 1992, 70, 2209-2214. (14) Carlson, H. A.; Briggs, J. M.; McCammon, J. A. J. Med. Chem. 1999, 42, 109-117. (15) Muth, G. W.; Ortoleva-Donnelly, L.; Strobel, S. A. Science 2000, 289, 947-950. 6919 J. Org. Chem. 2001, 66, 6919-6925 10.1021/jo010234g CCC: $20.00 © 2001 American Chemical Society Published on Web 09/20/2001