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A theoretical study of proton transfers in aqueous para-, ortho-hydroxypyridine and para-, ortho-hydroxyquinoline
13 September 1996
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 259 (1996) 647-653
A theoretical study of proton transfers in aqueous para-, ortho-hydroxypyridine and para-, ortho-hydroxyquinoline J i a h u W a n g , R u s s e l l J. B o y d Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 Received 6 May 1996; in final form 26 June 1996
Abstract
The structures and relative stabilities of the four different forms of hydroxypyridine and hydroxyquinoline (normal, protonated cation, deprotonated anion and zwitterion) in the gas phase have been calculated at the M¢ller-Plesset (MP) perturbation and coupled-cluster theory levels with basis sets up to 6-3 I+G**. The solvation free energies of the reactions were treated with the SMx series of aqueous solvation models by Cramer and Truhlar. By combining the PM3-SM3 model for solvation with the MP2/6-31 +G** level treatment for the gas-phase species, it is found that the free energy changes of the proton transfer reactions can be predicted reasonably well.
1. Introduction
Proton transfer is a very important chemical process in both chemical and biological systems [ 1,2]. It has been studied very extensively ever since it was discovered in 1924 [3]. It is one of the simplest chemical reactions that can provide valuable information about chemical kinetics, equilibria and isotope effects. In biological systems, many chemical species exchange protons with the solvent and this reversible mechanism plays vital roles for their biological functions. Proton transfers in hydroxypyridines and hydroxyquinolines have been studied quite early as their equilibrium constants lie in the range of convenient spectroscopic [4] and potentiometric [5] measurements. Since the above systems may serve as experimental models for proton relays and proton pumps in biological systems, they continue to attract attention from both experimental [ 6,7 ] and theoretical [ 8 ] communities. Both hydroxypyridine and hydroxyquinoline can
exist in four different forms in aqueous solutions: the normal (N), the protonated cation (C), the deprotohated anion (A) and the zwitterion (Z) [9] (see the following scheme for an illustration).
(c)
\
H
(z)
(A) H
Among these four forms, three unique prototropic equilibria can be established:
0009-2614/96/$12.00 Copyright (~) 1996 Elsevier Science B.V. All rights reserved. PH S 0 0 0 9 - 2 6 1 4 ( 9 6 ) 0 0 8 0 6 - 8
648
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
N~-Z,
( 1)
2. Computational details
N + H20 ~ A + H30 + ,
(2)
N+H30 + ~C+H20.
(3)
The GAUSSIAN 94 [23] program has been used to predict the structures and free energies of the normal (N), protonated cation (C), deprotonated anion (A) and zwitterion (Z) of paraand ortho-hydroxypyridine and para- and orthohydroxyquinoline in the gas phase. Geometry optimization for all structures was carried out with the 6-31G** basis set [17] at the Hartree-Fock (HF) level, also at the second-order M¢ller-Plesset (MP2) theory level for hydroxypyridines. The analysis of vibrational frequencies at the HF level confirms that all species have planar minima in the gas phase. For the species of para-, ortho-hydroxypyridine, relative energies have also been obtained through fourth-order (MP4SDQ) M011er-Plesset and coupled-cluster with single and double substitutions (CCSD) methods with the 6-31+G** basis sets. The chosen solvation model is the semi-empirical PM3-SM3 model proposed by Cramer and Truhlar [20]. It is based on a parameterized model (PM3) of a neglect-of-diatomic-differential-overlap (NDDO) Hamiltonian for the solute and a specially fitted solvation model (SM3) which includes not only the usual electronic, nuclear relaxation and polarization (ENP) terms but also cavity formation, dispersion and solvent-structure rearrangement (CDS). Cramer and Truhlar [20] used this model for the N and Z forms of para-, ortho-hydroxypyridine and found that the experimental aqueous free solvation energies can be well reproduced. The free solvation energies given below were obtained with version 3.5 of the AMSOL computer program [ 24]. The solute is allowed to relax, i.e. both the electronic wave function and nuclear geometry have been adjusted for the presence of solvent. The stable geometries of all para-, ortho-hydroxypyridine and para-, ortho-hydroxyquinoline have been found to be planar in solution.
The first reaction, proton transfer between N and Z, is commonly known as tautomerism and has been subjected to many experimental [10-12] and theoretical [13-16] studies. The other two reactions, however, have not been studied much theoretically. Under appropriate conditions of acidity, two or more of the above species coexist in solutions. The equilibrium constants governing the above three proton transfer processes have been measured by Mason [ 5]. Earlier theoretical studies have been essentially focused on the gas-phase chemical reactions [ 17,18]. Common quantum chemistry methodologies, such as the Hartree-Fock, M#ller-Plesset, configuration interaction and coupled-cluster methods have been employed and quite satisfactory results compared with experiment have been reported [ 19]. To study the equilibria ( 1 ) - ( 3 ) in aqueous solutions, we may view the solution chemical reaction as two separate steps: the gas-phase chemical reaction and the solvation of reactants and products. The standard free energy change of the chemical reaction in the aqueous solution A~aaq is given by AG~aq : A G~g+ AG~s(products) - AG~s(reactants),
(4) where AGOgis the standard free energy change of the gas-phase chemical reaction and AGes(reactants) and AG°(products) are the standard free solvation energies of the reactants and products, respectively. It is evident that to accurately predict a chemical equilibrium in aqueous solution, a reliable solvation model as well as sophisticated theoretical methods for predicting the gas phase reaction are required. In this Letter, we use correlated ab initio methods to predict the free energy change of the proton transfer reactions in the gas phase and semi-empirical solvation models (SMx) by Cramer and Truhlar [20,21] for predicting the solvation effects. This combined approach has been proven to be quite successful for tantomeric reactions [22] and we will extend it to treat reactions involving ionic species.
3. Results and discussion Calculated total and relative gas-phase energies of the N, Z, C, A forms are summarized in Tables 1, 2, 3 and 4 for para-, ortho-hydroxypyridine, and para-, ortho-hydroxyquinoline, respectively. Electronic ener-
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
649
Table I Calculated total and relative energies of para-hydroxypyridinein four different forms Level
N
Z
C
A
total energy (hartree) HF/6-31G**//HF/6-31G** MP2/6-31G** //HF/6-3 IG** MP4(SDQ)/6-3 IG**//HF/6-31G** CCSD/6-3 IG**//HF/6-31G** HF/6-3 IG**//MP2/6-31G** MP2/6-31G** //MP2/6-31G** MP4(SDQ)/6-31G** //MP2/6-3 IG** CCSD/6-3 IG**//MP2/6-31G** HF/6-31 +G** / / MP2/6-31G** MP2/6-31 +G** //MP2/6-3 IG** MP4(SDQ)/6-31 +G** //MP2/6-31G**
-321.58084 -322.57004 -322.60090 -322.60125 -321.57773 -322.57289 -322.60316 -322.60356 -321.58810 -322.59502 -322.62339
-321.57837 -322.56535 -322.60063 -322.59928 -321.57422 -322.56927 -322.60285 -322.60128 -321.58545 -322.59174 -322.62340
-321.94688 -322.92915 -322.96547 -322.96576 -321.94369 -322.93216 -322.96747 -322.96782 -321.94843 -322.94488 -322.97924
-320.98648 -321.98092 -322.00864 -322.00716 -320.98308 -321.98408 -322.01094 -322.00928 -321.00882 -322.02819 -322.05155
thermal corrections to free energy (hartree) HF/6-3 IG**//HF/6-31G**
0.07109
0.07124
0.08469
0.05586
solvation free energy (kcal/mol) PM3-SM3
-8.182
-12.464
-66.662
-69.309
-2.637 -1.248 -4.019 -2.953 -1.985 -1.916 -4.085 -2.758 -2.523 -2.131 -4.189 -4.04
-278.636 -274.263 -277.715 -277.678 -278.586 -274.389 -277.551 -277.521 -275.051 -268.482 -272.237 -272.07
302.285 298.997 300.967 302.116 302.471 300.685 300.746 302.746 292.825 285.009 288.159 278.83
relative free energy in aqueous solution (kcal/mol) HF/6-3 IG**//HF/6-3 IG** 0.000 MP2/6-3 IG**//HF/6-31G** 0.000 MP4(SDQ)/6-3 IG**//HF/6-31G** 0.000 CCSD/6-31G**/ ! HF/6-31G** 0.000 HF/6-31G**//MP2/6-3 IG** 0.000 MP2/6-31G** //MP2/6-31G** 0.000 MP4(SDQ)/6-31G** //MP2/6-3 IG** 0.000 CCSD/6-31G**//MP2/6-31G** 0.000 HF/6-31 +G** //MP2/6-31G** 0.000 MP2/6-31 +G** //MP2/6-3 IG** 0.000 MP4(SDQ)/6-31 +G**//MP2/6-31G** 0.000 exp. 15 ] 0.00
gies at both the H F / 6 - 3 1 G * * and M P 2 / 6 - 3 1 G * * optimized geometries are given. The thermal correction to the free energy of each species, which includes the entropy contribution, zero-point vibrational energies, etc., has been calculated at the H F / 6 - 3 1 G * * optimized geometry by the HF method. It is assumed that no extra thermal correction is needed for the solvated species. The calculated solvation energy of the Z form of each species is larger than that of the corresponding N form because the former has a more polar structure [ 11 ]. The C and A forms show an even larger sol-
vation effect due to the strong interaction of their electric charges with the solvent (which is accounted for in SMx models by a generalised Born term [25,26] ). The different solvation energies of these species contribute to the shift of the prototropic equilibria. For the tautomeric equilibrium ( 1 ), the free solvation energy differences between the Z and N forms are - 4 . 2 8 and - 5 . 8 6 kcal/mol for para-hydroxypyridine and ortho-hydroxyquinoline, respectively. These account for almost entirely the experimentally determined AG~aq (= - R T In K) of the above two equilibria,
650
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
Table 2 Calculated total and relative energies of ortho-hydroxypyridine in four different forms Level
N
Z
C
A
total energy (hartree) HF/6-31G** //HF/6-3 IG**
-321.56841
MP2/6-31G** //HF/6-3 IG**
-322.55797
-321.56156
-321.95458
-320.99180
-322.54860
-322.93782
MP4(SDQ)/6-31G**//HF/6-31G**
-321.98622
-322.58909
-322.58456
-322.97394
-322.01402
CCSD/6-31G** //HF/6-3 IG** HF/6-31G**//MP2/6-31G**
-322.58938 -321.56538
-322.58291 -321.55755
-322.97401 -321.95164
-322.01243 -320.98871 -321.98911
MP2/6-31G** //MP2/6-31G**
-322.56075
-322.55230
-322.94057
MP4(SDQ)/6-31G**//MP2/6-3 IG**
-322.59139
-322.58687
-322.97602
-322.01623
CCSD/6-31G** //MP2/6-31G**
-322.59172
-322.58495
-322.97611
-322.01448
HF/6-31 +G** //MP2/6-31G**
-321.57577
-321.56955
-321.95666
-321.01415
MP2/6-31 +G** //MP2/6-31G**
-322.58289
-322.57562
-322.95356
-322.03299
MP4(SDQ)/6-31 +G**//MP2/6-31G**
-322.61166
-322.60846
-322.98805
-322.05664
thermal corrections to free energy (hartree) HF/6-31G** / / HF/6-31G**
0.07063
0.07178
0.08563
0.057436
solvation free energy (kcal/mol) PM3-SM3
-9.277
-18.611
-66.194
-69.231
294.597
relative free energy in aqueous solution (kcal/mol) HF/6-31G** //HF/6-31G** 0.000
-4.312
-289.824
MP2/6-3 IG** //HF/6-31G**
0.000
-2.727
-285.860
291.550
MP4(SDQ)/6-3 IG**//HF/6-3 IG** CCSD/6-31G** //HF/6-31G**
0.000 0.000
-5.766
-289.001
293.631
-4.554
-288.863
294.810
HF/6-3 IG**//MP2/6-31G**
0.000
-3.701
-289.885
294.632
MP2/6-31G**//MP2/6-31G**
0.000
--3.309
-285.838
291.476
MP4(SDQ)/6-3 IG**//MP2/6-3 IG**
0.000
-5.776
-288.860
293.683
CCSD/6-31G** //MP2/6-31G**
0.000
-4.359
-288.712
294.993
HF/6-31 +G** //MP2/6-31G**
0.000
-4.709
-286.515
284.185
MP2/6-31 +G** //MP2/6-3 IG**
0.000
-4.051
-280.102
276.831
MP4(SDQ)/6-31 +G**//MP2/6-31G** exp. [5 ]
0.000 0.00
-6.606 -4.49
-283.693 -275.96
280.042 277.65
- 4 . 0 4 and - 5 . 7 2 kcal/mol. Therefore, it is the solvation effects that shift the equilibria to the right for parahydroxypyridine and ortho-hydroxyquinoline. Orthohydroxypyridine, which would appear as the N form in the gas phase, exists predominantly in the Z form in aqueous solution due to the large solvation energy of Z. The solvation energy also further shifts ( 1 ) to the right for para-hydroxyquinoline. We have used the value of 267 kcal/mol for the free energy change of H30 + ~ H20 in aqueous solution to obtain the experimental free energy change
involving the C and A forms. This is the value being used for the parametrization in the PM3-SM3 model [21 ]. With the solvation contribution included, AG~aq for the prototropic equilibrium (2) is predicted to be - 2 7 8 . 6 4 kcal/mol at the HF/6-31G** level for para-hydroxypyridine, compared with the experimental value of - 2 7 2 . 0 7 kcal/mol. However, the agreement between experiment and the results at the HF/631G** level for reactions involving other ionic species is not satisfactory. Including electron correlation at the MP2 level im-
J. Wang, R.J, Boyd/Chemical Physics Letters 259 (1996) 647-653
651
Table 3 Calculated total and relative energies of para-hydroxyquinoline in four different forms Level
N
Z
C
A
total energy (hartree) HF/6-31G**//HF/6-31G**
-474.24098
-474.24674
-474.62416
-473.65594
MP2/6-31G**//HF/6-31G**
-475.74482
-475.74799
-476.11997
-475.16667
HF/6-31+G**//HF/6-31G**
-474.25452
-474.26011
-474.63139
-473.68304
MP2/6-31+G**//HF/6-31G**
-475.77444
-474.77680
-476.13921
-475.21595
thermal corrections to free energy (hartree) HF/6-3 IG**//HF/6-31G** 0.11887
0.11874
0.13269
0.10356
solvation free energy (kcal/mol) PM3-SM3
-11.103
-59.788
-66.035
300.312
-9.937
relative free energy in aqueous solution (kcal/mol) HF/6-31G** //HF/6-3 IG** 0.000 MP2/6-31G** //HF/6-31G** 0.000
-5.966
-282.727
-4.338
-277,689
295.989
HF/6-31 +G**//HF/6-3 IG**
0.000
-5.860
-278.769
291.806
MP2/6-31 +G** //HF/6-31G**
0.000
-3.837
-271.183
283.651
exp. 151
0.00
-5.30
-271.88
277,74
Table 4 Calculated total and relative energies of ortho-hydroxyquinoline in four different forms Level
N
Z
C
A
total energy (hartree) HF/6-3 IG** //HF/6-31G**
-474.22648
-474.23031
-474.62259
-473.66195
MP2/6-3 IG** //HF/6-31G**
-475.73197
-475.73265
-476.12083
-475.17311
HF/6-3 I+G**//HF/6-31G**
-474.24001
-474.24383
-474.63007
-473.68823
MP2/6-31 +G** //HF/6-3 IG**
-475.76141
-474.76152
-476.14037
-475.22104
thermal corrections to free energy (hartree) HF/6-31G** //HF/6-3 IG** 0.11857
0.11853
0.13326
0.10420
solvation free energy (kcal/mol) PM3-SM3
-14.995
-58.699
-64.443
-9.140
relative free energy in aqueous solution (kcal/mol) HF/6-3 IG** //HF/6-3 IG** 0.000
-8.284
-288.903
289.928
MP2/6-31G** //HF/6-31G**
-6.306
--284.352
286.376
0.000
HF/6-31 +G** //HF/6-31G**
0.000
-8.278
-285.107
281.927
MP2/6-31 +G** //HF/6-31G** exp. 151
0.000 0.00
-5.949 -5.72
-278.136 -275.82
274.775 276.64
652
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
proves the agreement for all the reactions involving ionic species. For the proton-transfer reaction between the N and A forms of para-hydroxyquinoline, AG~aq drops to 295.99 kcal/mol from the HF value of 300.31 kcal/mol, closer to the experimental value of 277.74 kcal/mol (see Table 3). Geometry seems to play little role in the AG~aq prediction. In Tables 1 and 2, the relative free energies have been predicted at both the HF and MP2 optimized geometries. The differences are within the range of 1 kcal/mol. Augmenting the basis set with a set of diffuse functions on the heavy atoms improves the results dramatically. For ortho-hydroxyquinoline, the relative energies in aqueous solution between the A and N forms changes from 291.48 kcal/mol to 276.83 kcal/mol at the MP2 theory level by switching to the 6-31+G** basis sets. The latter is much closer to the experimental value, 277.65 kcal/mol. A reliable prediction of the three proton transfer reactions requires treating all species on an equal footing. This demands a high-level theoretical treatment in terms of both the basis set quality and the inclusion of electron correlation. Diffuse functions are also needed to describe properly the electronic structure of ionic species, especially the anions. With the inclusion of a set of sp diffuse functions in the 6-31+G** basis set, the agreement between theory and experiment becomes reasonable for both hydroxypyridines and hydroxyquinolines. The largest discrepancies are observed for equilibrium (3) at 5.91 kcal/mol for ortho-hydroxyquinoline and at 6.18 kcal /mol for parahydroxypyridine. In summary, with the theoretical approach of the MP2/6-3 I + G * * and PM3-SM3 methods, it is possible to predict the proton transfer reactions to an accuracy within the root-mean-square (RMS) error of the solvation model. The RMS error for the free energy of solvation changes involving ionic species equilibria is about 6.6 kcal/mol in the parameterization of PM3SM3 [21]. The present calculations on the proton transfer reactions of hydroxypyridine and hydroxyquinoline have comparable uncertainties.
4. Conclusions This letter presents a combined ab initio and semi-empirical solvation model study of proton trans-
fer reactions among the normal (N), the protonated cationic (C), the deprotonated anionic (A) and the zwitterionic (Z) forms of aqueous para-, orthohydroxypyridine and para-, ortho-hydroxyquinoline. All species are predicted to have planar minima in the gas phase and in aqueous solution. Among the factors examined, electron correlation and basis set quality are found to be much more important than the geometries of the species for the accurate prediction of the prototropic equilibria. With electron correlation included at the second-order M¢ller-Plesset level (MP2) and the basis sets up to 6-31 +G**, the free energy change of proton transfer equilibria involving all four forms can be predicted to the accuracy of the PM3-SM3 parameterization.
Acknowledgements This work has been supported by grants from the Natural Sciences and Engineering Research Council of Canada, NSERC (to RJB). JW thanks the Killam Trust for a Killam Postdoctoral Fellowship.
References [1] A.B. Kotlyar, N. Borovok, S. Kiryati and E. Nachliel, Biochemistry 33 (1994) 873. [2] M.L. Paddock, S.H. Rongey, A.J.EH. McPherson and M.Y. Okamura, Biochemistry33 (1994) 734, [3] J.N. Br6nsted and K. Pedersen, J. Chem. Soc. Perkin II (1976) 1428. [4] S.E Mason, J. Chem. Soc. (1957) 5010. [5] S.E Mason, J. Chem. Soc. (1958) 674. [6] M Kasha, J. Chem. Soc., FaradayTrans. II 82 (1986) 2379. [7] S.-I. Lee and D,-J. Jang, J. Phys. Chem. 99 (1995) 7537. [8] EJ. Luque, Y. Zhang, C.A. n, M. Bachs, J. Gao and M. Orozco, J. Phys. Chem. 100 (1996) 4269. 19] S.E Mason,J. Philp and B.E. Smith, J. Chem. Soc. A (1968) 3051. [10] J. Elguero, C. Marzin, A.R. Kartritzkyand E Linda, The tautomerism of heterocycles (Academic Press, New York, 1976). [ I l ] A.R. Katritzky, Handbook of heterocyclic chemistry (Pergamon, Oxford, 1985). [ 12] M.R. Nimlos,D.E Kellyand E.R. Bernstein, J. Phys. Chem. 93 (1989) 643. [ 13] M.M. Karelson,A.R. Katritzky,M. Szafranand M.C. Zemer, J. Org, Chem. 54 (1989) 6030. [ 14] M.M. Karelson,A.R. Katritzky,M. Szafranand M.C. Zerner, J. Chem. Soc. Perkin Trans. II (1990) 195.
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653 115] A.R. Katritzky and M.M. Karelson, J. Am. Chem. Soc. 113 (1991) 1561. [16] M.W. Wong, K.B. Wiberg and M.J. Frisch, J. Am. Chem. Soc. 114 (1992) 1645. 1"17] W.L Hehre, L. Radom, P. von R. Schleyer and J.A. Pople, Ab initio molecular orbital theory (Wiley, New York, 1986). 1181 J.A. Pople, M. Head-Gordon, D.J. Fox, K. Raghavachari and L.A. Curtiss, J. Chem. Phys. 90 (1989) 5622. I 191 L.A. Curtiss, K. Raghavachari, G.W. Trucks and J.A. Pople, J. Chem. Phys. 94 (1991) 7221. [201 C.J. Cramer and D,G. Truhlar, J. Comput. Chem. 13 (1992) 1089. 1211 C.J. Cramer and D.G. Truhlar, J. Comput. Aided Mol. Des. 6 (1992) 629. 1221 C.J. Cramer and D.G. Truhlar, J. Am. Chem. Soc. 115 (1993) 8810.
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[23] M.J. Frisch, G.W. Trucks, H.B. Schlegel, EW.W. Gill, B.G. Johnson, M.A. Robb, J.R. Cheeseman, T.A. Keith, G.A. Petersson, J.A. Montgomery, K. Raghavaehad, M.A. AI-Laham, V.G. Zakrzewski, J.V. Ortiz, JB. Foresman, J. Cioslowski, B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y. Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S. Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley, D.J, DeFrees, J. Baker, J.P. Stewart, M. Head-Gordon, C. Gonzalez and J.A. Pople, GAUSSIAN 94 (Gaussian, Inc., Pittsburgh, PA, 1995). [241 C.J. Cramer, G.C. Lynch, G.D. Hawkins and D.G. Truhlar, AMSOL, version 3.5, Quantum Chemistry Program Exchange, program No. 606. QCPE Bull. 13 (1993) 55. [25] M. Born, Z. Physik 1 (1920) 45. [26] G.J. Hoijtink, E. de Boer, P.H. van der Meij and W.P. Weijland, Rec. Trav. Chim. Pays-Bas 75 (1956) 487.
CHEMICAL PHYSICS LETTERS ELSEVIER
Chemical Physics Letters 259 (1996) 647-653
A theoretical study of proton transfers in aqueous para-, ortho-hydroxypyridine and para-, ortho-hydroxyquinoline J i a h u W a n g , R u s s e l l J. B o y d Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 Received 6 May 1996; in final form 26 June 1996
Abstract
The structures and relative stabilities of the four different forms of hydroxypyridine and hydroxyquinoline (normal, protonated cation, deprotonated anion and zwitterion) in the gas phase have been calculated at the M¢ller-Plesset (MP) perturbation and coupled-cluster theory levels with basis sets up to 6-3 I+G**. The solvation free energies of the reactions were treated with the SMx series of aqueous solvation models by Cramer and Truhlar. By combining the PM3-SM3 model for solvation with the MP2/6-31 +G** level treatment for the gas-phase species, it is found that the free energy changes of the proton transfer reactions can be predicted reasonably well.
1. Introduction
Proton transfer is a very important chemical process in both chemical and biological systems [ 1,2]. It has been studied very extensively ever since it was discovered in 1924 [3]. It is one of the simplest chemical reactions that can provide valuable information about chemical kinetics, equilibria and isotope effects. In biological systems, many chemical species exchange protons with the solvent and this reversible mechanism plays vital roles for their biological functions. Proton transfers in hydroxypyridines and hydroxyquinolines have been studied quite early as their equilibrium constants lie in the range of convenient spectroscopic [4] and potentiometric [5] measurements. Since the above systems may serve as experimental models for proton relays and proton pumps in biological systems, they continue to attract attention from both experimental [ 6,7 ] and theoretical [ 8 ] communities. Both hydroxypyridine and hydroxyquinoline can
exist in four different forms in aqueous solutions: the normal (N), the protonated cation (C), the deprotohated anion (A) and the zwitterion (Z) [9] (see the following scheme for an illustration).
(c)
\
H
(z)
(A) H
Among these four forms, three unique prototropic equilibria can be established:
0009-2614/96/$12.00 Copyright (~) 1996 Elsevier Science B.V. All rights reserved. PH S 0 0 0 9 - 2 6 1 4 ( 9 6 ) 0 0 8 0 6 - 8
648
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
N~-Z,
( 1)
2. Computational details
N + H20 ~ A + H30 + ,
(2)
N+H30 + ~C+H20.
(3)
The GAUSSIAN 94 [23] program has been used to predict the structures and free energies of the normal (N), protonated cation (C), deprotonated anion (A) and zwitterion (Z) of paraand ortho-hydroxypyridine and para- and orthohydroxyquinoline in the gas phase. Geometry optimization for all structures was carried out with the 6-31G** basis set [17] at the Hartree-Fock (HF) level, also at the second-order M¢ller-Plesset (MP2) theory level for hydroxypyridines. The analysis of vibrational frequencies at the HF level confirms that all species have planar minima in the gas phase. For the species of para-, ortho-hydroxypyridine, relative energies have also been obtained through fourth-order (MP4SDQ) M011er-Plesset and coupled-cluster with single and double substitutions (CCSD) methods with the 6-31+G** basis sets. The chosen solvation model is the semi-empirical PM3-SM3 model proposed by Cramer and Truhlar [20]. It is based on a parameterized model (PM3) of a neglect-of-diatomic-differential-overlap (NDDO) Hamiltonian for the solute and a specially fitted solvation model (SM3) which includes not only the usual electronic, nuclear relaxation and polarization (ENP) terms but also cavity formation, dispersion and solvent-structure rearrangement (CDS). Cramer and Truhlar [20] used this model for the N and Z forms of para-, ortho-hydroxypyridine and found that the experimental aqueous free solvation energies can be well reproduced. The free solvation energies given below were obtained with version 3.5 of the AMSOL computer program [ 24]. The solute is allowed to relax, i.e. both the electronic wave function and nuclear geometry have been adjusted for the presence of solvent. The stable geometries of all para-, ortho-hydroxypyridine and para-, ortho-hydroxyquinoline have been found to be planar in solution.
The first reaction, proton transfer between N and Z, is commonly known as tautomerism and has been subjected to many experimental [10-12] and theoretical [13-16] studies. The other two reactions, however, have not been studied much theoretically. Under appropriate conditions of acidity, two or more of the above species coexist in solutions. The equilibrium constants governing the above three proton transfer processes have been measured by Mason [ 5]. Earlier theoretical studies have been essentially focused on the gas-phase chemical reactions [ 17,18]. Common quantum chemistry methodologies, such as the Hartree-Fock, M#ller-Plesset, configuration interaction and coupled-cluster methods have been employed and quite satisfactory results compared with experiment have been reported [ 19]. To study the equilibria ( 1 ) - ( 3 ) in aqueous solutions, we may view the solution chemical reaction as two separate steps: the gas-phase chemical reaction and the solvation of reactants and products. The standard free energy change of the chemical reaction in the aqueous solution A~aaq is given by AG~aq : A G~g+ AG~s(products) - AG~s(reactants),
(4) where AGOgis the standard free energy change of the gas-phase chemical reaction and AGes(reactants) and AG°(products) are the standard free solvation energies of the reactants and products, respectively. It is evident that to accurately predict a chemical equilibrium in aqueous solution, a reliable solvation model as well as sophisticated theoretical methods for predicting the gas phase reaction are required. In this Letter, we use correlated ab initio methods to predict the free energy change of the proton transfer reactions in the gas phase and semi-empirical solvation models (SMx) by Cramer and Truhlar [20,21] for predicting the solvation effects. This combined approach has been proven to be quite successful for tantomeric reactions [22] and we will extend it to treat reactions involving ionic species.
3. Results and discussion Calculated total and relative gas-phase energies of the N, Z, C, A forms are summarized in Tables 1, 2, 3 and 4 for para-, ortho-hydroxypyridine, and para-, ortho-hydroxyquinoline, respectively. Electronic ener-
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
649
Table I Calculated total and relative energies of para-hydroxypyridinein four different forms Level
N
Z
C
A
total energy (hartree) HF/6-31G**//HF/6-31G** MP2/6-31G** //HF/6-3 IG** MP4(SDQ)/6-3 IG**//HF/6-31G** CCSD/6-3 IG**//HF/6-31G** HF/6-3 IG**//MP2/6-31G** MP2/6-31G** //MP2/6-31G** MP4(SDQ)/6-31G** //MP2/6-3 IG** CCSD/6-3 IG**//MP2/6-31G** HF/6-31 +G** / / MP2/6-31G** MP2/6-31 +G** //MP2/6-3 IG** MP4(SDQ)/6-31 +G** //MP2/6-31G**
-321.58084 -322.57004 -322.60090 -322.60125 -321.57773 -322.57289 -322.60316 -322.60356 -321.58810 -322.59502 -322.62339
-321.57837 -322.56535 -322.60063 -322.59928 -321.57422 -322.56927 -322.60285 -322.60128 -321.58545 -322.59174 -322.62340
-321.94688 -322.92915 -322.96547 -322.96576 -321.94369 -322.93216 -322.96747 -322.96782 -321.94843 -322.94488 -322.97924
-320.98648 -321.98092 -322.00864 -322.00716 -320.98308 -321.98408 -322.01094 -322.00928 -321.00882 -322.02819 -322.05155
thermal corrections to free energy (hartree) HF/6-3 IG**//HF/6-31G**
0.07109
0.07124
0.08469
0.05586
solvation free energy (kcal/mol) PM3-SM3
-8.182
-12.464
-66.662
-69.309
-2.637 -1.248 -4.019 -2.953 -1.985 -1.916 -4.085 -2.758 -2.523 -2.131 -4.189 -4.04
-278.636 -274.263 -277.715 -277.678 -278.586 -274.389 -277.551 -277.521 -275.051 -268.482 -272.237 -272.07
302.285 298.997 300.967 302.116 302.471 300.685 300.746 302.746 292.825 285.009 288.159 278.83
relative free energy in aqueous solution (kcal/mol) HF/6-3 IG**//HF/6-3 IG** 0.000 MP2/6-3 IG**//HF/6-31G** 0.000 MP4(SDQ)/6-3 IG**//HF/6-31G** 0.000 CCSD/6-31G**/ ! HF/6-31G** 0.000 HF/6-31G**//MP2/6-3 IG** 0.000 MP2/6-31G** //MP2/6-31G** 0.000 MP4(SDQ)/6-31G** //MP2/6-3 IG** 0.000 CCSD/6-31G**//MP2/6-31G** 0.000 HF/6-31 +G** //MP2/6-31G** 0.000 MP2/6-31 +G** //MP2/6-3 IG** 0.000 MP4(SDQ)/6-31 +G**//MP2/6-31G** 0.000 exp. 15 ] 0.00
gies at both the H F / 6 - 3 1 G * * and M P 2 / 6 - 3 1 G * * optimized geometries are given. The thermal correction to the free energy of each species, which includes the entropy contribution, zero-point vibrational energies, etc., has been calculated at the H F / 6 - 3 1 G * * optimized geometry by the HF method. It is assumed that no extra thermal correction is needed for the solvated species. The calculated solvation energy of the Z form of each species is larger than that of the corresponding N form because the former has a more polar structure [ 11 ]. The C and A forms show an even larger sol-
vation effect due to the strong interaction of their electric charges with the solvent (which is accounted for in SMx models by a generalised Born term [25,26] ). The different solvation energies of these species contribute to the shift of the prototropic equilibria. For the tautomeric equilibrium ( 1 ), the free solvation energy differences between the Z and N forms are - 4 . 2 8 and - 5 . 8 6 kcal/mol for para-hydroxypyridine and ortho-hydroxyquinoline, respectively. These account for almost entirely the experimentally determined AG~aq (= - R T In K) of the above two equilibria,
650
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
Table 2 Calculated total and relative energies of ortho-hydroxypyridine in four different forms Level
N
Z
C
A
total energy (hartree) HF/6-31G** //HF/6-3 IG**
-321.56841
MP2/6-31G** //HF/6-3 IG**
-322.55797
-321.56156
-321.95458
-320.99180
-322.54860
-322.93782
MP4(SDQ)/6-31G**//HF/6-31G**
-321.98622
-322.58909
-322.58456
-322.97394
-322.01402
CCSD/6-31G** //HF/6-3 IG** HF/6-31G**//MP2/6-31G**
-322.58938 -321.56538
-322.58291 -321.55755
-322.97401 -321.95164
-322.01243 -320.98871 -321.98911
MP2/6-31G** //MP2/6-31G**
-322.56075
-322.55230
-322.94057
MP4(SDQ)/6-31G**//MP2/6-3 IG**
-322.59139
-322.58687
-322.97602
-322.01623
CCSD/6-31G** //MP2/6-31G**
-322.59172
-322.58495
-322.97611
-322.01448
HF/6-31 +G** //MP2/6-31G**
-321.57577
-321.56955
-321.95666
-321.01415
MP2/6-31 +G** //MP2/6-31G**
-322.58289
-322.57562
-322.95356
-322.03299
MP4(SDQ)/6-31 +G**//MP2/6-31G**
-322.61166
-322.60846
-322.98805
-322.05664
thermal corrections to free energy (hartree) HF/6-31G** / / HF/6-31G**
0.07063
0.07178
0.08563
0.057436
solvation free energy (kcal/mol) PM3-SM3
-9.277
-18.611
-66.194
-69.231
294.597
relative free energy in aqueous solution (kcal/mol) HF/6-31G** //HF/6-31G** 0.000
-4.312
-289.824
MP2/6-3 IG** //HF/6-31G**
0.000
-2.727
-285.860
291.550
MP4(SDQ)/6-3 IG**//HF/6-3 IG** CCSD/6-31G** //HF/6-31G**
0.000 0.000
-5.766
-289.001
293.631
-4.554
-288.863
294.810
HF/6-3 IG**//MP2/6-31G**
0.000
-3.701
-289.885
294.632
MP2/6-31G**//MP2/6-31G**
0.000
--3.309
-285.838
291.476
MP4(SDQ)/6-3 IG**//MP2/6-3 IG**
0.000
-5.776
-288.860
293.683
CCSD/6-31G** //MP2/6-31G**
0.000
-4.359
-288.712
294.993
HF/6-31 +G** //MP2/6-31G**
0.000
-4.709
-286.515
284.185
MP2/6-31 +G** //MP2/6-3 IG**
0.000
-4.051
-280.102
276.831
MP4(SDQ)/6-31 +G**//MP2/6-31G** exp. [5 ]
0.000 0.00
-6.606 -4.49
-283.693 -275.96
280.042 277.65
- 4 . 0 4 and - 5 . 7 2 kcal/mol. Therefore, it is the solvation effects that shift the equilibria to the right for parahydroxypyridine and ortho-hydroxyquinoline. Orthohydroxypyridine, which would appear as the N form in the gas phase, exists predominantly in the Z form in aqueous solution due to the large solvation energy of Z. The solvation energy also further shifts ( 1 ) to the right for para-hydroxyquinoline. We have used the value of 267 kcal/mol for the free energy change of H30 + ~ H20 in aqueous solution to obtain the experimental free energy change
involving the C and A forms. This is the value being used for the parametrization in the PM3-SM3 model [21 ]. With the solvation contribution included, AG~aq for the prototropic equilibrium (2) is predicted to be - 2 7 8 . 6 4 kcal/mol at the HF/6-31G** level for para-hydroxypyridine, compared with the experimental value of - 2 7 2 . 0 7 kcal/mol. However, the agreement between experiment and the results at the HF/631G** level for reactions involving other ionic species is not satisfactory. Including electron correlation at the MP2 level im-
J. Wang, R.J, Boyd/Chemical Physics Letters 259 (1996) 647-653
651
Table 3 Calculated total and relative energies of para-hydroxyquinoline in four different forms Level
N
Z
C
A
total energy (hartree) HF/6-31G**//HF/6-31G**
-474.24098
-474.24674
-474.62416
-473.65594
MP2/6-31G**//HF/6-31G**
-475.74482
-475.74799
-476.11997
-475.16667
HF/6-31+G**//HF/6-31G**
-474.25452
-474.26011
-474.63139
-473.68304
MP2/6-31+G**//HF/6-31G**
-475.77444
-474.77680
-476.13921
-475.21595
thermal corrections to free energy (hartree) HF/6-3 IG**//HF/6-31G** 0.11887
0.11874
0.13269
0.10356
solvation free energy (kcal/mol) PM3-SM3
-11.103
-59.788
-66.035
300.312
-9.937
relative free energy in aqueous solution (kcal/mol) HF/6-31G** //HF/6-3 IG** 0.000 MP2/6-31G** //HF/6-31G** 0.000
-5.966
-282.727
-4.338
-277,689
295.989
HF/6-31 +G**//HF/6-3 IG**
0.000
-5.860
-278.769
291.806
MP2/6-31 +G** //HF/6-31G**
0.000
-3.837
-271.183
283.651
exp. 151
0.00
-5.30
-271.88
277,74
Table 4 Calculated total and relative energies of ortho-hydroxyquinoline in four different forms Level
N
Z
C
A
total energy (hartree) HF/6-3 IG** //HF/6-31G**
-474.22648
-474.23031
-474.62259
-473.66195
MP2/6-3 IG** //HF/6-31G**
-475.73197
-475.73265
-476.12083
-475.17311
HF/6-3 I+G**//HF/6-31G**
-474.24001
-474.24383
-474.63007
-473.68823
MP2/6-31 +G** //HF/6-3 IG**
-475.76141
-474.76152
-476.14037
-475.22104
thermal corrections to free energy (hartree) HF/6-31G** //HF/6-3 IG** 0.11857
0.11853
0.13326
0.10420
solvation free energy (kcal/mol) PM3-SM3
-14.995
-58.699
-64.443
-9.140
relative free energy in aqueous solution (kcal/mol) HF/6-3 IG** //HF/6-3 IG** 0.000
-8.284
-288.903
289.928
MP2/6-31G** //HF/6-31G**
-6.306
--284.352
286.376
0.000
HF/6-31 +G** //HF/6-31G**
0.000
-8.278
-285.107
281.927
MP2/6-31 +G** //HF/6-31G** exp. 151
0.000 0.00
-5.949 -5.72
-278.136 -275.82
274.775 276.64
652
J. Wang, R.J. Boyd/Chemical Physics Letters 259 (1996) 647-653
proves the agreement for all the reactions involving ionic species. For the proton-transfer reaction between the N and A forms of para-hydroxyquinoline, AG~aq drops to 295.99 kcal/mol from the HF value of 300.31 kcal/mol, closer to the experimental value of 277.74 kcal/mol (see Table 3). Geometry seems to play little role in the AG~aq prediction. In Tables 1 and 2, the relative free energies have been predicted at both the HF and MP2 optimized geometries. The differences are within the range of 1 kcal/mol. Augmenting the basis set with a set of diffuse functions on the heavy atoms improves the results dramatically. For ortho-hydroxyquinoline, the relative energies in aqueous solution between the A and N forms changes from 291.48 kcal/mol to 276.83 kcal/mol at the MP2 theory level by switching to the 6-31+G** basis sets. The latter is much closer to the experimental value, 277.65 kcal/mol. A reliable prediction of the three proton transfer reactions requires treating all species on an equal footing. This demands a high-level theoretical treatment in terms of both the basis set quality and the inclusion of electron correlation. Diffuse functions are also needed to describe properly the electronic structure of ionic species, especially the anions. With the inclusion of a set of sp diffuse functions in the 6-31+G** basis set, the agreement between theory and experiment becomes reasonable for both hydroxypyridines and hydroxyquinolines. The largest discrepancies are observed for equilibrium (3) at 5.91 kcal/mol for ortho-hydroxyquinoline and at 6.18 kcal /mol for parahydroxypyridine. In summary, with the theoretical approach of the MP2/6-3 I + G * * and PM3-SM3 methods, it is possible to predict the proton transfer reactions to an accuracy within the root-mean-square (RMS) error of the solvation model. The RMS error for the free energy of solvation changes involving ionic species equilibria is about 6.6 kcal/mol in the parameterization of PM3SM3 [21]. The present calculations on the proton transfer reactions of hydroxypyridine and hydroxyquinoline have comparable uncertainties.
4. Conclusions This letter presents a combined ab initio and semi-empirical solvation model study of proton trans-
fer reactions among the normal (N), the protonated cationic (C), the deprotonated anionic (A) and the zwitterionic (Z) forms of aqueous para-, orthohydroxypyridine and para-, ortho-hydroxyquinoline. All species are predicted to have planar minima in the gas phase and in aqueous solution. Among the factors examined, electron correlation and basis set quality are found to be much more important than the geometries of the species for the accurate prediction of the prototropic equilibria. With electron correlation included at the second-order M¢ller-Plesset level (MP2) and the basis sets up to 6-31 +G**, the free energy change of proton transfer equilibria involving all four forms can be predicted to the accuracy of the PM3-SM3 parameterization.
Acknowledgements This work has been supported by grants from the Natural Sciences and Engineering Research Council of Canada, NSERC (to RJB). JW thanks the Killam Trust for a Killam Postdoctoral Fellowship.
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