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AM1 and PM3 study of tautomerism of xanthine in the gas and aqueous phases
Journal of Molecular Structure (Theochem) 545 (2001) 7±15
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AM1 and PM3 study of tautomerism of xanthine in the gas and aqueous phases È . Civcir* P.U Ankara University, Faculty of Health Education, Ankara, Turkey Received 6 October 2000; accepted 1 November 2000
Abstract Heats of formation, entropies, Gibbs free energies, relative tautomerisation energies, tautomeric equilibrium constants, relative proton af®nities, dipole moments, and ionisation potentials for the fourteen possible tautomers of xanthine have been studied using semiempirical AM1 and PM3 quantum-chemical calculations at the SCF level in the gas and aqueous phases, with full geometry optimisation. The COSMO solvation model was employed for aqueous solution calculations. The calculations show that the two diketo tautomers X1,3,7 and X1,3,9 are the predominant species at room temperature in the gas and aqueous phase. But, the ®rst more stable tautomer is the dioxo-7H tautomer, X1,3,7. Comparison with available experimental data provides support for quality of results derived from theoretical computations. The entropy effect on the Gibbs free energy of the xanthine is very small and there is little signi®cance for the tautomeric equilibria of the base. The enthalpic term is dominant also in the determination of the equilibrium constant. q 2001 Elsevier Science B.V. All rights reserved. Keywords: AM1, PM3 semiempirical calculations; Dipole moment; Ionisation potential; Tautomerism; Tautomeric equilibrium constant; Xanthine
1. Introduction The oxopurines are of biological importance, because they are metabolic intermediate products of purine metabolism formed by degradation of nucleic acids. Alkylated xanthines are bronchodilators. Xanthine (3,7-dihydro-1H-purine-2,6-dione) is a purine base which is not common in ribonucleic acid or deoxyribonucleic acid, but deamination of guanine results in xanthine base, and this base is still able to pair with cytosine by two hydrogens. In man, the end product of purine metabolism is uric acid and xanthine oxidase. Actually, hypoxanthine, which formed by enzymatic degradation of nucleic acid, is * Tel.: 190-312-3808172; fax: 190-312-3575323. E-mail address: [email protected] (P.U. Civcir).
oxidised by the molybdenum- and iron-containing enzyme xanthine oxidase via xanthine to uric acid. This enzyme found in the liver, is capable of oxidising xanthine to uric acid [1]. Defects in purine metabolism result in an increase in the uric acid level and in the deposition of sodium hydrogen urate monohydrate crystals in joints. This disease known as gout and is clinically treated by allopurinol, which has also been used in conjunction with anticancer drugs combined with 6-mercaptopurine in treatment of leukaemia [2± 4]. Enzymes attack purines at preferred positions, and therefore the tautomerisation of the purine molecules may play an important role in the replication process and the equilibrium is strongly sensitive to the interaction of these molecules with their environment [5]. In an equilibrium, xanthine base exists in different tautomeric forms, the protropic tautomerism can
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166- 128 0( 00) 00821-6
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È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
Fig. 1. Representation of tautomers of xanthine considered in the present work.
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
occur in both rings (pyrimidine and imidazole) and thus two type of equilibria can be observed: keto Y enol and N(7)H Y N(9)H. Knowledge of the geometric and electronic structure as well as the relative stability of tautomeric forms provides a basis for understanding biological activity of oxopurine bases. In addition, knowing how these tautomerisation energies change in different environments can give an insight into the in¯uence of solvent effects on molecular stability. Several experiments and theoretical studies on the tautomerism of xanthine are reported in the literature [6±11]. The highest level calculations [9] published to date (MP2/6-31G(d) including zero point energy correction) suggest a similar stability for the N7(H) dioxo and N9(H) dioxo species in aqueous solution. This conclusion supported by results of UV and NMR measurements show that the xanthine is found mainly in the N7(H) dioxo tautomeric form in aqueous solution [6±8]. On the other hand, X-ray experiments show that the sodium salt of xanthine is found mainly in the N9(H) dioxo tautomeric form in the solid state [12]. Calculations by the CNDO method and ab initio method predict that the N7(H) dioxo tautomeric forms energetically favoured over N9(H) tautomeric form in the gas phase [9±11]. To our knowledge, there have not been reported experimental data on the tautomeric preference of xanthine in the gas phase. The ®rst aim is to provide a set of consistent theoretical data over large variety of DNA bases, which can hardly be obtained by experimental studies. As part of our continued interest in the tautomerism of nucleic acid bases and related compounds [13±16], we have carried out a theoretical study using the AM1 and PM3 methods for the fourteen possible tautomers of xanthine both in the gas and aqueous phase. Previous work on xanthine has also described the structures and the relative stabilities for different tautomers of the base. Most of these do not consider the effects of the entropy on the equilibrium. Analysis of the entropy effect allows for better understanding of the tautomerisation process. If several tautomers exist in comparable concentrations, the entropy contributions are important parts of relative Gibbs free energies. Because the exact equilibrium concentration depends on the Gibbs free energies of each tautomers. Both entropy and enthalpy should be included for a proper comparison of the calculated and experimental
9
tautomeric stability of the bases. Experimental information about the relative stability of two tautomeric forms of a molecule (a Y b) is obtained from the measurement of the tautomeric equilibrium constant Ka,b(T ). As a consequence, the Gibbs free energy of the tautomerisation DGa,b(T ) can be estimated at the de®ned temperature T. The present work is directly related to previous studies of Sponer and Leszczynski [9] who used the ab initio LCAO-MO method to investigate tautomerism of xanthine both in the gas phase and aqueous phase, but they have considered only eight tautomeric forms of xanthine. The second aim of this work is, therefore, to investigate the relative stability of this molecule as presented in Fig. 1, using semiempirical AM1 and PM3 methods, but also considering the effects of entropy on the equilibrium both in the gas and aqueous phases. We also extend the previous theoretical works [9±11] to include tautomeric equilibrium constants calculated from the Gibbs free energies of the xanthine. Also, there are no data available on the prediction of the tautomeric equilibrium constants for this molecule by means of quantum chemical calculations in the literature. The present paper reports the heats of formation, entropy, Gibbs free energy, relative stability, tautomeric equilibrium constants, relative proton af®nities, dipole moments and ionisation potentials for xanthine at 298.15 K. After having predicted the relative stability of tautomers, we have found the tautomeric equilibrium constants with respect to the more stable tautomer both in the gas phase and in aqueous solution. 2. Method of calculation Theoretical calculations were carried out at the restricted Hartree±Fock level (RHF) using AM1 [17] and PM3 [18] semiempirical SCF-MO methods with the Mopac 7.0 program [19], implemented on an Pentium II 300 MHz computer. In aqueous phase calculations, the COSMO (conductor-like screening model) solvation model [20] is used to construct a solvent accessible surface area based on Van der Waals radii. The relative permitivity of water was taken to be e 78:4 and the model incorporated up to 30 surface segments per atom, then we set the
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
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Table 1 The AM1 calculated thermodynamic properties for the tautomers of xanthine in the gas phase e 1 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
16.26 3.68 2.57 9.10 11.67 24.18 20.39 19.86 28.32 24.11 7.79 19.73 9.77 13.76
90.97 87.77 87.79 89.01 88.27 88.54 87.94 92.36 87.35 87.98 88.28 88.48 88.35 90.60
210.86 222.49 223.60 217.25 214.65 22.22 25.83 27.68 234.36 230.34 218.53 26.65 216.57 213.25
23.50 11.87 10.76 17.11 19.71 32.14 28.53 26.68 0.00 4.02 15.83 27.71 17.79 21.11
9.09 9.09 8.96 9.19 9.35 9.24 9.19 9.43 9.34 9.27 8.91 8.91 9.25 9.27
8.72 0.87 5.56 3.02 5.42 4.91 3.36 5.88 3.97 6.64 5.03 9.41 8.05 8.11
a
From DGf DHf2TDS.
parameters NPPA to 1082 and NSPA to 30. Initial geometry estimates of the all structures were obtained from a molecular mechanics calculation (CS Chem Of®ce) [21], and were followed by full optimisation of all geometrical variables. All structures were optimised to a gradient norm of ,0.2 in the gas phase and 0.1±2 in the aqueous phase, using the eigenvector method (EF) at PRECISE level. In order to calculate thermodynamic properties (DHf, DS) of the tautomers, the gradient norm is again reduced a value very close to zero. Entropy term is obtained from FORCE calculations for all the possible tautomers and the Gibbs free energies of the tautomerisation (DGf) at 298.15 K were predicted by adding the enthalpic (DHf) and entropic (TDS) terms.
3. Results and discussion 3.1. Relative stability Xanthine (X) is capable of existing in the fourteen tautomeric forms which are given in Fig. 1. To name a given tautomer we have used the following notations: Xi, j,k where i, j and k stand for the number of the nitrogen or oxygen atoms to which the hydrogens are attached. The AM1 and PM3 calculated relative stability energies, enthalpies, entropies and Gibbs free energies, dipole moments and ionisation potentials
for the tautomers of xanthine are given in Tables 1± 4. From Table 1, it can be inferred that xanthine can be found in the gas phase as a mixture of two predominant species: the two diketo tautomers X1,3,7 and X1,3,9. According to the present results, the tautomer X1,3,7, i.e. a diketo form containing a hydrogen attached to N7 of imidazolic ring, is 4.02 kcal mol 21 more stable than X1,3,9. The third most stable tautomer is the X1,9,10, which is 10.76 kcal mol 21 above the X1,3,7. According to Mezey et al. [22,23] a relative energy of 10 kcal mol 21 is a reasonable limit for the existence of the stable species and hence the two diketo tautomers is predicted to be detectable in the gas phase, the other tautomers would possess no signi®cant concentrations at room temperature. Tautomerism between six-membered ring nitrogens, N1 and N3, clearly favours the N1±H form, the only exception is presented by the dihydroxy tautomers X1,10,11 and X3,10,11. The relative free energy difference between tautomers X1,9,10 and X3,9,10 amounts to around 13 kcal mol 21. This is probably due to increased repulsion between the hydrogen atoms bound N3 and N9 in this latter form. The presented gas phase result is also in reasonable agreement with previous semiempirical results determined at the CNDO method [11] and also ab initio results determined at the HF/6-31G level [9,10]. However, there is no experimental data for the tautomeric preference of xanthine in the gas phase, preventing
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Table 2 The AM1 calculated thermodynamic properties for the tautomers of xanthine in aqueous phase e 78:4 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
221.25 226.75 227.75 222.99 215.50 27.14 28.10 213.94 238.93 238.33 224.15 222.80 225.04 223.58
88.83 87.83 87.95 88.72 88.81 89.03 88.46 88.86 87.56 87.57 87.92 88.18 87.70 88.11
247.73 252.94 253.97 249.44 241.98 233.68 234.66 240.43 265.04 264.44 250.36 249.09 251.19 249.85
17.31 12.10 11.07 15.60 23.06 31.36 30.38 24.61 0.00 0.60 14.68 15.95 13.85 15.19
9.37 9.34 9.26 9.44 9.48 9.43 9.46 9.59 9.39 9.32 9.24 9.30 9.37 9.47
19.64 1.32 9.58 6.05 8.34 9.89 6.24 9.70 6.36 11.48 9.14 17.51 13.63 14.64
a
From DGf DHf2TDS.
any comparison with the calculated values could be not made. The effect of the polar environment was estimated by the COSMO solvation model. These calculations did not change the gas phase stability order of the tautomers. The most important effect of COSMO solvation model is a signi®cant lowering of the energy gap between the two most stable diketo tautomers. However, the Gibbs free energy differences between
X1,3,7 and X1,3,9 decreased from 4.02 kcal mol 21 in the gas phase to 0.60 kcal mol 21 in aqueous phase (cf. Tables 1 and 2). The stability of the two diketo tautomers becomes more similar upon solvation and the changes are moderate. Only the diketo tautomers X1,3,7 and X1,3,9 can also exist in appreciable amounts at room temperature while the other tautomers can not exist in aqueous solution. The diketo forms (X1,3,7 and X1,3,9) would have a clear
Table 3 The PM3 calculated thermodynamic properties for the tautomers of xanthine in the gas phase e 1 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
222.05 238.52 239.27 230.02 234.54 216.40 223.72 226.70 249.97 243.04 232.00 223.01 232.11 231.28
93.07 89.55 89.61 91.46 90.20 90.62 89.73 91.09 89.25 92.87 90.21 89.94 91.43 91.43
249.80 265.22 265.99 257.29 261.43 243.42 250.47 253.86 276.58 270.73 258.90 249.83 259.37 258.54
26.78 11.36 10.59 19.10 15.15 33.16 26.11 22.72 0.00 5.85 17.68 26.75 17.21 18.04
9.51 9.08 9.02 9.34 9.36 9.28 9.30 9.30 9.22 9.28 8.74 8.96 9.21 9.12
9.87 1.59 5.31 4.73 4.96 5.47 3.60 5.82 4.09 6.68 4.64 8.14 8.07 8.20
a
From DGf DHf2TDS.
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Table 4 The PM3 calculated thermodynamic properties for the tautomers of xanthine in aqueous phase e 78:4 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
268.11 272.95 270.6 270.91 263.02 252.21 256.03 264.62 283.67 280.52 267.40 269.10 270.84 273.09
91.00 88.95 89.12 90.05 89.60 90.02 89.57 89.23 87.68 87.99 88.85 89.62 88.79 88.71
295.24 299.47 297.17 297.76 289.73 279.05 282.74 291.22 2109.81 2106.75 293.89 295.82 297.31 299.54
14.57 10.34 12.64 12.05 20.08 30.76 27.07 18.59 0.00 3.06 15.92 13.99 12.50 10.27
9.26 9.32 9.25 9.31 9.50 9.52 9.51 9.56 9.20 9.15 9.17 9.25 9.24 9.31
20.97 3.06 9.62 9.47 7.86 11.70 6.75 10.60 6.73 12.25 8.96 19.46 14.38 15.16
a
From DGf DHf2TDS.
predominance over the dienol and enol forms in both phases, most probably because of electronic stabilisation and thermal corrections. As we can see from Tables 1±4, the calculated entropy values are generally small (ca.87±93 cal/mol). These results indicate that the value of the entropy effect on the Gibbs free energy is very small and the entropy term and TDS value can be neglected for the tautomeric equilibria of xanthine. Thus, the enthalpic term is dominant in the determination of the equilibrium constant. Experimental evidence clearly indicates that xanthine exist as the N7(H) diketo species in aqueous solution [6±8]. Ultraviolet spectra reported by Cavalier and co-workers [7], and Ogston [8], suggest that the diketo tautomers are predominant in aqueous solution. NMR measurements reported by Lichtenberg and co-workers [6], which clearly indicates that the N7(H) diketo tautomer is most stable than N9(H) tautomer in dimethyl sulphoxide and deuterium oxide. This result is also in reasonable agreement with previous ab initio calculation result determined at the HF/6-31G level in aqueous solution by Sponer and Leszczynski [9]. The PM3 calculations give the same order of tautomer stability for the xanthine. As previously noted, the AM1 method performs better than PM3 method in six-membered nitrogen heterocycles [24].
3.2. Dipole moments and ionisation potentials The calculated dipole moments and the ®rst ionisation potentials of xanthine tautomers are also listed in Tables 1±4. The calculated dipole moments for the most stable tautomers of xanthine, X1,3,7 and X1,3,9 are 3.97 and 6.64 debye, respectively (cf. Table 1). There is no experimental dipole moment for xanthine, because of the solubility in non-polar solution. Dipole moment measurements for distinguishing between different tautomeric forms, in particular, between the N7±H and N9±H tautomer are dif®cult by the physicochemical techniques. However, in order to make possible determination of the dipole moments of the xanthine derivatives, it is necessary to introduce a solubilising substituent (the decylthio-group) at C-8 position. In the reasonable assumption that the introduction of the same group at the same position in all compounds will not affect the sequence of the physical properties of the various substance. The results obtained for derivatives of 8-decylthioxanthine [11] are in good agreement with our results calculated by AM1 and PM3 method. Dipole moments determined by semiempirical CNDO method for the tautomers X1,3,7 and X1,3,9 are 4.0 and 7.9 debye, respectively. However, our calculated dipole moments are quite close to the
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U Table 5 The AM1and PM3 predicted tautomeric equilibrium constants with respect to the most stable tautomers of xanthine in the gas phase e 1 and in aqueous solution e 78:4 at 298.15 K Tautomeric equilibrium
X1,3,7±X3,9,10 X1,3,7±X1,7,10 X1,3,7±X1,9,10 X1,3,7±X3,7,10 X1,3,7±X9,10,11 X1,3,7±X1,10,11 X1,3,7±X3,10,11 X1,3,7±X7,10,11 X1,3,7±X1,3,9 X1,3,7±X1,9,11 X1,3,7±X1,7,11 X1,3,7±X3,9,11 X1,3,7±X3,7,11 a
pKT a (e 1)
pKT a (e 78.4)
AM1
PM3
AM1
PM3
17.23 8.70 7.89 12.54 14.45 23.56 20.92 19.56 2.95 11.61 20.31 13.04 15.48
19.63 8.33 7.76 14.14 11.11 24.31 19.14 16.66 4.29 12.96 19.61 12.62 13.23
12.69 8.87 8.12 11.44 16.91 22.99 22.27 18.04 0.44 10.76 11.69 10.15 11.14
10.68 7.58 9.27 8.83 14.72 22.55 19.85 13.63 2.24 11.67 10.26 9.16 7.53
pKT 2log KT.
results determined from ab initio calculations [9,25], which are 3.97 and 6.87 debye for the most stable diketo tautomers. As we can see from Tables 1±4, the calculated dipole moments are substantially higher in moving from the gas phase e 1 to solution e 78:4 and the dipole moments are sensitive to the polarity of the medium. The calculated dipole moments are substantially higher in a medium of high relative permitivity, mainly due to major charge redistribution in the molecule, and also by changes in the distances between the charge separations. The magnitude of the in¯uence of the solvent reaction ®eld on electronic structure is different in different tautomers. This may also explain the great variation of the calculated dipole moments of the tautomers. The ionisation potentials for the tautomers of xanthine were obtained from the energies of the highest occupied molecular orbitals using Koopmans' theorem. The ®rst vertical ionisation potentials for the most stable tautomers of xanthine are in good agreement with the experimental value. The experimental ionisation potential for xanthine is 9.30 ^ 0.2 eV [26] and the CNDO calculations values reported by Pullman and Pullman [11] are 10.8 and 10.4 eV for the more stable diketo tautomers. As previously noted, CNDO calculations overestimate
13
the stability of nitrogen atom lone-pair orbitals relative to the manifold of p-type orbitals [27]. Calculated dipole moments by PPP method reported by Pullman and Pullman [11] are 8.8 and 8.7 eV for the most stable diketo tautomers. Experimental ionisation potential for xanthine is closer to our calculated AM1 and PM3 values, and in better agreement than those of the CNDO and PPP values. As previously noted, the ionisation potentials are systematically overestimated AM1 as well as MNDO by ca. 0.5 eV for p-type orbitals [28]. Results obtained by the PM3 method are not too different from those obtained by AM1. However, the PM3 method yields somewhat lower values for ionisation from pyridine-like lone pairs and, thus, in better agreement with experimental values than AM1. 3.3. Tautomeric equilibrium constants The AM1 and PM3 calculated tautomeric equilibrium constants with respect to the most stable tautomers of xanthine both in the gas and in aqueous solution are listed in Table 5. The pKT values of the studied molecules were calculated by means of the following equation pKT
dDG 2:303RT
Calculated values for the equilibrium between the tautomers X1,3,7 and X1,3,9 of xanthine in the gas phase show that the diketo form N7(H) is more dominant than the diketo form N9(H), with a pKT value of 2.95. The calculation for the aqueous phase of xanthine, X1,3,7 Y H1,3,9 tautomeric equilibrium again suggest that the diketo form NH(7) with hydrogen atoms at N1, N3 and N7 is more dominant tautomer than the diketo form with hydrogen atoms at N1, N3 and N9 with a pKT value of 0.44. Calculations also show that two diketo forms of xanthine are most stable than all other forms in aqueous solution. Generally, 1H tautomers are more stable than the corresponding 3H tautomers, the only exception is presented by the dihydroxy tautomers in the gas phase, which implies that the proton at N1 is more acidic than that of N3. There is no experimental evidence for the equilibrium constants of the investigated compound, preventing any comparison with the calculated pKT values could be not made.
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Table 6 The AM1 and PM3 calculated relative proton af®nities (d PA) with respect to the most stable tautomer of xanthine (in kcal mol 21) Tautomeric equilibrium
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11 a
d PA a e 1
d PA a e 78:4
AM1
PM3
AM1
PM3
24.58 12.00 10.89 17.42 19.99 32.50 28.71 28.18 4.21 16.11 28.05 18.09 22.08
27.92 11.45 10.70 19.95 15.43 33.57 26.25 23.27 6.93 17.97 26.96 17.86 18.69
17.68 12.18 11.18 15.94 23.43 31.79 30.83 24.99 0.60 14.78 16.13 13.89 15.35
15.56 10.72 13.07 12.76 20.65 31.46 27.64 19.05 3.15 16.27 14.57 12.83 10.58
d PA d DH DH(B) 2 DH(A).
proton af®nities for xanthine in order to put in a more reliable basis the qualitative results inferred from the AM1 and PM3 calculations. Xanthine may be protonated at different nitrogen atoms or oxygen atom, but experimentally it is not possible to discriminate between the various possibilities. The protonation energetics depend on the chemical surrounding, and so theoretical investigations represent a practicable way for obtaining information about the energetics of proton attachment to the different sites of xanthine and to establish which of these are favoured. The predicted relative proton af®nities are collected in Table 6 for AM1 and PM3 methods in both phases. The relative proton af®nities (d PA), which is the difference between proton af®nities of molecules A and B, can be calculated as
dPA dDH PA B 2 PA A or dPA dDH DH B 2 DH A
Furthermore, comparison of the gas phase equilibrium constants with solution phase values implies that large changes may occur on going from gas phase to solution. This can be explained by solvent effects. Solvent effects have been ascribed to two major components: electrostatic solvent±solute interaction and hydrogen bonding. The hydrogen bonding effects can not be estimated in a quantitative manner from the solvation model, further large-scale calculations. A semiquantitative estimation of the solvation differences can be obtained from COSMO solvation model. The electrostatic solvent±solute effects, however, are readily estimated by the dielectric continuum model [29]. Application of the COSMO solvation model leads to an explanation of the change in order of tautomeric stability on going from gas phase to solution. However, such a treatment lacks explicit consideration of base±water hydrogen bonding effects, tautomeric equilibrium constants predicted in water are considerably less reliable than those predicted in the gas phase.
where DH(B) and DH(A) are the heats of formation values of tautomers A and B taken from Tables 1±4. As we stated before, the two-diketo forms X1,3,7 and X1,3,9 species possess comparable relative energies. This implies that the ®rst protonation of xanthine is imidazole ring, i.e. the N7 (in X1,3,9) and N9 (in X1,3,7). This is in good agreement with 15N, 1H and 13C NMR experimental results in DMSO, which show that xanthine is protonated preferentially at imidazole ring [31,32]. Generally, 1H tautomers are more stable than the corresponding 3H tautomers, the only exception is presented by the dihydroxy tautomers in the gas phase, which implies that the proton at N1 is more acidic than that of N3. Thus, the second protonation site of xanthine is the N1 or N3. Predicted relative proton af®nities show that C2O is more acidic than the C6O, which shows that third protonation site of xanthine is C2O, then C6O. The above proton af®nity order also follows a logical trend in the sense that the endocyclic nitrogens will be protonated ®rst, then the oxygen, which is less basic centre.
3.4. Relative proton af®nities
4. Conclusions
Since protonation of nucleic acid bases plays an important role in many biochemical (i.e. enzymatic reactions, stabilisation of triplex structures) and mutagenic process [30], we have calculated the relative
Several conclusions can be made on the basis of the results of the present theoretical study. 1. The results clearly indicate that xanthine both in
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
2. 3.
4. 5. 6.
7.
the gas phase and in aqueous phase exists predominantly in the two diketo forms X1,3,7 and X1,3,9. This result is in agreement with available experimental and theoretical studies. The energy difference between X1,3,7 and X1,3,9 is predicted to be signi®cantly lowered by the polar solvent. The results presented in this paper con®rm our earlier observations about the applicability of the AM1 method for the quantitative prediction of relative stability of nucleic acid bases in solution. AM1 also gives a good representation of the charge distribution in molecules in terms of calculated dipole moments. The inclusion of the solvent reaction ®eld in quantum-chemical theory is obligatory for accurate results in solution. The entropy effect on the Gibbs free energy of xanthine tautomers is very small and there is little signi®cance for the tautomeric equilibria of the base. The enthalpic term is dominant also in the determination of the equilibrium constant. The protonation of xanthine in both phases occurs at the imidazole nitrogens (N7 or N9), then pyrimidine nitrogens (N1 or N3).
Acknowledgements I would like to thank Prof. Knut Faegri and Prof. Einar Uggered for their helpful comments and discussions. References [1] D.T. Hurst, An Introduction to the Chemistry and Biochemistry of Pyrimidines, Purines and Pteridines, Wiley, New York, 1980 (pp. 179±203). [2] E.J. Stiefel, Prog. Inorg. Chem. 23 (1977) 211. [3] R.W. Rundless, J.B. Wyngaarden, G.H. Hitchings, G.B. Elion, H.P. Silberman, Trans. Assoc. Am. Phys. 76 (1963) 126.
15
[4] G.B. Elion, S. Callahan, G.H. Hitchings, R.W. Rundles, J. Laszlo, Cancer Chemother. Rep. 16 (1962) 1971. [5] M.J. Scanlan, I.H. Hillier, J. Am. Chem. Soc. 106 (1984) 3837. [6] D. Lichtenberg, F. Bergmann, Z. Neiman, J. Chem. Soc., C (1971) 1676. [7] L.F. Cavalieri, J.J. Fox, A. Stone, N. Chang, J. Am. Chem. Soc. 76 (1954) 1119. [8] A.G. Ogston, J. Chem. Soc. (1935) 1376. [9] J. Sponer, J. Leszczynski, Struct. Chem. 6 (4/5) (1995) 281. [10] M. Nonella, G. Hanggi, E. Dubler, J. Mol. Struct. (Theochem) 279 (1993) 173. [11] B. Pullman, A. Pullman, Adv. Heterocycl. Chem. 13 (1971) 77. [12] M. Mizuno, T. Fujiwara, K. Tomita, Bull. Chem. Soc. Jpn 42 (1969) 3099. [13] P.U. Civcir, J. Mol. Struct. (Theochem) 532 (1±3) (2000) 157. [14] P.U. Civcir, J. Phys. Org. Chem. 14 (2001) 171. [15] P.U. Civcir, J. Mol. Struct. (Theochem) 535 (2001) 121. [16] P.U. Civcir, J. Mol. Struct. (Theochem) 536 (2001) 161. [17] M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, J.J.P. Stewart, J. Am. Chem. Soc. 107 (1985) 366. [18] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. [19] J.J.P. Stewart, Mopac 7.0, Quantum Chemistry Program Exchange, University of Indiana, Bloomington, IN, USA. [20] A. Klamt, G. Schuurmann, J. Chem. Soc. Perkin Trans. 2 (1993) 799. [21] CS Chem Of®ce, Pro. For Microsoft Windows, Cambridge Scienti®c Computing Inc., 875 Massachusetts Avenue, Suite 61, Cambridge, MA 02139, USA. [22] P.G. Mezey, J.J. Ladik, Theor. Chim. Acta 52 (1979) 129. [23] P.G. Mezey, J.J. Ladik, M. Barry, Theor. Chim. Acta 54 (1980) 251. [24] J. Garcia, J. Villarrasa, Heterocycles 27 (1988) 1083. [25] N.El-B. Kassimi, A.J. Thakkar, J. Mol. Struct. (Theochem) 366 (1996) 185. [26] C. Lifschitz, E.D. Bergmann, B. Pullman, Tetrahedron Lett. 46 (1967) 4583. [27] J. Lin, C. Yu, S. Peng, I. Akiyama, K. Li, L. Kao-Lee, P.R. LeBreton, J. Phys. Chem. 84 (1980) 1006. [28] M.J.S. Dewar, Y. Yamaguchi, S. Doraiswamy, S.D. Sharma, S.H. Suck, Chem. Phys. 41 (1979) 21. [29] A. Klamt, G. Schuurmann, J. Chem. Soc. Perkin Trans. 2 (1993) 799. [30] S.M. Mirkin, Annu. Rev. Biophys. Biomol. Struct. 24 (1995) 319. [31] R.L. Benoit, M. Frechette, Can. J. Chem. 63 (1985) 3053. [32] R.M. Izatt, J.J. Christensen, J.H. Ryttine, Chem. Rev. 71 (1971) 439.
www.elsevier.nl/locate/theochem
AM1 and PM3 study of tautomerism of xanthine in the gas and aqueous phases È . Civcir* P.U Ankara University, Faculty of Health Education, Ankara, Turkey Received 6 October 2000; accepted 1 November 2000
Abstract Heats of formation, entropies, Gibbs free energies, relative tautomerisation energies, tautomeric equilibrium constants, relative proton af®nities, dipole moments, and ionisation potentials for the fourteen possible tautomers of xanthine have been studied using semiempirical AM1 and PM3 quantum-chemical calculations at the SCF level in the gas and aqueous phases, with full geometry optimisation. The COSMO solvation model was employed for aqueous solution calculations. The calculations show that the two diketo tautomers X1,3,7 and X1,3,9 are the predominant species at room temperature in the gas and aqueous phase. But, the ®rst more stable tautomer is the dioxo-7H tautomer, X1,3,7. Comparison with available experimental data provides support for quality of results derived from theoretical computations. The entropy effect on the Gibbs free energy of the xanthine is very small and there is little signi®cance for the tautomeric equilibria of the base. The enthalpic term is dominant also in the determination of the equilibrium constant. q 2001 Elsevier Science B.V. All rights reserved. Keywords: AM1, PM3 semiempirical calculations; Dipole moment; Ionisation potential; Tautomerism; Tautomeric equilibrium constant; Xanthine
1. Introduction The oxopurines are of biological importance, because they are metabolic intermediate products of purine metabolism formed by degradation of nucleic acids. Alkylated xanthines are bronchodilators. Xanthine (3,7-dihydro-1H-purine-2,6-dione) is a purine base which is not common in ribonucleic acid or deoxyribonucleic acid, but deamination of guanine results in xanthine base, and this base is still able to pair with cytosine by two hydrogens. In man, the end product of purine metabolism is uric acid and xanthine oxidase. Actually, hypoxanthine, which formed by enzymatic degradation of nucleic acid, is * Tel.: 190-312-3808172; fax: 190-312-3575323. E-mail address: [email protected] (P.U. Civcir).
oxidised by the molybdenum- and iron-containing enzyme xanthine oxidase via xanthine to uric acid. This enzyme found in the liver, is capable of oxidising xanthine to uric acid [1]. Defects in purine metabolism result in an increase in the uric acid level and in the deposition of sodium hydrogen urate monohydrate crystals in joints. This disease known as gout and is clinically treated by allopurinol, which has also been used in conjunction with anticancer drugs combined with 6-mercaptopurine in treatment of leukaemia [2± 4]. Enzymes attack purines at preferred positions, and therefore the tautomerisation of the purine molecules may play an important role in the replication process and the equilibrium is strongly sensitive to the interaction of these molecules with their environment [5]. In an equilibrium, xanthine base exists in different tautomeric forms, the protropic tautomerism can
0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166- 128 0( 00) 00821-6
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È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
Fig. 1. Representation of tautomers of xanthine considered in the present work.
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
occur in both rings (pyrimidine and imidazole) and thus two type of equilibria can be observed: keto Y enol and N(7)H Y N(9)H. Knowledge of the geometric and electronic structure as well as the relative stability of tautomeric forms provides a basis for understanding biological activity of oxopurine bases. In addition, knowing how these tautomerisation energies change in different environments can give an insight into the in¯uence of solvent effects on molecular stability. Several experiments and theoretical studies on the tautomerism of xanthine are reported in the literature [6±11]. The highest level calculations [9] published to date (MP2/6-31G(d) including zero point energy correction) suggest a similar stability for the N7(H) dioxo and N9(H) dioxo species in aqueous solution. This conclusion supported by results of UV and NMR measurements show that the xanthine is found mainly in the N7(H) dioxo tautomeric form in aqueous solution [6±8]. On the other hand, X-ray experiments show that the sodium salt of xanthine is found mainly in the N9(H) dioxo tautomeric form in the solid state [12]. Calculations by the CNDO method and ab initio method predict that the N7(H) dioxo tautomeric forms energetically favoured over N9(H) tautomeric form in the gas phase [9±11]. To our knowledge, there have not been reported experimental data on the tautomeric preference of xanthine in the gas phase. The ®rst aim is to provide a set of consistent theoretical data over large variety of DNA bases, which can hardly be obtained by experimental studies. As part of our continued interest in the tautomerism of nucleic acid bases and related compounds [13±16], we have carried out a theoretical study using the AM1 and PM3 methods for the fourteen possible tautomers of xanthine both in the gas and aqueous phase. Previous work on xanthine has also described the structures and the relative stabilities for different tautomers of the base. Most of these do not consider the effects of the entropy on the equilibrium. Analysis of the entropy effect allows for better understanding of the tautomerisation process. If several tautomers exist in comparable concentrations, the entropy contributions are important parts of relative Gibbs free energies. Because the exact equilibrium concentration depends on the Gibbs free energies of each tautomers. Both entropy and enthalpy should be included for a proper comparison of the calculated and experimental
9
tautomeric stability of the bases. Experimental information about the relative stability of two tautomeric forms of a molecule (a Y b) is obtained from the measurement of the tautomeric equilibrium constant Ka,b(T ). As a consequence, the Gibbs free energy of the tautomerisation DGa,b(T ) can be estimated at the de®ned temperature T. The present work is directly related to previous studies of Sponer and Leszczynski [9] who used the ab initio LCAO-MO method to investigate tautomerism of xanthine both in the gas phase and aqueous phase, but they have considered only eight tautomeric forms of xanthine. The second aim of this work is, therefore, to investigate the relative stability of this molecule as presented in Fig. 1, using semiempirical AM1 and PM3 methods, but also considering the effects of entropy on the equilibrium both in the gas and aqueous phases. We also extend the previous theoretical works [9±11] to include tautomeric equilibrium constants calculated from the Gibbs free energies of the xanthine. Also, there are no data available on the prediction of the tautomeric equilibrium constants for this molecule by means of quantum chemical calculations in the literature. The present paper reports the heats of formation, entropy, Gibbs free energy, relative stability, tautomeric equilibrium constants, relative proton af®nities, dipole moments and ionisation potentials for xanthine at 298.15 K. After having predicted the relative stability of tautomers, we have found the tautomeric equilibrium constants with respect to the more stable tautomer both in the gas phase and in aqueous solution. 2. Method of calculation Theoretical calculations were carried out at the restricted Hartree±Fock level (RHF) using AM1 [17] and PM3 [18] semiempirical SCF-MO methods with the Mopac 7.0 program [19], implemented on an Pentium II 300 MHz computer. In aqueous phase calculations, the COSMO (conductor-like screening model) solvation model [20] is used to construct a solvent accessible surface area based on Van der Waals radii. The relative permitivity of water was taken to be e 78:4 and the model incorporated up to 30 surface segments per atom, then we set the
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
10
Table 1 The AM1 calculated thermodynamic properties for the tautomers of xanthine in the gas phase e 1 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
16.26 3.68 2.57 9.10 11.67 24.18 20.39 19.86 28.32 24.11 7.79 19.73 9.77 13.76
90.97 87.77 87.79 89.01 88.27 88.54 87.94 92.36 87.35 87.98 88.28 88.48 88.35 90.60
210.86 222.49 223.60 217.25 214.65 22.22 25.83 27.68 234.36 230.34 218.53 26.65 216.57 213.25
23.50 11.87 10.76 17.11 19.71 32.14 28.53 26.68 0.00 4.02 15.83 27.71 17.79 21.11
9.09 9.09 8.96 9.19 9.35 9.24 9.19 9.43 9.34 9.27 8.91 8.91 9.25 9.27
8.72 0.87 5.56 3.02 5.42 4.91 3.36 5.88 3.97 6.64 5.03 9.41 8.05 8.11
a
From DGf DHf2TDS.
parameters NPPA to 1082 and NSPA to 30. Initial geometry estimates of the all structures were obtained from a molecular mechanics calculation (CS Chem Of®ce) [21], and were followed by full optimisation of all geometrical variables. All structures were optimised to a gradient norm of ,0.2 in the gas phase and 0.1±2 in the aqueous phase, using the eigenvector method (EF) at PRECISE level. In order to calculate thermodynamic properties (DHf, DS) of the tautomers, the gradient norm is again reduced a value very close to zero. Entropy term is obtained from FORCE calculations for all the possible tautomers and the Gibbs free energies of the tautomerisation (DGf) at 298.15 K were predicted by adding the enthalpic (DHf) and entropic (TDS) terms.
3. Results and discussion 3.1. Relative stability Xanthine (X) is capable of existing in the fourteen tautomeric forms which are given in Fig. 1. To name a given tautomer we have used the following notations: Xi, j,k where i, j and k stand for the number of the nitrogen or oxygen atoms to which the hydrogens are attached. The AM1 and PM3 calculated relative stability energies, enthalpies, entropies and Gibbs free energies, dipole moments and ionisation potentials
for the tautomers of xanthine are given in Tables 1± 4. From Table 1, it can be inferred that xanthine can be found in the gas phase as a mixture of two predominant species: the two diketo tautomers X1,3,7 and X1,3,9. According to the present results, the tautomer X1,3,7, i.e. a diketo form containing a hydrogen attached to N7 of imidazolic ring, is 4.02 kcal mol 21 more stable than X1,3,9. The third most stable tautomer is the X1,9,10, which is 10.76 kcal mol 21 above the X1,3,7. According to Mezey et al. [22,23] a relative energy of 10 kcal mol 21 is a reasonable limit for the existence of the stable species and hence the two diketo tautomers is predicted to be detectable in the gas phase, the other tautomers would possess no signi®cant concentrations at room temperature. Tautomerism between six-membered ring nitrogens, N1 and N3, clearly favours the N1±H form, the only exception is presented by the dihydroxy tautomers X1,10,11 and X3,10,11. The relative free energy difference between tautomers X1,9,10 and X3,9,10 amounts to around 13 kcal mol 21. This is probably due to increased repulsion between the hydrogen atoms bound N3 and N9 in this latter form. The presented gas phase result is also in reasonable agreement with previous semiempirical results determined at the CNDO method [11] and also ab initio results determined at the HF/6-31G level [9,10]. However, there is no experimental data for the tautomeric preference of xanthine in the gas phase, preventing
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
11
Table 2 The AM1 calculated thermodynamic properties for the tautomers of xanthine in aqueous phase e 78:4 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
221.25 226.75 227.75 222.99 215.50 27.14 28.10 213.94 238.93 238.33 224.15 222.80 225.04 223.58
88.83 87.83 87.95 88.72 88.81 89.03 88.46 88.86 87.56 87.57 87.92 88.18 87.70 88.11
247.73 252.94 253.97 249.44 241.98 233.68 234.66 240.43 265.04 264.44 250.36 249.09 251.19 249.85
17.31 12.10 11.07 15.60 23.06 31.36 30.38 24.61 0.00 0.60 14.68 15.95 13.85 15.19
9.37 9.34 9.26 9.44 9.48 9.43 9.46 9.59 9.39 9.32 9.24 9.30 9.37 9.47
19.64 1.32 9.58 6.05 8.34 9.89 6.24 9.70 6.36 11.48 9.14 17.51 13.63 14.64
a
From DGf DHf2TDS.
any comparison with the calculated values could be not made. The effect of the polar environment was estimated by the COSMO solvation model. These calculations did not change the gas phase stability order of the tautomers. The most important effect of COSMO solvation model is a signi®cant lowering of the energy gap between the two most stable diketo tautomers. However, the Gibbs free energy differences between
X1,3,7 and X1,3,9 decreased from 4.02 kcal mol 21 in the gas phase to 0.60 kcal mol 21 in aqueous phase (cf. Tables 1 and 2). The stability of the two diketo tautomers becomes more similar upon solvation and the changes are moderate. Only the diketo tautomers X1,3,7 and X1,3,9 can also exist in appreciable amounts at room temperature while the other tautomers can not exist in aqueous solution. The diketo forms (X1,3,7 and X1,3,9) would have a clear
Table 3 The PM3 calculated thermodynamic properties for the tautomers of xanthine in the gas phase e 1 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
222.05 238.52 239.27 230.02 234.54 216.40 223.72 226.70 249.97 243.04 232.00 223.01 232.11 231.28
93.07 89.55 89.61 91.46 90.20 90.62 89.73 91.09 89.25 92.87 90.21 89.94 91.43 91.43
249.80 265.22 265.99 257.29 261.43 243.42 250.47 253.86 276.58 270.73 258.90 249.83 259.37 258.54
26.78 11.36 10.59 19.10 15.15 33.16 26.11 22.72 0.00 5.85 17.68 26.75 17.21 18.04
9.51 9.08 9.02 9.34 9.36 9.28 9.30 9.30 9.22 9.28 8.74 8.96 9.21 9.12
9.87 1.59 5.31 4.73 4.96 5.47 3.60 5.82 4.09 6.68 4.64 8.14 8.07 8.20
a
From DGf DHf2TDS.
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
12
Table 4 The PM3 calculated thermodynamic properties for the tautomers of xanthine in aqueous phase e 78:4 Tautomer
DHf (kcal mol 21)
DS (cal mol 21 K 21)
DGf a (kcal mol 21)
d DGf (kcal mol 21)
IP (eV)
m (debye)
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,7 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11
268.11 272.95 270.6 270.91 263.02 252.21 256.03 264.62 283.67 280.52 267.40 269.10 270.84 273.09
91.00 88.95 89.12 90.05 89.60 90.02 89.57 89.23 87.68 87.99 88.85 89.62 88.79 88.71
295.24 299.47 297.17 297.76 289.73 279.05 282.74 291.22 2109.81 2106.75 293.89 295.82 297.31 299.54
14.57 10.34 12.64 12.05 20.08 30.76 27.07 18.59 0.00 3.06 15.92 13.99 12.50 10.27
9.26 9.32 9.25 9.31 9.50 9.52 9.51 9.56 9.20 9.15 9.17 9.25 9.24 9.31
20.97 3.06 9.62 9.47 7.86 11.70 6.75 10.60 6.73 12.25 8.96 19.46 14.38 15.16
a
From DGf DHf2TDS.
predominance over the dienol and enol forms in both phases, most probably because of electronic stabilisation and thermal corrections. As we can see from Tables 1±4, the calculated entropy values are generally small (ca.87±93 cal/mol). These results indicate that the value of the entropy effect on the Gibbs free energy is very small and the entropy term and TDS value can be neglected for the tautomeric equilibria of xanthine. Thus, the enthalpic term is dominant in the determination of the equilibrium constant. Experimental evidence clearly indicates that xanthine exist as the N7(H) diketo species in aqueous solution [6±8]. Ultraviolet spectra reported by Cavalier and co-workers [7], and Ogston [8], suggest that the diketo tautomers are predominant in aqueous solution. NMR measurements reported by Lichtenberg and co-workers [6], which clearly indicates that the N7(H) diketo tautomer is most stable than N9(H) tautomer in dimethyl sulphoxide and deuterium oxide. This result is also in reasonable agreement with previous ab initio calculation result determined at the HF/6-31G level in aqueous solution by Sponer and Leszczynski [9]. The PM3 calculations give the same order of tautomer stability for the xanthine. As previously noted, the AM1 method performs better than PM3 method in six-membered nitrogen heterocycles [24].
3.2. Dipole moments and ionisation potentials The calculated dipole moments and the ®rst ionisation potentials of xanthine tautomers are also listed in Tables 1±4. The calculated dipole moments for the most stable tautomers of xanthine, X1,3,7 and X1,3,9 are 3.97 and 6.64 debye, respectively (cf. Table 1). There is no experimental dipole moment for xanthine, because of the solubility in non-polar solution. Dipole moment measurements for distinguishing between different tautomeric forms, in particular, between the N7±H and N9±H tautomer are dif®cult by the physicochemical techniques. However, in order to make possible determination of the dipole moments of the xanthine derivatives, it is necessary to introduce a solubilising substituent (the decylthio-group) at C-8 position. In the reasonable assumption that the introduction of the same group at the same position in all compounds will not affect the sequence of the physical properties of the various substance. The results obtained for derivatives of 8-decylthioxanthine [11] are in good agreement with our results calculated by AM1 and PM3 method. Dipole moments determined by semiempirical CNDO method for the tautomers X1,3,7 and X1,3,9 are 4.0 and 7.9 debye, respectively. However, our calculated dipole moments are quite close to the
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U Table 5 The AM1and PM3 predicted tautomeric equilibrium constants with respect to the most stable tautomers of xanthine in the gas phase e 1 and in aqueous solution e 78:4 at 298.15 K Tautomeric equilibrium
X1,3,7±X3,9,10 X1,3,7±X1,7,10 X1,3,7±X1,9,10 X1,3,7±X3,7,10 X1,3,7±X9,10,11 X1,3,7±X1,10,11 X1,3,7±X3,10,11 X1,3,7±X7,10,11 X1,3,7±X1,3,9 X1,3,7±X1,9,11 X1,3,7±X1,7,11 X1,3,7±X3,9,11 X1,3,7±X3,7,11 a
pKT a (e 1)
pKT a (e 78.4)
AM1
PM3
AM1
PM3
17.23 8.70 7.89 12.54 14.45 23.56 20.92 19.56 2.95 11.61 20.31 13.04 15.48
19.63 8.33 7.76 14.14 11.11 24.31 19.14 16.66 4.29 12.96 19.61 12.62 13.23
12.69 8.87 8.12 11.44 16.91 22.99 22.27 18.04 0.44 10.76 11.69 10.15 11.14
10.68 7.58 9.27 8.83 14.72 22.55 19.85 13.63 2.24 11.67 10.26 9.16 7.53
pKT 2log KT.
results determined from ab initio calculations [9,25], which are 3.97 and 6.87 debye for the most stable diketo tautomers. As we can see from Tables 1±4, the calculated dipole moments are substantially higher in moving from the gas phase e 1 to solution e 78:4 and the dipole moments are sensitive to the polarity of the medium. The calculated dipole moments are substantially higher in a medium of high relative permitivity, mainly due to major charge redistribution in the molecule, and also by changes in the distances between the charge separations. The magnitude of the in¯uence of the solvent reaction ®eld on electronic structure is different in different tautomers. This may also explain the great variation of the calculated dipole moments of the tautomers. The ionisation potentials for the tautomers of xanthine were obtained from the energies of the highest occupied molecular orbitals using Koopmans' theorem. The ®rst vertical ionisation potentials for the most stable tautomers of xanthine are in good agreement with the experimental value. The experimental ionisation potential for xanthine is 9.30 ^ 0.2 eV [26] and the CNDO calculations values reported by Pullman and Pullman [11] are 10.8 and 10.4 eV for the more stable diketo tautomers. As previously noted, CNDO calculations overestimate
13
the stability of nitrogen atom lone-pair orbitals relative to the manifold of p-type orbitals [27]. Calculated dipole moments by PPP method reported by Pullman and Pullman [11] are 8.8 and 8.7 eV for the most stable diketo tautomers. Experimental ionisation potential for xanthine is closer to our calculated AM1 and PM3 values, and in better agreement than those of the CNDO and PPP values. As previously noted, the ionisation potentials are systematically overestimated AM1 as well as MNDO by ca. 0.5 eV for p-type orbitals [28]. Results obtained by the PM3 method are not too different from those obtained by AM1. However, the PM3 method yields somewhat lower values for ionisation from pyridine-like lone pairs and, thus, in better agreement with experimental values than AM1. 3.3. Tautomeric equilibrium constants The AM1 and PM3 calculated tautomeric equilibrium constants with respect to the most stable tautomers of xanthine both in the gas and in aqueous solution are listed in Table 5. The pKT values of the studied molecules were calculated by means of the following equation pKT
dDG 2:303RT
Calculated values for the equilibrium between the tautomers X1,3,7 and X1,3,9 of xanthine in the gas phase show that the diketo form N7(H) is more dominant than the diketo form N9(H), with a pKT value of 2.95. The calculation for the aqueous phase of xanthine, X1,3,7 Y H1,3,9 tautomeric equilibrium again suggest that the diketo form NH(7) with hydrogen atoms at N1, N3 and N7 is more dominant tautomer than the diketo form with hydrogen atoms at N1, N3 and N9 with a pKT value of 0.44. Calculations also show that two diketo forms of xanthine are most stable than all other forms in aqueous solution. Generally, 1H tautomers are more stable than the corresponding 3H tautomers, the only exception is presented by the dihydroxy tautomers in the gas phase, which implies that the proton at N1 is more acidic than that of N3. There is no experimental evidence for the equilibrium constants of the investigated compound, preventing any comparison with the calculated pKT values could be not made.
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
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Table 6 The AM1 and PM3 calculated relative proton af®nities (d PA) with respect to the most stable tautomer of xanthine (in kcal mol 21) Tautomeric equilibrium
X3,9,10 X1,7,10 X1,9,10 X3,7,10 X9,10,11 X1,10,11 X3,10,11 X7,10,11 X1,3,9 X1,9,11 X1,7,11 X3,9,11 X3,7,11 a
d PA a e 1
d PA a e 78:4
AM1
PM3
AM1
PM3
24.58 12.00 10.89 17.42 19.99 32.50 28.71 28.18 4.21 16.11 28.05 18.09 22.08
27.92 11.45 10.70 19.95 15.43 33.57 26.25 23.27 6.93 17.97 26.96 17.86 18.69
17.68 12.18 11.18 15.94 23.43 31.79 30.83 24.99 0.60 14.78 16.13 13.89 15.35
15.56 10.72 13.07 12.76 20.65 31.46 27.64 19.05 3.15 16.27 14.57 12.83 10.58
d PA d DH DH(B) 2 DH(A).
proton af®nities for xanthine in order to put in a more reliable basis the qualitative results inferred from the AM1 and PM3 calculations. Xanthine may be protonated at different nitrogen atoms or oxygen atom, but experimentally it is not possible to discriminate between the various possibilities. The protonation energetics depend on the chemical surrounding, and so theoretical investigations represent a practicable way for obtaining information about the energetics of proton attachment to the different sites of xanthine and to establish which of these are favoured. The predicted relative proton af®nities are collected in Table 6 for AM1 and PM3 methods in both phases. The relative proton af®nities (d PA), which is the difference between proton af®nities of molecules A and B, can be calculated as
dPA dDH PA B 2 PA A or dPA dDH DH B 2 DH A
Furthermore, comparison of the gas phase equilibrium constants with solution phase values implies that large changes may occur on going from gas phase to solution. This can be explained by solvent effects. Solvent effects have been ascribed to two major components: electrostatic solvent±solute interaction and hydrogen bonding. The hydrogen bonding effects can not be estimated in a quantitative manner from the solvation model, further large-scale calculations. A semiquantitative estimation of the solvation differences can be obtained from COSMO solvation model. The electrostatic solvent±solute effects, however, are readily estimated by the dielectric continuum model [29]. Application of the COSMO solvation model leads to an explanation of the change in order of tautomeric stability on going from gas phase to solution. However, such a treatment lacks explicit consideration of base±water hydrogen bonding effects, tautomeric equilibrium constants predicted in water are considerably less reliable than those predicted in the gas phase.
where DH(B) and DH(A) are the heats of formation values of tautomers A and B taken from Tables 1±4. As we stated before, the two-diketo forms X1,3,7 and X1,3,9 species possess comparable relative energies. This implies that the ®rst protonation of xanthine is imidazole ring, i.e. the N7 (in X1,3,9) and N9 (in X1,3,7). This is in good agreement with 15N, 1H and 13C NMR experimental results in DMSO, which show that xanthine is protonated preferentially at imidazole ring [31,32]. Generally, 1H tautomers are more stable than the corresponding 3H tautomers, the only exception is presented by the dihydroxy tautomers in the gas phase, which implies that the proton at N1 is more acidic than that of N3. Thus, the second protonation site of xanthine is the N1 or N3. Predicted relative proton af®nities show that C2O is more acidic than the C6O, which shows that third protonation site of xanthine is C2O, then C6O. The above proton af®nity order also follows a logical trend in the sense that the endocyclic nitrogens will be protonated ®rst, then the oxygen, which is less basic centre.
3.4. Relative proton af®nities
4. Conclusions
Since protonation of nucleic acid bases plays an important role in many biochemical (i.e. enzymatic reactions, stabilisation of triplex structures) and mutagenic process [30], we have calculated the relative
Several conclusions can be made on the basis of the results of the present theoretical study. 1. The results clearly indicate that xanthine both in
È . Civcir / Journal of Molecular Structure (Theochem) 545 (2001) 7±15 P.U
2. 3.
4. 5. 6.
7.
the gas phase and in aqueous phase exists predominantly in the two diketo forms X1,3,7 and X1,3,9. This result is in agreement with available experimental and theoretical studies. The energy difference between X1,3,7 and X1,3,9 is predicted to be signi®cantly lowered by the polar solvent. The results presented in this paper con®rm our earlier observations about the applicability of the AM1 method for the quantitative prediction of relative stability of nucleic acid bases in solution. AM1 also gives a good representation of the charge distribution in molecules in terms of calculated dipole moments. The inclusion of the solvent reaction ®eld in quantum-chemical theory is obligatory for accurate results in solution. The entropy effect on the Gibbs free energy of xanthine tautomers is very small and there is little signi®cance for the tautomeric equilibria of the base. The enthalpic term is dominant also in the determination of the equilibrium constant. The protonation of xanthine in both phases occurs at the imidazole nitrogens (N7 or N9), then pyrimidine nitrogens (N1 or N3).
Acknowledgements I would like to thank Prof. Knut Faegri and Prof. Einar Uggered for their helpful comments and discussions. References [1] D.T. Hurst, An Introduction to the Chemistry and Biochemistry of Pyrimidines, Purines and Pteridines, Wiley, New York, 1980 (pp. 179±203). [2] E.J. Stiefel, Prog. Inorg. Chem. 23 (1977) 211. [3] R.W. Rundless, J.B. Wyngaarden, G.H. Hitchings, G.B. Elion, H.P. Silberman, Trans. Assoc. Am. Phys. 76 (1963) 126.
15
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