Density Functional Study of Intrinsic and Environmental Effects in the

J. Phys. Chem. 1995,99, 15062-15068

15062

Density Functional Study of Intrinsic and Environmental Effects in the Tautomeric Equilibrium of 2-Pyridone Vincenzo Barone” Dipartimento di Chimica, Universitd di Napoli “Federico II”, via Mezzocannone 4,I-80134Napoli, Italy

Carlo Adamo Dipartimento di Chimica, Universith della Basilicata, via N. Sauro 85, I-85100Potenza, Italy Received: May 22, 1995;In Final Form: July 17, 1995@

The mechanism of oxo/hydroxy tautomerization in 2-pyridone has been investigated by means of a selfconsistent density functionMartree-Fock (HF) hybrid method with particular attention to the role of solvent effects. The computed structural parameters, reaction heats, and energy barriers are in good agreement with the values obtained from post-HF models. Specific interactions with a single water molecule strongly enhance the reaction rate and shift the equilibrium toward the lactam form, while the effect of bulk solvent is comparatively negligible. Zero point and entropy effects do not modify the above general trends. The interaction between both tautomeric forms and a water molecule has been analyzed by means of the so called natural bond orbital approach.

1. Introduction The protomeric tautomerism in the system 2-pyridone/2hydroxypyridine (2Py/2Hy) has been extensively studied since it can be considered as a model of similar equilibria occurring in a wide range of heterocyclic molecules, many of which are of biological importance. From an experimental point of view,‘-{’ this system is one of the few where the energy difference between the tautomeric forms is sufficiently small that both species are observed in the gas phase8 and in inert matrices6 A great variety of experimental measurements (including UV and IR spectroscopy,2X-ray and UV photoelectron spectroscopy? and IR spectroscopy in inert gas matrices6%“) indicates that the free energy difference between the hydroxy (2Hy) and the oxo (2Py) forms is 1-2 kcaVmol in favor of the first tautomer. Polar solvents shift the tautomeric equilibrium toward 2Py, which, in water, becomes more stable than 2Hy by about 1 k c a l / m ~ l . ~ %This ~ - ” behavior has been interpreted in terms of the larger dipole moment of the oxo form and, in protic solvent, of its ability to form stronger H-bonds with one or more solvent molecules.I2 This last point was investigated by Held and Pratt,I3 who analyzed in detail the rotationally resolved S 1 SOfluorescence excitation spectra of the monoand disolvated water complexes of 2Py. This investigation provides an estimation of the intermolecular geometrical parameters for the 2Py-H20 adduct and some evidence of the geometrical rearrangment of 24, upon complexation with one or two water molecules. This large amount of experimental work has caused a contemporary bloom of theoretical analyses, focused both on the thermochemistry and on the mechanism of tautomerizat i ~ n . ’ ~ -These ~ * investigations have underlined how solutesolvent interactions not only determine the relative stability of the two tautomeric forms but can also influence the interconversion m e c h a n i ~ m . ’ ~ , As ~ * ,a~ ~matter of fact amphiprotic solvents, like water, can act as bifunctional catalysts; Le., they can accept a proton from the donor site of the solute molecule and transfer a different proton to the acceptor site on the solute. The overall result is a strong reduction of the activation energy of the tautomeric reaction.I2.l6

-

@

Abstract published in Advance ACS Absrracts, September 15, 1995.

0022-365419512099-15062$09.0010

From a methodological point of view, it is well-known that electron correlation plays a non-negligible role in determining the relative stabilities of the two tautomeric forms and the activation energy governing proton transfer. This is even more important for the weak H-bond interactions between solute and solvent molecules. In particular, it has been found that low-order Moller-Plesset perturbation theory, the most popular method to include correlation energy, does not predict the appropriate endothemicity for the oxohydroxy interconversion, and more sophisticated post-Hartree-Fock (HF) methods are needed to achieve good agreement with experimental data.33.34 In this scenario the use of a computational approach resting on the density functional (DF) theory can be considered as a valid altemative to more conventional methods. These protocols are, today, routinely and successfully applied to predict geometrical and thermochemical properties of organic systems, and their ability to model various classes of reactions is being ~ o n f m e d . In ~ ~particular . ~ ~ a growing interest has been devoted to the application of DF methods to the study of intra- and intermolecular H-bonded complexes and of the associated proton transfer (PT) reaction^.^'-^^ Conventional DF approaches, especially in the generalized gradient version (GGA), describe with some accuracy the structures of the energy minima and the formation enthalpies of these complexes. On the other hand, several a ~ t h o r s ~ ’have - ~ ~ stressed that these methods provide too low activation energies for PT reactions. Following these lines, we have recently applied a selfconsistent hybrid (SCH) approach, which includes density gradient corrections and some Hartree-Fock (HF) exchange, to the study of the physicochemical properties of some small H-bonded c o m p l e ~ e s .We ~ ~ have ~ ~ ~ found that a particular implementation (hereafter referred to as B3LYP)43*44 corrects some of the faults of standard DF methods and gives promising results also in the evaluation of potential energy profiles goveming FT.39,41 So we thought it interesting to extend our investigationto H-bonded complexes and PT reactions involving biologically significant systems. As a first step in this direction, we studied the most stable conformers of gaseous g l y ~ i n e . 4 ~ 3 ~ ~ On this difficult playground, we found that the B3LYP approach outperforms all the current DF protocols in the evaluation of 0 1995 American Chemical Society

Tautomeric Equilibrium of 2-Pyridone

J. Phys. Chem., Vol. 99,No. 41, I995 15063 density functional. The B3LYP variant is obtained using the Becke gradient correction to exchange,52and the Lee-YangParr ( L W ) correlation functional.53 Since the LYP functional contains both a local part and a gradient correction, only the latter contribution should be used to obtain a coherent implementation. It is, however, expedient to use the approximation

c6

AEc %

- EZWN

A number of test^^^,^ showed that values of the three semiempirical coefficients appearing in eq 1 near 0.80 provide the best results, irrespective of the particular form of the different functionals. We will use here the values = 8.0, ax = 0.72, and ac = 0.81 determined by Becke from a best fitting of the Figure 1. Atom numbering and schematic drawings of direct and heats of formation of a standard set of molecule^.^' assisted mechanisms for proton transfer in 2-pyridone. On the basis of previous e x p e r i e n ~ e and ~ ~ ,of ~ some tests with large grids, the standard fine grid54 in Gaussian 92" the relative stabilities of the different conformers, providing has been selected for all DF calculations. This grid was results close to the most sophisticated (but much more expenproduced from a basic grid having 75 radial shells and 302 sive) post-HF methods. To gain further insight in the application angular points per radial shell for each atom and by reducing of the SCH approach to the analysis of the FT mechanism in the number of angular points for different ranges of radial shells, biological systems, we have studied the PT ruled 2Hy/2Py leaving about 7000 points per atom while retaining an accuracy interconversion, both in the gas phase and in aqueous solution. similar to the original (75 302) grid. This system has been chosen because, together with its intrinsic Two different basis sets have been used in the computations. interest discussed above, it is one of the most used models for The first is the standard and well tested 6-31G(d,p) basis set tautomerism in nucleic acid bases. Furthermore, lactam-lactim (hereafter referred to as SVP),55whereas the second is a full tautomeric equilibria are great challenges for conventional DFT triple-f basis set with a double set of polarization functions methods: in the particular case of 2-pyridone, although the (hereafter referred to as TZ2P), already tested for DF computaabsolute errors (- 1.1 and - 1.2 kcaymol) are relatively small, tion~.~~ both local and gradient-correctedcalculations predict incorrectly that 2Py should be more stable than 2Hy in the gas p h a ~ e . ~ ~ . ~ The ~ effect of nonspecific solute-solvent interactions was taken into account via the SCRF m ~ d e l . ~ 'In. ~this ~ model, the The influence of water on the kinetics and the thermodynamcharge distribution of the solute (modeled by a dipole excluding ics of the tautomerization reactions was taken into account at the solvent from a suitable spherical region) induces a polarizatwo different levels: the molecule directly involved in the PT tion in the dielectric mimicking the solvent, so that a reaction mechanism was explicitly included in the computations,whereas field is generated, which acts in turn on the solute. The process the remaining part of the solvent was modeled as a polarizable is iterated until the charge density and the reaction field become continuum, using the simple self-consistent reaction field mutually consistent. The solvation energy computed in this way (SCRF) a p p r ~ a c h . ~Since ~ . ~a~carbonyl group may be involved corresponds to the electrostatic contribution, which plays a in further hydrogen bonds with water, some test computations dominant role in tautomerization reactions. Behind its simplichave been performed for selected adducts containing two water ity, the SCRF model presents several advantages. From a molecules. technical point of view, the reaction field can be considered as a perturbation of the Hamiltonian of the isolated molecule, 2. Method allowing, thus, an easy implementationin the SCF scheme which The calculations reported here are based on the Kohn-Sham preserves all the standard SCF facilities, such as analytical first (KS) approach to the density functional theory as implemented and second derivative^.^^ Moreover, it has been found57that in the Gaussian 92DFT package.49 Among the characteristics this simple model can reproduce correctly solute-solvent of this code are the use of Gaussian basis functions, the interactions for rigid molecules bearing large dipole moments avoidance of auxiliary functions, the implementation of large (like those reported here), whereas it fails when the dipole grids, and the availability of analytical first and second moment is small and higher multipole moments dominate the derivatives. solute-solvent interactions. The only adjustable parameter in In hybrid m e t h o d ~ ~the ~ ,exchange-correlation ~' energy (EX,) the SCRF model is the radius of the spherical cavity embedding is represented by the following general equation: the solute. Here the radius has been computed scaling the 0.001 au electron density surface by 1.33 to obtain an estimate of E,, = a & y f (1 - a,)EY f axAEx 44- achEc molecular volume and next augmenting the radius of the isovolumetric sphere by 0.5 A, to account for the nearest (1) approach of solvent molecule^.^^ It has been found that this where E!EG is the density functional for the exchange energy method provides a better estimate of uo than the approach based is the corresponding corof the uniform electron gas, on the experimental molar volume. The radii obtained by this procedure are 3.80, 4.10, and 4.33 8, for 2Py, 2Py(HzO), and relation contribution, E F is the Hartree-Fock exchange, and 2Py(H20)2, respectively, and do not change for the correspondthe AE terms are the GGA contributions to exchange and ing saddle points or hydroxy tautomeric forms. correlation. Geometry optimizations were carried out with the SVP basis A hybrid method is further qualified as self-consistent when set for all the stationary points characterizing direct intramogradient corrections and HF exchange are not simply computed lecular and water assisted tautomerizations of 2Py in the gas using a converged LSD wave function (or, more traditionally, phase. All the structures were characterized by computing LSD and GGA contributions added to a converged HF wave harmonic frequencies, which are used also to compute zero point function), but the SCF process is performed with the complete

eG

EF

Barone and Adamo

15064 J. Phys. Chem., Vol. 99, No. 41, 1995

TABLE 1: Bond Lengths (A) and Valence Angles (deg) of the Stationary Points Characterizing Tautomerization of 2-Pyridone 2PY SP 2HY HF B3LYPDZ HF MP2" B3LYPlDZ HF MP2" B3LYPDZ exptb 1.331 1.366 1.311 1.331 1.352 1.404 1.414 1.401 1-c2 1.390 1.353 1.289 1.358 1.385 1.229 1.234 1.227 1.236 c2-03 1.221 1.404 1.413 1.390 1.399 1.396 1.449 1.453 1.444 c2-c4 1.452 1.387 1.387 1.375 1.386 1.370 1.367 1.366 1.334 c4-c6 1.340 1.401 1.412 1.391 1.398 1.405 1.422 1.428 1.421 c6-cS 1.436 1.391 1.387 1.372 1.388 1.370 1.363 1.364 1.371 CS-ClO 1.338 2.239 2.327 2.234 1.286 1.305 1.011 1.013 NI-HIZ 1.om 0.970 1.371 0.967 0.969 1.357 2.440 2.441 Hi2-03 2.439 117.3 118.3 103.8 105.3 120.4 119.9 121.3 NI-C~-O~, 120.6 124.1 124.3 123.1 119.8 120.0 112.6 112.8 112.7 NI-C~-C~ 123.3 117.4 117.6 117.6 116.8 116.7 122.1 121.7 122.3 c2-c4-c6 121.8 119.6 119.3 119.9 122.2 121.2 121.5 122.2 122.1 c4-c6-c8 121.3 117.5 119.2 123.7 123.4 125.3 125.6 124.9 C2-Nl-Clo 173.0 174.8 159.8 161.7 120.2 120.5 HIZ-NI-CIO 120.1 (I

Reference 19. Reference 62.

TABLE 2: Relevant Bond Lengths (A) and Valence Angles (deg) of the Stationary Points Characterizing Tautomerization of the 2-Pyridone Complex with One Water Moleculd atoms N1-G cz-03

Ni-His HIS-013 NI-013 O3-Hl2 03-013

0n-H~ oi3-H~

NI -C2-03 H12-013-Hi5 013-HIZ-03 Hn-013-Hi4

2pv 1.401 1.244 1.030 1.872 2.190 1.816 2.725 0.986 0.965 120.2 79.2 151.8 104.7

SP 1.371 1.292 1.272 1.235 2.423 1.226 2.396 1.212 0.967 118.2 82.8 157.9 108.7

2Hv 1.342 1.337 1.908 0.986 2.764 0.993 2.700 1.741 0.966 119.1 81.0 161.1 110.0

All of the results have been obtained at the B3LYP/SVP level. The computed OH bond length and HOH valence angle in H20 are 0.965 8, and 103.83", respectively. (I

energies (ZPEs). The effect of bulk solvent on 2Hy/2Py tautomerization was computed without reoptimizing the above geometries. For purposes of reference all the molecules and the adducts with one water molecule have been optimized at the Hartree-Fock level, employing the same SVP basis set. Using these geometries, single point computations have been carried out by second-order many-body perturbation theory employing the Moller-Plesset partitioning of the electronic Hamiltonian (MP2).59 Hydrogen bond features were analyzed in terms of the natural bond orbital (NBO)

3. Results and Discussion 3.1. Geometrical Parameters. The optimized geometries of 2Py and 2Hy and of the corresponding first-order saddle point (SP) are collected in Table 1. For purposes of comparison, also HF and the available MP2 geometries are reported. For 2Py the crystal structural data62are also included. Since intramolecular angles and distances of the water complexes are essentially the same as in the bare molecules, only some of them are shown in Table 2, together with the intermolecular waterpyridone geometrical parameters. In a recent paper,I0 Nimlos et al. have suggested that a nonplanar structure of 2Py could explain the presence of two different bands in the time-of-flight mass spectroscopic and dispersed emission spectra. This hypothesis was not confmed by a subsequent microwave study.8 Furthermore semiempiri-

call2 and ab i n i t i ~ ' ~ , ' *calculations , ~ ~ ~ * ~ indicate that the planar structures of 2Py and 2Hy tautomers correspond to true energy minima, and inclusion of correlation energy at the MP2 level does not change this c o n c l ~ s i o n .On ~ ~ this line, our B3LYP computations do not give any indication of nonplanarity for either of the two tautomers. With regard to the bare molecules there is an overall good agreement between the geometrical parameters computed by MF'2 and B3LYP methods, also regarding H-bond geometrical features, while there are sensible differences with the HF results on ring parameters. As expected, all the bond lengths sensibly change as the tautomerization proceeds. In particular in 2Py the N1 -C2 bond length is reduced from 1.414 to 1.331 A, while the C2-03 distance increases from 1.227 to 1.353 A, in going from 2Py to 2HY. The corresponding bond lengths in the SP are, of course, intermediate, being 1.366 and 1.289 A, for the CN and CO distances, respectively. This is consistent with the breaking of the CO double bond and the corresponding formation of the n CN bond. From an electronic point of view, tl-+ rearrangement involves, from one side, the u backbone with the N I - H ~bonding ~ orbital, its corresponding u* orbital and the 0 lone pair n and, from the other side, the NCO ~d orbital network, which includes the n bonding and n* antibonding orbitals (involving N and C) and nonbonding n orbitals (localized on N). Similar behavior is preserved in the adduct with one water molecule, even if there is a slight variation of some geometrical parameters, due to the intermolecular H-bond formation. So, in agreement with e~periment,'~ complexation with one water molecule induces sensible changes in some intramolecular geometrical parameters of 2Py. Changes in the pyridone geometry include a small increase of 0.03 and 0.02 A in the N-H and C=O distances and a small variation of 0.4" in the NCO angle. In 2Hy, the OH bond length increases, with respect to the corresponding value in the bare molecule, by 0.02 A, whereas the NCO angle decreases by 1.8'. Of course, significant changes are also found in the water molecule. For instance, in the 2Py(H20) complex, there are increases of 11.3' in the H-0-H angle of the water and of 0.02 8, in the hydrogenbonded OH bond. This lengthening of the OH bond is not unexpected and is related to the well-known shift of the OH stretching frequency toward lower values, associated with hydrogen b ~ n d i n g . ~On ' the other hand, the 013-Hld bond length retains the same value as that in the free water molecule, the Hi4 atom being only tilted out of the molecular plane in order to allow better interaction between one of the lone pairs of the oxygen atom and the NH antibonding orbital. The experimental study of ref 13 indicates that the hydrogen is not

Tautomeric Equilibrium of 2-Pyridone

J. Phys. Chem., Vol. 99, No. 41, I995 15065

TABLE 3: Computed Rotational Constants (MHz) for 2-Pyridone and Its Complex with a Water Molecule €3 3LYPISVP

2PY 2HY 2Py-H20

experimental"

A

B

C

A

B

C

5647 5820 3941

2775 2762 1427

1860 1873

5644 5825

1051

3997

2794 2768 1394

1869 1876 1035

Reference 13. in the plane of the aromatic ring but it tilted about 37", which corresponds to a C-0-0-H dihedral angle of 143". The B3LYP result is 149'. Special attention must be devoted to the intermolecular parameters, since some recent ~ t u d i e s on ~ ~small . ~ ~ H-bonded systems have shown that standard DF approaches, overestimating H-bond interactions, predict too short distances between donor and acceptor atoms involved in the H-bonding and too long X-H bond lengths. Our results show that the B3LYP model gives results in good agreement with the available MP2 data3' and the experimental indication^.'^ For instance, the B3LYP 0 3 - 0 1 3 distance for 2Py-H20 is 2.73 A,close to the MP2 result (2.75 A) and to the experimental estimate (2.77 A), while the NI-013 bond length is slightly shorter than both MP2 (2.79 vs 2.84 A, for B3LYP and MP2, respectively) and experimental (2.86 8)data. Neither MP2 nor experimental data are available for the 2Hy-H20 adduct, so a direct comparison with our results is not possible. The overall quality of the B3LYP geometrical parameters is further confirmed by a comparison between the computed and experimental rotationals constant^*^^^ of 2 4 , 2Hy, and 2PyH2O (see Table 3). The mean deviation for the rotational constants of 2Py predicted at the B3LYP level (10, MHz) is lower than that obtained at the MP2 level (20 M H z ) . ~ ~In particular the largest difference between the computed and experimental values (*l%) is found for the B constant of 2Py. The same trends are observed in 2Hy and in 2Py-H20. In Table 4 are collected the harmonic frequencies in wavenumbers for all the considered molecules. It is well-known that MP2 values can be considered as reference marks in the evaluation of vibrational frequencies. This statement is confirmed, for the bare 2Py and 2Hy molecules, by the good agreement between the MP2/SVP results and the experimental spectra.6 So, it is gratifying that the B3LYP vibrational IR spectra are only a few cm-' different from those computed at the MP2 level. Since the detailed analysis carried out by Kwiatkowski and L e s ~ c y n s k for i ~ ~their MP2 computations is applicable also to our B3LYP results, we only note that, as aforementioned, the geometrical rearrangement observed upon complexation is reflected in a red shift of the vibrational frequencies connected with the bonds involved in the H-bridge formation. So, in 2Py, the NH stretching frequency goes from 3608 cm-I in the bare molecule to 3291 cm-l in the adduct with one water molecule, while in 2Hy the OH stretching changes from 3772 to 3285 cm-I, upon complexation. 3.2. Relative Stability of the Tautomeric Forms and PT Energetics. The thermochemistry of direct and water assisted tautomerization is summarized in Table 5 . We start the discussion from the relative stability of the two bare tautomers, which has been long debated in past years, also from a theoretical point of view. From a methodologicalpoint of view, it is now well e ~ t a b l i s h e d ' ~that . ~ ~electronic .~~ correlation plays a significant role in determining the relative stability of the two tautomeric forms. Several papers have been devoted to analyzing this point,'8s19,29,30 showing also how the results are very sensitive to the employed model. In fact, the theoretical

predictions of the exothermicityfor the 2Py/2Hy tautomerization are widespread, ranging between 0.9 kcal/mol (at the QCISD(T)/DZP levelIg) and 0.01 kcdmol (at the MP4/SVP This latter result is particularly convincing since, contrary to all the other computations which employ geometries optimized at the HF level, energy evaluations have been performed using MP2/SVP geometries, which are much closer to experimental data (see Table 1). Anyway all the employed post-HF methods indicate that 2Hy is the most stable tautomer in the gas phase, in agreement with experimental findings. Very recently, it has been f o ~ n d that ~ ~ standard , ~ ~ DF calculations, even gradient corrected, fail to properly treat the 2Py/2Hy equilibrium. As a matter of fact, all the DF calculations predict incorrectly that in the gas phase 2Py is more stable than 2Hy by about 1.0 kcal/mol. Our B3LYP results represent a significant improvement since the hydroxy form is now marginally more stable than the oxo one (see Table 5). It must be also noted that the MP2/SVP model sensibly overestimates the stability of 2Py, which is predicted to be more stable than 2Hy by 2.2 kcal/mol. The situation is more involved for the activation energy, for which only a few data are available in the literature. The only available post-HF data are those of Field and Hillier (obtained at the CISD/3-21G level, using HF/3-21G geometries),I6 which give an energy barrier of 44.9 kcal/mol. On the other hand, our B3LYP/SVP activation energy (35.3 kcal/mol) is very close to the MP2 result obtained with the same basis sets (35.0 kcal/mol). The extended basis set, TZ2P, stabilizing sensibly 2Py with respect to both 2Hy and SP, induces an increase of both endothemicity and activation energy (-0.1 and 37.4 kcaymol, respectively). Going to the adducts with one water molecule, we find that both 2Py-H20 and the corresponding SP are stabilized by H-bond interactions. At the B3LYP/SVP level 2Py-H20 is predicted to be more stable than 2Hy-H20 by about 1 kcal/ mol, and the energy barrier is reduced to about one-third of the previous value (12.5 kcdmol). Although the absolute value of the B3LYP energy difference between 2Hy and 2Py isomers is lower than that obtained in previous CISD computationsI6 (3.1 kcal/mol), the effect of the water molecule in displacing the tautomeric equilibrium is essentially the same (1 kcal/mol) at the MP2, CISD, and B3LYP levels. Also the activation energy computed at the B3LYP/SVP level (12.5 kcaymol) is close to the ME/SVP (13.3 kcal/mol) and CISD/3-21G (13.4 kcal/mol) values. Extension of the basis set slightly modifies the relative energies and the energy barriers, while the ZPE has no sensible effect on the thermodynamics of the process. In the same Table 5 are reported the solvation contributions (evaluated either at the HF or B3LYP level) to the endothermicities and to the activation energies. Inclusion of nonspecific solute-solvent interactions enhances the effect of the first solvent molecule. More precisely, bulk solvent, stabilizing the molecule with the higher dipole moment (3.65 and 2.59 D for 2Py and 2Hy, respectively, at the B3LYP/SVP level), increases the energy difference between the oxo and the hydroxy forms. It is noteworthy that these interactions influence also the PT energy barrier, but the effect is larger for the direct process (1.O kcal/mol) than for the assisted one (0.4 kcaymol). Also the magnitude of the solvent effect is very similar at the HF and B3LYP levels. Continuum solvent models cannot, of course, describe the specific effects of hydrogen bonding. In the present context this means that we need to consider at least a further explicit water molecule interacting with the CO group of the aromatic ring. This has been investigated by optimizing the intermolecular parameters for the 2Py-HzO adduct and for the

15066 J. Phys. Chem., Vol. 99, No. 41, 1995

Barone and Adamo

TABLE 4: B3LW/SVP Harmonic Frequencies (cm-l) of the Stationary Points Characterizing Direct and Water Assisted Tautomerization of 2-Pyridone 3608,3242,3231,3216,3185, 1793, 1679, 1596, 1502, 1459, 1388, in-p 1ane 24r 1246, 1224, 1168, 1113, 1024,997,823,617,547,453 out-of-plane 1007,937,857,770,737,698488,389, 178 SP in-plane 3241,3235,3213,3192,2142, 1690, 1605, 1561, 1496, 1420, 1341, 1280, 1179, 1144, 1044, 1015,900,674,608,496,1837i out-of-plane 1126,999,957,853,164,729,487,412, 192 3772,3238,3220,3194,3174, 1666, 1642, 1527, 1503, 1379, 1347, in-plane 2HY 1332,1213, 1171, 1114, 1068, 1007,867,640,568,423 out-of-plane 997,974,879,791,755,577,509,424,219 3865,3465,3291,3242,3234,3216,3190, 1761, 1688, 1673, 1601, 2Py-H2O 1522, 1484, 1405, 1283, 1245, 1174, 1133, 1034, 1009, 1001,983,929, 861,859,840,172,737,626,558,519,487,420,400,330,206, 189, 171,75 3835,3234,3230,3197,3191, 1962, 1709, 1684, 1592, 1567,1515, SP-HzO 1503, 1432, 1410, 1338, 1318, 1287, 1179, 1147, 1055, 1010, 1004,957,870, 869,783,750,722,649,605,581,548,514,474,415,337,211, 108, I524i 3859,3485,3285,3230,3222,3195,3176, 1684, 1671, 1638, 1538, 1529, 1447, 2Hy-HzO 1368, 1330, 1285, 1174, 1126, 1068, 1012,1001,969,925,877,871,830,791, 752,646,576,536,485,433,382,352,216,214,174,72 TABLE 5: Reaction Energies (hE) and Activation Energies (A@) for the Tautomerization of 2-Pyridone in the Gas Phase and Solvation Contributions in Aqueous Solutiona gas-phase energies solvation contributions HFtSVP MP2tSVP B3LYPtSVPb B3LYPRZ2P AZPEb HFtSVP B3LYPtSVPb -0.1 -0.1 2.7 2.5 -0.03 AEintra -1.6 -2.2 37.4 -3.1 0.8 1.o 49.5 35.0 35.3 APmtra 1.4 -0.1 0.8 1.0 (1.2) 0.8 (3.3) 0.1 -1.3 AEmer APmter 28.0 13.3 12.5 (13.5) 14.6 -3.8 0.4 0.4 (1.O) ~~

All of the values are in kilocalories per mole, and negative values of AE indicate that 2-hydroxypyridineis more stable than 2-pyridone. The values in parentheses have been obtained using the adducts with two water molecules (see Figure 2). (i

Figure 2. Structures of the adducts with two water molecules corresponding to energy minima and the first-order saddle point for assisted proton transfer in 2-pyridone. corresponding saddle point and hydroxy tautomer. The resulting structures (see Figure 2) indicate that, as expected, the CO group of the aromatic ring is involved in a second hydrogen bond. Furthermore the second water molecule adopts an orientation (the 03-H17-0,6-H18 dihedral angle is about 90') which maximizes the interaction between one of the oxygen lone pairs and one hydrogen atom of the ring. The effect of the second water molecule on the thermodynamics and kinetics of tautomerization is quite significant. In particular the energy barrier is increased by about 1 kcdmol, and the oxo form is further stabilized by about 2.5 kcdmol. Further inclusion of nonspecific solvent effects increases the energy barrier by 1 kcaYmo1 and the reaction energy by 1.2 kcaYmol (see Table 5). It is particularly noteworthy that the overall (supermolecule f continuum) stabilization of the oxo form by water (4.6 kcaY mol) is very near those obtained from molecular dynamics simulations (5.2 kcaYmo1)64and from experimental estimates (4.8kcal/m01).~~ The general picture emerging from the above computations is in nice agreement with experimental evidence in suggesting

that the hydroxy form is more stable in the gas phase and the equilibrium is shifted toward the oxo form in polar, especially protic, solvents. Furthermore, the significance of an assisted PT mechanism is confirmed by the finding of quite low activation energies (13- 15 kcaYmo1). An efficient assisted PT can operate, however, only if the adducts 2Py-H20 or 2HyHzO have a sufficient lifetime in aqueous solution. Although a complete assessment of this point would require dynamic simulations, a strong indication in this sense is provided by a comparison between the complexation energies and the corresponding dimerization energy of H20 (see next section). 3.3. Analysis of the Interactions with Water. The significant effects induced by specific interactions with one water molecule on the thermodynamics and kinetics of tautomerization prompted us to investigate in deeper detail the origin of this behavior. In Table 6 are reported the binding energies for the adducts of 2Py and 2Hy with one water molecule. The binding energy is 14.8 kcaYmol for 2Py and 14.0 kcaYmo1 for 2Hy at the B3LYPlSVP level, while the corresponding values obtained with the TZ2P basis set are 12.1

J. Phys. Chem., Vol. 99, No. 41, 1995 15067

Tautomeric Equilibrium of 2-Pyridone TABLE 6: Computed Binding Energies for the 2Py-H20 and 2Hy-H20 Complexes" B3LYPlSVP B3LYPRZ2P Dea

D,'

DdC

D,'

Dea

Dlb

24r-Hz0 14.83 11.92 9.18 11.94 12.08 11.12 13.98 11.39 8.74 12.67 10.84 10.08 2Hy-Hz0 Binding energy. Binding energy including BSSE correction. Binding energy including BSSE and ZPE corrections. Binding energy including solvent effects. TABLE 7: NBO Energy Analysis of the 2-Pyridine-Water Interactions at the B3LYP/SVP Levela AECT

2Py-Hz0 2Hy-Hz0

-42.06 -50.10

24r-H20 2Hy-HzO

-42.60 -50.43

AENCT AEA-w

Gas Phase -19.88 27.23 36.12 -17.22 Solution -20.37 30.70 37.76 -17.55

AEw-A

Aqb

-16.31 -24.89

-0.006 0.015

-15.88 -24.84

-0.012 0.012

" All of the energies are in kilocalories per mole. Charge transferred from the ring to the water molecule in 1e-l. and 10.8 kcaYmo1, respectively. Since variational evaluations of small binding energies can be seriously affected by the basis set superpositionerror (BSSE), the counterpoise method of Boys and B e m ~ d was i ~ ~used to correct the above values. The correction for BSSE decreases the binding energies of 2pYH20 and 2Hy-H20 to 11.9 and 11.4 kcdmol, respectively, with the smaller basis set and to 11.1 and 10.1 kcaYmo1 with the larger set, leading to similar results for the interaction energies. A further reduction of the interaction energy is obtained if ZPEs are also included, the final value being 9.2 kcaYmol for 2Py-H20 and 8.7 kcal/mol for 2Hy-H20. So the B3LYP approach indicates that in the gas phase 2pY interacts more strongly than 2Hy with a single water molecule. On the contrary, nonspecific solvent effects favor the H20-2Hy interaction with respect to the H20-2Py one. In fact the corresponding binding energies are 12.7 kcaYmo1 for 2HyH20 and 11.9 kcal/mol for 2Py-H20. We note incidentally that the dimerization energy of water computed at the same level is about 6 kcdmol. This gives further support to the hypothesis made in the preceding section that the pyridone-water adducts have a sufficiently long life time to allow water-assisted proton transfer. A detailed analysis of the binding energies can be done in the framework of the NBO mode1.60.6' In this approach, the binding energy of two fragments (here heteroaromatic ring and water molecule) can be decomposed into a charge transfer (CT) and a no-CT (NCT) contribution. The CT energy term essentially represents the energy related to the electron transfer from one of the lone pairs of the electron donor atom to the antibonding B* empty orbital of the X-H bond and is evaluated by deleting matrix elements connecting the manifold of filled orbitals of one partner to the unfilled orbitals of the other and noting the change in the total energy. The NCT term is due to exclusion repulsion and electrostatic (induction and polarization) interactions and is obtained as the difference between AE and UCT.

As a first point, we note that HF and B3LYP methods lead to very similar trends in the NBO analysis, so that only the latter results are presented in Table 7. In both complexes the largest contribution comes from the CT term, which, in tum, is lower in the oxo than in the hydroxy tautomer (42.1 vs 50.1 kcdmol for 2Py and 2Hy, respectively). This trend is, however, more than counterbalanced by the NCT term, which, although smaller in absolute value (27.2 kcdmol in 2Py and 36.1 kcaV

mol in 2Hy), determines the overall larger stability of the 2PyH20 complex. Concerning the CT term, a second-order perturbative analysis revealed only two strong intermolecular stabilizing interactions, AEA-w and AEw-A, respectively, connected to n B* charge transfer from and to the aromatic ring. These two interactions are, at this level of perturbation theory, responsible for about 85% of AEcT. The relative weight of the two mechanisms (n u* from ring to water and n B* from water to ring) in the overall CT process depends on the energy differences between the donor and acceptor orbitals. The first interaction is larger in 2Py than in 2Hy (19.9 vs 17.2 kcdmol), since the oxygen lone pairs are closer in energy to the antibonding orbital of the OH bond in water than to the lone pair of the nitrogen atom. On the contrary, the CT process from water to ring is more significant in 2Hy (16.3 and 24.9 kcaYmol in 2Py and 2Hy, respectively), since the lone pair of the water oxygen is energetically nearer to the OH antibonding orbital than to the NH antibonding orbital. The extent of CT is well evidenced by the total charge on the two fragments. So the charge on water has a very small negative value in 2Py-H20 (-0.0061el) but increases to 0.0151el in 2Hy-H20, in agreement with a significant CT from water to 2Hy. The NBO analysis also allows one to interpret the variation of the binding energies on going from vacuum to solution. In fact, nonspecific solutesolvent interactions sensibly increase the energies associated with the charge transfer process, AEcT, being now 42.6 and 50.4 kcaYmol for 2Py-H20 and 2Hy-H20, respectively. This trend can be explained by taking into account that the field by the bulk solvent stabilizes, albeit by different amounts, the orbitals of both 2pY and 2Hy with respect to those of the water molecule. In fact in both complexes the perturbation energies associated with the A W process increase, whereas those connected to the W A process decrease. Anyway, the energy gained through CT is lost by NCT terms, especially with regard to the oxo complex. The net result is a sensible decrease of the dissociation energies in both adducts, with a larger reduction in 2Py-H20.

-

-

-

- -.

4. Conclusion We have performed a comprehensive study of intrinsic and solvent effects on the kinetics and thermodynamics of direct and solvent assisted proton transfer in 2Py. On the one hand, both specific and nonspecific solute-solvent interactions influence the thermodynamics of the reaction, but for different reasons. Bulk solvent stabilizes the molecule with the higher dipole moment (Le., 2Py), whereas the specific interaction with a water molecule stabilizes 2Py, due to its ability to give, in the gas phase, stronger H bonds. These results are consistent with the experimental findings, which indicate that 2Py is the most stable tautomer in polar solvents. On the other hand, nonspecific solvent effects are nearly identical for the oxo form and the saddle point structure, so that the activation barrier to proton transfer is reduced only by the catalytic effect of a water molecule. From a methological point of view, we have found that selfconsistent hybrid approaches correct several faults of conventional density functional methods and give results close to the most sophisticated post-Hartree-Fock models. What is even more promising is that all the general trends affected by correlation effects are correctly reproduced. Since only Hartree-Fock computations were previously feasible for large biomolecules, this opens the route to much more reliable information in the field of chemical reactivity in biological systems.

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