- Email: [email protected]
2 study
Che@cd Physics-27(1978) 389-397.
0 Nor+lolIand
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:
Publishing Company
: WATER ENVIRONMENTAL -. OF 2- AND.4-6XOPYRIDINES; .J.S. KWIATKOWSKI Institute
EFFECT ON TAUTOMERIC EQUILIBRIA A eNDO/
STUDY*
of Physics, Nicholas Copernicus University, 87-IO0 Tomi, Poland
%d B. SZCZODROWSKA Agricultural Academy, 71-424 Szczecin. Poland Received 26 January 1977 Revised manuscript received 20 September
1977
The supermolecule approach is proposed to evaluate the shift of the tautomeric equilibrium of a molecule when going from the vapour phase to water solution. According to the model, a comparison of the stabilization (hydration) energies
of different tautomers of a molecule surrounded by water molecules predicts changes in tautomeric equilibrium upon solvation. An application of the model (within the CNDO/Z method) to 2-and 4-osopyridine shows that the lactam tautomers of the niolecules are more stabilized by water molecules than the corresponding Iactim forms by about 7-8 kcaI/moIe.
1. Introduction The presence of solvent molecules does not only change the physico-chemical properties of the solute molecules in their ground states, but it also shifts the bak of their absorption spectra and changes the stability of conformers as well as the tautomeric equilibrium conditions. Therefore in the last few years there has been observed a development in studies concerning the ways of including the solvent effects (in particular the influence of water) into tbe quantummechanical calculations of molecular properties. The studies on solvent effect within theoretical calculations are carried out, broadly speaking, in two
different kinds of approaches. In the first case, the solvent is treated as a h&mogeneous medium (with a given.dklectric constant E) in which the considered molecule is immersed. In the second approach the solvent effect is.included immediately into calculatiqns by considering a “supermolecule” system, i.e.. a complex consi&ng.of the solutk molecule sur* Based ore a part of the Ph.D. Thesis by B. Szczodrowska, Nicholas Copernicus University, To&
1975.
rounded by one or several solvent molecules. The latter approach has been satisfactorily applied to predict the hydration sites of several biomolecules as well as to explain the change of the conformational properties of biomolecules upon solvation [l] _ The purpose of this paper is an attempt to apply thy super-molecule approach to evaluate the influence of the water environment on the change of the tautomeric equilibrium of a molecule when going from the vapour phase to water solution. The application of the model to the study of the particular case of the lactim-lactam tautomeric equilibrium in oxopyridines, made in this paper, is due to the importance of this kind of tautomerism of nucleic acid bases in biological processes as RNA transcription or DNA replication. It is worth noting that the model proposed here
has been satisfactorily applied in other papers [2,3] to interpret the change of the tautomeric equilibrium observed for the monoanions of uracil upon solvation.
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AT. Kwkzrkowski, B. Szczodrowsk/Watereffect on tautqmericequilibti
2. The solvation effect on tautomeric equilibrium the supermolecule approach In order to interpret the effect of water molecules on the shift of the tautomeric equilibrium. A * B (we consider the solute molecule existing in two forms either A or B), we propose to use the supermolecule approach in two steps. (1) For both types of tautomers we calculate the hy&atiun spheres. Using non-empirical or a defined semi-empirical method we shouId calculate the total energy of the complex of tautomer A (or tautomer B) with one water molecule placed at different positions in the space surrounding the tautomer. For a defined position of the water oxygen the most probable geometricat structure of the supermolecule should be calculated by changing the configuration of the water relative to a tautomer and rotating it around the O-H bonds. Since the water oxygen is placed at both different directions and different distances from the atoms of the tautomer; we are able to determine the hydration sphere for each tautomer as the points of the space revealing the energetically preferred water-tautamer configurations. Each point of the hydration sphere is characterized by the configuration of the water molecule relative to the tautomer and by the value of the stabilization (hydration) energy (the difference between the total energy of the compIex of the tautomer with the water and the total energies of the components of the complex). In the case of the study of the solvent effect on tautomeric equilibrium of planar n-electronic molecules, instead of the whole hydration sphere one can calculate it only in the plane of the tautomers, i.e. one can calculate the hydration surface being a part of the hydration sphere at the points of space lying in the plane of the tautomer, and so we do in the present paper. The calculations, for which the oxygen atom of the water molecule is located out of the plane of the tautomer, can be not carried on because several non-empirical calculations indicate that the interaction energy between water and a molecule for this case is small* [ I] . This of course does not sufficiently justify the use of the hydration surfaces in the plane of the tautomers instead of their hydration spheres. In some cases the differences between the small values of the stabiliza-
tion energies calculated for the.watei molecules fxed out of the plane for both tautomers can be of the same order ofmagnitude as those for-the stabuation energies ckulated in the plane of‘the tautomers. Farticularly, these differences cti be untiegligibh when comparing the hydration in the regions of the space surrounding the proton acceptor centres of both tautomers (e.g. in the case of the lactim-lactam tautomerism: the oxygen of the hydroxyl and carbonyl groups, the pyridinic and pyrrok nitrogens Of the rings). Unfortunately, as far as we are aware, there is no in the literature this type of comparison of hydrations made on an ab initio level (our preliminary calculations on the out-of-plane interactions between water and 4-pyridone [4] are only the first step made in this direction because they were concerned with one type of tautome$. On the other hand, an application of semi-empirical methods to study of the out-of_pIane interactions mentioned above is very questionable. For example, the CNDO/2 method overestimates the energies of these interactions in the case of the complex of 4pyridone f H-JO for about ten times comparing to the corresponding energies from ab initio calculations [4] (some other aspects of the application of the CNDO/2 method to the salvation problem will be discussed later). Because of all these reasons the hydration surface of a tautomer as poitulated here should be rather treated as the first approximation of its hydration sphere. As we are interested in the difference between the hydration energies of both tautomers we can use an additional approximation. There is no need to carry on calculations for the whole hydration surface (in general hydration sphere) for each tautomer - we should make it only in those areas, ivhich show significant qualitative differences for both tautomers. This approximation is obvious, and the examples of the calculations presented here for oxopyridines and some other calculations on hydration of uracti monoanions are goodillustrations justifyingthis approach [2;3]. + The sameconclusionhas been drawn in our very recent ab initio study of p1ana1and nonplanar complexesof the lactam form of rl-oxopyridine(4-pyridone)and water [4]. We found that the in-plane interaction between the waterand 4-pyridonemoleculeswas3-6 times (or even more) strongerthan out-of-planeinteractions @articularlysmall valuesof interaction energieswere for the caseswhen water was placedabove the ring of 4-pyridone).
J.S. Kwridowski,
B. Szczodrowska/Water
(2) For each tautomer we fuc several water molecules at the local energetic minima of hydration spheres (or hydration surfaces) and for each case we calculate the stabilization energy of the tautomer with all water molecules simultaneously. In the calculation of this step we shouId change simultaneously the positions of all water molecules moving them out of the hydration sphere (surface) to find the energetically preferred structure of the firsth@retion shelf for each tautomer. A determination of the exact arrangement of the water molecules in the hydration shell for a molecule is, of course, complicated. But in the study of the polyhydration effect on the tautomeric equilibrium, it seems reasonable to perform the calculation for those parts of the hydration shell of tautomers, for which there are differences in hydration spheres or even only in hydration surfaces in the plane of the tautomers [see step (l)] . For both tautomers, a comparison of the stabillzation energies of the polyhydrated tautomers determines the trend of the influence of the water on the tautomeric equilibrium. Since determination of the exact structure of the first hydration shell (or even of its part) is complicated (particularly on an ab initio level), one can use an approximate hydration shell determined by a set of water molecules placed at the local minima of hydration spheres (or hydration surfaces). In this approximation, the stabilization energies of the poly hydrated tautomers are calculated by the additivity rule taking into account the water-tautomer and water-water interactions. Our recent calculations within the PCILO method for the polyhydrated monoanions of uracil [3] show no significant difference in the evaluation of the polyhydration effect on the tautomeric equilibrium when using either the exact or approximate hydration shells.
3. The results of calctdations and discussion (the case of 2- and 4-oxopyridine) It is well known that 2- and 4-oxopyridine indicate the property of the lactim-Iactam tautomerism, i.e. the lactim forms (1) or (3) exist in tautomeric equilibrium with the corresponding lactam tautomers (2) or (4)
effecton tautomeric equilibria
dW
/ 4
W
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0 K$3=
[4)/[3) -ii
I I .i! (9
having the proton on the ring nitrogen [5,6]. Until very recently, numerous experimental data [5,7] indicated that 2.oxopyridlne in the crystalline state as well as in solution existed predominantly in the lactam forms. However, the tautomeric ratio evaluated from ionization constants [5,8] , Kf-’ = 340-9 10, does not indicate a great predominance of the lactams over the lactims in water solution. Several experimental data show that in some appropriate conditions it is possible to observe the shift of the tautomerlc equilibrium (1) + (2) towards the lactim forms. For instance, very recent 14N NMR studies [9] indicate that the predominance of the lactam forms of 2-oxopyridie over the lactim ones in nonaqueous solution like methanol or acetone is small [K:’ (methanol) = 24, Kt2.l (acetone) = 121. It is also worth to note that the aromatic substitution at carbon of 2-oxopyiidine (particularly at the 6th position) shifts the tautomeric equilibrium (1) * (2) towards the lactim forms [l&l l] _ Some time ago Levln and Radionova [ 123 suggested from the IR measurements that Zoxopyridine in the vapour phase exists as a mixture of comparable amounts of forms (1) and (2). Recent studies of the vapour of the compound by mass spectrometry [13, 141 confirmed this conclusion. Very recent ultraviolet and infrared spectrscopy studies by Beak et al. [lS,l6] have also revealed that the lactim tautomers of 2-oxop ridine are the major forms in the vapour phase [KtJ1* (gas) =0.4-OS] . The difference between the tautomeric ratio in the vapour phase and that in the solution can, of course, be ascribed to the effect of the medium on the equilibrium of the lactim and lactam tautomers of 2oxopyridine. When going from vapour phase to aqueous
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J.S. Kwiatkowski, B..Szczodrowska/Wnter~effect on tautomeric~quilibria
solution the tautomeric ratio changes by about three orders of magnitude, and the stabilization energy of the lactam form upon solvation is higher than that of the Iactim one by about 3.5-U kcal/moIe
El71Analogously to the case of 2-oxopyridine, tautomeric ratio K:3 for Goxopyridine varies with the nature of the solvent from the value of 2200 in aqueous solution [8,16] to the values of 9 and 5 in methanol and acetone, respectively [9]. In the vapour phase the lactim forms (3) predominate over the lactam ones (4) by a factor of more than ten (AT3 < 0.1) 1161. Infrared, ultraviolet and mass spectrometry measurements [13,14,16] confirm the predominance of the lactims (3) over the lactams (4) in the vapour phase. Thus, in the case of 4-oxopyridine, analogously to the case of 2_oxopyridine, a medium changes the lactim-lactam tautomeric equilibrium. Similarly as in the case of 2-oxopyridine [ 171, from the comparison of the tautomeric ratios K:3 (vapour) z 10-t and Kt4s3 (water) z2 X 103 we conclude that the stabilization energy of the Iactam form (4) upon sohation is higher than that of the lactim one (3) by about 5.0-5.5 kcal/mole. In order to interpret the effect of water environment on the change of the tautomeric equilibria (1)+ (2)and (3) * (4), we have used the supermolecule approach as described in section 2. However, we did not calculate the exact structures of the hydration shells for the tautomers [see step (2)], but tentatively we considered approximate hydration shells using the hydration surfaces determined in step (1). The calcuIations have been performed within the framework of the original CND0/2 method [18] _ Concerning the input data, the individual geometries of the 2- and 4-oxopyridine tautomers and water molecute have been kept constant in all calculations of the hydration surfaces. The experimental geometry was used for water. In the case of the oxopyridines in question, the geometries of their la&m forms are not known. The positions of the heavy atoms and those of the hydrogens joined to the carbon of the ring were assumed to be the same as those ln pyridine itself as shown in the study by Bak et al. [19]. The geometry of the external group C-OH (rcO = 1.33 A, ‘OH = 0.86 A) was assumed to be the same as that in an X-ray investigation of the lactim form of 6cNoro-2-oxopyridine 11I] _The X-ray method,
however, gives unrealistic positions for hydrogen at: oms, and the O-H bond lengthused in the-present . work seems to be-too short_(atleast of.about 0,l a).: Therefore, we performed some additional calculations of the part of the hydration.surface for the lactim form of 2.oxopyridine using the bond ledgthroH-= ; 0.96 A. The geometry of the lactam forms of the molecules, were the same as those used in our previousCND0/2 study on tautomerism in monosubstituted pyridines and pyrimidines [20]. The choice of the geometries of the lactim and lactam tautomers of oxopyridines (in general, the geometries of the tautomers A and B of a molecule) deserves some comment. It seems it would be better to perform the geometry optimization for both tautomers ofeachmolecule, and to compare the energies of the tautomers after the optimization procedure_ . It seems also that the estimation of the water environment effects (e.g. the calculation of hydration spheres or surfaces) should be made with the geome-
try optimization for the whole complex (tautomer + HzO) or at least-for optimized geometries of the tautomers. However, for a variety of reasons we did not perform the optimization procedure neither for the geometries of the isolated tautomers nor for their complexes with water. The calculations on an ab initio level with the geometry optimization are, of course, too expensive. On the other hand, semi-empirical methods very often are not successful in the prediction of molecular geometries. For instance, recent CND0/2calculations carried out by Tosato et al. 1211 for the isoIated.2oxopyridine tautomers have shown that we should not expect a reliable prediction of the experimental results for vapour phase by means of the calculated difference of the total energies of both tautomes. Moreover, as it was already stated, we are interested in the prediction of the relative stabilization effects. In our very recent ab initio study on 2- and 4oxopyridine tautomers [41 we evaluated the hydration of distinct tautomers by calculation of the electrostatic component of the interaction energy between water and tautomers using their ab initio wavefunctions. We have shown that even when one uses different geometries of the hydroxyl group for the hCfiIIlS(f~_OH
=1.33&f,,
=0.86h.W,_,, =
1.36 A, ‘OH = 0.96.Q the hydration energies are not changed signiticantiy. The changes of solvation effects
J.S.Kwiatkowski. 8. Szczodrowska/Water effect on tcrutomen’c equilibria
on the tautomeric equilibrium due to the different geometries were of one order of magnitude smaller (= 1 k&/mole) than the changes of the total energy differences (;r: 23 kcal/mole) between the lactim forms having different geometries and the corresponding lactarn forms. The same order of changes due to the differences in geometries is found in the present CNDO/2 study for the 2-oxopyridine tautomers (see below). Therefore, it does not seem necessary to apply the geometry optimization procedure for whole hydrated tautomers (or for isolated tautomers) in the study of the solvent effect on tautomeric equilibrium. At this point it is also worth to underiie the failure of the CND0/2 method with the geometry optimization to predict the hydration sites of the tautomess under study. As we have discussed recently [4] such calculations give not only the overestimated hydration energies for the Ppyridone + Hz0 complex when comparing with the ab initio results (e.g. out-of-plane interactions are overestimated about IS times), but they incorrectly predict nonplanar configurations of the complex to be more stable than the planar ones. It is due to the well known failure of the CND0/2 method in prediction of the stable conformecs found for a number of conjugated molecules [23]. The hydration surfaces for the lactim and lactam tautomers of oxopyridines calculated in the way described in section 2 [step (l)] are shown in figs. 1 and 2. The shapes of hydration surfaces for both
393
tautomets in each case are very similar to each other. In the case of 2.oxopytidine the equilibrium distances between the nitrogen or oxygen atoms of the tautomers and the oxygen of the water molecule placed at positions a,@, 0, @(see fig. 1) are equal to 2.55 8. For the other regions of the hydration surfaces the equilibrium distances are equal to 2.95 A in the case of the lactim tautomer and 2.90 A in the case of the lactam one. As to the shape nsfthe hydration surfaces of 4oxopyridine tautomers, the calculations show that the equilibrium distances between the oxygen atom of the tautomers and’that of the water molecule (fixed e.g. at the positions@,@ for the lactim or@, @ for the lactam, fig. 2) ate also equal to 2.55 A. The equilibrium distances between the oxygen of the water and the nitrogen atoms of the ring of the tautomers ate er:ual to 2.60 A being slightly longer than in the case of hydration surfaces for 2.oxopyidine. For the other regions of the hydration surfaces of the 4oxopyridiie tautomers the equilibrium distances are equal to 2.90-2.95 A as in the case of the 2-0~0 isomer. It may be interesting to compare the hydration of the corresponding lactim and lactam forms for each compound. In the case of the lactam of 2-oxopyridine there exists the most probable hydration site in the region between N-H and C=O groups (-11.5 kcal/ mole). In the corresponding lactim tautomer there exists the energetic minimum (-10.1 k&/mole) in the
-4.9
6 2.7)
(- 7.6)
Fig. 1. Hydration of the 2-oxopyridine tautomersin their planes (hydration surfaces). Stabilization energies in kcal/mole. Water molecule with full and dotted line for O-H bonds indicatesthat the water p1ar.e is perpendicular to the tautomer plane. Hydration energies given in the parentheses have been calculated For the distance of 2.85 A between the water oxygen and the heavy atoms of the tautomers (see text).
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J.S. Kwiatkowski, B. SzczodrowskajWatereffect on tautomeric&uilibria
II.
@-i.8 7,
/\N/
r
-1.8
0
0
I c\H -2’5F
J -8.7
Fig. 2. Hydrationof the Il-oxopyridinetautomersin their planes(hydration surfaces).Stabilizationenergiesin kcal/mole. same region of space, but the arrangement of the water molecule relative to the lactim tautomer is different from that for the lactam one. It is also to underline that in the region of the carbonyl oxygen there is a great region of depth minimum (-10-l 1 kcall mole), while the region in the neighbourhood of the hydroxyl group of the lactim form has a quite different hydration energies. Similar differences in the hydration surfaces are observed for the 4-oxopyridine tautomers. In the case of the lactim form of 2-oxopyridine we have performed additional calculations of the hydration energies using the bond length rOH = 0.96 w (the increase of the OH bond length of the lactim tautomer from 0.86 to 0.96 A increases the difference between the total energies of the lactam and lactim forms by about 30 k&/mole in favour of the latter form). In accordance with expectation the hydration energies are changed significantly only for water placed in the region of hydration surface surrounding the O-H bond. For example, the hydration energies for the water placed at positions @and @ decrease to -12 and -3 k&/mole, respectively, while for waters@ and 0 the energies are decreased by less than about 0.2 kcal/mole. The differences mentioned above have no significant influence on the relative water stabilization effect of 2-oxopyridine tautomers (see below). It would be interesting to compare the calculations presented in figs; 1 and 2 with the results of ab initio calculations to see how both the water-tautomer distances and interaction energies calculated by minimizing the supermolecule total energies are related
within the two schemes. The comparison may be, however, made in a very limited way because of lack of appropriate ab initio results. Our ab initio SCF MO calculation [4] for the planar complex of4-pyridone with the water having one O-H bond lying on the line passing through the N-H and C=O bonds gives the value of -5.33 kcal/ mole at the equilibrium distance between the oxygens R,_, = 2.95 A, while the corresponding value from the CNDO/2 calculation is -10.2 kcal/mole at the equilibrium distance Rg_0 = 2.55 A. Thus in this case the CND0/2 calculation overestimates about twice the in-plane interaction energies, and gives too short equilibrium water-tautomer distance when comparing with ab initio results. This is in accordance with general opinion about the application of the CNDO/2 method to study of the molecular systems interacting through hydrogen bond. For instance, Schuster [24] has suggested that CNDO/Z is an appropriate method for the calculation of such small energy differences, which are necessary to describe hydrogen bonding. However, +I order to calculate the hydrogen bonding energies comparable with experimental values, according to Schuster, one should use the experimentally determined geometry for the complex of a molecule with water, particularly the experimental equilibrium distance between a molecule and water. Otherwise, the CNDO/Z calculations minimizing the total energies of the complex overestimate almost twice the hydrogen bonding energies. Thus, the hydration energies preserited in figs. 1 and 2 seem- to be too high by this factor. Sirice the equilibrium distances between the com-
IS. Kwtitkowski,
B. Szczodrowska/Water
ponents of a hydrated molecule predicted by CNDO/2 supermolecule approach are usually too short by about 0.3 a, we have performed additional calculations for the hydration energies of 2-oxopyridine tautomers maintaining the distance of 2.85 A between the oxygen of water and heavy atoms of the tautomers. The results presented in fig. 1 (the numbers in the. parentheses) show that in this case the hydration energies are significantly lower (particularly in the region of probable hydration sites of the tautomers) than the energies calculated for estimated equilibrium distances, and they are, it is worth to underline, closed to the corresponding electrostatic components of the interaction energies calculated from ab initio wavefunctions of water and tautomers [41Comparing the hydration energies of the tautomers of each compound (figs. 1 and 2) we see that they are quite different from one another only for the surroundings of the ring nitrogen and the exocyclic oxygen. Fixing a few water molecules at the local minima of the hydration surfaces in the region mentioned above one can easily estimate that the lactam tautomers are more stabilized by waters than the corresponding lactim ones. The location of the water molecules on the hydration surfaces should be, however, made with caution, remembering water-water interactions as well as limitations of the method used to describe these interactions. Unfortunately, an ab initio calculation has not been carried out for the co-planar dimers of water so the results of the CND0/2 calculations for these dimers have been tentatively used in order t,o evaluate the contributions of the water-water interactions to stabilization effects of both tautomers. The CND0/2 calculations for the water dimers having different mutual arrangement of the water molecules [2] have shown that the dimerization energy of the water dlmer for the oxygen-oxygen distance of 3.5-4.0 A is about 1.O-2.0 kcal/mole not depending on the mutual arrangement of the water molecules. On the other hand, the interaction energies between the waters having ro_o = 2.5-3.0 A do strongly depend on the mutual arrangement of the molecules. Of course, it must be kept in mind that this statement which is true for CNDO/2 calculations, may become ratherquestionable if one performs an ab initio supermolecule calculation for the water dimer.
effect on tautomnic
equilibTin
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In the case of 2-oxopyridine, fixing two water molecules at positions @ (the most probable hydraiion sites of the tautomers) and @ (fig. 1) we see that the contribution of the water-tautomer interactions to the polyhydration energy is greater for the lactam tautomer than for the lactim one by = 5.7 kcal/mole. Since the contribution of the water @-water @ interactions for both tautomers is of the same order (the distances between the water molecules are z 5 a), two water molecules fixed at positions @and @ stabiiize the lactam tautomer more than the lactim one by = 5.7 kcal/mole. As the region between the nitrogen atom and the neighbouring C-H bond shows difference in the hydration surfaces of both ‘tautomers, we should additionally locate one water molecule in these regions for each case. When the waters are located at positions@, the polyhydration energy of the lactam tautomer is increased to 6.6 kcal/mole relative to that of the lactim one (the contribution of the water @water@ interaction to the pqlyhydration energy in both cases is the same). More precisely, the water molecules located in the regions mentioned above should be rather moved from positions @ towards positions@ or@ in the lactim and lactam forms, respectively. In the case of the Iactim form for instance, the water should not be, however, exactly fied at position @ as indicated in fig. 1. Because of the repulsion between water @ and water 0, the latter one should not only be rotated around its O-H bond changing the hydration energy from the value of -6.9 kcal/ mole to -6.0 kcal/mole, but it should be moved towards position 0. The CND0/2 calculations on the water-water interaction suggest that the additional water molecule should be placed in the region between positions @ and@ at the distance of x 2.85 w from water 0. The same case is for the lactam form of 2.oxopyridine. Although the water-tautomer interaction energy for the water placed at this position is greater for the lactim form by a!>out 1 kcaljmole, the total contribution of this water to the polyhydration energy is greater for the lactam tautomer by about 1.5 kcal/ mole relative to ihe lactim one. It is due to the more favourable mutual arrangement of the water considered and water @ in the case of the lactam form when comparing with the lactim one (in the first case the
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J.S. Kwiatkowski, B. Szczodrowska/Water effect &I tautomer& equiIfb&
.- :
water-water @ interaction energy is greater by about 2.5 k&/mole comparing to the second case). It is interesting that the total re!ative contribution to the stabilization energy of the third water mole-. cuIe placed in the region mentioned above is not changed when moving it from the position 2.85 A distant from water @ towards position @ (the contribution is of the order of 0.9-1.5 kcaI/mole always in favour of the lactam form). Thus, the polyhydration energy of the lactam tautomer with two water molecules fied at positions 0, @ end the third water in the region between the nitrogen atom and the C-H bond is greater by = 7 k&/mole than the corresponding energy of the lactim form with three waters placed in the same positions_ It is to note that because the distances between waters @and @ are of the order of 5 A, an additional water cannot be fixed in these regions of the hydration surfaces. The water-water interaction will fLuthe additional water out of the hydration surface defined above (i.e. the water will be placed in the second hydration shell). Although the contributions to the polyhydration energy of the tautomers due to the second hydration shell are omitted here, it is evident (see fig. 1) that the water molecule from this shell placed in the region considered above will stabilize the lactam form more than the lactim one. It is also to note that three water molecules placed in the regions discussed previously still more stabilize the lactam form than the lactim one when using the hydration surface calculated for the lactim form with rOH = 0.96 A (the relative stabilization effect is slightly reduced to = 5 kcal/mole). Remembering that the hydration energies presented in fig. 1 are overestimated almost twice, the presented evaluation of the water stabilization effects of both tautomers (a 7 kcal/mole) is in a very good agreement with the experimental quantity (3.5-4.0 kcallmole) estimated from the experimental tautomeric ratios in water and vapour phase. It is worth to underline that using the hydration energies calculated for the distance of 2.85 A between the water oxygen and the heavy atoms of the tautomers one obtains more rea-
In the case of 4-oxopyridinedfigXive water molecules at positions-a to @ on &hydration suifaces (fig. 2), considering &water-tautdmer as well as water-water inter&ions, we evaluated-that the lactam tautomer ismore stabilized. by water thanthe lactim one by = 8 kcal/tnole.~The~influence ofthe water molecules placed at the other regions of the hydration surfaces on the stabilization of the tautomers was omitted, because the hydration energies of these waters are the same. As we see, the calculated differences of the stab& zation energies for both tautomers of 2- and 4-0x0pyridines are in a good agreement with the experimental data..Of course,- the comparison should be made with a great caution. Both the quantities, the theoretical and experimental ones, differ in kind. The theoretical quantities have been evaluated on the microscopic level; while the experimental ones are derived from the macroscopic measurements. We should also remember that the model proposed here is a very approximate one, and the CNDO/2 method is limited in prediction of hydration energies. However, the main conclusion of our estimation that the lactam forms of 2- and 4-oxopyridines are stronger stabilized by water environment than the corresponding lactim forms seems to be true. The similar evaluation made very recently by us [22] on the ab initio level gave the same order of the relative stabilization effects (4.5 and 4.1 k&/mole for 2- and 4-oxopyridines, respectively). Thus, although the presented evaluation of the stabilization energies should rather not be used in a quantitative way (because of the numerous uncertainties related to the approximations used in the cab culations such as geometries of the tautomers, the limitation of the solvent effect to the influence of the first hydration shell, the use of the additivity rule for stabilization effects etc.), quantitatively it appears to account correctly for the general nature of the solvent effect on the tautomeric equilibrium of 2- and 4oxopyridines.
sonable values (= 3.5 kcaljmole) of the relative stabi-
Acknowledgement
lization effects. But it is not unexpected when remembering about the relation between CNDO/Z calculations and experimental values of the hydrogen bonding energies (see previous discussion and ref. [24] )_
This work was supported by the Polish Academy of Sciences within the project 09.7.1.
1..
LS. Kwiatkowski,
B. Srczodrowska/Water
References [I] A. Pullman and B. Pullman, Quart. Rev. Biophys. 7 (1975) 505. [2) B. Szczodrowska, Ph.D. Thesis, Nicholas Copernicus University, Toru6, Poland (1975). (Published in Polish as Preprint No. 284 issued by Institute of Physics, N. Copernicus University, Toru6,1975). [3] J.S. Kwiatkowski and B. Pullman, Theoret. Chim. Acta 42 (1976) 83. [4] J.S. Kwiatkowski, D. Pcrahia, A. Pullman and B. Pullmann, submitted for pu_blication. [5] A.R. Katritzky and !.M- Lagowski, Advan. Heterocycl. Chem. 1 (1963) 339. [6] J.S. Kwiatkowski and M. Berndt, in: Synthesis, structure and the properties of the heterocyclic compounds, proceedings of International Conference; Poznafi (Poland), July 24-26,1973 (A. Mickiewicz Univ. Press, PoznaB, 1975) p- 173. [7] R.H. Cox and A.A. Bothner-By, J. Phys. Chem. 73 (1969) 2465, and references therein. [8] A. Albert and J.N. Philips, J. Chem. Sot. (1956) 1294; S.F. Mason, J. Chem. Sot. (1958) 674; A. Albert, in: Physical methods of hererocyclic chemistry, Vol. 1, cd. A.R. Katritzky (Academic Press, New York, 1963) p. 1. [9] L. Stefaniak, Tetrahedron 32 (1976) 1065. [lo] P. Beak, T.S. Woods and D.S. hfueller, Tetrahedron 28 (1972) 5507; S.S.T. King, W.L. Dilling and N.B. Tefertiller, Tetrahedron 28 (1972) 5859; A. Kvick and I. Olovsson, Arkiv. Kemi 30 (1968) 7 1. [ll] 1. Almliiff, A. Kvick and I. Olovsson, Acta Cryst. B27 (1971) 1201. [12] ES. Levin and G.N. Radionova, Dokl. Akad. Nauk SSR 164 (1965) 584; 174 (1967) 1132.
effect on tautonwric equilibria
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1131 T. Grannenberg and K. Undheim, Org. Mass Spectry. 6 (1972) 823. [ 141 A. Maquestiau, Y. van Haverbeke, C. de Meyer, A.R. Katritzky. M.J. Cook and A.D. Page, Can. J. Chem. 53 (1975) 490. [IS] P. Beak and F.S. Fry Jr., J. Am. Chcm. Sot. 95 (1973) 1700. [16] P. Beak, F,S. Fry Jr., J. Lee and F. Steele, J. Am. Chem. Sot. 98 (1976) 111. [17] J.S. Kwiatkowski, Studia Biophysics 46 (1974) 79. [18] J.A. PopIe and D.L. Beveridge, Approximate molecular orbital theory (McGraw-Hill, New York, 1970). [19] B. Bak, L. Hansen-Nygaard and J. RastrupAndcrscn, J. Mol. Spectry. 2 (1958) 136. [20] M. Bemdt, J.S. Kwiatkowski, J. Bud&ski and B. Szczodroivska, Chem. Phys. Letters 19 (1973) 246. [21] M.L. Tosato, M. Cignitti and L. Paoloni. Caz. Chim. ital. 105 (197.5) 335, and unpublished results. 1221 J.S. Kwiatkowski, submitted for publication. [23] 0. Gropen and H.M. Seip, Chem. Phys. Letters lI(1971) 445; D. Pcrahia and A. Pullman, Chcm. Phys. Letters 19 (1973) 73; H.-J. Hoffman, H.-J. Khhler, K. Thieroff and P. Uhlmann, J. Prakt. Cheni. 316 (1974) 659; A. Veillard, Chem. Phys. Letters 33 (1975) 15; C. Sieiro, P. Gonzalez-Diaz and Y.G. Smeyers, J. Mol. Struct. 24 (1975) 345;. T. Weller, D. Kliiper and H.-J. KShlcr, Chem. Phys. Letters 36 (1975) 475. [24] P. Schuster, Int. J. Quantum Chem. 3 (1969) 851; P. Schuster, in: The hydrogen bond - recent developments in theory and experiments, cds. P. Schuster, G. Zundel and C. Sandorfy (North-Holland, Amsterdam, 1976) p. 25.
0 Nor+lolIand
.-
:
Publishing Company
: WATER ENVIRONMENTAL -. OF 2- AND.4-6XOPYRIDINES; .J.S. KWIATKOWSKI Institute
EFFECT ON TAUTOMERIC EQUILIBRIA A eNDO/
STUDY*
of Physics, Nicholas Copernicus University, 87-IO0 Tomi, Poland
%d B. SZCZODROWSKA Agricultural Academy, 71-424 Szczecin. Poland Received 26 January 1977 Revised manuscript received 20 September
1977
The supermolecule approach is proposed to evaluate the shift of the tautomeric equilibrium of a molecule when going from the vapour phase to water solution. According to the model, a comparison of the stabilization (hydration) energies
of different tautomers of a molecule surrounded by water molecules predicts changes in tautomeric equilibrium upon solvation. An application of the model (within the CNDO/Z method) to 2-and 4-osopyridine shows that the lactam tautomers of the niolecules are more stabilized by water molecules than the corresponding Iactim forms by about 7-8 kcaI/moIe.
1. Introduction The presence of solvent molecules does not only change the physico-chemical properties of the solute molecules in their ground states, but it also shifts the bak of their absorption spectra and changes the stability of conformers as well as the tautomeric equilibrium conditions. Therefore in the last few years there has been observed a development in studies concerning the ways of including the solvent effects (in particular the influence of water) into tbe quantummechanical calculations of molecular properties. The studies on solvent effect within theoretical calculations are carried out, broadly speaking, in two
different kinds of approaches. In the first case, the solvent is treated as a h&mogeneous medium (with a given.dklectric constant E) in which the considered molecule is immersed. In the second approach the solvent effect is.included immediately into calculatiqns by considering a “supermolecule” system, i.e.. a complex consi&ng.of the solutk molecule sur* Based ore a part of the Ph.D. Thesis by B. Szczodrowska, Nicholas Copernicus University, To&
1975.
rounded by one or several solvent molecules. The latter approach has been satisfactorily applied to predict the hydration sites of several biomolecules as well as to explain the change of the conformational properties of biomolecules upon solvation [l] _ The purpose of this paper is an attempt to apply thy super-molecule approach to evaluate the influence of the water environment on the change of the tautomeric equilibrium of a molecule when going from the vapour phase to water solution. The application of the model to the study of the particular case of the lactim-lactam tautomeric equilibrium in oxopyridines, made in this paper, is due to the importance of this kind of tautomerism of nucleic acid bases in biological processes as RNA transcription or DNA replication. It is worth noting that the model proposed here
has been satisfactorily applied in other papers [2,3] to interpret the change of the tautomeric equilibrium observed for the monoanions of uracil upon solvation.
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AT. Kwkzrkowski, B. Szczodrowsk/Watereffect on tautqmericequilibti
2. The solvation effect on tautomeric equilibrium the supermolecule approach In order to interpret the effect of water molecules on the shift of the tautomeric equilibrium. A * B (we consider the solute molecule existing in two forms either A or B), we propose to use the supermolecule approach in two steps. (1) For both types of tautomers we calculate the hy&atiun spheres. Using non-empirical or a defined semi-empirical method we shouId calculate the total energy of the complex of tautomer A (or tautomer B) with one water molecule placed at different positions in the space surrounding the tautomer. For a defined position of the water oxygen the most probable geometricat structure of the supermolecule should be calculated by changing the configuration of the water relative to a tautomer and rotating it around the O-H bonds. Since the water oxygen is placed at both different directions and different distances from the atoms of the tautomer; we are able to determine the hydration sphere for each tautomer as the points of the space revealing the energetically preferred water-tautamer configurations. Each point of the hydration sphere is characterized by the configuration of the water molecule relative to the tautomer and by the value of the stabilization (hydration) energy (the difference between the total energy of the compIex of the tautomer with the water and the total energies of the components of the complex). In the case of the study of the solvent effect on tautomeric equilibrium of planar n-electronic molecules, instead of the whole hydration sphere one can calculate it only in the plane of the tautomers, i.e. one can calculate the hydration surface being a part of the hydration sphere at the points of space lying in the plane of the tautomer, and so we do in the present paper. The calculations, for which the oxygen atom of the water molecule is located out of the plane of the tautomer, can be not carried on because several non-empirical calculations indicate that the interaction energy between water and a molecule for this case is small* [ I] . This of course does not sufficiently justify the use of the hydration surfaces in the plane of the tautomers instead of their hydration spheres. In some cases the differences between the small values of the stabiliza-
tion energies calculated for the.watei molecules fxed out of the plane for both tautomers can be of the same order ofmagnitude as those for-the stabuation energies ckulated in the plane of‘the tautomers. Farticularly, these differences cti be untiegligibh when comparing the hydration in the regions of the space surrounding the proton acceptor centres of both tautomers (e.g. in the case of the lactim-lactam tautomerism: the oxygen of the hydroxyl and carbonyl groups, the pyridinic and pyrrok nitrogens Of the rings). Unfortunately, as far as we are aware, there is no in the literature this type of comparison of hydrations made on an ab initio level (our preliminary calculations on the out-of-plane interactions between water and 4-pyridone [4] are only the first step made in this direction because they were concerned with one type of tautome$. On the other hand, an application of semi-empirical methods to study of the out-of_pIane interactions mentioned above is very questionable. For example, the CNDO/2 method overestimates the energies of these interactions in the case of the complex of 4pyridone f H-JO for about ten times comparing to the corresponding energies from ab initio calculations [4] (some other aspects of the application of the CNDO/2 method to the salvation problem will be discussed later). Because of all these reasons the hydration surface of a tautomer as poitulated here should be rather treated as the first approximation of its hydration sphere. As we are interested in the difference between the hydration energies of both tautomers we can use an additional approximation. There is no need to carry on calculations for the whole hydration surface (in general hydration sphere) for each tautomer - we should make it only in those areas, ivhich show significant qualitative differences for both tautomers. This approximation is obvious, and the examples of the calculations presented here for oxopyridines and some other calculations on hydration of uracti monoanions are goodillustrations justifyingthis approach [2;3]. + The sameconclusionhas been drawn in our very recent ab initio study of p1ana1and nonplanar complexesof the lactam form of rl-oxopyridine(4-pyridone)and water [4]. We found that the in-plane interaction between the waterand 4-pyridonemoleculeswas3-6 times (or even more) strongerthan out-of-planeinteractions @articularlysmall valuesof interaction energieswere for the caseswhen water was placedabove the ring of 4-pyridone).
J.S. Kwridowski,
B. Szczodrowska/Water
(2) For each tautomer we fuc several water molecules at the local energetic minima of hydration spheres (or hydration surfaces) and for each case we calculate the stabilization energy of the tautomer with all water molecules simultaneously. In the calculation of this step we shouId change simultaneously the positions of all water molecules moving them out of the hydration sphere (surface) to find the energetically preferred structure of the firsth@retion shelf for each tautomer. A determination of the exact arrangement of the water molecules in the hydration shell for a molecule is, of course, complicated. But in the study of the polyhydration effect on the tautomeric equilibrium, it seems reasonable to perform the calculation for those parts of the hydration shell of tautomers, for which there are differences in hydration spheres or even only in hydration surfaces in the plane of the tautomers [see step (l)] . For both tautomers, a comparison of the stabillzation energies of the polyhydrated tautomers determines the trend of the influence of the water on the tautomeric equilibrium. Since determination of the exact structure of the first hydration shell (or even of its part) is complicated (particularly on an ab initio level), one can use an approximate hydration shell determined by a set of water molecules placed at the local minima of hydration spheres (or hydration surfaces). In this approximation, the stabilization energies of the poly hydrated tautomers are calculated by the additivity rule taking into account the water-tautomer and water-water interactions. Our recent calculations within the PCILO method for the polyhydrated monoanions of uracil [3] show no significant difference in the evaluation of the polyhydration effect on the tautomeric equilibrium when using either the exact or approximate hydration shells.
3. The results of calctdations and discussion (the case of 2- and 4-oxopyridine) It is well known that 2- and 4-oxopyridine indicate the property of the lactim-Iactam tautomerism, i.e. the lactim forms (1) or (3) exist in tautomeric equilibrium with the corresponding lactam tautomers (2) or (4)
effecton tautomeric equilibria
dW
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W
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0 K$3=
[4)/[3) -ii
I I .i! (9
having the proton on the ring nitrogen [5,6]. Until very recently, numerous experimental data [5,7] indicated that 2.oxopyridlne in the crystalline state as well as in solution existed predominantly in the lactam forms. However, the tautomeric ratio evaluated from ionization constants [5,8] , Kf-’ = 340-9 10, does not indicate a great predominance of the lactams over the lactims in water solution. Several experimental data show that in some appropriate conditions it is possible to observe the shift of the tautomerlc equilibrium (1) + (2) towards the lactim forms. For instance, very recent 14N NMR studies [9] indicate that the predominance of the lactam forms of 2-oxopyridie over the lactim ones in nonaqueous solution like methanol or acetone is small [K:’ (methanol) = 24, Kt2.l (acetone) = 121. It is also worth to note that the aromatic substitution at carbon of 2-oxopyiidine (particularly at the 6th position) shifts the tautomeric equilibrium (1) * (2) towards the lactim forms [l&l l] _ Some time ago Levln and Radionova [ 123 suggested from the IR measurements that Zoxopyridine in the vapour phase exists as a mixture of comparable amounts of forms (1) and (2). Recent studies of the vapour of the compound by mass spectrometry [13, 141 confirmed this conclusion. Very recent ultraviolet and infrared spectrscopy studies by Beak et al. [lS,l6] have also revealed that the lactim tautomers of 2-oxop ridine are the major forms in the vapour phase [KtJ1* (gas) =0.4-OS] . The difference between the tautomeric ratio in the vapour phase and that in the solution can, of course, be ascribed to the effect of the medium on the equilibrium of the lactim and lactam tautomers of 2oxopyridine. When going from vapour phase to aqueous
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J.S. Kwiatkowski, B..Szczodrowska/Wnter~effect on tautomeric~quilibria
solution the tautomeric ratio changes by about three orders of magnitude, and the stabilization energy of the lactam form upon solvation is higher than that of the Iactim one by about 3.5-U kcal/moIe
El71Analogously to the case of 2-oxopyridine, tautomeric ratio K:3 for Goxopyridine varies with the nature of the solvent from the value of 2200 in aqueous solution [8,16] to the values of 9 and 5 in methanol and acetone, respectively [9]. In the vapour phase the lactim forms (3) predominate over the lactam ones (4) by a factor of more than ten (AT3 < 0.1) 1161. Infrared, ultraviolet and mass spectrometry measurements [13,14,16] confirm the predominance of the lactims (3) over the lactams (4) in the vapour phase. Thus, in the case of 4-oxopyridine, analogously to the case of 2_oxopyridine, a medium changes the lactim-lactam tautomeric equilibrium. Similarly as in the case of 2-oxopyridine [ 171, from the comparison of the tautomeric ratios K:3 (vapour) z 10-t and Kt4s3 (water) z2 X 103 we conclude that the stabilization energy of the Iactam form (4) upon sohation is higher than that of the lactim one (3) by about 5.0-5.5 kcal/mole. In order to interpret the effect of water environment on the change of the tautomeric equilibria (1)+ (2)and (3) * (4), we have used the supermolecule approach as described in section 2. However, we did not calculate the exact structures of the hydration shells for the tautomers [see step (2)], but tentatively we considered approximate hydration shells using the hydration surfaces determined in step (1). The calcuIations have been performed within the framework of the original CND0/2 method [18] _ Concerning the input data, the individual geometries of the 2- and 4-oxopyridine tautomers and water molecute have been kept constant in all calculations of the hydration surfaces. The experimental geometry was used for water. In the case of the oxopyridines in question, the geometries of their la&m forms are not known. The positions of the heavy atoms and those of the hydrogens joined to the carbon of the ring were assumed to be the same as those ln pyridine itself as shown in the study by Bak et al. [19]. The geometry of the external group C-OH (rcO = 1.33 A, ‘OH = 0.86 A) was assumed to be the same as that in an X-ray investigation of the lactim form of 6cNoro-2-oxopyridine 11I] _The X-ray method,
however, gives unrealistic positions for hydrogen at: oms, and the O-H bond lengthused in the-present . work seems to be-too short_(atleast of.about 0,l a).: Therefore, we performed some additional calculations of the part of the hydration.surface for the lactim form of 2.oxopyridine using the bond ledgthroH-= ; 0.96 A. The geometry of the lactam forms of the molecules, were the same as those used in our previousCND0/2 study on tautomerism in monosubstituted pyridines and pyrimidines [20]. The choice of the geometries of the lactim and lactam tautomers of oxopyridines (in general, the geometries of the tautomers A and B of a molecule) deserves some comment. It seems it would be better to perform the geometry optimization for both tautomers ofeachmolecule, and to compare the energies of the tautomers after the optimization procedure_ . It seems also that the estimation of the water environment effects (e.g. the calculation of hydration spheres or surfaces) should be made with the geome-
try optimization for the whole complex (tautomer + HzO) or at least-for optimized geometries of the tautomers. However, for a variety of reasons we did not perform the optimization procedure neither for the geometries of the isolated tautomers nor for their complexes with water. The calculations on an ab initio level with the geometry optimization are, of course, too expensive. On the other hand, semi-empirical methods very often are not successful in the prediction of molecular geometries. For instance, recent CND0/2calculations carried out by Tosato et al. 1211 for the isoIated.2oxopyridine tautomers have shown that we should not expect a reliable prediction of the experimental results for vapour phase by means of the calculated difference of the total energies of both tautomes. Moreover, as it was already stated, we are interested in the prediction of the relative stabilization effects. In our very recent ab initio study on 2- and 4oxopyridine tautomers [41 we evaluated the hydration of distinct tautomers by calculation of the electrostatic component of the interaction energy between water and tautomers using their ab initio wavefunctions. We have shown that even when one uses different geometries of the hydroxyl group for the hCfiIIlS(f~_OH
=1.33&f,,
=0.86h.W,_,, =
1.36 A, ‘OH = 0.96.Q the hydration energies are not changed signiticantiy. The changes of solvation effects
J.S.Kwiatkowski. 8. Szczodrowska/Water effect on tcrutomen’c equilibria
on the tautomeric equilibrium due to the different geometries were of one order of magnitude smaller (= 1 k&/mole) than the changes of the total energy differences (;r: 23 kcal/mole) between the lactim forms having different geometries and the corresponding lactarn forms. The same order of changes due to the differences in geometries is found in the present CNDO/2 study for the 2-oxopyridine tautomers (see below). Therefore, it does not seem necessary to apply the geometry optimization procedure for whole hydrated tautomers (or for isolated tautomers) in the study of the solvent effect on tautomeric equilibrium. At this point it is also worth to underiie the failure of the CND0/2 method with the geometry optimization to predict the hydration sites of the tautomess under study. As we have discussed recently [4] such calculations give not only the overestimated hydration energies for the Ppyridone + Hz0 complex when comparing with the ab initio results (e.g. out-of-plane interactions are overestimated about IS times), but they incorrectly predict nonplanar configurations of the complex to be more stable than the planar ones. It is due to the well known failure of the CND0/2 method in prediction of the stable conformecs found for a number of conjugated molecules [23]. The hydration surfaces for the lactim and lactam tautomers of oxopyridines calculated in the way described in section 2 [step (l)] are shown in figs. 1 and 2. The shapes of hydration surfaces for both
393
tautomets in each case are very similar to each other. In the case of 2.oxopytidine the equilibrium distances between the nitrogen or oxygen atoms of the tautomers and the oxygen of the water molecule placed at positions a,@, 0, @(see fig. 1) are equal to 2.55 8. For the other regions of the hydration surfaces the equilibrium distances are equal to 2.95 A in the case of the lactim tautomer and 2.90 A in the case of the lactam one. As to the shape nsfthe hydration surfaces of 4oxopyridine tautomers, the calculations show that the equilibrium distances between the oxygen atom of the tautomers and’that of the water molecule (fixed e.g. at the positions@,@ for the lactim or@, @ for the lactam, fig. 2) ate also equal to 2.55 A. The equilibrium distances between the oxygen of the water and the nitrogen atoms of the ring of the tautomers ate er:ual to 2.60 A being slightly longer than in the case of hydration surfaces for 2.oxopyidine. For the other regions of the hydration surfaces of the 4oxopyridiie tautomers the equilibrium distances are equal to 2.90-2.95 A as in the case of the 2-0~0 isomer. It may be interesting to compare the hydration of the corresponding lactim and lactam forms for each compound. In the case of the lactam of 2-oxopyridine there exists the most probable hydration site in the region between N-H and C=O groups (-11.5 kcal/ mole). In the corresponding lactim tautomer there exists the energetic minimum (-10.1 k&/mole) in the
-4.9
6 2.7)
(- 7.6)
Fig. 1. Hydration of the 2-oxopyridine tautomersin their planes (hydration surfaces). Stabilization energies in kcal/mole. Water molecule with full and dotted line for O-H bonds indicatesthat the water p1ar.e is perpendicular to the tautomer plane. Hydration energies given in the parentheses have been calculated For the distance of 2.85 A between the water oxygen and the heavy atoms of the tautomers (see text).
394
J.S. Kwiatkowski, B. SzczodrowskajWatereffect on tautomeric&uilibria
II.
@-i.8 7,
/\N/
r
-1.8
0
0
I c\H -2’5F
J -8.7
Fig. 2. Hydrationof the Il-oxopyridinetautomersin their planes(hydration surfaces).Stabilizationenergiesin kcal/mole. same region of space, but the arrangement of the water molecule relative to the lactim tautomer is different from that for the lactam one. It is also to underline that in the region of the carbonyl oxygen there is a great region of depth minimum (-10-l 1 kcall mole), while the region in the neighbourhood of the hydroxyl group of the lactim form has a quite different hydration energies. Similar differences in the hydration surfaces are observed for the 4-oxopyridine tautomers. In the case of the lactim form of 2-oxopyridine we have performed additional calculations of the hydration energies using the bond length rOH = 0.96 w (the increase of the OH bond length of the lactim tautomer from 0.86 to 0.96 A increases the difference between the total energies of the lactam and lactim forms by about 30 k&/mole in favour of the latter form). In accordance with expectation the hydration energies are changed significantly only for water placed in the region of hydration surface surrounding the O-H bond. For example, the hydration energies for the water placed at positions @and @ decrease to -12 and -3 k&/mole, respectively, while for waters@ and 0 the energies are decreased by less than about 0.2 kcal/mole. The differences mentioned above have no significant influence on the relative water stabilization effect of 2-oxopyridine tautomers (see below). It would be interesting to compare the calculations presented in figs; 1 and 2 with the results of ab initio calculations to see how both the water-tautomer distances and interaction energies calculated by minimizing the supermolecule total energies are related
within the two schemes. The comparison may be, however, made in a very limited way because of lack of appropriate ab initio results. Our ab initio SCF MO calculation [4] for the planar complex of4-pyridone with the water having one O-H bond lying on the line passing through the N-H and C=O bonds gives the value of -5.33 kcal/ mole at the equilibrium distance between the oxygens R,_, = 2.95 A, while the corresponding value from the CNDO/2 calculation is -10.2 kcal/mole at the equilibrium distance Rg_0 = 2.55 A. Thus in this case the CND0/2 calculation overestimates about twice the in-plane interaction energies, and gives too short equilibrium water-tautomer distance when comparing with ab initio results. This is in accordance with general opinion about the application of the CNDO/2 method to study of the molecular systems interacting through hydrogen bond. For instance, Schuster [24] has suggested that CNDO/Z is an appropriate method for the calculation of such small energy differences, which are necessary to describe hydrogen bonding. However, +I order to calculate the hydrogen bonding energies comparable with experimental values, according to Schuster, one should use the experimentally determined geometry for the complex of a molecule with water, particularly the experimental equilibrium distance between a molecule and water. Otherwise, the CNDO/Z calculations minimizing the total energies of the complex overestimate almost twice the hydrogen bonding energies. Thus, the hydration energies preserited in figs. 1 and 2 seem- to be too high by this factor. Sirice the equilibrium distances between the com-
IS. Kwtitkowski,
B. Szczodrowska/Water
ponents of a hydrated molecule predicted by CNDO/2 supermolecule approach are usually too short by about 0.3 a, we have performed additional calculations for the hydration energies of 2-oxopyridine tautomers maintaining the distance of 2.85 A between the oxygen of water and heavy atoms of the tautomers. The results presented in fig. 1 (the numbers in the. parentheses) show that in this case the hydration energies are significantly lower (particularly in the region of probable hydration sites of the tautomers) than the energies calculated for estimated equilibrium distances, and they are, it is worth to underline, closed to the corresponding electrostatic components of the interaction energies calculated from ab initio wavefunctions of water and tautomers [41Comparing the hydration energies of the tautomers of each compound (figs. 1 and 2) we see that they are quite different from one another only for the surroundings of the ring nitrogen and the exocyclic oxygen. Fixing a few water molecules at the local minima of the hydration surfaces in the region mentioned above one can easily estimate that the lactam tautomers are more stabilized by waters than the corresponding lactim ones. The location of the water molecules on the hydration surfaces should be, however, made with caution, remembering water-water interactions as well as limitations of the method used to describe these interactions. Unfortunately, an ab initio calculation has not been carried out for the co-planar dimers of water so the results of the CND0/2 calculations for these dimers have been tentatively used in order t,o evaluate the contributions of the water-water interactions to stabilization effects of both tautomers. The CND0/2 calculations for the water dimers having different mutual arrangement of the water molecules [2] have shown that the dimerization energy of the water dlmer for the oxygen-oxygen distance of 3.5-4.0 A is about 1.O-2.0 kcal/mole not depending on the mutual arrangement of the water molecules. On the other hand, the interaction energies between the waters having ro_o = 2.5-3.0 A do strongly depend on the mutual arrangement of the molecules. Of course, it must be kept in mind that this statement which is true for CNDO/2 calculations, may become ratherquestionable if one performs an ab initio supermolecule calculation for the water dimer.
effect on tautomnic
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In the case of 2-oxopyridine, fixing two water molecules at positions @ (the most probable hydraiion sites of the tautomers) and @ (fig. 1) we see that the contribution of the water-tautomer interactions to the polyhydration energy is greater for the lactam tautomer than for the lactim one by = 5.7 kcal/mole. Since the contribution of the water @-water @ interactions for both tautomers is of the same order (the distances between the water molecules are z 5 a), two water molecules fixed at positions @and @ stabiiize the lactam tautomer more than the lactim one by = 5.7 kcal/mole. As the region between the nitrogen atom and the neighbouring C-H bond shows difference in the hydration surfaces of both ‘tautomers, we should additionally locate one water molecule in these regions for each case. When the waters are located at positions@, the polyhydration energy of the lactam tautomer is increased to 6.6 kcal/mole relative to that of the lactim one (the contribution of the water @water@ interaction to the pqlyhydration energy in both cases is the same). More precisely, the water molecules located in the regions mentioned above should be rather moved from positions @ towards positions@ or@ in the lactim and lactam forms, respectively. In the case of the Iactim form for instance, the water should not be, however, exactly fied at position @ as indicated in fig. 1. Because of the repulsion between water @ and water 0, the latter one should not only be rotated around its O-H bond changing the hydration energy from the value of -6.9 kcal/ mole to -6.0 kcal/mole, but it should be moved towards position 0. The CND0/2 calculations on the water-water interaction suggest that the additional water molecule should be placed in the region between positions @ and@ at the distance of x 2.85 w from water 0. The same case is for the lactam form of 2.oxopyridine. Although the water-tautomer interaction energy for the water placed at this position is greater for the lactim form by a!>out 1 kcaljmole, the total contribution of this water to the polyhydration energy is greater for the lactam tautomer by about 1.5 kcal/ mole relative to ihe lactim one. It is due to the more favourable mutual arrangement of the water considered and water @ in the case of the lactam form when comparing with the lactim one (in the first case the
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J.S. Kwiatkowski, B. Szczodrowska/Water effect &I tautomer& equiIfb&
.- :
water-water @ interaction energy is greater by about 2.5 k&/mole comparing to the second case). It is interesting that the total re!ative contribution to the stabilization energy of the third water mole-. cuIe placed in the region mentioned above is not changed when moving it from the position 2.85 A distant from water @ towards position @ (the contribution is of the order of 0.9-1.5 kcaI/mole always in favour of the lactam form). Thus, the polyhydration energy of the lactam tautomer with two water molecules fied at positions 0, @ end the third water in the region between the nitrogen atom and the C-H bond is greater by = 7 k&/mole than the corresponding energy of the lactim form with three waters placed in the same positions_ It is to note that because the distances between waters @and @ are of the order of 5 A, an additional water cannot be fixed in these regions of the hydration surfaces. The water-water interaction will fLuthe additional water out of the hydration surface defined above (i.e. the water will be placed in the second hydration shell). Although the contributions to the polyhydration energy of the tautomers due to the second hydration shell are omitted here, it is evident (see fig. 1) that the water molecule from this shell placed in the region considered above will stabilize the lactam form more than the lactim one. It is also to note that three water molecules placed in the regions discussed previously still more stabilize the lactam form than the lactim one when using the hydration surface calculated for the lactim form with rOH = 0.96 A (the relative stabilization effect is slightly reduced to = 5 kcal/mole). Remembering that the hydration energies presented in fig. 1 are overestimated almost twice, the presented evaluation of the water stabilization effects of both tautomers (a 7 kcal/mole) is in a very good agreement with the experimental quantity (3.5-4.0 kcallmole) estimated from the experimental tautomeric ratios in water and vapour phase. It is worth to underline that using the hydration energies calculated for the distance of 2.85 A between the water oxygen and the heavy atoms of the tautomers one obtains more rea-
In the case of 4-oxopyridinedfigXive water molecules at positions-a to @ on &hydration suifaces (fig. 2), considering &water-tautdmer as well as water-water inter&ions, we evaluated-that the lactam tautomer ismore stabilized. by water thanthe lactim one by = 8 kcal/tnole.~The~influence ofthe water molecules placed at the other regions of the hydration surfaces on the stabilization of the tautomers was omitted, because the hydration energies of these waters are the same. As we see, the calculated differences of the stab& zation energies for both tautomers of 2- and 4-0x0pyridines are in a good agreement with the experimental data..Of course,- the comparison should be made with a great caution. Both the quantities, the theoretical and experimental ones, differ in kind. The theoretical quantities have been evaluated on the microscopic level; while the experimental ones are derived from the macroscopic measurements. We should also remember that the model proposed here is a very approximate one, and the CNDO/2 method is limited in prediction of hydration energies. However, the main conclusion of our estimation that the lactam forms of 2- and 4-oxopyridines are stronger stabilized by water environment than the corresponding lactim forms seems to be true. The similar evaluation made very recently by us [22] on the ab initio level gave the same order of the relative stabilization effects (4.5 and 4.1 k&/mole for 2- and 4-oxopyridines, respectively). Thus, although the presented evaluation of the stabilization energies should rather not be used in a quantitative way (because of the numerous uncertainties related to the approximations used in the cab culations such as geometries of the tautomers, the limitation of the solvent effect to the influence of the first hydration shell, the use of the additivity rule for stabilization effects etc.), quantitatively it appears to account correctly for the general nature of the solvent effect on the tautomeric equilibrium of 2- and 4oxopyridines.
sonable values (= 3.5 kcaljmole) of the relative stabi-
Acknowledgement
lization effects. But it is not unexpected when remembering about the relation between CNDO/Z calculations and experimental values of the hydrogen bonding energies (see previous discussion and ref. [24] )_
This work was supported by the Polish Academy of Sciences within the project 09.7.1.
1..
LS. Kwiatkowski,
B. Srczodrowska/Water
References [I] A. Pullman and B. Pullman, Quart. Rev. Biophys. 7 (1975) 505. [2) B. Szczodrowska, Ph.D. Thesis, Nicholas Copernicus University, Toru6, Poland (1975). (Published in Polish as Preprint No. 284 issued by Institute of Physics, N. Copernicus University, Toru6,1975). [3] J.S. Kwiatkowski and B. Pullman, Theoret. Chim. Acta 42 (1976) 83. [4] J.S. Kwiatkowski, D. Pcrahia, A. Pullman and B. Pullmann, submitted for pu_blication. [5] A.R. Katritzky and !.M- Lagowski, Advan. Heterocycl. Chem. 1 (1963) 339. [6] J.S. Kwiatkowski and M. Berndt, in: Synthesis, structure and the properties of the heterocyclic compounds, proceedings of International Conference; Poznafi (Poland), July 24-26,1973 (A. Mickiewicz Univ. Press, PoznaB, 1975) p- 173. [7] R.H. Cox and A.A. Bothner-By, J. Phys. Chem. 73 (1969) 2465, and references therein. [8] A. Albert and J.N. Philips, J. Chem. Sot. (1956) 1294; S.F. Mason, J. Chem. Sot. (1958) 674; A. Albert, in: Physical methods of hererocyclic chemistry, Vol. 1, cd. A.R. Katritzky (Academic Press, New York, 1963) p. 1. [9] L. Stefaniak, Tetrahedron 32 (1976) 1065. [lo] P. Beak, T.S. Woods and D.S. hfueller, Tetrahedron 28 (1972) 5507; S.S.T. King, W.L. Dilling and N.B. Tefertiller, Tetrahedron 28 (1972) 5859; A. Kvick and I. Olovsson, Arkiv. Kemi 30 (1968) 7 1. [ll] 1. Almliiff, A. Kvick and I. Olovsson, Acta Cryst. B27 (1971) 1201. [12] ES. Levin and G.N. Radionova, Dokl. Akad. Nauk SSR 164 (1965) 584; 174 (1967) 1132.
effect on tautonwric equilibria
397
1131 T. Grannenberg and K. Undheim, Org. Mass Spectry. 6 (1972) 823. [ 141 A. Maquestiau, Y. van Haverbeke, C. de Meyer, A.R. Katritzky. M.J. Cook and A.D. Page, Can. J. Chem. 53 (1975) 490. [IS] P. Beak and F.S. Fry Jr., J. Am. Chcm. Sot. 95 (1973) 1700. [16] P. Beak, F,S. Fry Jr., J. Lee and F. Steele, J. Am. Chem. Sot. 98 (1976) 111. [17] J.S. Kwiatkowski, Studia Biophysics 46 (1974) 79. [18] J.A. PopIe and D.L. Beveridge, Approximate molecular orbital theory (McGraw-Hill, New York, 1970). [19] B. Bak, L. Hansen-Nygaard and J. RastrupAndcrscn, J. Mol. Spectry. 2 (1958) 136. [20] M. Bemdt, J.S. Kwiatkowski, J. Bud&ski and B. Szczodroivska, Chem. Phys. Letters 19 (1973) 246. [21] M.L. Tosato, M. Cignitti and L. Paoloni. Caz. Chim. ital. 105 (197.5) 335, and unpublished results. 1221 J.S. Kwiatkowski, submitted for publication. [23] 0. Gropen and H.M. Seip, Chem. Phys. Letters lI(1971) 445; D. Pcrahia and A. Pullman, Chcm. Phys. Letters 19 (1973) 73; H.-J. Hoffman, H.-J. Khhler, K. Thieroff and P. Uhlmann, J. Prakt. Cheni. 316 (1974) 659; A. Veillard, Chem. Phys. Letters 33 (1975) 15; C. Sieiro, P. Gonzalez-Diaz and Y.G. Smeyers, J. Mol. Struct. 24 (1975) 345;. T. Weller, D. Kliiper and H.-J. KShlcr, Chem. Phys. Letters 36 (1975) 475. [24] P. Schuster, Int. J. Quantum Chem. 3 (1969) 851; P. Schuster, in: The hydrogen bond - recent developments in theory and experiments, cds. P. Schuster, G. Zundel and C. Sandorfy (North-Holland, Amsterdam, 1976) p. 25.