Theoretical Models for Quantitative Description of the AcidâBase

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Theoretical Models for Quantitative Description of the Acid-Base Equilibria of the 5,6-Substituted Uracils Margarita G. Ilyina, Edward M. Khamitov, Sergey Petrovich Ivanov, Akhat G. Mustafin, and Sergey L. Khursan J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b09330 • Publication Date (Web): 07 Dec 2017 Downloaded from http://pubs.acs.org on December 8, 2017

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The Journal of Physical Chemistry

Theoretical Models for Quantitative Description of the Acid-Base Equilibria of the 5,6Substituted Uracils Margarita G. Ilyina a, c, Edward M. Khamitov a, b, c, Sergey P. Ivanov b, Akhat G. Mustafin a, b, and Sergey L. Khursan b, * a

Bashkir State University Chemical Faculty, Department of Physical Chemistry and Chemical Ecology, 32 Zaki Validi Str., Ufa 450074, Russia

b

Ufa Institute of Chemistry, Russian Academy of Sciences, Laboratory of Chemical Physics, 69 Prospekt Oktyabrya, Ufa 450054, Russia c

Institute of Petroleum Refining and Petrochemistry, Laboratory of quantum chemistry and

molecular dynamics of the Department of Chemistry and Technology, 12 Initsiativnaya Str., Ufa 450065, Republic of Bashkortostan, Russia e-mail: [email protected]

*

Corresponding author. Present address: Ufa Institute of Chemistry, Russian Academy of Sciences, 71 Prospekt Oktyabrya, Ufa 450054, Russia.

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Abstract The acidities of 18 5,6-substituted uracils have been numerically estimated as pKa values in terms of three theoretical models. The first scheme includes the calculation of the gas-phase acidity of uracil with the G3MP2B3 method and taking into account the solvent effect using the polarizable continuum approximation PCM(SMD)-TPSS/aug-cc-pVTZ. The second model is one-step and implies calculating of the free Gibbs energies of the hydrate complex of uracil (and its anion) with 5 water molecules by the TPSS/aug-cc-pVTZ method. This model accounts the solvent effect corresponding to both specific and nonspecific solvation. The third scheme required high time and computational resources and includes the strong features of the two previous schemes. Here, the theoretical estimation of pKa is performed by the CBS-QB3 composite method. As in the second approach, both specific (as pentahydrate) and nonspecific solvent effects are accounted. We have analyzed the advantages and model restrictions of the considered schemes for the pKa calculations. All models have the systematic errors, which have been corrected with the linear empirical regression relations. Herewith, the absolute mean deviations of the pKa values of uracils dissociating via the N1-H bonds diminish to 0.25, 0.28 and 0.23 pKa units (respectively, for I, II, and III models) that corresponds to ~0.3 kcal/mol on the energy scale. The applicability of our computational schemes to uracils dissociating via N3-H, O-H (orotic acids) and C-H bonds is discussed.


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1. Introduction As known, 5- and 6-substituted uracils (Figure 1) are the biologically important pyrimidines. Uracil and thymine (5-methyluracil) enter the set of five bases of nucleic acids. Due to the high biological significance of pyrimidine derivatives in general and uracils in particular, the formation of the labile intermediates for their neutral molecules (e.g., under the radiation damage to DNA and RNA) were investigated. The properties of the radical particles generated from uracil and its derivatives1-4 and their further chemical fate were studied.5-7 The cationic intermediates (the ionized forms of uracils) were also considered.2, 3, 8-11.

Figure 1. The set of uracils used in this study.

5,6-Substituted uracils are weak dibasic acids dissociating via N–H bonds (Figure 1). It is noteworthy that both N-H bonds (N1–H, in position 1 of the pyrimidinedione, and N3–H, in position 3) usually reveal similar acidic properties depending on the structure of the uracil and the solvent. This fact creates significant obstacles for understanding the chemical properties of uracils because the alternative anionic states with different structure and reactivity coexist. The situation is even more complicated if the R5 and/or R6 substituents are prone to undergo the dissociation too. Previously,12 the relative stability of the N1 и N3 anionic states of diverse uracil derivatives were studied but the data obtained seem insufficient to rationalize the relations between the uracil structures and their acid-base properties. Dissociation of the uracils via the N-H bonds is a key factor that define their reactivity. This is very important for biological systems and the synthetic strategies for producing uracil derivatives. Thus, 6-methyluracil is known as an antiulcer pharmaceutical, also applied to 3 ACS Paragon Plus Environment


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treatment of hepatitis and pancreatitis.13 5-Halogenouracils have antiviral and antitumor activities.14 Acidity is numerically estimated as pKa values and defines in what form uracil and its derivatives are presented under certain conditions. Currently, the experimental pKa values of uracils

(See

Supplementary

spectrophotometric16,

22-28

Material)

have

been

obtained

with

potentiometric,15-21

and argentometric titration.29 A good agreement is observed for the

results obtained by different techniques (with rare exceptions). However, the experimental pKa values of uracils provide no information about the structures of their ionized forms. Such information may be obtained with the quantum chemical calculations. The identification of the most stable deprotonated states of uracils in aqueous solutions and, consequently, theoretical assessing the pKa values is a nontrivial task for computational chemistry. This becomes more evident due to the fact that the “chemical accuracy” of usual thermochemical estimates, equal to 1 kcal/mol, correspond to the error of 0.74 pKa units. Such an error is unacceptably high as compared with the experimental measurements. The solvent effect in this case is the main source of the error of the calculations. For example, the calculations of free Gibbs energy of hydration of monovalent ions have the mean absolute deviation of 4 kcal/mol.30,

31

The errors arise due to the model restrictions within the dielectric continuum

models.32-34 Generally, these errors may be minimized using the hybrid schemes of cluster continuum,35-39 in which the dissolved substance and the first solvate shell are explicitly described whereas the remaining solvent is simulated in terms of the aforementioned dielectric continuum. The performance of the cluster continuum schemes strongly depends on the choice of the method describing the electronic structure, the solvation model and other factors. The pKa values have been measured for a wide list of uracils16, 18, 21-26, 28, 40-45 and diverse schemes for their theoretical predictions have been proposed.46-57 The diversity of the models is primarily caused by the recent advances in computational methods of quantum chemistry that lead to the opportunity of more accurate pKa assessment. An interest in accurate prediction of the pKa values of uracil and its derivatives remains. Thedeveloped models should take into account the presence of several deprotonation sites in the molecule and possible tautomeric interconversions. In the present work, we compare three approaches to the theoretical pKa estimates. The first computational scheme is based on the high-level G3MP2B3 calculations of the gas-phase acidities of uracils with the DFT-calculated correction to solvent effect. Thus, this scheme does not explicitly account the solvent. The second approach implies the DFT simulation on the first solvate shell of uracil made up with 5 water molecules with the applied polarizable continuum 4 ACS Paragon Plus Environment

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model. The third approach is based on the explicit solvate model of uracil as the pentahydrate cluster calculated with the CBS-QB3 composite method. We should mention the features of the present work that make it different from the previous studies. First, it is a diversity of the studied compounds: the list includes 19 uracils with different substituents. Second, we take into account possibility of the uracil deprotonation via N-H, O-H and C-H bonds according to the structure and tautomeric transitions. Third, the pentahydrate shell is used. This model required for the description of the specific solvation has been justified and analyzed in details in previous work.58 2. Computational details The DFT and ab initio calculations were performed using the program package Gaussian09 Revision D59 and the cluster supercomputer of the Institute of Petroleum Refining and Petrochemistry. The visualization of the results was made in the VMD program.60 The wave functions of the molecules and ions were studied in terms of the restricted Hartree–Fock or Kohn–Sham methods (the wave functions of the closed electron shells). All calculations correspond to the standard conditions (298.15 K, 1 atm). All the presented structures correspond to minima on the potential energy surface as it was evidenced by the absence of imaginary vibrational frequencies in the Hessian calculation. 2.1 Method I. Estimation of pKa in terms of the G3MP2B3 + DFT approximation with indirect taking into account the solvent effect For the theoretical estimation of pKa, the following thermodynamic cycle is introduced (Figure 2).34, 46, 48, 50, 61-65

Figure 2. Thermodynamic cycle for calculation of pKa.

In Figure 2, ∆G°deprot, g and ∆G°deprot, aq are the standard free energies of deprotonation in gas and condensed phases, respectively; ∆G°solv, HU, ∆G°solv, U- and ∆G°solv, H+ are standard free 5 ACS Paragon Plus Environment


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energies of solvation of uracil, its anion and Н+, respectively. The pKa constant is calculated according to the equation: pKa = ∆G°deprot,aq/2.303RT

(1)

∆G°deprot,aq = ∆G°deprot,g + {∆G°solv, U- +∆G°solv, H+ + ∆G°solv, HU}

(2)

∆G°deprot,g = ∆G°g, U- - ∆G°g, HU

(3)

where

The standards free Gibbs energies of each molecules and anions (G°g, HU and G°g, U-) are obtained according to the equation: G° = E0K + ZPE + ∆G0→298K

(4)

The total energies of the molecules and ions at 0 K (E0K), zero-point energies (ZPE) and changes in free Gibbs energies from 0 to 298 K were obtained using the full optimization of the studied structures and calculations of the vibration mode frequencies by the G3MP2B3 method.66-68 All found structures correspond to the minima on the potential energy surfaces (confirmed with the only positive eigenvalues of the hessians). To consider the solvent effect, we applied the Tomasi polarizable continuum model IEFPCM69, 70 with the SMD option.71, 72 Single-point calculations PCM were performed using the τ-dependent density functional TPSS with gradient correction.73 The latter was used in combination with flexible and moderately thrift triple-valence split basis set augmented with diffuse and polarization functions of d- and p-types aug-cc-pVTZ.74-79 Reoptimization of the structures found with the composite method (at B3LYP/6-31G(d) level) in the TPSS/aug-ccpVTZ approximation does not noticeably improve the description of the solvent effect and has almost no effect on the resulting acidity indices of uracils. To calculate pKa, we need to know the standard free energy of proton ∆G°solv, H+. This fundamental quantity was scrutinized by the series of works. The results of the ∆G°solv, H+ measurements lie in the interval from -253 to -271 kcal/mol. The “best” value, to our knowledge, equals -270.30 kcal/mol. This value was obtained according to the equation: ∆G°solv, H+ = G°g, H+ + ∆G1 atm→1M + ∆G*solv, H+, where G°g,

+ H

is the standard gas-phase energy of proton; ∆G1

(5) atm→1M

= 1.89 kcal/mol is the

contribution from the change of the state from 1 atm to 1M; ∆G*solv, H+ is the free energy of proton in the condensed phase, equal to -265.9 kcal/mol. The standard gas-phase energy of proton G°g

+ H equals

-6.28 kcal/mol34, 61, 80 that follows from the equation:

G°g, H+ = H°g, H+ - TS°g,

(6)

where H°g, H+ = 5/2 RT = 1.48 kcal/mol and S°g°= 26.05 kcal/(mol K).


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However, the model restrictions induce some systematic error in the calculations. To correct it and compare with the calculations within the other computational schemes, we find the effective value of standard free energy of proton that is deduced from the relation with the known pKa value of the simplest uracil (Equation 7). In other words, uracil is used as ‘reference acid’ (RA) in the pKa calculations of other uracils; this approach was showed to be useful for the compounds having similar structures and deprotonation centers, see Ref. 81. ∆G°RA = 2.303⋅RT⋅pKa - ∆G°solv, U- + ∆G°solv, HU

(7)

For this model, we have found ∆G°RA = -274.53 kcal/mol. 2.2 Method II. Calculating the pKa values by the TPSS/aug-cc-pVTZ with explicit taking into account the solvent effect The composite calculations of the uracil molecules and their ions were the most resourcecost stage in the previous scheme. Replacing this stage by the thrift DFT approximation should unavoidably reduce the reliability of the pKa estimates. , However, the accuracy loss may be compensated with more thorough description of the solvation of the uracil molecule and its anion. This may be performed within the model of cluster continuum, in which the supermolecule of the dissolved substance surrounded with the solvent molecules is placed into the isotropic dielectric medium of the solvent. In this case, the ∆G°deprot, aq, required for the estimation of pKa according to equation, is calculated as follows: ∆G°deprot,aq = ∆G°solv, U- +∆G°solv, H+ + ∆G°solv, HU

(8)

where ∆G°solv, U- and ∆G°solv, HU are the absolute standard free Gibbs energies of the anions and molecule, respectively, calculated by the TPSS/aug-cc-pVTZ + IEFPCM method as supermolecules (aqua complexes). The ∆G°solv, H+ has the same sense as in the first approach. Hydration affects the stability of the anion forms of uracils. Herewith, both specific and nonspecific solvation effects matter. The most vague issue of the specific solvation models deals with the choosing the number of the solvent molecules of the first solvation shell to achieve the reliable description of the properties. Previously, we have investigated this question in details.58 According to the cited work, five is the minimal number of the water molecules in the first hydration shell that is sufficient to describe tautomeric and anion forms of uracil within the single model (Figure 3). The nonspecific solvation was accounted in terms of the IEFPCM model including the SMD option. As shown above, the simplification of the computational model induces the systematic error. To correct it, the free hydration energy of proton was treated as the effective value calculated according to equation (7). In terms of this models, ∆G°RA = -273.01 kcal/mol. 7 ACS Paragon Plus Environment


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Figure 3. The first hydration shells of 5,6-disubstituted uracils and the corresponding N1and N3-anions. 2.3 Method III. Calculation of pKa in terms of the CBS-QB3 approximation with explicit taking into account the solvent effect Method III combines the advantages of the two schemes above: the high-level approximation of the cluster continuum in terms of the reliable composite method with the simultaneous is combined with the cluster continuum model for more correct description of the medium. Apparently, the resource demands of Method III is the highest among the three models. However, these are still acceptable as applied to uracil derivatives due to the advances in computational technology. When calculating by the G3MP2B3 composite method, we found that B3LYP/6-31G(d) used for the optimization within the composite approach incorrectly describes the hydrate shell of the uracil anions. Indeed, the hydrate shells were collapsed near the deprotonated nitrogen atoms upon the optimization procedure. This unwelcome effect is caused by the weakness of the 6-31G(d) basis set, so it may be eliminated by improving the basis set. Other composite methods utilize for optimization the triple-valence split basis sets with augmented polarization components. For example, there is B3LYP/cc-pVTZ+1 in the W1 (Weizmann-1) approximation and B3LYP/6-311G(2df, p) in the CBS-QB3 composite method. As the Wn methods are not applicable to our systems due to the excessive resource demands, we have chosen Petersson’s CBS-QB3 method combining the high accuracy of the calculations (mean absolute deviation equals 1.1 kcal/mol for testing set G2) and moderate resource requirements. The calculation scheme of Method III is similar to Method I. The pKa values are calculated according to equations (1–3) with the reservation that indices HU and U- relate to the pentahydrate clusters shown in Figure 3. The hydration energy of reference acid (see above) calculated via equation 7 is ∆G°RA = -270.05 kcal/mol. The nonspecific solvation of the clusters 8 ACS Paragon Plus Environment

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have been described using the IEFPCM-SMD model in the B3LYP/6-311G(2df, p) approximation. We should mention that the models above are not perfect. Thus, the predicted pKa values still differ from the experimental ones. To eliminate the remaining deviation, we have corrected the calculated pKa values via the linear regression with the corresponding experimental data: pKa,exp = a·pKa,theor + b

(9)

3. Results and discussion We have calculated the free Gibbs energies of 19 uracils and all their possible anions using three computational schemes. Based on these calculations, we have defined the series of the thermodynamic stability of the anions of each uracil. Thus, in our set, there are 11 compounds, for which the N1 anions are the most stable, i.e. the first stage of their dissociation most probably occurs via the N1–H bond. Two other species, 5-hydroxyuracil and 5-hydroxy-6methyluracil, were classified as N3–H acids because water medium efficiently stabilizes the N3 anions of these compounds. This inverts the stabilities of the N1 and N3 anions as compared to the compounds in the gas phase. It should be noted that the N1 and N3 anions of some uracils (5OHU, 5OH6CH3U, 5-halogenuracils) have the close Gibbs energies. In these cases, both anionic forms are presented in the solutions in comparable amounts, hence the attribution of these uracils to the N1–H or N3–H becomes ambiguous. Indeed, the recent paper52 reports on the ratio of the anions N1 : N3 = 2:3 in the water caustic solutions of 5FU. Nevertheless, such an uncertainty does not influence significantly on the calculated pKa values whereas the indistinctive situations, i.e. the transits between the dissociation sites and coexisting alternative anionic forms sometimes unavoidable. The presence in the uracil’s structure the readily dissociating carboxyl group expectedly decreases the pKa values of the corresponding uracils (4 compounds). These uracil derivatives are attributed to the O–H acids. Finally, 6-hydroxyuracil and 5,6-dihydroxyuracil are the minor tautomers of barbituric and dialuric acids, respectively. In aqueous solutions, these compounds are presented as pyrimidinetriones with highly polarized C5–H bonds and, therefore, attributed to the C–H acids. Though barbituric and dialuric acids are conditionally considered as uracils, the calculation of their acidities (and the carboxyl-containing uracils) is relevant to testing the accuracy of our methods and assessing their limitations. 3.1 Uracils dissociating via the N1-H bonds For the theoretical estimations of the pKa values of organic acids dissociating via the O-H, C-H, N-H or S-H bonds, the systematic error is regularly varied for the compound of one class.50, 63 This allows using the equations (9) for similar compounds to minimize the deviation 9 ACS Paragon Plus Environment


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of the computational data from the experimental values. As consequence, this enhances the prognostic potential of the model applied to the structures yet unstudied. Guiding the considerations above, we have chosen 11 uracils (Figure 1) from the overall set. The selected structures dissociates mainly via the N1–H bonds. The pKa values for this subset are varied in the wide range from 4 to 10 that is required to obtain the trustworthy correlations. Our three methods applied to the N1-subset provide the pKa values summed up in Table 1. Table 1 The pKa values of uracils dissociating via the N1-H bonds Compound 6FU 5NO2U 6ClU 5FU 5ClU 5BrU 6NH2U 5NH2U U 6CH3U 5CH3U

pKa, exp

na

G3MP2B3+DFT

TPSS/aug-cc-pVTZ pKa

CBS-QB3

4.03 5.35 ± 0.19 5.67 7.89 ± 0.15 7.97 ± 0.05 8.03 ± 0.13 8.39 9.30 b 9.42 ± 0.09 9.57 ± 0.16 9.87 ± 0.07

1 3 1 5 4 4 1 1 8 2 7

4.33 4.93 5.93 8.09 7.79 7.83 8.44 9.77 9.10 9.66 9.63

4.56 5.01 5.60 8.14 7.66 7.75 8.60 9.40 9.16 10.00 9.62

4.41 5.25 5.45 8.16 8.05 7.50 8.59 9.28 9.14 9.92 9.74

Deviation MAD 0.25 0.28 0.23 MAX d 0.47 0.53 0.53 Correlation 0.63 ± 0.03 0.73 ± 0.04 0.77 ± 0.04 a 3.19 ± 0.25 2.32 ± 0.32 1.86 ± 0.31 b Re 0.99 0.99 0.99 a Footnotes: The relevant pKa value is the average from n independent measurements (the used results of experimental works are shown as Supporting Information). b 9.68 ± 0.04 (measured in the present work). c MAD is the mean absolute deviation on the testing set. d MAX is the maximal absolute deviation. e R is the correlation coefficient. c

The results of the theoretical determination of pKa of the N1-dissociating uracils by the three independent computational techniques are well agree and, in general, correspond to each other and the relevant experimental data. As expected, the better description of the testing set is achieved in the case of the highest-cost cluster continuum method CBS-QB3 + DFT. Methods I and II demonstrate almost the same quality of the pKa calculations. The reliability of the prognostic potential are demonstrated below on the example of 5-amino uracil. Its experimental acidity values taken from the literature significantly differ (9.30 ACS Paragon Plus Environment

28

vs. 5.65

44

). Our results 10

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obtained in terms of three methodologies favors to the first value. Besides, we have preformed our own measuring the pKa value of this compound using the potentiometric titration and found it equal to 9.68 ± 0.04. The last value is close to the estimate of work28 and our calculations. Mean absolute (MAD) and maximal (MAX) deviation of our calculations on the N1-testing samples are shown in Table 1. The experimental error of the acidity measurements also influences their accuracies. Typically, the highest deviations are observed in the case of the pKa values presented by the only estimate. We consider that the additional measurements should be performed to obtain the trustworthy values. A comparative analysis of the methods used allows to elucidate some shortcomings which are worth to discuss briefly. As it was expected a priori, enhancing of the calculation scheme gives better results. Going from Method I to III we obtain consecutive increasing in slope of linear fitting – 0.63 – 0.73 – 0.77 and opposite trend for interception – 3.19 – 2.32 – 1.86 (Table 1). Note, an ideal method would give slope of unity and zero interception. As it may see, systematic deviation even for most sophisticated method remains remarkable. The MAD value for Method III was found to be only slightly reduced (0.23) as compared with Method I (0.25) and II (0.28). Since Method III does not show significant improvement compared to simpler methods, it may suppose that some problems in the calculation scheme remains uncovered. To our mind, the first candidate to improve calculation scheme is enhancing of the first hydration shell, especially for uracils having hydrophilic substituents. However, this approach leads to the non-uniformity of the hydration shell for different uracils, It means that new methods should not use linear fitting to reduce systematic error of calculation. In view of this challenge, further study on the pKa theoretical prediction is obviously needed. Nevertheless, it is worth to say that even now the value of MAD obtained by Methods I - III is quite small and comparable with usual experimental error of pKa determination, thus we have nearly achieved natural limit of MAD. 3.2. Uracils dissociating via the N3-H, O-H and C-H bonds The functional groups, which are prone to heterolytic dissociation, in 5 and/or 6 position of the pyrimidine cycle may significantly influence the experimental pKa values due to the change of the deprotonation site. This case is presented by 8 compounds from our uracil set (Figure 1). We have calculated their pKa values to estimate the limitations of the approaches used. We should mention that for 6 compounds, which are the O–H and C–H acids, the dissociation occur via the sites, which are not considered within Methods II and III. This is, of course, weak points of the computational schemes. Nevertheless, we think that these schemes are still applicable to the mentioned cases due to two reasons. First, all the schemes contain the PCM 11 ACS Paragon Plus Environment


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solvation component, i.e. the nonspecific are take into account by default. Second, in the ionized state, the electron density is redistributed in the molecule, so the pentahydrate supermolecule model should describe the specific solvation (at least, partly). Indeed, we have found that three models provide qualitatively the same estimates for this subset of uracils. The resulting pKa values without the correction of the systematic error are shown in Figure 4 on the example of the scheme CBS-QB3. A new subset of uracils may be divided into 3 parts.

pKa exp 10

8

N-H

6

O-H 4

2 0

2

4

6

8 pKa calc (not corrected)

10

12

Figure 4. The correlation of experimental and computational pKa values of uracils dissocianting via the N1-H (black circles), N3-H (white circles), O-H (white triangles) and C-H (black triangles) bonds. The calculated values are obtained within Method III (CBS-QB3).

Thus, the study of different variants of deprotonation of uracils reveals that two uracils, 5OHU and 5OH6CH3U, undergo the heterolysis mainly via the N3-H bond. As the model hydrate shell allows describing the stabilization of the N3 anionic states, the calculation of the corresponding pKa values was performed using the correlation parameters shown in Table 1. The theoretical prognosis of the pKa value 5OH6CH3U fits into the deviation magnitude found for the N1–H-dissociating uracils (Table 2). The deviation of the theoretical estimate of pKa of 5hydroxyuracil equals 0.82 (CBS-QB3). Obviously, our calculations do not take into account the hydration of the hydroxyl group while the latter influences the acidic properties of 5OHU. 12 ACS Paragon Plus Environment

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A completely different situation is observed in the case of the O–H and C–H uracil acids. If uracil derivative contains the carboxylic group, it becomes a tribasic acid, which dissociates via COOH group on the first stage. The change of the dissociation site in orotic (5R6COOHU) and iso-orotic (5COOHU) acids in addition to the indirect consideration of the hydration of the carboxylic groups leads to the changes in the parameters of the correlation between the experimental and computational data (Figure 4). Nevertheless, a linear behavior of the correlation for the O–H acids remains. The found regression coefficients are shown in Table 2. As it is seen, their use leads to a good agreement with the experiment. It seems that the analogous situation takes place in the case of the C–H acids. However, the lack of the experimental data that does not allow defining the regression coefficients to obtain the corrected acidity estimates of barbituric and dialuric acids. Table 2. The pKa values of uracils dissociating via the C-H, O-H and N3-H bonds. Compound

pKa, exp

G3MP2B3+DFT C-H 5OH6OHU 2.83 – 6OHU 3.90 – O-H a 6COOHU 3.16±0.52 3.10 5OH6COOHU a 3.12±0.09 3.36 a 5NH26COOHU 3.48±0.06 3.33 5COOHU 4.16 4.14 0.24 ± 0.06 a 3.00 ± 0.16 b e R 0.94 N3-H 5OHU 8.11 9.02 5OH6CH3U 8.54 9.51 Footnote: a Measured in the present work.

TPSS/aug-cc-pVTZ

CBS-QB3

– –

– –

3.21 3.36 3.22 4.12 0.24 ± 0.08 2.96 ± 0.21 0.90

3.08 3.20 3.51 4.14 0.31 ± 0.03 2.58 ± 0.10 0.99

9.14 9.30

8.93 8.94

A comparative analysis of our present results on pKa of uracils with the previous findings 46-49, 51, 63

should be done. The cited works were devoted entirely to 5-substituted uracils.

Herewith, the works were studying up to 5 compounds, except of work47 investigated the set of 8 uracils. Thus, the number of the samples in the present work is more than twice larger. The previous estimates were performed within the density functional theory with the B3LYP calculations, except of work51 used the BP functional, in combination with the double- and triple-split polarization basis sets augmented by the diffuse functions. The solvent effect was taken into account in terms of diverse continuum models. The moderate level of theory (B3LYP/PVD(T)Z) sometime led to the ambiguous results. Particularly, works46, ACS Paragon Plus Environment

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that uracil and thymine dissociate via the N3–H bonds. However, accounting the systematic error using equation (9) allowed decreasing MAD of the pKa calculations in those works to 0.4 – 0.6.46, 48, 63 The imperfectness of the used theoretical level can be partly compensated by improving the PCM models, e.g. with the use of COSMO-RS model51 or 3 different models CPCM.47 The explicit model of the hydration of thymine and uracil was applied in work.49 The authors found that the increase in the number of water molecules in the first solvation shell enhances matching of theory and experiment. The deviation of the tetrahydrate model shell applied to 1-methylated nucleobases equals 1.7 pKa units. The necessity of the description of non-specific hydration for improving the quality of the pKa calculation model was fully supported by our results. By ignoring explicit water in the Method II, we have found that linear correlation (9) is characterized by slope a = 0.53 and interception b = 3.23; error of pKa calculation becomes larger, MAD = 0.41, MAX = 1.01. Even worse performing was obtained when we simplified Method I by using DFT instead of composite approach to estimate gas-phase acidities: a = 0.48 and b = 4.86, MAD = 0.39, MAX = 1.29. All these examples refer to N1-dissociating uracils, see Table 1 for comparison. In general, in the present work, 3 theoretical models based on the high-level quantum chemical calculations were applied to the wide set of uracil 5- and 6-substituted derivatives, which are able to dissociate via diverse bonds. The agreement between the theoretical and experimental values is generally better than in the previous works. 4. Conclusion The application of the developed methods of the pKa calculation to the testing set of uracils and their comparison with the relevant experimental data leads to the following conslusions. First, the schemes used can be applied to the accurate estimation of pKa. Here, the choice of the scheme depends on the aims of the study, experimental conditions and computational facilities. Second, none of the proposed schemes is devoid the disadvantages. Therefore, the results of the calculations within each scheme contain the systematic error (Figure 4). This causes the necessity of correction to the calculated pKa values using the coefficients of the linear regression (a and b, Tables 1 and 2). The values of the regression coefficients depend on the method used for the calculation of acidities and, additionally, on the type of the dissociating bond. The systematic correction leads to the reliable description of the acidities of uracils. The errors of the computational schemes are characterized with the maximal absolute (MAX) and mean absolute deviations (MAD) from the corresponding experimental values. As found, MAX and MAD equal to 0.47 and 0.25 (Method I), 0.53 and 0.28 (Method II) and 0.53 and 0.23 (Method III) (all values in pKa units). Analyzing the deviation values, one should 14 ACS Paragon Plus Environment

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remember that that these values also include the experimental deviations of the pKa measurements. In the present work, we have anew measured the acidity constants (by the potentiometric titration) for some uracils, for which previous values seemed untrusty. In summary, the proposed computational schemes for assessing pKa correspond to one quarter of the conventional quantum chemical error and equal to ~0.3 kcal/mol. This low values open opportunities for studying the chemical properties of uracils in aqueous solutions taking into account their acid-base equilibria and tautomeric interconversions. 5. Supporting Information Supplementary materials contain an exhaustive set of experimental values of pKa for uracils under study, both experimental and theoretical values of standard free Gibbs energy of proton hydration, absolute free Gibbs energies for uracils and corresponding anions calculated by different methods. 6. References (1) Wetmore, S. D.; Boyd, R. J.; Eriksson, L. A. Radiation Products of Thymine, 1Methylthymine, and Uracil Investigated by Density Functional Theory. J. Phys. Chem. B 1998, 102, 5369-5377. (2) Wetmore, S. D.; Boyd, R. J.; Eriksson, L. A. A Theoretical Study of 5-Halouracils: Electron Affinities, Ionization Potentials and Dissociation of the Related Anions. Chem. Phys. Lett. 2001, 343, 151-158. (3) Tureček, F.; Wolken, J. K. Energetics of Uracil Cation Radical and Anion Radical Ion−Molecule Reactions in the Gas Phase. J. Phys. Chem. A 2001, 105, 8740-8747. (4) Wolken, J. K.; Syrstad, E. A.; Vivekananda, S.; Tureček, F. Uracil Radicals in the Gas Phase: Specific Generation and Energetics. J. Am. Chem. Soc. 2001, 123, 5804-5805. (5) Deeble, D. J.; Das, S.; Von Sonntag, C. Uracil Derivatives: Sites and Kinetics of Protonation of the Radical Anions and the UV Spectra of the C(5) and C(6) H-Atom Adducts. J. Phys. Chem. 1985, 89, 5784-5788. (6) Harańczyk, M.; Dábkowska, I.; Rak, J.; Gutowski, M.; Nilles, J. M.; Stokes, S.; Radisic, D.; Bowen, K. H. Excess Electron Attachment Induces Barrier-Free Proton Transfer in Anionic Complexes of Thymine and Uracil with Formic Acid. J. Phys. Chem. B 2004, 108, 6919-6921. (7) Cole, C. A.; Wang, Z. C.; Snow, T. P.; Bierbaum, V. M. Anionic Derivatives of Uracil: Fragmentation and Reactivity. Phys. Chem. Chem. Phys. 2014, 16, 17835-17844. (8) Nguyen, V. Q.; Tureček, F. Protonation Sites in Pyrimidine and Pyrimidinamines in the Gas Phase. J. Am. Chem. Soc. 1997, 119, 2280-2290. (9) Wolken, J. K.; Tureček, F. e. Proton Affinity of Uracil. A Computational Study of Protonation Sites. J. Am. Soc. Mass. Spectrom. 2000, 11, 1065-1071. (10) Chandra, A. K.; Uchimaru, T.; Zeegers-Huyskens, T. Theoretical Study on Protonated and Deprotonated 5-Substituted Uracil Derivatives and Their Complexes with Water. J. Mol. Struct. 2002, 605, 213-220. (11) Pedersen, S. O.; Byskov, C. S.; Turecek, F.; Brondsted, N. S. Structures of Protonated Thymine and Uracil and Their Monohydrated Gas-Phase Ions from Ultraviolet Action Spectroscopy and Theory. J. Phys. Chem. A 2014, 118, 4256-4265. (12) Ilyina, M. G.; Khamitov, E. M.; Ivanov, S. P.; Mustafin, A. G.; Khursan, S. L. Anions of Uracils: N1 or N3? That Is the Question. Comput. Theor. Chem. 2016, 1078, 81-87.



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(13) Gimadieva, A. R.; Myshkin, V. A.; Mustafin, A. G.; Chernyshenko, Y. N.; Borisova, N. S.; Zimin, Y. S.; Abdrakhmanov, I. B. Preparation and Antihypoxic Activity of Complexes of Uracil Derivatives with Dicarboxylic Acids. Pharm. Chem. J. 2014, 48, 93-96. (14) Hanus, M.; Kabeláč, M.; Nachtigallová, D.; Hobza, P. Mutagenic Properties of 5Halogenuracils: Correlated Quantum Chemical Ab Initio Study. Biochem. 2005, 44, 1701-1707. (15) Taqui Khan, M. M.; Satyanarayana, S.; Jyoti, M. S.; Lincoln, C. A. Thermodynamic Quantities Associated with Interaction of Thymine, Uracil, Cytosine, Adenine and Hypoxantine with Metal Ions Indian J. Chem. 1983, 22, 357-363. (16) Jonáš J.; J., G. Nucleic Acids Components and Their Analogues. XVI. Dissociation Constants of Uracil, 6-Azauracil and Related Compounds. Collect. Czech. Chem. Commun. 1962, 27, 716-723. (17) Srivastava, R. C.; Srivastava, M. N. Formation, Stability and Thermodynamic Functions of Beryllium(II) and Mercury(II) Complexes of Uracil and Thymine. J. Inorg. Nucl. Chem. 1978, 40, 1439-1442. (18) Levene, P. A.; Bass, L. W.; Simms, H. S. The Ionization of Pyrimidines in Relation to the Structure of Pyrimidine Nucleosides. J. Biol. Chem. 1926, 70, 229-241. (19) Tyagi, S.; Kumar, R.; Singh, U. P. Solution Studies of Some Binary and Ternary Lanthanide Complexes. J. Chem. Eng. Data 2005, 50, 377-382. (20) Tucci, E. R.; Doody, B. E.; Li, N. C. Acid Dissociation Constants and Complex Formation Constants of Several Pyrimidine Derivatives. J. Phys. Chem. 1961, 65, 1570-1574. (21) Stankevich, E. I.; Popelis, Y. Y.; Grinshtein, A. Y.; Dubur, G. Y. The Constants of Acidic Dissociation of Some Nitrogen-Containing Polynuclear Systems. Chem. Heter. Compd. 1970, 1, 122-124 (in Russian). (22) Gukovskaya, A. S.; Sukhorukov, B. I.; Prokop'eva, T. M.; Antonovskii, V. L. Spectrophotometric Investigation of the Protonation and Deprotonation of Thymine, Uracil, and Its 5-Haloderivatives. Bull. Acad. Sci. of the USSR, Div. Chem. Sci. 1972, 21, 2614-2619. (23) Privat, E. J.; Sowers, L. C. A Proposed Mechanism for the Mutagenicity of 5Formyluracil. Mutat Res 1996, 354, 151-156. (24) Wempen, I.; Fox, J. J. Spectrometric Studies of Nucleic Acid Derivatives and Related Compounds. VI. On the Structure of Certain 5- and 6-Halogenouracils and -Cytosines. J. Am. Chem. Soc. 1964, 86, 2474-2477. (25) Wittenburg, E. Untersuchung Der Tautomeren Struktur Von Thymin Und Seinen Alkylderivaten Mit Hilfe Von UV-Spektren. Chem. Ber. 1966, 99, 2391-2398. (26) Albert, A.; Phillips, J. N. Ionization Constants of Heterocyclic Substances. Part II. Hydroxy-Derivatives of Nitrogenous Six-Membered Ring-Compounds. J. Chem. Soc. (Resumed) 1956, 1294-1304. (27) Amorati, R.; Valgimigli, L.; Pedulli, G. F.; Grabovskiy, S. A.; Kabal'nova, N. N.; Chatgilialoglu, C. Base-Promoted Reaction of 5-Hydroxyuracil Derivatives with Peroxyl Radicals. Org. Lett. 2010, 12, 4130-4133. (28) Mori, M.; Teshima, S.-I.; Yoshimoto, H.; Fujita, S.-I.; Taniguchi, R.; Hatta, H.; Nishimoto, S.-I. OH Radical Reaction of 5-Substituted Uracils: Pulse Radiolysis and Product Studies of a Common Redox-Ambivalent Radical Produced by Elimination of the 5-Substituents. J. Phys. Chem. B 2001, 105, 2070-2078. (29) Buzlanova, M. M. Potentiometic Study on Some Imides and the Substituted Uracil with Ion-Selective Electrodes. Russ. J. Anal. Chem. 1988, 43, 1515-1517 (in Russian). (30) Cramer, C. J.; Truhlar, D. G. A Universal Approach to Solvation Modeling. Acc. Chem. Res. 2008, 41, 760-768. (31) Klamt, A.; Mennucci, B.; Tomasi, J.; Barone, V.; Curutchet, C.; Orozco, M.; Luque, F. J. On the Performance of Continuum Solvation Methods. A Comment on “Universal Approaches to Solvation Modeling”. Acc. Chem. Res. 2009, 42, 489-492.


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(52) Abdrakhimova, G. S.; Ovchinnikov, M. Y.; Lobov, A. N.; Spirikhin, L. V.; Ivanov, S. P.; Khursan, S. L. 5-Fluorouracil Solutions: NMR Study of Acid–Base Equilibrium in Water and Dmso. J. Phys. Org. Chem. 2014, 27, 876-883. (53) Bachrach, S. M.; Dzierlenga, M. W. Microsolvation of Uracil and Its Conjugate Bases: A DFT Study of the Role of Solvation on Acidity. J. Phys. Chem. A 2011, 115, 5674-5683. (54) Chen, E. C.; Wiley, J. R.; Chen, E. S. The Electron Affinities of Deprotonated Adenine, Guanine, Cytosine, Uracil, and Thymine. Nucleosides, Nucleotides & Nucleic Acids 2008, 27, 506-524. (55) Huang, Y.; Kenttämaa, H. Theoretical Estimations of the 298 K Gas-Phase Acidities of the Pyrimidine-Based Nucleobases Uracil, Thymine, and Cytosine. J. Phys. Chem. A 2003, 107, 4893-4897. (56) Kurinovich, M. A.; Lee, J. K. The Acidity of Uracil and Uracil Analogs in the Gas Phase: Four Surprisingly Acidic Sites and Biological Implications. J. Am. Soc. Mass. Spectrom. 2002, 13, 985-995. (57) Miller, T. M.; Arnold, S. T.; Viggiano, A. A.; Stevens Miller, A. E. Acidity of a Nucleotide Base: Uracil. J. Phys. Chem. A 2004, 108, 3439-3446. (58) Lukmanov, T.; Ivanov, S. P.; Khamitov, E. M.; Khursan, S. L. Relative Stability of KetoEnol Tautomers in 5,6-Substituted Uracils: Ab Initio, DFT and PCM Study. Comput. Theor. Chem. 2013, 1023, 38-45. (59) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A., et al. Gaussian 09, Revision D.1, Gaussian, Inc.: Wallingford CT, 2009. (60) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graphics 1996, 14, 33-38. (61) Topol, I. A.; Tawa, G. J.; Burt, S. K.; Rashin, A. A. Calculation of Absolute and Relative Acidities of Substituted Imidazoles in Aqueous Solvent. J. Phys. Chem. A 1997, 101, 1007510081. (62) Ho, J.; Coote, M. L. A Universal Approach for Continuum Solvent pKa Calculations: Are We There Yet? Theor. Chem. Acc. 2009, 125, 3-21. (63) Klicić, J. J.; Friesner, R. A.; Liu, S.-Y.; Guida, W. C. Accurate Prediction of Acidity Constants in Aqueous Solution Via Density Functional Theory and Self-Consistent Reaction Field Methods. J. Phys. Chem. A 2002, 106, 1327-1335. (64) Ho, J. Predicting pKa in Implicit Solvents: Current Status and Future Directions. Aust. J. Chem. 2014, 67, 1441-1460. (65) Ho, J. Are Thermodynamic Cycles Necessary for Continuum Solvent Calculation of pKa`s and Reduction Potentials? Phys. Chem. Chem. Phys. 2015, 17, 2859-2868. (66) Baboul, A. G.; Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. Gaussian-3 Theory Using Density Functional Geometries and Zero-Point Energies. J. Chem. Phys. 1999, 110, 7650-7657. (67) Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A. Gaussian-3 (G3) Theory for Molecules Containing First and Second-Row Atoms. J. Chem. Phys. 1998, 109, 7764-7776. (68) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K.; Rassolov, V.; Pople, J. A. Gaussian-3 Theory Using Reduced Möller-Plesset Order. J. Chem. Phys. 1999, 110, 4703-4709. (69) Tomasi, J.; Persico, M. Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent. Chem. Rev. 1994, 94, 2027-2094. (70) Tomasi, J.; Mennucci, B.; Cammi, R. Quantum Mechanical Continuum Solvation Models. Chem. Rev. 2005, 105, 2999-3094. (71) Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions. J. Phys. Chem. B 2009, 113, 6378-6396.


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TOC Graphic


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Figure 1. The set of uracils used in this study. 252x116mm (300 x 300 DPI)

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Thermodynamic cycle for calculation of pKa. 14x7mm (600 x 600 DPI)


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The first hydration shells of 5,6-disubstituted uracils and the corresponding N1- and N3-anions. 50x15mm (600 x 600 DPI)



The correlation of experimental and computational pKa values of uracils dissocianting via the N1 H (black circles), N3 H (white circles), O H (white triangles) and C H (black triangles) bonds. The calculated values are obtained within Method III (CBS-QB3). 11x9mm (600 x 600 DPI)


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