3.1. Relationship between Tautomeric, Deprotonated and Protonated forms of 5FU
5-Fluorouracil is a compound which not only possesses two potential sites of deprotonation, but also occurs in four tautomeric forms (T1, T2, T3 and T4 presented in
Scheme 3 and
Scheme 4, respectively). Additionally, each of the deprotonated forms of 5FU is described by a few resonance structures. Moreover, deprotonation of two different tautomeric forms of 5FU may provide the same deprotonated species. Thus, when the N1-H is deprotonated from the tautomeric form T1 and when the O2-H is deprotonated from the tautomeric form T2, the same deprotonated species DN1 is formed (
Scheme 3). Analogously, when the N2-H is deprotonated from the tautomeric form T1 and when the O4-H is deprotonated from the tautomeric form T3, the same deprotonated species, DN3, is formed. In turn, deprotonation of the tautomeric form T4 provides tautomeric forms of DN1 and DN3, respectively. The succeeding deprotonation of 5FU provides one dianion (DD), irrespective of the starting tautomer and singly deprotonated species.
The situation is similarly complicated in the case of 5FU protonation, where starting from different tautomers, one may achieve the same protonated form. Thus, protonation of the both T1 and T2 tautomeric forms may provide the same PO2
T1,T2 species, whereas protonation of the both T1 and T3 tautomeric forms may provide the same PO4
T1,T3 species (
Scheme 4). Analogously, protonation of the both T3 and T4 tautomeric forms may provide the same PO2
T3,T4 species, whereas protonation of the both T2 and T4 tautomeric forms may provide the same PO4
T2,T4 species.
Presented systems of the connected equilibriums show the complexity of the theoretical considerations on acidity and basicity of 5FU.
3.3. Deprotonated and Protonated Forms of 5FU in the Gas Phase
The relative energies for the DN1 and DN3 single-deprotonated, as well as for the PO2 and PO4 protonated forms of 5FU were calculated at different levels of theory (
1–
9,
Table 2).
All of the methods used herein indicate that the DN1 anion is much more stable than the DN3 anion in the gas phase. The difference in stability of DN1 and DN3 is about 10 kcal/mol (Δ
GA). The greater stability of the DN1 anion results from advantageous delocalisation of the negative charge. In fact, the DN1 anion is represented by four resonance structures (
Scheme 3), which illustrate delocalisation of the negative charge onto the N1, O2, C5 and O4 atoms. In turn, the DN3 anion is represented by three resonance structures, which illustrate delocalisation of the negative charge onto the N3, O2 and O4 atoms only. Additionally, an inductive effect caused by the fluorine atom should much more effectively delocalise the negative charge on the DN1 anion than on the DN3 anion due to the close proximity of the negative charge on the C5 atom and the fluorine atom in DN1.
To gain a deeper insight into the negative charge delocalisation in DN1 and DN3 anions, the NBO and ESP analyses were carried out at the B3LYP/6-311++G** (
1) and M062X/6-311++G** (
3) levels of theory, respectively (
Table 3). The results of these analyses confirm that the DN1 anion possesses a better-delocalised negative charge than the DN3 anion since there is less of a negative charge on the N1 atom in the DN1 anion than on the N3 atom in the DN3 anion. For example, the NBO analysis with M062X/6-311++G** method (
3) shows that the negative charge on the N1 atom in DN1 anion is −0.65680, whereas the negative charge on the N3 atom in the DN3 anion is −0.69441. In both the DN1 and DN3 anions, the negative charge is delocalised onto the O2 (−0.72892 and −0.74066, respectively) and O4 oxygens (−0.70419 and −0.68767, respectively), which is in agreement with the resonance structures (
Scheme 3). However, the O2 oxygen takes a more negative charge (from −0.71649 to −0.79926, depending on method) than the O4 oxygen (from −0.67777 to −0.74247, depending on method) in both the DN1 and DN3 anions. Importantly, the presented results confirm that the negative charge is delocalised onto the C5 carbon atom in the DN1 anion, which is not the case in the DN3 anion. Respective charges on the C5 carbon are always smaller (NBO) or even negative (ESP) for the DN1 anion compared with the DN3 anion. For example, the charge of the C5 atom is 0.16543 in DN1, whereas it is 0.26248 in the DN3 anion, according to the NBO analysis with the M062X/6-311++G** method (
3). A slightly greater negative charge on the fluorine atom in the DN1 anion than in the DN3 anion may be evidence that an inductive effect of the fluorine atom stabilises the former anion. For example, the charge on the fluorine atom in DN1 is −0.37704, whereas it is −0.36861 in the DN3 anion, according to the NBO analysis with the M062X/6-311++G** method (
3).
In case of protonation of 5FU, two orientations of the hydrogen atom are considered for both protonated forms (
Figure 2). These are assigned: PO2 (protonated at the O2 oxygen with hydrogen directed towards the N3-H site), PO2’ (protonated at the O2 oxygen with hydrogen directed towards the N1-H site), PO4 (protonated at the O4 oxygen with hydrogen directed towards the F atom) and PO4’ (protonated at the O4 oxygen with hydrogen directed towards the N3-H site). Irrespective of the hydrogen orientation, the O4 oxygen atom shows a greater affinity to proton than the O2 oxygen atom in a gas phase. This is demonstrated by the calculated relative energies of the cationic forms (
Table 2). According to all of the methods used, the PO4 form is the most stable. Changing the hydrogen orientation, PO4→PO4’, increases the energy by 4.91–5.44 kcal/mol, depending on the method used. Greater stability of the PO4 form over the PO4’ form probably results from the electrostatic interactions between the electronegative fluorine atom and the hydrogen atom. Nevertheless, the PO4’ form is still more stable than both forms protonated at the O2 oxygen (PO2 and PO2’). The Δ
GC value for the PO2 protonated form is in the range of 6.96 to 7.91 kcal/mol, whereas for the PO2’ protonated form is in the range of 7.92 to 8.95 kcal/mol.
The fact that the O4 oxygen atom in 5FU is preferentially protonated, regardless of the hydrogen orientation, is due to the more advantageous delocalisation of the positive charge in the PO4 cation than in the PO2 cation. As shown in
Scheme 4, protonation of the O4 oxygen in the T1 tautomeric form allows positive charge to be delocalised onto the five atoms (O4, C4, N3, C6 and N1). In the case of the O2 oxygen protonation in the T1 tautomeric form, delocalisation is reduced to the four atoms (O2, C2, N1 and N3). To verify the charge distribution in the protonated forms of 5FU, the NBO and ESP analyses were carried out at the B3LYP/6-311++G** (
1) and M062X/6-311++G** (
3) levels of theory, respectively (
Table 4). The more stable PO4 and PO2 structures were used for these studies. The results of the performed calculations are discussed below as an example of the NBO analysis with the M062X/6-311++G** method (
3).
Protonation of the O2 oxygen atom in 5FU results in the PO2 cationic form with positive charge delocalisation involving the C2=O2 carbonyl group and the neighbouring N1 and N3 nitrogen atoms (
Scheme 4). Therefore, the positive charge on the C2 carbon atom (0.85539,
Table 4) is much bigger than the positive charge on the C4 carbon atom in the PO2 form (0.63262). However, protonation of the O4 oxygen in 5FU, which gives the PO4 form, does not cause a bigger accumulation of the positive charge on the C4 carbon atom (0.64624) than the C2 carbon atom (0.82381). This indicates that the positive charge in the cationic PO4 form is delocalised in the larger area. As illustrated in
Scheme 4, the C6 carbon atom takes place in the delocalisation of the positive charge in the PO4 form, which is not the case in the PO2 form. Indeed, comparison of the C6 carbon atom charges in the PO4 (0.12090) and PO2 (−0.01960) forms confirms that the positive charge in the former cation is partially located at the C6 carbon atom. This is also reflected in the comparison of the H
C hydrogen positive charge, which is slightly bigger in the PO4 (0.26711) than in the PO2 (0.26595) form.
3.5. Calculations of the pKa Values
Based on the Gibbs free energies obtained with different DFT methods, the p
Ka values for the all possible acidic equilibria concerning the T1 tautomeric form of 5FU (
Scheme 5a) were calculated. Two methodologies of p
Ka calculations, direct (
D) and relative (
R), were applied. The results of our investigations (
Table 6) show that the calculated p
Ka values, related to the specific acid equilibrium, strongly depend on the DFT method (
1–
8), solvation model (
a–
c) and thermodynamic cycle (
D or
R). These show how difficult it is to find the most applicable DFT method for the accurate p
Ka calculation of such a multi-faceted compound as 5FU. It does not change the fact that the calculated p
Ka values for deprotonation of the N1 nitrogen in the T1 tautomer of 5FU (T1⇌DN1) are, generally, slightly lower than the p
Ka values for deprotonation of the N3 nitrogen (T1⇌DN3). This is due to the above-demonstrated better stabilization and lower energy of the DN1 deprotonated form compared with the DN3 deprotonated form in water (
Table 5). The p
Ka values for the T1⇌DN1 acid equilibrium in methodology
D are in the range of 6.65 to 11.49 (9.56 on average), whereas in methodology
R in the range of 1.75 to 8.25. (5.25 on average). In turn, the p
Ka values for the T1⇌DN3 acid equilibrium in methodology
D are in the range of 6.64 to 13.25 (10.21 on average) whereas in methodology
R, they are in the range of 2.22 to 8.92 (6.60 on average). Generally, methodology
D provides higher p
Ka values than methodology
R.
There are seven methodologies among those tested herein, which provide the p
Ka T1→A value of 5FU in the range of 7.51–8.20, which is close to the experimentally measured value of 7.93 [
6] or 8.05 [
7] (
Table 6). Four of them, the
3cD,
5bR,
6bR and
7bD methods, give the clearly lower p
Ka values for deprotonation of the N1 nitrogen (7.76, 7.51, 8.18 and 8.15, respectively) than for deprotonation of the N3 nitrogen (8.23, 8.75, 8.92 and 8.80, respectively). Three remaining methods, namely
5cR,
6cR, and
8bD provide almost the same p
Ka T1→A value for deprotonations of the N1 and N3 nitrogens, indicating that both nitrogens are equally likely to be deprotonated in water. Such results are due to small differences in stability of the DN1 and DN3 anions, calculated with these methodologies (
Table 5). Taking into account the averaged results of all methodologies used here, the lower p
Ka value is provided for the T1⇌DN1 equilibrium than for the T1⇌DN3 equilibrium (∆p
Ka = 0.65 and 1.35 for methodology
D and
R, respectively).
Since the DN1 anion is more stable than the DN3 anion (
Table 5), the second deprotonation related to the DN3⇌DD equilibrium is expected to occur more easily than deprotonation related to the DN1⇌DD equilibrium (
Scheme 5b). Therefore, the calculated p
Ka values for the DN1⇌DD equilibrium are generally higher than those calculated p
Ka values for the DN3⇌DD equilibrium (
Table 6). The former ones are in a range of 16.92 to 29.08 (21.10 on average), whereas the latter in the range of 16.70 to 26.90 (20.44 on average) when methodology
D is used. In methodology
R, these values are in the range of 11.19 to 23.55 (18.19 on average) and 10.72 to 21.37 (17.28 on average), respectively. It does not change the fact that the second p
Ka value of 5FU must be related to the DN1⇌DD equilibrium if the first p
Ka value of 5FU is related to the DN1 anion.
Looking at the
3cD method, which provides the first p
Ka value of 5FU (7.76) in accordance with the experimental value (7.93 [
6] or 8.05 [
7]), we may state that the second p
Ka value of 5FU is 17.17, and is related to the DN1⇌DD equilibrium. Six other above-mentioned methodologies, which provide the first p
Ka value of 5FU close to the experimental p
Ka value, place the second p
Ka value in the range of 17.24 to 18.93. The second p
Ka value of 5FU in the range of 17.24 to 18.93 seems to be reasonable, given that the dianion needs to be created. It must be added that the available literature data on the second p
Ka value of 5FU differ from these reported herein and are 9.0 [
22] or 13.0 [
26]. On the other hand, a p
Ka value higher than 14 is not measured in water, which might explain why the data on the second p
Ka of 5FU are limited. Importantly, based on the second p
Ka values of 5FU calculated here, we may state that the dianionic form of 5FU is strongly limited in aqueous media, even if it is the alkaline aqueous solution.
It was demonstrated above that the O4 carbonyl oxygen is more easily protonated than the O2 carbonyl oxygen. Therefore, the O2 protonated 5FU is expected to be a stronger acid than the O4 protonated 5FU. In fact, the calculated pKa values for the PO4⇌T1 equilibrium are higher than the calculated pKa values for the PO2⇌T1 equilibrium, irrespective of the methodology used. The pKa values for PO4⇌T1 equilibrium are in the range from −20.50 to 8.24 (−6.43 on average), whereas for the PO2⇌T1 equilibrium, they are in the range from −22.23 to 7.63 (−7.20 on average) when methodology D is used. In methodology R, these values are in the range from −27.99 to 4.96 (−12.40 on average) and from −29.72 to 4.34 (−13.42 on average), respectively. Particular pKa values concerning the protonated forms of 5FU differ widely depending on the calculation method used. In our opinion, some of them are underestimated, these are the pKa values obtained with the 1aD, 3aD and 1aR–4aR methods, which quite often are below value −20. On the other hand, some are overestimated, these are the pKa values obtained with the 5b, 5c, 6b and 6c methods, for both the R and D thermodynamic cycles, which are found within the range of 3.80–8.24. Such a range of the pKa values for the protonated form of 5FU is hard to accept. Thus, the WB97XD methods (5b,c and 6b,c), which provide very accurate pKa values for deprotonation of the neutral 5FU when the relative methodology (R) is used, do not work in the case of pKa calculations of the cationic form of 5FU. Three other effective methods in deprotonation calculations of the neutral 5FU, namely the 3cD, 7bD and 8bD, provide pKa values of −13.01, −11.72 and −12.71, respectively, for the PO4⇌T1 equilibrium, and pKa values of −13.23, −12.17 and −13.02, respectively, for the PO2⇌T1 equilibrium. It is difficult to verify these values because, to our knowledge, the pKa value of the protonated 5FU has not been measured. This is due to the fact that the protonated 5FU must be a strong acid with a pKa value that is impossible to measure in a water solution. Importantly, based on the pKa values of the protonated 5FU calculated here, we may state that both the protonated forms of 5FU, PO2 and PO4 are strongly limited in aqueous media, even if it is the acidic aqueous solution.