5-Fluorouracil—Complete Insight into Its Neutral and Ionised Forms

5-Fluorouracil (5FU), a common anti-cancer drug, occurs in four tautomeric forms and possesses two potential sites of both protonation and deprotonation. Tautomeric and resonance structures of the ionized forms of 5FU create the systems of connected equilibriums. Since there are contradictory reports on the ionized forms of 5FU in the literature, complex theoretical studies on neutral, protonated and deprotonated forms of 5FU, based on the broad spectrum of DFT methods, are presented. These indicate that the O4 oxygen is more willingly protonated than the O2 oxygen and the N1 nitrogen is more willingly deprotonated than the N3 nitrogen in a gas phase. Such preferences are due to advantageous charge delocalization of the respective ions, which is demonstrated by the NBO and ESP analyses. In an aqueous phase, stability differences between respective protonated and deprotonated forms of 5FU are significantly diminished due to the competition between the mesomeric effect and solvation. The calculated pKa values of the protonated, neutral and singly deprotonated 5FU indicate that 5FU does not exist in the protonated and double-deprotonated forms in the pH range of 0–14. The neutral form dominates below pH 8 and the N1 deprotonated form dominates above pH 8.


Introduction
The anti-cancer drugs are a widely applied group of pharmaceuticals. These are hazardous to humans due to their cytotoxicity, genotoxicity, mutagenicity and teratogenicity. Extensively consumed anti-cancer drugs are detected in the environment in increasing amounts, where they are hazardous to wildlife [1,2]. Among anti-cancer drugs, 5-fluorouracil (5FU) is one of the most commonly used [3]. It is an analogue of natural thymine and has been proven useful in the chemotherapy of different cancers [4]. 5FU is also known to act as an antifungal drug [5].
5-Fluorouracil is a weak acid with a measured pK a of 7.93 [6] or 8.05 [7]. This means that 5FU is, to a great extent, deprotonated at physiological and intracellular pH, as well as at environmental pH, particularly when it is slightly basic (some soils, seawater). The ionized form of 5FU influences its mobility in the body fluid [8] and in the environment [9]. Interaction with the proteins [10] and crossing the cell membranes [11][12][13] also depend on the form (ionized or neutral) of 5FU. In the case of tumours, the ability of drugs to cross the cell membrane is strongly dependent on the plasmalemmal pH gradient [14,15]. It has been demonstrated that the tumour extracellular environment is acidic, whereas the intracellular environment is neutral to alkaline [16]. According to the Henderson-Hasselbalch equation, different pH outside and inside of a tumor cell means different concentrations of the neutral and deprotonated forms of an acidic drug in these places. Therefore, it is crucial to know how the deprotonated form of 5FU looks. It was demonstrated that the form of 5FU influences the rate of its sum of the total energy (Etot) and the ZPE gave the zero-point-corrected total energy, E0. Calculation of the enthalpy at 298. 15 K was based on the equation H298 = E298 + RT, where E298 is the sum of the electronic energy and the thermal correction to the energy (E0 + E(0-298)). Calculation of the Gibbs free energy (sum of the electronic and thermal free energies) at 298. 15 K was based on the equation G298 = H298 − TS298.
The atomic charge distribution was determined by fitting to the electrostatic potential at points selected according to the Kollman's scheme (ESP) for the optimised anions [42]. Additionally, the natural bond orbital (NBO) analysis was carried out for the optimised ions using version 3.1 of the NBO package [43] included in the Gaussian 09 program at the B3LYP/6-311++G** and M062X/6-311++G ** levels of theory in the gas phase.

Methods of the pKa Evaluations
In order to calculate the pKa values of 5FU, two methodologies were applied, i.e., the direct and relative method, both with PCM and SMD solvation models, respectively.
The direct method is the most common and, conceptually, the simplest method of pKa calculation, which is based on the process of abstraction of the proton from the acid to form the conjugate base A − and H + [37,40,[44][45][46][47][48] This method involves a thermodynamic cycle that combines the gas-phase Gibbs free energy of deprotonation (ΔGg) and the solvation energies (ΔGs) of all particles (Scheme 1). Scheme 1. A thermodynamic cycle in which an acid species HA is dissociated into its conjugated base A − and a proton.
The Gibbs free energy change of HA deprotonation in aqua (Gaq) was calculated according to Equation (1): Gaq = Gg + Gs + 1.89 kcal/mol (1) where Gg as the change of Gibbs free energy of HA deprotonation in a gas phase is calculated according to Equation (2): whereas G s is defined in Equation (3): where Gs (HA), Gs (A -) and Gs (H + ) are the changes of Gibbs free energies of HA, Aand H + hydrations.
Having ΔGaq , a required pKa value can be calculated using Equation (6): Scheme 1. A thermodynamic cycle in which an acid species HA is dissociated into its conjugated base A − and a proton.
The Gibbs free energy change of HA deprotonation in aqua (∆G aq ) was calculated according to Equation (1): ∆G aq = ∆G g + ∆∆G s + 1.89 kcal/mol (1) where ∆G g as the change of Gibbs free energy of HA deprotonation in a gas phase is calculated according to Equation (2): whereas ∆∆G s is defined in Equation (3): where ∆G s (HA), ∆G s (A − ) and ∆G s (H + ) are the changes of Gibbs free energies of HA, A − and H + hydrations. Since the calculation of ∆G g uses a reference standard state of 1 atm and the calculations of ∆G s use a reference standard state of 1 M concentration, converting the ∆G g reference state from 1 atm to 1 M is accomplished using Equations (4) and (5) [49]: RT ln 24.4654 = 1.89 kcal/mol The values of −6.28 kcal/mol for G (H + ) g and −265.9 kcal/mol for ∆G s (H + ) were derived from the literature [50,51].
Having ∆G aq , a required pK a value can be calculated using Equation (6): The relative (also known as an isodesmic) [52] method we used is based on the process in which acid HA donates a proton to the selected base (here acetate ion) to yield its conjugated base A − and another acid, conjugated with the base used (here, acetic acid). This method involves a thermodynamic cycle, in which the same number of molecules is found on both sides of the reaction equation (Scheme 2). Such a situation gives an advantage over the cycle used in the direct method since solvation energy errors are largely cancelled out, which should improve the accuracy of the pK a predictions [53][54][55][56]. This cancellation of errors is expected to be maximised when the molecular and electronic structures of acids and conjugated bases are similar. The relative (also known as an isodesmic) [52] method we used is based on the process in which acid HA donates a proton to the selected base (here acetate ion) to yield its conjugated base A − and another acid, conjugated with the base used (here, acetic acid). This method involves a thermodynamic cycle, in which the same number of molecules is found on both sides of the reaction equation (Scheme 2). Such a situation gives an advantage over the cycle used in the direct method since solvation energy errors are largely cancelled out, which should improve the accuracy of the pKa predictions [53][54][55][56]. This cancellation of errors is expected to be maximised when the molecular and electronic structures of acids and conjugated bases are similar. Scheme 2. Thermodynamic cycle in which an acid HA donates a proton to CH3COO − to yield the conjugated base A − and CH3COOH.
In the relative method, the pKa of the acid considered is expressed in terms of the acidity of another acid, for which the experimental pKa is known (here, acetic acid), according to Equation (7): The pKa value of 4.76 was used for CH3COOH [57]. The same two methodologies, based on Equation (8) (direct method) and Equation (9) (relative method), were used in the case of protonated 5FU.

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 Schemes 3 and 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. Scheme 2. Thermodynamic cycle in which an acid HA donates a proton to CH 3 COO − to yield the conjugated base A − and CH 3 COOH.
In the relative method, the pK a of the acid considered is expressed in terms of the acidity of another acid, for which the experimental pK a is known (here, acetic acid), according to Equation (7): The pK a value of 4.76 was used for CH 3 COOH [57]. The same two methodologies, based on Equation (8) (direct method) and Equation (9) (relative method), were used in the case of protonated 5FU.

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 Schemes 3 and 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. Scheme 3. System of connected equilibriums between tautomeric and deprotonated forms of 5FU. The latter are described by respective resonance structures. T1-T4-tautomeric forms; DN1 and DN3-forms deprotonated at the N1 and N3, respectively; DD-double-deprotonated form; TDN1 and TDN3-tautomeric forms of DN1 and DN3, respectively.
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 PO2T1,T2 species, whereas protonation of the both T1 and T3 tautomeric forms may provide the same PO4T1,T3 species (Scheme 4). Analogously, protonation of the both T3 and T4 tautomeric forms may provide the same PO2T3,T4 species, whereas protonation of the both T2 and T4 tautomeric forms may provide the same PO4T2,T4 species.
Presented systems of the connected equilibriums show the complexity of the theoretical considerations on acidity and basicity of 5FU. Scheme 3. System of connected equilibriums between tautomeric and deprotonated forms of 5FU. The latter are described by respective resonance structures. T1-T4-tautomeric forms; DN1 and DN3-forms deprotonated at the N1 and N3, respectively; DD-double-deprotonated form; TDN1 and TDN3-tautomeric forms of DN1 and DN3, respectively.
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. Scheme 4. System of connected equilibriums between tautomeric and protonated forms of 5FU. The latter are described by respective resonance structures. T1-T4-tautomeric forms; PO2T1,T2-form protonated at the O2, derived from tautomeric forms T1 or T2; PO2T3,T4-form protonated at the O2, derived from tautomeric forms T3 or T4; PO4T1,T3-form protonated at the O4, derived from tautomeric forms T1 or T3; PO4T2,T4-form protonated at the O4, derived from tautomeric forms T2 or T4.

Stability of the Tautomeric Forms of 5FU
At the beginning, geometry optimisations of the four tautomeric forms of 5FU were performed using a broad spectrum of DFT methods and one CBS-QB3 method. Our results show the advantaged stability of the T1 tautomer, which is 7.32-10.38 kcal/mol (gas phase) or 6.48-11.68 kcal/mol (water) more stable than the second most stable T2 tautomer (Table 1). Tautomer T3 is the least stable in a gas phase with GT in the range of 10.88-13.82 kcal/mol, depending on the method used (Table 1). In turn, the T4 form is the least stable in water with GT in the range of 10.67-16.70 kcal/mol ( Table 1). The M052X functional (smd, α=1,2) is excluded from the latter range since it smooths out differences between T2-T4 forms in water. Our results, concerning stability of the tautomeric forms of 5FU, are in agreement with the results demonstrated by Markova et al. [58]. Thus, the T1 tautomer appears to be fundamental ( Figure 1) for analysis of the protonated and deprotonated forms of 5FU and is used for further consideration.

Stability of the Tautomeric Forms of 5FU
At the beginning, geometry optimisations of the four tautomeric forms of 5FU were performed using a broad spectrum of DFT methods and one CBS-QB3 method. Our results show the advantaged stability of the T1 tautomer, which is 7.32-10.38 kcal/mol (gas phase) or 6.48-11.68 kcal/mol (water) more stable than the second most stable T2 tautomer (Table 1). Tautomer T3 is the least stable in a gas phase with ∆G T in the range of 10.88-13.82 kcal/mol, depending on the method used (Table 1). In turn, the T4 form is the least stable in water with ∆G T in the range of 10.67-16.70 kcal/mol ( Table 1). The M052X functional (smd, α=1,2) is excluded from the latter range since it smooths out differences between T2-T4 forms in water. Our results, concerning stability of the tautomeric forms of 5FU, are in agreement with the results demonstrated by Markova et al. [58]. Thus, the T1 tautomer appears to be fundamental ( Figure 1) for analysis of the protonated and deprotonated forms of 5FU and is used for further consideration.

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 (∆G A ). 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 ∆G C 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. 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 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.

PO2
PO2' PO4 PO4' 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).  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.

Deprotonated and Protonated Forms of 5FU in Water
The exchange of the gas phase by water solution distinctly impacts stabilities of the anionic and cationic forms of 5FU. This is because in a gas phase, the energy of charge delocalisation solely influences the anionic and cationic forms stabilities, whereas in water, the energy of their hydration must be additionally taken into account. Typically, the ions with a better delocalised charge possess smaller dipole moment than those of a worse delocalised charge. Therefore, the latter are better hydrated. Thus, there is a competition between two factors stabilizing the anionic and cationic forms of 5FU in the aqueous phase.
The presented calculations, irrespective of the method used, indicate that the DN1 deprotonated form of 5FU is still more stable than the DN3 deprotonated form in water (Table 5). However, the energy difference between the DN1 and DN3 forms is significantly reduced in an aqueous phase compared with a gas phase and is in the range of 0.56 to 4.10 kcal/mol, depending on the method used (2.08 kcal/mol on average). Such a result differs from that result reported by Jang et al., who found the DN3 anion of 5FU to be 2.44 kcal/mol more stable than the DN1 anion in water [19].  1-8, the solvation models are assigned by letters a-c.
The differences between energy of the protonated forms of 5FU are also significantly reduced in an aqueous phase compared with a gas phase due to the competition between charge delocalisation and hydration. However, the PO4 cation remains the most stable protonated form both in the gas and aqueous phases. The difference between the PO4 form and the second most stable form in water is in a range of 0.37 to 2.65 kcal/mol (Table 5), depending on the method used (1.43 kcal/mol on average). The remaining protonated forms do not noticeably differ in terms of the relative energies and the order of their stability in water depends on the method used.

Calculations of the pK a Values
Based on the Gibbs free energies obtained with different DFT methods, the pK a values for the all possible acidic equilibria concerning the T1 tautomeric form of 5FU (Scheme 5a) were calculated. Two methodologies of pK a calculations, direct (D) and relative (R), were applied. The results of our investigations ( Table 6) show that the calculated pK a values, related to the specific acid equilibrium, strongly depend on the DFT method (1)(2)(3)(4)(5)(6)(7)(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 pK a calculation of such a multi-faceted compound as 5FU. It does not change the fact that the calculated pK a values for deprotonation of the N1 nitrogen in the T1 tautomer of 5FU (T1 DN1) are, generally, slightly lower than the pK a 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 pK a 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 pK a 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 pK a values than methodology R.  1-8, the solvation models by letters a-c. b "A" means anionic forms: DN1 or DN3. c "C" means cationic forms: PO2 or PO4.
There are seven methodologies among those tested herein, which provide the pKa 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 pKa 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 pKa 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 pKa value is provided for the T1 DN1 equilibrium than for the T1 DN3 equilibrium (∆pKa = 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 pKa values for the DN1 DD equilibrium are generally higher than those calculated pKa values for the DN3 DD equilibrium ( Table 6) Looking at the 3cD method, which provides the first pKa value of 5FU (7.76) in accordance with the experimental value (7.93 [6] or 8.05 [7]), we may state that the second pKa value of 5FU is 17.17, and is related to the DN1 DD equilibrium. Six other above-mentioned methodologies,  There are seven methodologies among those tested herein, which provide the pK a 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 pK a 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 pK a 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 pK a value is provided for the T1 DN1 equilibrium than for the T1 DN3 equilibrium (∆pK a = 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 pK a values for the DN1 DD equilibrium are generally higher than those calculated pK a 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 pK a value of 5FU must be related to the DN1 DD equilibrium if the first pK a value of 5FU is related to the DN1 anion.
Looking at the 3cD method, which provides the first pK a value of 5FU (7.76) in accordance with the experimental value (7.93 [6] or 8.05 [7]), we may state that the second pK a value of 5FU is 17.17, and is related to the DN1 DD equilibrium. Six other above-mentioned methodologies, which provide the first pK a value of 5FU close to the experimental pK a value, place the second pK a value in the range of 17.24 to 18.93. The second pK a 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 pK a value of 5FU differ from these reported herein and are 9.0 [22] or 13.0 [26]. On the other hand, a pK a value higher than 14 is not measured in water, which might explain why the data on the second pK a of 5FU are limited. Importantly, based on the second pK a 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 pK a values for the PO4 T1 equilibrium are higher than the calculated pK a values for the PO2 T1 equilibrium, irrespective of the methodology used. The pK a 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 pK a 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 pK a 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 pK a 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 pK a values for the protonated form of 5FU is hard to accept. Thus, the WB97XD methods (5b,c and 6b,c), which provide very accurate pK a values for deprotonation of the neutral 5FU when the relative methodology (R) is used, do not work in the case of pK a 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 pK a values of −13.01, −11.72 and −12.71, respectively, for the PO4 T1 equilibrium, and pK a 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 pK a 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 pK a value that is impossible to measure in a water solution. Importantly, based on the pK a 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.

Conclusions
5-Fluorouracil, a drug with two potential sites of protonation and two potential sites of deprotonation, occurs in four tautomeric forms, among which the 2,4-dioxo tautomer (T1) is evidently the most stable. The protonated and deprotonated forms of 5FU, respectively, create systems of connected equilibriums with the tautomeric forms of 5FU. The gas-phase calculations indicate that the O4 carbonyl oxygen of 5FU is much more easily protonated than the O2 carbonyl oxygen, and the N1 nitrogen is much more easily deprotonated than the N3 nitrogen. The demonstrated preferences result from advantageous charge delocalisation of the respective ions. In an aqueous phase, stability differences between respective protonated and deprotonated forms are significantly diminished due to solvation. However, the O4 oxygen is shown to be slightly more easily protonated than the O2 oxygen and the N1 nitrogen is slightly more easily deprotonated than the N3 nitrogen. Calculations of the pK a of protonated, neutral and singly deprotonated 5FU provided wide ranges of respective values, which strongly depend on the method used. It shows how difficult it is to find the most applicable DFT method for accurate pK a calculation of such a multi-faceted compound like 5FU. Importantly, all the obtained pK a values are in line with the calculated stabilities of the protonated and deprotonated forms of 5FU in the aqueous phase. The M062X/6-311++G**, M052X/6-311++G** and M052X/6-31+G** methods with SMD solvation models and direct thermodynamic cycles, namely 3cD, 7bD and 8bD, provide the most accurate pK a values for all of the considered acid equilibriums. The 3cD and 7bD methods clearly indicate that the N1 nitrogen is more willingly deprotonated than the N3 nitrogen, which is in accordance with the averaged results from all the methods tested herein. In turn, the 8bD method indicates that both nitrogens are equally likely to be deprotonated in water. Based on the 3cD and 7bD methods, the acidic equilibriums concerning 5FU are expected to be shaped as follows: PO4 T1 DN1 DD (Scheme 5) with the following pK a values: −13.01 (3cD) or −11.72 (7bD) for the PO4 form, 7.76 (3cD) or 8.15 (7bD) for the T1 form and 17.17 (3cD) or 19.00 (7bD) for the DN1 form. However, it cannot be missed that a few methods presented here, being in the minority, do not exactly fit into this scheme. These indicate that the O2 and O4 atoms of 5FU are equally willingly protonated and N1 and N3 atoms are equally willingly deprotonated. It does not change the fact that 5FU does not exist in the protonated and double-deprotonated forms in a pH range of 0-14, which is characteristic of water. The neutral form of 5FU dominates below pH 8 and the N1 deprotonated form of 5FU dominates above pH 8.