2.1. Energy of Uracil Tautomers and Its Derivatives
In the first step, the geometries and energies of all possible tautomers of uracil and its 5-halogen derivatives are calculated in the gas phase and in water environment, modelled by the polarizable continuum model (PCM) and the solvent model density (SMD). The obtained relative energies and dipole moments for the studied tautomers are presented in
Table 1. It follows that for all studied compounds, tautomer 5XU1 clearly has the lowest energy, both in the gas phase and in water. This is in agreement with earlier reports [
26,
57]. The second lowest energy tautomer 5XU5 is higher by more than 10 kcal/mol. The energy order of 5XU tautomers in vacuum for most of the studied compounds is as follows:
and only for 5-bromouracil is the order of the two highest energy tautomers, 4 and 3, reversed. In water, the stability order of high-energy tautomers is more diverse.
Analyzing the influence of a polar solvent on the energy of uracil tautomers and its derivatives, we noticed that the solvent stabilization energy, i.e., the energy difference for a given molecule in water and in vacuum, increases with its dipole moment. To illustrate this relationship, in
Figure S1, the approximately linear solvent stabilization (estimated by PCM and SMD methods) dependence on the dipole moment of uracil and its 5-halogen derivatives in vacuum is shown. The R
2 correlation coefficient for the PCM method is 0.84, and for the SMD model it is 0.77. Solvent stabilization energies calculated by the SMD method are about 5 kcal/mol higher than the analogous values estimated by the PCM method. However, the patterns observed from
Figure S1 for PCM and SMD results are similar. Thus, in the next stages of our study we limited ourselves to the first method only (some results of SMD method are included in the Supporting Material).
In a polar environment, modelled by PCM method, the dipole moment of the studied molecules increased by 0.03 to 3.33 D. Tautomers 6 of all uracil derivatives show the lowest dipole moments in vacuum and water induces the smallest increase in their dipole moments. On the contrary, the largest calculated dipole moments are observed for tautomers 3 and 4 (see
Table 1). Obviously, for these tautomers, one could notice the strongest impact of polar solvent on their dipole moments. The directions of the dipole moment vectors of uracil tautomers and the maps of electrostatic potential around these molecules are shown in
Figure 3.
It is apparent from
Figure 3 that the position of the exchangeable proton in all the studied tautomers is crucial and it decides on the distribution of electrostatic potential (and electron density), which is manifested by the direction and magnitude of the total dipole moment. This should control the tautomer stability, as well as the NMR parameters, which are dependent on the magnitude of magnetic field shielding by local electron density. The NMR properties of the studied tautomers will be discussed in detail in a subsequent section.
Analyzing the tautomer energies of uracil and its halogen derivatives, the following question arises: what is the reason for the high stability of tautomer 1? From
Figure 3, we could speculate that this is due to the favorable configuration of two C=O and two N-H groups, which in this tautomer form three intramolecular dipole–dipole attractions due to the anti-parallel arrangement of N-H and O=C bond dipoles. In other tautomers, there is a repulsion of negative charges of free electron pairs of oxygen and nitrogen atoms lying close together.
To check whether dipole interactions are responsible for the particularly high stabilization of tautomer 1 of the studied compounds, we performed additional B3LYP-D3/aug-cc-pVQZ calculations on N-formylformamide as a model molecule. The corresponding three tautomeric forms of N-formylformamide in the gas phase are shown in
Figure S2. The calculations showed that tautomer I is about 17 kcal/mol more stable than II, and 22 kcal/mol more stable than III. These results confirm that the mutual arrangement of the C=O, N-H, -OH and >N: groups in uracil molecule can change the energy of the system by about 20 kcal/mol. In addition, it can be seen that the dipole moment vectors in tautomers 1 and 2 of uracil have the same directions as in tautomers I and II of N-formylformamide, i.e., it suggests that this fragment of the molecule determines the electron density distribution in uracil.
2.2. Aromaticity of Uracil, 5XU and Their Tautomers
It is generally accepted that planarity and stability of benzene in comparison to other unsaturated ring compounds is due to aromaticity [
58]. However, there is a long lasting controversy about aromaticity of uracil [
59,
60,
61]. Therefore, to get more hints about the structural stability of 5XU1, we additionally considered three isomers of diazines. The calculated magnetic and geometric indexes of aromaticity for 5XU1, diazines and model aromatic compound (benzene and pyridine) are shown in
Table 2. In the supporting information, the NICS and HOMA parameters for all 5XU tautomers in vacuum and water, modelled with PCM and SMD methods, are gathered in
Table S1. In the case of diazines, NICS(0) indexes are smaller than for benzene, included here as the best model of an aromatic compound. However, NICS(1), NICS(1)
zz and HOMA values for diazines and benzene are similar, which indicates a comparable magnitude of aromaticity. Both NICS and HOMA indexes have a negligible decrease in water (
Table 2).
NICS(0), NICS (1) and NICS (1)
zz values of tautomer
1 of uracil are negative and their absolute values are significantly smaller than for benzene, indicating its very low degree of aromaticity (
Table 2). In addition, HOMA is only about 0.5, which also suggests a small aromaticity of uracil (tautomer U1). There is a controversy about the relative aromaticity of U1 and 5XU1, as apparent from data shown in
Table 2. Thus, the NICS (0) and NICS (1) indexes of 5-halogeno derivatives 5XU1 are slightly more negative, indicating a negligible pronounced aromaticity, but NICS (1)
zz and HOMA somehow decrease, which points towards the lowering of their aromaticity. However, all indexes agree about increased aromaticity due to the presence of a polar solvent.
In the case of 5XU tautomers in the gas phase and water (see
Table S1), the applied indexes of aromaticity show a significant diversity. Thus, the tautomers
1 and
4 for all compounds are the least aromatic according to NICS (0), NICS (1), NICS (1)
zz, as well as HOMA parameters. On the contrary, tautomer
6 is characterized by large NICS indexes and its HOMA is close to unity, and therefore is considered the most aromatic one. The halogen substituent at C5 position slightly increases the ring aromaticity according to NICS indexes but lowers the HOMA parameter. Water enhances the aromaticity of all uracil tautomers except tautomer 6, for which the polar environment reduces the aromaticity measured by HOMA and NICS parameters. However, the magnitude of changes of the calculated indexes are relatively small.
2.3. Chemical Shifts and Indirect Spin-Spin Coupling Constants of Uracil and 5-Fluorouracil
Proton and carbon NMR spectra reflect the structural and electronic features of the studied uracil derivatives. Below we studied in detail the possibility of selected theoretical approaches to model their NMR parameters. Due to the fact that only tautomer
1 was observed in the experiment and calculated as the most stable form, we are analyzed the NMR data only for this form. Initially, we used three basis sets, STO(1M)−3G, 6−311+G (2d, p) and aug-cc-pVQZ, for the prediction of nuclear shieldings and the chemical shift of uracil and 5FU. These basis sets significantly differ by size, expressed by the number of basis functions (for example, No of b. f. = 165, 261 and 856 for 5FU) and completeness. In
Tables S2 and S3, the differences between calculated and experimental chemical shifts of uracil and 5-fluorouracil tautomer
1 in vacuum and water using B3LYP functional in combination with compact STO(1M)−3G, standard 6−311+G(2d, p) and a very large aug-cc-pVQZ basis set are presented. The RMS values for carbon and proton chemical shifts, calculated with 6−311 + G (2d, p), are between those, obtained with STO(1M)−3G and aug-cc-pVQZ basis sets. The subsequent NMR calculations were conducted using a new, modified STO−3G basis set and a good quality aug-cc-pVQZ one. In order to compare the performance of xOPBE density functional with traditional B3LYP one, we conducted GIAO NMR studies in vacuum and water for uracil and 5FU (see
Table 3 and
Table 4).
In the case of heterocyclic compounds, the prediction of chemical shifts could be quite challenging. As can be seen from the data collected in
Table 3, both density functionals, B3LYP and xOPBE, are able to fairly accurately predict chemical shifts of uracil with RMS (C, H) below 7 and 5 ppm in vacuum and water, respectively (see
Figure 4 Left). Interestingly, a small and compact STO(1M)−3G basis set, specially designed for calculation of magnetic shieldings, performs very well (RMS (C, H) of 2.7 and 3.0 ppm) in comparison to the very expensive aug-cc-pVQZ one. The importance of the inclusion of the solvent effect is also apparent from
Table 3. The PCM approach, though very simplified, produces nearly two times better agreement between the predicted
13C and
1H chemical shifts and the experiment. The presence of the solvent effect also improves the quality of
17O chemical shifts and only xOPBE/STO(1M)−3G produces worse agreement with the experiment in water. On the contrary, for all studied theory levels, the
15N chemical shifts calculated in water are less accurate than for uracil in the gas phase. However, one should notice that in the case of
17O and
15N NMR, no experimental data in water are available.
As for 5-fluorouracil, theoretically predicted carbon and proton chemical shifts (
Table 4) reproduce the experimental data in water very well, as evidenced by RMS (C, H) from 1.9 to 5.0 ppm. The inclusion of water via PCM significantly improves the quality of proton and carbon chemical shifts. For example, the RMS (C, H) values of isolated 5FU and in water calculated with B3LYP and xOPBE combined with STO(1M)−3G basis set decrease from 2.6 to 1.9. and from 2.4 to 1.9 ppm, respectively. As before, the small basis set STO(1M)−3G is able to accurately model 5FU shifts. Both density functionals work equally well with the modified STO−3G basis set. A surprisingly good performance of the STO(1M)−3G basis set in the prediction of heteronuclear chemical shifts, in particular in combination with B3LYP density functional, is apparent from
Table 4. For example, the calculated
19F deviations in water are below 3 ppm.
The second most important parameter analyzed in NMR spectra is J-coupling. The so-called indirect spin–spin coupling constants (SSCC) are more difficult than nuclear shieldings to predict accurately. This is mainly due to the fact that basis sets designed to predict energy and chemical reactions are well defined for valence electrons, far from the nuclei. However, in case of SSCC, it is necessary to account for accurate description of electron density at and near the nuclei.
In
Table 5, deviations from the experiment of theoretically predicted SSCC values of uracil calculated with B3LYP and xOPBE density functionals combined with small STO(1M)−3G basis set and a very large aug-cc-pVQZ basis set are presented. In both cases, we used the option “mixed” to adjust the basis set for the accurate prediction of the dominating Fermi contact term in SSCC. In the case of B3LYP/aug-cc-pVQZ calculations, all deviations from the experiment are fairly small. The RMS values are 1.1 to 2.7 Hz (without
1J(C5H5) results) in vacuum and water, respectively (see
Figure 4 Right). B3LYP/STO(1M)−3G predicted coupling constants which are significantly less accurate and the RMS values are about 11.2 to 8.8 Hz. This is caused by a very large underestimation of one-bond C-H couplings by about 20–30 Hz. In the case of xOPBE density functional combined with both a large basis set and a small one, the predicted coupling constants are significantly worse than those obtained with B3LYP. Similarly as above, this is mainly due to one-bond C-H coupling underestimation by about 40 and 15 Hz for small and large basis sets, respectively.
In
Table 6, deviations from the experiment of theoretically predicted SSCC values of 5FU calculated with B3LYP and xOPBE density functionals combined with two basis sets are presented. The presence of a fluorine atom in 5FU significantly complicates the modeling of SSCC parameters. First of all, a very large one bond coupling is visible—the experimentally observed
1J (C5F5) in DMSO reaches 227 Hz and for two bond carbon–fluorine couplings, the values are also high: 31 and 25 Hz for
2J (F5C6) and
2J (F5C4), respectively. The combination of B3LYP with the large basis set allows for very accurate prediction of SSCC parameters (RMS of 1.4 and 3.5 Hz in vacuum and water) and only the in case of
1J (C5F5) does the theory markedly overestimate the experiment (by 86 and 70 Hz). A surprisingly good performance of STO(1M)−3G basis set in prediction of
1J (C5F5), with deviation of 8.7 and −4.6 Hz in vacuum and water, in comparison to the Dunning-type basis set (86.1 and 69.6 Hz, respectively) is also apparent from
Table 6. However, in combination with B3LYP and xOPBE density functionals, this basis set underestimates the observed
1J (C6H6) by about 25 and 40 Hz. The latter density functional combined with the very large basis set somehow produces a larger RMS (7.5 and 5 Hz in vacuum and water) than B3LYP.
It is apparent from the quality of the predicted SSCC parameters for uracil and 5-fluorouracil that inclusion of water could significantly improve the results. The STO(1M)−3G basis set gives larger deviations than the aug-cc-pVQZ one. However, this was expected since the former basis set was designed for good prediction of nuclear magnetic shieldings and the option “mixed” could not improve basis functions close to nuclei. In addition, the xOPBE density functional, recently designed for the prediction of nuclear shieldings, yielded somehow larger deviations from the experiment than B3LYP.