Study of binding energies using DFT methods, vibrational frequencies and solvent effects in the interaction of silver ions with uracil tautomers

3.1 Optimized structures and energies of uracil tautomers

First, all uracil (U) tautomers were optimized and their relative energies and molecular parameters were extracted. Nine tautomers for uracil (U1–U9) and twenty U-Ag⁺ complexes (obtained from the interaction of uracil tautomers with silver ions) were considered in these calculations. In the previous studies, only 6–8 tautomers were presented for uracil (Tian et al., 1999; Jalbout et al., 2007). The general structures of uracil tautomers are shown in Fig. 1. For more simplicity, conformational isomers of uracil tautomers were neglected in this study; but in some complexes in which there were meaningful differences between interaction energies and different isomers, these isomers were considered. Fig. 2 presents the optimized structures of uracil tautomers and U-Ag⁺ complexes. In most of the reported studies on uracil, U1 under the title of pyrimidine-2,4(1H,3H)-dione has been the major and most stable tautomer of uracil and this tautomer has been only observed in different media. The present calculations at both levels of theory confirmed this observation. Fig. 3 shows the relative Gibbs free energies of all uracil tautomers at B3LYP/6-311++G^∗∗ and B3LYP/3-21G levels of theory.

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Figure 1 General structures of nine tautomers of uracil.

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Figure 2 Optimized structures of nine uracil tautomers and twenty uracil-Ag⁺ complexes.

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Figure 3 Graphical representation for sorted relative Gibbs free energies of all uracil tautomers at B3LYP/6-311++G^∗∗ and B3LYP/3-21G levels of theory.

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According to this figure, the relative energies of uracil tautomers at the higher basis set (6-311++G^∗∗) were found to be as U1 < U2 < U8 < U4 < U9 < U6 < U5 < U7 < U3. Two major tautomers increasing in energy level from U1 to U2 and U5 to U7 could be observed. Inspection in the structures of tautomers displayed that aromatic ring, keto tautomer (versus enol tautomer), N–H bond (versus C–H bond) and C⚌N double bond (versus N⚌N double bond) were stabilizing factors for determining the relative stabilities of tautomers. For example, U1 and U4 consisting of two carbonyl groups were the first and forth tautomers and U8 with aromatic ring was the third tautomer in the stability ranking. However, U2 was the second tautomer in stability because it had three conjugated π-bonds. Moreover, since various tautomerism classes between nine uracil tautomers could be observed, the energy differences for each class of tautomerism could be obtained from Fig. 3. The keto-enol, imine-enamine and amide-iminol tautomerism could be observed in uracil tautomers. For the first case, U5 was enol tautomer of U4 (keto) with 7.05 kcal/mol higher energy level. However, U8 was the enol tautomer of U7 with 18.70 kcal/mol lower energy level because U8 was aromatic (like phenol). Additionally, U4, U3 and U7 are imine tautomers of U1, U2 and U6, respectively. In all of them, the enamine tautomer was more stable than the imine. Moreover, U2, U3 and U9 were the iminol tautomers of U1, U4 and U1 with a higher energy level, respectively.

3.2 Optimized structures and energies of complexes of uracil tautomers with Ag⁺

After optimization of uracil tautomers, their interactions with silver ions were studied in all possible ways. By considering all active places in each uracil tautomer in the interaction with silver ions, twenty stable U-Ag⁺ complexes were found. The optimized structures of these complexes are shown in Fig. 2 and the most important optimized parameters are listed in Table 1. To save space, only some of the parameters that were more important are shown in the table. In addition, the same numbering scheme was employed for defining molecular parameters in all tautomers and complexes and this numbering scheme is depicted in Fig. 4.

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Figure 4 The numbering scheme used for definition of parameters in all structures.

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The most important parameter for complexes is the distance between silver ion and the atom in uracil tautomer connected to it. This distance can be used as a criterion of the strength of interaction between uracil and silver ion. The range of this distance lay between 2.184 and 2.831 Å for Ag–O distance and between 2.239 and 2.496 Å for Ag–N distance. The normal bond length between Ag and N or O was two angstroms. Therefore, these low distances might be due to the interaction between silver ion and nitrogen or oxygen of uracil tautomers (this claim will be discussed more by interaction energies and other interaction parameters).

Since this paper focused on the interaction of uracil tautomers and silver ions, the relative energies of different complexes might be important. Table 2 consists of relative Gibbs free energies of all U-Ag⁺ complexes at both levels of theory. For better representation of energy data, all complexes were sorted by relative energies and the results are depicted in Fig. 5. According to these data, although U1 was the most stable tautomer, two U2-Ag⁺ complexes were the most stable complexes because, in U2, silver ions interacted with both oxygen and nitrogen while, in U1, it only interacted with oxygen. Therefore, the more powerful interactions existing in the U2 complexes made them more stable. The relative stabilities of all complexes at the higher energy level were found to be: U2-Ag-2 > U2-Ag-1 > U1-Ag-2 > U6-Ag-1 > U8-Ag-1 > U1-Ag-1 > U5-Ag-1 > U4-Ag-1 > U8-Ag- > U9-Ag-2 > U8-Ag-3 > U7-Ag-3 > U9-Ag-1 > U3-Ag- > U7-Ag-1 > U3-Ag-2 > U4-Ag-2 > U3-Ag-3 > U7-Ag-2 > U6-Ag-2. Two parameters affected these stabilities. The first factor is the relative energy of tautomer (like U1 and U2 complexes) and the second is the number and strength of interaction between tautomers and silver ions. All complexes except U6-Ag-2 had a planar interaction that showed more powerful interaction in the planar state and only the non-planar complex was the least stable one. Another important aspect of these complexes is the nonlinear interaction of silver ion oxygen and nitrogen. For example, in U9-Af-1, U4-Ag-2 and both complexes of U1, the angle of C–O–Ag was in the range of 143–157 degrees. These nonlinear interactions showed that the nature of interaction between silver ions and uracil tautomers is non-electrostatic or covalent interaction because, in the electrostatic interaction, this angle should be closed up to 180 degrees. However, it seems that, in various complexes of one tautomer, the less hindered complex is more stable than the complex of the more hindered tautomer.

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Figure 5 Sorted relative Gibbs free energies of all uracil-Ag⁺ complexes at B3LYP/6-311++G^∗∗ and B3LYP/3-21G levels of theory.

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3.3 Vibrational spectra of uracil tautomers and their complexes

IR frequencies have important contributions to many research areas in chemistry because of the sensitivity of IR spectra to the structure of molecules and environmental factors that is different from one tautomer to another. Therefore, it can provide fingerprint information and has been used to study various tautomeric systems (Chen et al., 2002). In this study, the IR frequencies for all tautomers and complexes were calculated but only some data were selected for presentation.

The graphical representation of the simulated IR spectra of three low-energy tautomers and complexes in comparison with the experimental spectrum (SDBSweb, 2011) are shown in Fig. 6 and Table 3. The data presented in this figure showed that the U1 (as a major tautomer) had the nearest spectrum to the experiment. However, some vibrational modes in other tautomers seemed to be the same as the experiment. This observation was a reason for the existence of other stable tautomers in equilibrium with the major tautomer. There is not much discussion on the IR spectra of tautomers in this paper because these spectra have been fully considered in previous studies and the focus of this study was on U-Ag⁺ complexes (Ten et al., 2010).

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Figure 6 Simulated IR spectra of three low-energy tautomers (respectively from up to down: U1, U2 and U8) of uracil at the B3LYP/6-311++G^∗∗ level of theory in comparison with real spectrum (below).

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Fig. 7 presents graphical description of the simulated IR spectra of three low-energy complexes of uracil tautomers and silver ions. Moreover, to gain better insight and to discuss the important vibrational frequencies in all complexes, Table 3 presents the corrected IR frequencies for NH and OH, existed double bonds (C⚌C, C⚌N or C⚌O) and the relative vibrations of silver ions versus uracil tautomer (only in complexes). It is important to note that in all calculations, intramolecular hydrogen bonding was not considered; therefore, in all IR spectra (like the spectra shown in Figs. 6 and 7), NH or OH vibrations are sharper and have higher values than the one in the experiment. The top two spectra shown in Fig. 7 belonged to two conformational isomers (U2-Ag-1 and U2-Ag-2, which were different only in the angle of OH bond versus main ring). Despite this, the presented spectra showed that, in U-Ag⁺ complexes, because of the effective interaction between silver ions and uracil tautomers, the spectra of the two conformers were different in most of the vibrational modes. In addition, the comparison between vibrational modes of U3-Ag-2 versus U3-Ag-3 and U7-Ag-1 versus U7-Ag-3 (each pair consisting of two conformers of one molecule) demonstrated some meaningful differences between them and the data shown in Table 3 confirm these differences. In other complexes, the conformers are not considered and only these three cases are discussed here.

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Figure 7 Simulated IR spectra of non scaled) of three low-energy complexes respectively from up to down: U2-Ag-2, U2-Ag-1 and U1-Ag-2) of uracil-Ag⁺ at the B3LYP/6-311++G^∗∗ level of theory.

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The comparison between the spectra of complexes in Fig. 7 with their tautomers’ spectra in Fig. 6 revealed another important aspect of Fig. 7 (and also Table 3) which was the shifting of most vibrations of complexes to the lower values versus the parent tautomer. This effect rose from the absorption of bonding electrons by silver ions, which made the bond weaker. The value of wave number’s shift was more intensive (between 76 and 85 cm⁻¹) in the carbonyl groups of U1 and U2 which are connected directly to the silver ion (C4–O8 in U1-Ag-2 and C2–O7 in both U2-Ag complexes) because π-bonds are looser than δ-bonds and were more easily attracted by silver ions. Interestingly, frequency value of another carbonyl group of U1-Ag-2 (C2–O7) that is placed away from the silver ion in complex is more than that in tautomer. From the data listed in Table 3, the same observations are found in all frequencies related to the C–O bonds (single or double) away from the silver ion because, in these cases, silver withdrew the oxygen lone pairs via C–O bond and this bond degree and also its frequency increased.

The frequencies of all NH or OH bonds in complexes are more than those in the parent tautomer, regardless to its distance from silver ion because, in these bonds, hydrogen does not have a lone pair. In all situations, silver withdraw electrons of δ-bond and made it weaker. The final part of Table 3 (rows 5 and 6 for complexes) consist of relative vibration of the whole uracil tautomer versus silver ion and vice versa. The simple representations of these vibrations are depicted in Fig. 8.

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Figure 8 A schematic presentation of intramolecular vibrational modes. Mode 1 was shown from besides of molecule.

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These frequencies shown in Fig. 8 are out-of-plane bending, in-plane bending and stretching. Out-of-plane bending in all complexes lay in the range of 21.4–84.4 cm⁻¹, in-plane bending lay between 37.4 and 108.4 cm⁻¹ and stretching modes were in the range of 150.2–209.5 cm⁻¹. It seems that the strength of these vibrations, especially stretching modes, could be related to the strength of the interaction because the value of each vibration is a function of harmonic oscillator strength. In the next section (interaction energies), this relation will be discussed. As a result, these vibrations confirm the existence of effective interaction between uracil tautomers and silver ion. Since the values of those frequencies are lower than the normal bond vibrations, the strengths of these interactions are weaker than that in the normal covalent bonds.

3.4 Interactions and their energies in the gas phase and solvent

In this section (and the next section), to continue the discussion on the interaction energies, the quantity and quality of binding energies are discussed. Moreover, since many biological processes happened in solvents, the solvent effect on the calculation of binding energies is also considered. The binding energies are calculated for all complexes in the gas phase and in four different solvents and the results are listed in Table 4.

It can be found in the above table that the binding energies (ΔG_BE) in the gas phase were in general more negative than the ones in the solvents because, in the solvent, the solvation of each molecule or ion prevented from their effective interaction. This postulate confirms the present data that showed, in all solvents except water, ΔG_BE has more positive value with the increase of solvent’s dielectric constant. Water is an exception because solvation energy in water is more complex than another solvent and additional factors such as hydrogen bonding have extensive effects on the solvation energies in water. The values of ΔG_BE in the gas phase are between −67.53 and −24.21 kcal/mol, in cyclohexane are between −37.04 and +1.63 kcal/mol, in chloroform between −26.04 and +12.85, in acetone between −20.40 and +19.69 and in water between −19.18 and 9.12. In all the solvents and in the gas phase, U6-Ag-2 has the most positive amount of ΔG_BE. Among all the studied complexes, these complexes have an exclusive non-planar interaction between uracil and silver ion; therefore, these complexes have the least stable tautomer (see Table 2) and, more importantly, their solvations are very effective (because of its non-planar interaction). These reasons can be responsible for its binding energies. Moreover, the complexes with only O–Ag interaction like U1-Ag1, U1-Ag-2, U4-Ag-2 and U9-Ag-1 have less negative binding energies than other complexes with both O–Ag and N–Ag interactions.

In addition, a linear-like relation is found between the binding energies in all the solvents and in the gas phase and the frequency of stretching vibrations of U-Ag⁺ (Table 3). These relations for the gas phase and three solvents are shown in Fig. 9. Although these relations are not completely planar, they demonstrated that stretching vibrations of uracil tautomer and silver ion is related to the binding energies of these two species and, with the increase in frequency, the binding energy became more negative. In other words, these stretching vibrations could be used as a criterion of interaction efficiency.

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Figure 9 Graphical representation for the linear relationship between binding energies ΔG_BE, in (kcal/mol) and the frequency of stretching vibrations of U-Ag⁺ in (cm⁻¹) in the gas phase (top left), cyclohexane (top right), chloroform below (left) and water below (right).

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3.5 Interaction parameters from AIM and NBO calculations

AIM and NBO calculations are used as two useful methods for studying the interaction between uracil tautomers and silver ion. The theory of atom in molecules (AIM) considered separated atoms and their electron densities for obtaining the interactions and other desired parameters. This simple and fast method is one of the best methods for studying intermolecular interactions. Three important values extracted from AIM calculations are electron density (ρ) at the bond critical point, Laplacian of electron density ρ (▾2ρ) and ellipticity parameter (ε). These parameters for the interaction between uracil tautomers and silver in all complexes are listed in Table 5. In addition, NBO charges are extracted from the calculations, but to save space, these data were moved to the supplementary materials, Table S1.

The parameter listed in Table 5 can be employed for each bond or interaction. Since in this study, only the interactions of silver ion and uracil tautomers (at oxygen or nitrogen atoms) are important, these parameters are extracted for the critical point between each uracil tautomer and silver ion. Moreover, in the present U-Ag⁺ complexes, the interactions of silver ion with oxygen atom (O7 or O8) and with nitrogen atom (N1 or N3) are obtained in all complexes and in most (16 complexes) complexes, respectively.

The electronic density at critical point, ρ, is a positive value related to the strength of the interaction between each two atoms and with the increase in the interaction strength, ρ increases. In the current complexes, the value for O–Ag interaction and for N–Ag interaction lay in the range of 2.89 × 10⁻²–7.52 × 10⁻² au (0.029–0.075) and between 3.27 × 10⁻²–6.73 × 10⁻² au, respectively. These values show the effective interaction between uracil tautomers and silver ion. Moreover, the increase in ρ value of O–Ag interaction was the reason for the decrease in the ρ of N–Ag interaction and the other way around. For example, ρ_O–Ag in U1-Ag1, U1-Ag-2, U4-Ag-2 and U9-Ag-1 have the highest values because, in these complexes, only the O–Ag interaction is possible and also ρ_O–Ag in U7-Ag-2, U8-Ag-1, U8-Ag-3 and U9-Ag-2 have the lowest values because, in these complexes, ρ_N–Ag had the highest values. In addition, increase or decrease in ρ for each interaction is related to the distance of atoms involved in the interaction (Table 1).

The Laplacian of ρ (▾²ρ) at critical points is a negative value related to the shared interaction of bond or interactions and shows a charge concentration between two interacted atoms. When the electron density between the two adjacent atoms increased, its value became more negative. The value of ▾²ρ followed the same pattern as that of ρ, meaning that the complexes with the highest and lowest values (for both O–Ag and N–Ag interactions) are the same with the complexes with the highest and lowest ρ values. The ▾²ρ value for O–Ag interaction lay in the range of −2.82 × 10⁻² to −1.05 × 10⁻¹ au and, as far as N–Ag interaction is concerned, it lay between −2.40 × 10⁻²–7.67 × 10⁻² au.

The last parameter, ellipticity (ε), is the criterion of π-bond character which increased in the single bond when the interaction strength increased (by conjugation or other phenomena). The value of ε for O–Ag interaction and N–Ag interaction lay in the range of 8.97 × 10⁻⁴–1.76 × 10⁻¹ au and between 4.56 × 10⁻³ and 1.00 × 10⁻¹ au, respectively. Since this parameter is a function of more variables such as conjugation with adjacent π-bond or lone pair, the values of this parameter did not obey the same pattern as that of the previous parameters and its values had a wider range. For example, the second highest ε value is observed in the N–Ag interaction of U6-Ag-2 (0.100) because this complex consisted of a non-linear interaction between uracil and silver ion. No meaningful relationship is obtained between ε values and structural aspects of the present complexes.

In the final part of this study, NBO calculations are employed to obtain important interaction energies between the orbitals of uracil tautomers and silver ion. Moreover, NBO charges and hybridizations are calculated via the NBO method; however, to save space, the results are transferred to the supplementary materials (Table S1). Table 6 consists of a number of second-order perturbation energies for charge transfer between uracil tautomers and silver ion in the complexes. All over Table 6, the silver ion acted as an acceptor and the interactions with more than 2 kcal/mol energy are listed. As was expected, the most important donors are oxygen (O7 or O8) and nitrogen (N1 or N3) lone pairs because the major interaction of silver ion with uracil tautomers was occurred with oxygen and nitrogen. Both oxygen lone pairs are electron donors in the charge transfer interaction with the silver ion. Furthermore, in U1-Ag1, U1-Ag-2, U4-Ag-2 and U9-Ag-1, instead of nitrogen atom, the π-orbital of C⚌O bond acted as an electron donor. It is obvious that, in these complexes, silver ion only interacted with oxygen and it did not interact with nitrogen atoms (Fig. 2 and Table 1). Therefore, both oxygen lone pair and C⚌O π-bond acted as a donor in the charge transfer to the silver ion. The quantity of interaction energy of each donor is related to the interaction strength. In most complexes, there is a charge transfer with the interaction energy, which is more than 8 kcal/mol. These data are the final proof for the stabilizing effect of silver ion with uracil tautomer and could be used to define the most important tautomer of uracil in the interaction with uracil.

3.6 Calculation of excited states and magnetic properties: UV–Vis and NMR spectra

To finish our study, NMR chemical shifts (¹³C and ¹H) and UV–Vis electronic absorptions were calculated and compared with the reported experimental values (SDBSWeb, 2011 and Chernyshova et al., 2012). The results for NMR chemical shifts are listed in Table 7 and for UV–Vis absorption values are shown in Table 8.

The calculated NMR chemical shifts of two most stable tautomers (U1 and U2) show that both tautomers can play an important role in the structure of uracil and our data have a good agreement with the reported data. However, a large difference between calculated and observed NH and OH chemical shifts is obtained because, in real spectrum, there is hydrogen bonding between OH or NH hydrogens and oxygen or nitrogen atom. Therefore, the chemical shifts of these hydrogens will be shifted to higher values while in theoretical methods, single molecule is considered and hydrogen bonding is neglected. When we compare the chemical shifts of tautomer with complexes (fifth and sixth rows), for complexes, because of coordination to silver ion, the average of chemical shift (and most of them) shifts to the higher frequency. The value of this shift in U2-Ag-2 complex is much higher than that in U1-Ag-2 because in the first complex, silver ion is coordinated via two atoms and has more effective interaction with uracil. This observation is in agreement with the more stability of U2-Ag-2 versus U1-Ag-2.

Table 8 shows a good agreement between experimental λ_max (244.1 nm) with a calculated value for U1 (251.8 nm). It is noticeable that the other calculated absorptions have oscillator strengths equal to or near zero and their absorption cannot be observed (they have low ε in real spectra) and both real and calculated spectra show one predominant absorption signal. Although our calculations show that, the UV–Vis absorption shows a red shift after coordination of uracil to silver ion the oscillator strength of absorption reduces after complexation.