Using Chou’s 5-Step Rule to Evaluate the Stability of Tautomers: Susceptibility of 2-[(Phenylimino)-methyl]-cyclohexane-1,3-diones to Tautomerization Based on the Calculated Gibbs Free Energies

Gibbs free energies, based on DFT (Density Functional Theory) calculations, prove that enaminone (2-(anilinemethylidene)cyclohexane-1,3-dione) and ketamine (2-[(phenylimino)-methyl]cyclohexane-1,3-dione) are the most and least stable tautomeric forms of the studied systems, respectively. 1H and 13C NMR spectra prove that 2-(anilinemethylidene)cyclohexane-1,3-diones are the only tautomeric species present in dimethylsulfoxide solution (a very weak signal can be seen only for the p-methoxy derivatives). The zwitterionic character of these enaminones is strengthened by naphthoannulation and by the insertion of the electron-withdrawing substituent into the benzene ring (the latter weakens the intramolecular hydrogen bond in the compound). Substituent and naphtoannulation have no effect on the stability of the studied tautomers. Slight twisting of the benzene ring, with respect to the CArNC plane (seen in the crystalline state), was proven to also take place in vacuum and in solution.

drugs. Therefore, aside from experimental methods, computational methods have also been used in our research.

Materials and Methods
To make research clearer, easier to follow, and to predict results for similar systems, Chou's 5step rule was followed [60]. Therefore, it was necessary to: (1) select or construct a valid benchmark dataset to train and test the predictor; (2) represent the samples with an effective formulation that truly reflects their intrinsic correlation with the target to be predicted; (3) introduce or develop a powerful algorithm to conduct the prediction; (4) properly perform cross-validation tests to objectively evaluate the anticipated prediction accuracy; and (5) establish a user-friendly web-server for the predictor that is accessible to the public. The advantages of this principle are: logic and transparency in action, the possibility for other researchers to repeat research, ease in developing methods and improving shortcomings, and, most importantly, convenience for use by other The substituent and naphthoannulation [57][58][59] are expected to affect the tautomeric preferences of these compounds [11][12][13]. Thus, 1 H and 13 C NMR experimental studies and quantum-chemical calculations were undertaken, to discover if some other (than those detected earlier) tautomers are stable enough to be present in solution.  The substituent and naphthoannulation [57][58][59] are expected to affect the tautomeric preferences of these compounds [11][12][13]. Thus, 1 H and 13 C NMR experimental studies and quantum-chemical calculations were undertaken, to discover if some other (than those detected earlier) tautomers are stable enough to be present in solution.

Materials and Methods
To make research clearer, easier to follow, and to predict results for similar systems, Chou's 5step rule was followed [60]. Therefore, it was necessary to: (1) select or construct a valid benchmark dataset to train and test the predictor; (2) represent the samples with an effective formulation that truly reflects their intrinsic correlation with the target to be predicted; (3) introduce or develop a powerful algorithm to conduct the prediction; (4) properly perform cross-validation tests to objectively evaluate the anticipated prediction accuracy; and (5) establish a user-friendly web-server for the predictor that is accessible to the public. The advantages of this principle are: logic and transparency in action, the possibility for other researchers to repeat research, ease in developing methods and improving shortcomings, and, most importantly, convenience for use by other

Materials and Methods
To make research clearer, easier to follow, and to predict results for similar systems, Chou's 5-step rule was followed [60]. Therefore, it was necessary to: (1) select or construct a valid benchmark dataset to train and test the predictor; (2) represent the samples with an effective formulation that truly reflects their intrinsic correlation with the target to be predicted; (3) introduce or develop a powerful algorithm to conduct the prediction; (4) properly perform cross-validation tests to objectively evaluate the anticipated prediction accuracy; and (5) establish a user-friendly web-server for the predictor that is accessible to the public. The advantages of this principle are: logic and transparency in action, the possibility for other researchers to repeat research, ease in developing methods and improving shortcomings, and, most importantly, convenience for use by other researchers. Therefore, the role of Chou's 5-step method in conducting proteome/genome analyses, drug development, and research on bioorganic compounds, is unusual and amazing [61][62][63][64][65][66][67][68][69][70][71].
The graphical approach to the study of organic, biological, and medical systems, provides an intuitive understanding of the methodology and research results to the reader, and allows the reader to draw useful insights. Therefore, the methodology of our research is presented in Figure 4. researchers. Therefore, the role of Chou's 5-step method in conducting proteome/genome analyses, drug development, and research on bioorganic compounds, is unusual and amazing [61][62][63][64][65][66][67][68][69][70][71].

Results and Discussion
Due to the very long relaxation times of quaternary carbon atoms, the respective signals were not observed in the NMR spectra. Unfortunately, as seen in Table 1, numerous chemical shifts for Energies 2020, 13, 183 5 of 14 the compounds studied are lacking. The GIAO calculations come to our aid. The experimental and calculated values of chemical shifts in the NMR spectra correspond well with each other (Table 1). 13 C NMR chemical shift of C2 in typical 1,3-diketo systems is equal to 52-68 ppm [53,75,85,86].
A very weak signal in this range can be seen only in the 13 C NMR spectra of p-methoxy derivatives, 1Ka (55.58 ppm) and 1Kb (55.53 ppm). Thus, 2-[(phenylimino)methyl]cyclohexane-1,3-diones (K) are practically absent in DMSO solutions 1-5. On the other hand, the separate C3 and C1 signals seen in the spectra of compounds 1a, 2a, 4a and 5a (Table 1) show that the respective E forms are present there [12,53]. The GIAO calculations confirm the experimental results. It can be effectively predicted that 3Ea is also present in the DMSO solution. The values of the chemical shifts of C1 and C3 carbon for this tautomer are in the same range as the other "a" compounds. The carbonyl carbons in 1b also resonate at different magnetic fields (Table 1). Since their signals are shielded, with respect to those seen in the spectra of compounds 1a, 2a, 4a and 5a (Table 1), one may assume that the order of the C1-O1 and C3-O3 bonds in 1Eb is lower (longer bonds) than that in the other compounds studied. This implies that 1Eb has an increased zwitterionic character (Z in Figure 5). Unfortunately, the signals of carbonyl carbons are not seen in the spectra of other compounds of this series, but one may assume that the molecules of 2Eb-5Eb are even more zwitterionic. The GIAO analysis confirms this assumption. We can clearly see the shift of C1 and C3 signals in NMR spectra of Eb tautomers, which means they have more zwitterionic character than Ea.  H8 signals in the spectra of compounds 1b-4b are seen at the significantly lower field, than those in the spectra of 1a-4a (Table 1). Thus, the intramolecular hydrogen bonds in the former compounds are exceptionally strong. Similar effects to the naphthalene moiety on the chemical shift of acidic hydrogen atoms has been observed in some related compounds [53]. As shown by the significantly low chemical shift of H8 (Table 1), the intramolecular hydrogen bond in 5b was exceptionally weak. Lack of the important 13 C chemical shifts (Table 1) precludes our ability to draw more detailed conclusions on its molecular structure. However, one may see that the very much differentiated effectiveness of the charge transfer in their molecules results in the significant differences in the zwitterionic character of 3Zb and 5Zb ( Figure 6). Zwitterionic character of the enaminone tautomer can be evaluated, at least in the crystalline state. The X-ray data show that the order of the C7-N8 single bond in 3Ea is higher (≈1.7) than that of the C2=C7 double bond (≈1.5) [55]. Furthermore, the C1-C2 (1.455 Å) and C2-C3 (1.438 Å) bonds are significantly shorter than the standard C(sp 2 )-C(sp 2 ) single bond (1.48 Å). On the other hand, both C3=O3′ (1.234 Å) and C1=O1′ (1.257 Å) carbonyl bonds are longer than the standard C=O bond (1.20-1.22 Å) [55]. These findings imply that there is an extensive π-electron transfer from N8 to the carbonyl groups, and proves that electron distribution in the molecule of 3Ea reflects that shown in the zwitterionic resonance structure (Z in Figure 5). From this point of view, 2-(anilinemethylidene)cyclohexane-1,3-dione is similar to 3-(pyridin-2(1H)-ylidene)cycloalkane-2,4diones [53]. X-ray measurements show that the benzene ring in the molecule of 3Ea is slightly twisted, with respect to the CArNC moiety (C10C9N8C7 dihedral angle is equal to 16.2°) [55].
Density functional calculations are known to often be very helpful in the evaluation of the relative stability of different tautomers [13,53,[87][88][89]. The results presented in Table 2 prove, that independently of substituent and series, the most stable form is always enaminone. Due to its very high value of Gibbs free energy, no one expected ketimine would equilibrate with this tautomer, both in vacuum and in DMSO solution. We can see a slight change in the stability of individual tautomers in vacuum and solution. Relative values of Gibbs free energies show that in DMSO solution, the respective On tautomers are less stable than in vacuum. The opposite is true in the case of Kn tautomers, which are more stable in DMSO than in vacuum ( Table 2). H8 signals in the spectra of compounds 1b-4b are seen at the significantly lower field, than those in the spectra of 1a-4a (Table 1). Thus, the intramolecular hydrogen bonds in the former compounds are exceptionally strong. Similar effects to the naphthalene moiety on the chemical shift of acidic hydrogen atoms has been observed in some related compounds [53]. As shown by the significantly low chemical shift of H8 (Table 1), the intramolecular hydrogen bond in 5b was exceptionally weak. Lack of the important 13 C chemical shifts (Table 1) precludes our ability to draw more detailed conclusions on its molecular structure. However, one may see that the very much differentiated effectiveness of the charge transfer in their molecules results in the significant differences in the zwitterionic character of 3Zb and 5Zb ( Figure 6). H8 signals in the spectra of compounds 1b-4b are seen at the significantly lower field, than those in the spectra of 1a-4a (Table 1). Thus, the intramolecular hydrogen bonds in the former compounds are exceptionally strong. Similar effects to the naphthalene moiety on the chemical shift of acidic hydrogen atoms has been observed in some related compounds [53]. As shown by the significantly low chemical shift of H8 (Table 1), the intramolecular hydrogen bond in 5b was exceptionally weak. Lack of the important 13 C chemical shifts (Table 1) precludes our ability to draw more detailed conclusions on its molecular structure. However, one may see that the very much differentiated effectiveness of the charge transfer in their molecules results in the significant differences in the zwitterionic character of 3Zb and 5Zb ( Figure 6). Zwitterionic character of the enaminone tautomer can be evaluated, at least in the crystalline state. The X-ray data show that the order of the C7-N8 single bond in 3Ea is higher (≈1.7) than that of the C2=C7 double bond (≈1.5) [55]. Furthermore, the C1-C2 (1.455 Å) and C2-C3 (1.438 Å) bonds are significantly shorter than the standard C(sp 2 )-C(sp 2 ) single bond (1.48 Å). On the other hand, both C3=O3′ (1.234 Å) and C1=O1′ (1.257 Å) carbonyl bonds are longer than the standard C=O bond (1.20-1.22 Å) [55]. These findings imply that there is an extensive π-electron transfer from N8 to the carbonyl groups, and proves that electron distribution in the molecule of 3Ea reflects that shown in the zwitterionic resonance structure (Z in Figure 5). From this point of view, 2-(anilinemethylidene)cyclohexane-1,3-dione is similar to 3-(pyridin-2(1H)-ylidene)cycloalkane-2,4diones [53]. X-ray measurements show that the benzene ring in the molecule of 3Ea is slightly twisted, with respect to the CArNC moiety (C10C9N8C7 dihedral angle is equal to 16.2°) [55].
Density functional calculations are known to often be very helpful in the evaluation of the relative stability of different tautomers [13,53,[87][88][89]. The results presented in Table 2 prove, that independently of substituent and series, the most stable form is always enaminone. Due to its very high value of Gibbs free energy, no one expected ketimine would equilibrate with this tautomer, both in vacuum and in DMSO solution. We can see a slight change in the stability of individual tautomers in vacuum and solution. Relative values of Gibbs free energies show that in DMSO solution, the respective On tautomers are less stable than in vacuum. The opposite is true in the case of Kn tautomers, which are more stable in DMSO than in vacuum (Table 2). Zwitterionic character of the enaminone tautomer can be evaluated, at least in the crystalline state. The X-ray data show that the order of the C7-N8 single bond in 3Ea is higher (≈1.7) than that of the C2=C7 double bond (≈1.5) [55]. Furthermore, the C1-C2 (1.455 Å) and C2-C3 (1.438 Å) bonds are significantly shorter than the standard C(sp 2 )-C(sp 2 ) single bond (1.48 Å). On the other hand, both C3=O3 (1.234 Å) and C1=O1 (1.257 Å) carbonyl bonds are longer than the standard C=O bond (1.20-1.22 Å) [55]. These findings imply that there is an extensive π-electron transfer from N8 to the carbonyl groups, and proves that electron distribution in the molecule of 3Ea reflects that shown in the zwitterionic resonance structure (Z in Figure 5). From this point of view, 2-(anilinemethylidene)cyclohexane-1,3-dione is similar to 3-(pyridin-2(1H)-ylidene)cycloalkane-2,4-diones [53]. X-ray measurements show that the benzene ring in the molecule of 3Ea is slightly twisted, with respect to the C Ar NC moiety (C10C9N8C7 dihedral angle is equal to 16.2 • ) [55].
Density functional calculations are known to often be very helpful in the evaluation of the relative stability of different tautomers [13,53,[87][88][89]. The results presented in Table 2 prove, that independently of substituent and series, the most stable form is always enaminone. Due to its very high value of Gibbs free energy, no one expected ketimine would equilibrate with this tautomer, both in vacuum and in DMSO solution. We can see a slight change in the stability of individual tautomers in vacuum and solution. Relative values of Gibbs free energies show that in DMSO solution, the respective On Energies 2020, 13, 183 7 of 14 tautomers are less stable than in vacuum. The opposite is true in the case of Kn tautomers, which are more stable in DMSO than in vacuum (Table 2). Table 2.
Calculated (M06-2X/def2-TZVP) relative [kcal/mol] Gibbs free energies for 2-(aniline-methylidene)cyclohexane-1,3-diones and its tautomers a . The optimized structure (Table 3) shows that lengths of the C3=O3 and C1=O1 bonds in 3Ea are less differentiated than shown by the respective X-ray data [55]. The benzene ring in its molecule is slightly twisted with respect to the C7N8C9 plane (according to the X-ray data, this twisting was also observed in the crystalline state [55]-see comparison of X-ray data with DFT in Figure 7). The extent of this deformation increases for the more electron-donating substituents. It is considerably more significant in "a" compounds than in "b" compounds (Table 3).  The optimized structure (Table 3) shows that lengths of the C3=O3′ and C1=O1′ bonds in 3Ea are less differentiated than shown by the respective X-ray data [55]. The benzene ring in its molecule is slightly twisted with respect to the C7N8C9 plane (according to the X-ray data, this twisting was also observed in the crystalline state [55]-see comparison of X-ray data with DFT in Figure 7). The extent of this deformation increases for the more electron-donating substituents. It is considerably more significant in "a" compounds than in "b" compounds (Table 3). Analyzing geometrical parameters of the studied tautomers (Table 3), we can observe that lengths of individual bonds in the vacuum and in DMSO are different. Namely, N8-C7, C2-C3, and C2-C1 are shorter in DMSO than in vacuum; and N8-N9, C7-C2, C3-O3′, and C1-O1′ are longer in DMSO solution. This shows a slight change in the character of these bonds: N8-C7, C2-C3, and C2- Analyzing geometrical parameters of the studied tautomers (Table 3), we can observe that lengths of individual bonds in the vacuum and in DMSO are different. Namely, N8-C7, C2-C3, and C2-C1 are shorter in DMSO than in vacuum; and N8-N9, C7-C2, C3-O3 , and C1-O1 are longer in DMSO solution. This shows a slight change in the character of these bonds: N8-C7, C2-C3, and C2-C1 in DMSO obtain the characteristics of double bonds; and N8-N9, C7-C2, C3-O3 , and C1-O1 , characteristics of single bonds. This confirms that in DMSO, the studied E tautomers have more zwitterionic character (as shown in Figure 5). Additionally, the studied tautomers are stabilized by the intramolecular hydrogen bond N8-H8···O3 , which is shorter by 0.023-0.027 Å in vacuum. The second order Fock matrix was carried out to confirm the charge transfer in studied systems in the NBO analysis. The calculated stabilization energies (E(2)) [90] for the selected donor (i) -acceptor (j) interactions corresponding to i→j electron delocalization, are shown in Table 4. They confirm that there is charge transfer in all studied systems. The higher the E(2) value, the more intense the donor-acceptor interaction is. Based on E(2) values, we can see that in DMSO solution, the charge transfer in E tautomers is more effective (in DMSO solutions, E tautomers are more zwitterionic in character, than in vacuum). It can be also observed that the intensity of electron transfer is highest for compounds with strong electron-donating substituent (-OMe) in the benzene ring (1Ea and 1Eb). The naphthoannulation of diketone moiety has a slight influence on the electron transfer of N8(LP)→C7-C2(π*); E(2) values for the respective Ea and Eb are similar. On the other hand, the delocalization of the electrons C7-C2(π)→C3-O3 (π*) and C7-C2(π)→C1-O1 (π*) is more effective for "b" compounds. In the case of the compound 1Eb in DMSO, a strongly stabilizing (73.06 kJ/mol) charge transfer to carbonyl carbon atom C3 was found.
The calculated NBO charges ( Table 5) also confirm that in DMSO solutions all the E forms are more zwitterionic than in vacuum. In general, charge separation in "b" compounds is more effective than in "a" compounds. Table 5. NBO charges (M06-2X/def2-TZVP) for selected 2-(aniline-methylidene)cyclohexane-1,3-diones in vacuum (regular font) and solution in DMSO (italics).