Role of Topological Charge Stabilization in Protomeric Tautomerism

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Role of Topological Charge Stabilization in Protomeric Tautomerism Masashi Hatanaka J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b00133 • Publication Date (Web): 25 Jan 2015 Downloaded from http://pubs.acs.org on January 30, 2015

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The Journal of Physical Chemistry

Title: Role of Topological Charge Stabilization in Protomeric Tautomerism

Author: Masashi Hatanaka School of Engineering, Tokyo Denki University, 5 Senju-Asahi-cho, Adachi-ku, Tokyo 120-8551 E-mail: [email protected]

Abstract: Protomeric tautomerism is analyzed in view of the topological charge stabilization rules. Based on Hückel molecular orbital considerations and modern DFT calculations, it was found that the branching of amino or hydroxyl groups significantly contributes to the stability of major species through the first- and second-order perturbations with respect to the isoelectronic hydrocarbon. While amino-imino tautomerism is almost completely dominated by topological charge stabilization, hydroxyl-oxo tautomerism is affected by changes in the resonance integral of C−O/C=O bonds. Nevertheless, apart from side effects such as hydrogen bonds or solvent effects, a quantitative preference rule for the prediction of the tautomeric stability can be developed using topological π-electron energetics. As well as the analyses of simple bases, applications to complex or extended systems are exemplified analyzing purine bases, polyguanide, and polyuret. The present approach can be useful in conjunction with chemical intuition that comes from conventional valence bond theory.

1. INTRODUCTION Protomeric tautomerism has been of interest to many chemists since a long time.1,2 The theoretical and experimental aspects of protomeric tautomerism have provided valuable insights into the electronic states of many organic compounds.3,4 Keto-enol equilibrium in vinyl alcohols is a classic prototype of protomeric tautomerism. Amino-imino conversion and hydroxyl-oxo conversion and their hybrid have been found in many conjugated systems, heterocyclic compounds, and bioactive molecules.1,2 The energy gaps between the most stable tautomer and the next most stable one vary over a wide range of magnitudes, and are often expressed using an equilibrium constant KT, or the logarithm of the reciprocal thereof (pKT). However, the determination of KT is often difficult because energy gaps, which lead to the simultaneous detection of two or more tautomers, are 1

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generally small. In solutions, solvent effects or possible dimerization through the hydrogen bonds make it difficult to establish accurate values. When the energy gaps are large, the minor tautomer species is present in an amount that is below the detection limit at room temperature. In such a case, the macroscopic properties of the system can be determined only for the most stable tautomer. Therefore, the acidity or basicity of the solutions (pKa or pKb) are important indexes in the study of the structural chemistry of protomeric tautomerism.5 Nevertheless, in some heterocyclic compounds, photo-radiation techniques have made it possible to convert the most stable tautomer into the next most stable one through the excitation states of a single molecule6-8 or through double proton transfer in dimeric systems.9 Moreover, the interest in protomeric tautomerism is increasing because of its biological importance in connection with base pairing,10,11 along with the growing interest in the structural or thermo-chemical problems of protomeric tautomerism. Therefore, systematic estimation of the magnitude of tautomeric energy gaps is a fundamental issue in the field of organic chemistry, photochemistry, and biochemistry. In the light of such new developments, it seems meaningful to understand the relationship between the topological character of molecules and the tautomeric energy gaps. In this study, amino-imino tautomerism and hydroxyl-oxo/amino-imino hybrid tautomerism in fully conjugated compounds are analyzed in view of the topological charge stability rules. Once a quantitative rule is established, we can understand the origin of the tautomeric preference and approximately predict the most stable tautomer, without requiring any complicated calculations. Amino-imino tautomerism is often found in ureas, heterocycles with two or more nitorogen atoms, purine or pyrimidine bases, and more complicated biochemical compounds. Its biological importance has increased in relation to DNA damage and the resultant mutation.10 In general, tautomerism with large energy gaps (over ca. 10 kcal/mol) cannot be observed under usual conditions at room temperature. Regarding heterocycles, amino preference has been empirically experienced in the field of organic chemistry.1,2 The origin of the amino preference has also been analyzed using simple bond energetics and the molecular orbital (MO) method employing semi-empirical SCF calculations.3 However, the studies conducted so far have been unable to relate the magnitude of the amino-imino energy gaps to the topological features of the systems; they have also not well predicted the subtle tautomerism with small energy gaps (less than ca. 5 kal/mol), even by ab initio calculations with large basis sets. In recent times, however, the use of density-functional 2


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theory (DFT) has made it possible to estimate the thermodynamic properties of organic compounds with high accuracy. In combination with reliable numerical calculations, it would be meaningful to establish a preference rule for predicting amino-imino energy gaps by the molecular skeleton alone. In many cases, the effects of entropy on the energy gaps are negligible, because the change in the density of states in the vibration levels is small. The magnitude of the change in the entropy term T∆S is less than 1 kcal/mol.12,13 This is due to the invariance in molecular skeletons except for the active proton-transfer sites. Thus, zero-point and/or thermal corrections are not essential to determine the empirical rule for protomeric tautomerism. Hydroxyl-oxo tautomerism is another prototype of protomeric tautomerism, which occurs in combination with amino-imino or methyne-methylene conversions. The former is seen in pyridones, quinolinol, etc. The latter is seen in phenols, aldehydes, and vinyl alcohols. In classical resonance theory, it has been shown that hydroxyl-oxo tautomerism is not dominated by resonance energy only. Instead, the change in the bond energies plays an important role in determining the most stable form.2 Nevertheless, if the bond energies are properly calibrated, we can expect that the rest of stability should originate from the resonance energy of the conjugated electrons. For simplicity, only fully conjugated planar molecules are suitable for our study. Nonplanar systems are not handled here, because they are explained by introducing side effects such as hyperconjugation.13 In this study, the tautomeric energy gaps of amino-imino and hydroxyl-oxo/amino-imino tautomerism are analyzed in view of the topological charge stabilization rules. We theoretically showed that branching of amino or hydroxyl groups significantly contributes to the stability of the major species through the first- and second-order perturbations with respect to the isoelectronic hydrocarbon. We also showed that the origin of the stability is related to the amplitude pattern of the nonbonding molecular orbitals (NBMOs) of the isoelectronic hydrocarbons, in which the orbital coefficients at the branching positions are relatively large. We have also exemplified applications to extended systems and complex compounds.

2. METHODS To develop a meaningful preference rule based on π-electron energetics only, we should select the compounds whose energy gaps are not much affected by additional side effects such as hydrogen bonds, steric hindrance, hyperconjugation, and solvent effects. For example, the enol form of 3



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acetylacetone is stabilized by intramolecular hydrogen bonds to a large extent.14,15 The enol preference of phloroglucinol is due to the keto instability caused by the hyperconjugation of the three methylene groups.13 The stabilities of polar molecules with low symmetries are probably affected by solvation energies to a large extent. Thus, we focused only on nearly planar compounds, in which the degree of such side effects can be neglected or cancelled out if any exist between the most stable one and the next most stable one. We carefully selected 16 compounds for the analysis of amino-imino tautomerism (Figure 1), and 13 compounds for analyzing hydroxyl-oxo/amino-imino hybridized tautomerism (Figure 2). In the former case, the protons transfer from an amino group to an imino group, and vice versa. In the latter case, the active hydrogen atoms transfer from hydroxyl groups to imino groups, or conversely, from amino groups to carbonyl groups. As a result, some tautomers have biradicaloid-zwitterionic resonance structures. Both types of tautomerism approximately conserve the planarity of the systems. It has been pointed out by many workers that semi-empirical and ab initio Hartree-Fock (HF) methods are not sufficient for the estimation of energy gaps in protomeric tautomerism.13-15 However, geometry optimization under configuration interactions (CI) or perturbation methods, e.g., the Møller–Plesset perturbation level of theory, is not realistic even today. Nowadays, DFT is probably the most suitable method to estimate the energetics without using highly complicated calculations. Thus, in the present study, the computations were performed under the B3LYP/6-311+G(d,p)//B3LYP/6-311+G(d,p) level of theory16-18 by using the GAMESS program.19 The polarization functions on the s and p atomic orbitals are essential to describe subtle energy gaps.13

4


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1a

NH

H2 N

1b

NH2 N

NH2

H2N

NH2 N H

NH

2b

2a O H2N

NH

NH2 N

O

NH2

H2N

3a

6a

NH2 N H

NH

N H

NH

4b

N

HN

N

NH2

N H

N H

NH2

5b

HN

11a

N

NH2

NH2

N H

N H

14a

N H

11b

N

N H

14b

H2N

NH2 NH2

NH

9b N

10b N

N H

NH

N H

10a

HN

NH

8b

9a N

NH

NH

N

N

5a

N H

7b

8a

N

HN

NH

NH

NH

NH2

NH2

NH2

H2N

4a

N

N

7a

NH2

6b

N

H2N

3b N

N

HN

NH

N

N H

NH HN

N

N H

N H

NH

15a

15b H2N

N

HN

N H

N H

16a

12a

NH2

12b

16b

NH N H

N NH2

N

13a

13b

NH2

NH

NH

N H

N H

N

NH

N H

Figure 1. Molecular structures of amino and imino tautomers for 1-16. 5



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17b

17a

OH

22a N

18a

N H

OH

OH

18b

OH

N

O

O

19b

HO

N N

HN OH

O

N

20a

NH2

NH2

OH

O

N H

N

O

N H

21b

N H

25a

O

OH

25b

O

HN N

O

N H

26a

O

O

OH

20b

N HO

N H

N N

21a

O

24b

N H

N HO

N H

OH

24a N

O

NH

23b

23a

N H

N H

N

19a

O

O

22b

N

26b

OH

O

N

N H

27b

27a HO

O

N

N H O

N H

28b

28a HO

N

O

N H

29b

29a

N H

N O

OH

N H O

Figure 2. Molecular structures of hydroxyl and oxo tautomers for 17-29. 6


N H

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After the computations, π-electron energetics was analyzed by the first- and second-order perturbation theory with respect to the isoelectronic hydrocarbons. The first perturbation is known as Gimarc’s topological charge stabilization.20-22 The total energy of the system is given by:

E = E 0 + ∑ q r δα r ,

(1)

r

where E0 is the energy of the reference isoelectronic hydrocarbon, qr is the π-electron density of the reference hydrocarbon, and δαr is the change in the Coulomb integral on the r-th site. In this study, the second-order perturbation was also considered, and we extended Gimarc’s idea to high-order approximations. The second-order perturbation is approximately expressed by atom polarizability πr,s and self-atom polarizability πr,r, which represent contributions of the excited states of the reference hydrocarbons. When perturbation of the deviation of resonance integral β is also included, the total energy of the system can be expressed as:23 1 E = E 0 + ∑ q r δα r + ∑ π r , s δα r δα s + ⋅ ⋅ ⋅ + ∑ δEbond (δβ r , s ) r r ,s 2 r ,s 1 ≅ E 0 + ∑ q r δα r + ∑ π r ,r (δα r ) 2 + ∑ δEbond (δβ r , s ), r r 2 r ,s

(2)

where πr,s is the atom polarizability given by: occ unocc

π r , s = 4∑ ∑ j

C jr C kr C js C ks

k

ε j −εk

.

(3)

We noted that the second-order cross terms can be approximately neglected, because the r- and s-th sites with nonzero δα are never adjacent to each other in protomeric tautomers. When the last term as a function of δβr,s is small, both the first and second perturbations are “additive” for each site by using the self-atom polarizability, given by: occ unocc

π r , r = 4∑ ∑ j

k

2

C jr C kr

ε j −εk

2

.

(4)

Both the first- and second-order perturbations are usually negative. Given that the second-order terms are additively proportional to the square of the change in the Coulomb integral (δαr)2, and thus, the term “topological charge stabilization” is used for both the first- and/or second-order perturbations hereafter. All the reference Hückel wavefunctions and perturbations were calculated for each molecule, and the DFT energy gaps ∆EDFT were plotted versus the difference in topological 7



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charge stabilization ∆ET: ∆E DFT = Eb ( DFT ) − E a ( DFT ),

(5)

and

∆ET = Eb ( topological) − E a ( topological) = ∑ q r {(δα r ) b − (δα r ) a } + r

1 ∑ π r ,r (δα r ) 2 b − (δα r ) 2 a 2 r

{

}

(6)

+ ∑ {δEbond (δβ r , s ) b − δEbond (δβ r , s ) a }, r ,s

where subscripts a and b denote forms a and b in the tautomeric schemes (Figures 1 and 2). We noted that qr and πr,r have the same values for a and b, and that the energy of the reference hydrocarbon E0 is cancelled out. The following standard values were used as the changes in the Coulomb integral:24 δαr(amino -NH2 or –NH-) = 1.5β, δαr(imino =NH or =N−) = 0.5β, δαr(hydroxyl -OH) = 2.0β, and δαr(carbonyl oxygen =O) = 1.0β, where the resonance integral β is common (β < 0). In view of the valence bond (VB) description, the numbers of π-electrons on the amino, imino, hydroxyl, and keto groups are 2, 1, 2, and 1, respectively. This is parallel to the magnitude of each δαr. In some tautomers with biradicaloid-zwitterionic resonance structures, the parameters were allocated based on the biradicaloid resonance structure. The validity of this parametrization is confirmed later by the clear relationship between the DFT results and the differences in the topological charge stabilities. The molecular maps of each reference isoelectronic hydrocarbon are shown in Figure 3 with the π-electron densities qr and self-atom polarizations πr,r. We noted that all the reference species are anionic, because HOMOs are doubly occupied. Some of the compounds share the same skeleton.

8


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qr

π r ,r

1.625

0.3425 0.2973

1 1.500

0.3125

1.625

0.3425

0.3933 1

1.143

0.4291

1.143

0.4689 0.3076

1 1.571

0.4116 0.3878

1

0.4432

1.250 1

0.3058 1.583

1.333

0.3963

0.4415

1.400 1

0.3037 1.600

1.338

1.229

0.3710

0.3878 0.3737

0.3896

1.120

0.3148

1.746 1.035 1.059

0.4447

1.252

0.3321

1.112

1

1

1.059 1

0.4218

1 1.235

1.059

0.3952

0.4299

0.4372 1.059

1

0.3954

0.4075

1.099

1.059

0.2301

0.3267

0.4047

0.4668

1.529

1

1.050

0.5013

0.5891 0.4239

1 1.045 1 1

1

0.3092 0.5107

1.450

1.050

0.4761

0.3495

1.200

0.4208

0.3284

0.4005

0.4563

1.200

0.3212 0.4610

0.3661

0.3947 0.4580

Figure 3. Data showing π-electron density distribution qr and self-atom polarizability πr,r (in units of 1/β) of isoelectronic reference hydrocarbons (hydrocarbon anions) for 1-29.

3. RESULTS AND DISCUSSION 3.1. Amino-Imino Tautomerism. In the case of amino-imino tautomerism, the relationship between the differences in topological charge stabilization ∆ET and DFT results are straightforward. The perturbation term with respect to β can be neglected, because the number of C=N and C−N bonds is invariant both before and after the tautomerism. Thus: active

∆ET =

∑ q {(δα r

r

r ) b − (δα r ) a } +

active

1 ∑ 2 π {(δα r ,r

r

}

) 2 b − (δα r ) 2 a .

r

9


(7)


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We noted that we only have to take the summation within the proton-transfer active sites, because the terms for the rest of the inactive sites cancelled out. The molecules considered are biguanide 1 and amidonourea 2 as cyanamide derivatives; pyridines 3-5, guanamine 6, melamine 7, 3(5)-aminopyrazole 8, and 7-azaindole 9 as five-membered ring-containing systems; and aminoquinolines 10-16. In 8 and 9, the “amino” or “imino” forms cannot be specified intuitively, and we formally regard forms a and b in Figures 1 and 2 as the amino and imino form, respectively. Figure 4 shows a plot of the imino-amino energy gap (∆EDFT = Eb−Ea) obtained by the DFT calculations versus difference of topological charge stabilization ∆ET. Within the first-order approximation (Figure 4a), we see a nearly linear relationship between the topological parameter and the calculated energy gap, in which the correlation coefficient R = 0.9291 (the coefficient of determination R2 = 0.8633 is the square of the correlation coefficient). The correlation is strong, and thus, the energetics of amino-imino tautomerism is essentially determined by topological charge stabilization only. This is due to the invariance in the number of amino- and imino-type nitrogen atoms before and after the tautomerization. When the second-order perturbation is included (Figure 4b), the linearity is further improved to R = 0.9573, and the coefficient of determination becomes R2 = 0.9165. Thus, we see amino preference because amino groups are more prevalent than imino groups.

10


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(a) 1st-order imino-amino gaps

ΔE DFT (kcal/mol)

40

R = 0.9291 R 2 = 0.8633

30 20 10 0 0

0.2

0.4

0.6

0.8

(｜ β ｜) ΔE T (｜β

(b) 2nd-order imino-amino gaps 40

ΔE DFT (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


R = 0.9573 R 2 = 0.9165

30 20 10 0 0

0.2

0 .4

0 .6

0 .8

(｜ β ｜) ΔE T (｜β

Figure 4. Plot of imino-amino tautomeric energies from DFT calculations versus the differences in topological charge stabilizations ∆ET for 1-16. (a) The first-order, (b) the second-order approximation.

In this section, we pay attention to the relationship between the amino stability and the molecular skeletons. The amplitude pattern of the NBMOs becomes important for establishing the preference rule. Aminopyridines 3-5 are good examples to show the origin of the amino preference in amino/imino tautomerism. The corresponding isoelectronic hydrocarbon is the benzyl radical anion with eight π-electrons. Figure 5 shows the skeleton of the benzyl anions, its NBMO, π-electron density qr, and self-atom polarization πr,r. The skeleton consists of a “bipartite lattice”; the carbon atoms are classified into “starred” and “unstarred” atoms that are not adjacent to each other. The 11



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NBMO becomes the HOMO, in which two π-electrons are accommodated. There is one terminal carbon at the benzyl position. The NBMO amplitude at the terminal is relatively large. This is a kind of edge effect, in which the frontier electrons localize at the terminal region rather than at the normal region, as is often seen in two-dimensional materials. It naturally follows that π-electrons near the terminal positions are less itinerant due to the lower connectivity. As shown later, this situation can also be deduced from symmetry considerations.

*

*

NBMO

1 7

1 7

−

2

*

*

1

−

qr

7

7

π r ,r 0.3933 1

1.143

0.4291

1.143

0.4689 0.3076

1 1.571

0.4116

*

*

NBMO3

NBMO2

1 2

−

1 2

*

*

NBMO1

−

*

1 2

1 2

−

qr

1 2

1 2

1 2

−

1 2

π r ,r

1.625

−

1 8

−

1 8

type 1

−

1 8

8

0.2973 0.3125

1.625

0.3425

type 2

Ct

Ct Cn

1 8

0.3425

1 1.500

2

−

Ct'

Cn'

Node Cn

Node

Figure 5. Two types of terminal effect. Ct and Cn are NBMO coefficients. 12


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Biguanide 1 and amidinourea 2 are also good examples for investigating the terminal effect of amino preference. The isoelectronic hydrocarbon corresponding to biguanide and amidinourea is tetramethylenepropane trianion (TMP3-) with ten π-electrons. Neutral TMP has five starred and two unstarred atoms, as depicted in Figure 5. Then, as is well known from the theories of non-Kekulé molecules, there are three NBMOs at the frontier level.25 In TMP3-, six π-electrons are accommodated in the three degenerate NBMOs. Figure 5 shows the π-electron density qr and self-atom polarizability πr,r of TMP3- calculated by the simple Hückel method. One can see that the π-electron density is large at the branched positions, and small at the trunk positions. This situation originates from the so-called zero-sum rule of non-Kekulé molecules.24 In general, the coefficients for the NBMOs at the starred atoms (often terminal positions) become large, and those at the unstarred atoms are zero. Thus, the terminal sites contribute most to the total π-electron densities. According to the topological charge stability rule, such an inhomogeneous distribution of qr matches the pattern of electronegativity of atoms in the perturbed system.20-22 That is, positions with large π-electron density correspond to “negative” sites with negatively large Coulomb integrals. The Coulomb integral of amino groups (δα = 1.5β) is negatively larger than that of imino groups (δα = 0.5β). Thus, we can expect that amino groups should be located at as many branched positions as possible. In other words, terminal imino groups are unstable, and Schiff-base nitrogen is preferred instead. Indeed, imino compounds are very rare in organic chemistry, except when one of the active hydrogens is deliberately substituted by heavy groups such as methyl groups.26 Here, we show the origin of the terminal effects from symmetry consideration of NBMOs. In the benzyl anion, there is one terminal position in the skeleton, depicted as type 1, at the bottom of Figure 5. For the moment, we assume that the topological skeleton of the system has at least a two-fold axis of symmetry. Then, we assume that there exists a mirror plane σv that contains the terminal position, perpendicular to the molecular plane. Each molecular orbital is classified by its symmetric or antisymmetric character with respect to the σv plane. If the NBMO is not degenerate, then it should be symmetric, because the serial number of the molecular orbitals counted from the lowest orbital should be odd and the lowest one is symmetric. We denote the NBMO coefficients on the terminal and normal (nonterminal) moieties as Ct and Cn, respectively, at the bottom of Figure 5. Then, from the zero-sum rule, we obtain the following: 13



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C t + C n + C n ' = 0,

(8)

and 2

2

C t − (C n + C n ' 2 ) = 2C n C n ' ,

(9)

where Ct ≠ 0. Given that the orbital is symmetric, Cn and Cnʹ have the same sign, and CnCnʹ > 0. Then, 2

2

2

Ct > C n + C n '2 >

Cn + Cn '2 2 = Cn , 2

(10)

where the last term is the average of the square of the coefficients on the nonterminal sites. This inequality represents the terminal effects, i.e., Ct2 > Cn2 on average (one might be reminded of the eyʹ orbital of trimethylenemethane). This inequality is true even if the symmetry is broken, because the conditions Ct ≠ 0 and CnCnʹ > 0 are satisfied in most cases. Strictly speaking, π-conjugated systems that contain odd-membered rings do not have NBMOs in the classical sense. However, even in such a case, the HOMO also has an approximately nonbonding character, and thus, the terminal effects always appear, similarly to that found above. When NBMOs are degenerate, the situation is somewhat complex, because the NBMOs are unitarily transformable, and the amplitude patterns are not determined uniquely.27 Degenerate NBMOs have appeared in systems with multiple type-1 edges, or in edges with two terminal sites depicted as type 2 shown at the bottom of Figure 5.27 The terminal effect above can no longer be clearly

proven.

However,

except

for

in

rare

cases

(for

example,

dianion

of

1,3-dimethylenecyclobutadiene27), contributions from the normal (nonterminal) positions to the total π-electron densities do not exceed those from the terminal positions when all the contributions from NBMOs are added together. This is in agreement with the chemical intuition that electrons are much more likely to be localized at terminal sites with lower connectivity rather than at nonterminal sites. This can also be deduced from the case of TMP3-, Figure 5. Thus, in most cases, we can conclude that terminal effects (Ct2 > Cn2 on average) are guaranteed by the nonbonding character of the NBMOs. The discussion above is essentially correct when the symmetry of the system is slightly deviated. An exceptionally rare case is discussed later in relation to the convergence problem of the perturbation. It is not difficult to show that the second-order perturbation also contributes to the stability of the branched amino groups, because the magnitude of self-atom polarizability πr,r is also large at the 14


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branched positions. This is due to the large amplitudes of the NBMOs, similar to the effect found for the first-order perturbation term. In addition, the absolute value of the denominator in Eq. (4) is minimized when the formal one-electron excitation occurs between the NBMO and the LUMO, and the second-order stability is maximized. Thus, the significant amplitudes of the NBMOs on the branched positions are essentially responsible for the amino preference. Judging from the coefficient of determination, the contribution from the second-order perturbation is ca. 5%, and the higher-order term is almost negligible. Table 1 shows a summary of the DFT results and perturbation calculations.

3.2. Hydroxyl-Oxo/Amino-Imino Hybrid Tautomerism. Hydroxyl/oxo tautomerism is seen in some aldehydes, phenols, and aza-aromatic phenols. In this study, however, compounds with nonconjugated fragments such as methylene or methyl groups are not considered for simplicity. We analyze hydroxyl-oxo/amino-imino hybrid tautomerism in some aza-aromatic phenols as comparative examples of the amino-imino tautomerism above. The tautomeric pairs that are considered are selected so that the hydrogen-bonding effects do not influence the energetics much. The selected molecules are pyridones 17-19, cytosine 20 and uracil 21 as pyrimidine bases, cyanuric acid 22, and quinolinols 23-29. Table 2 is a summary of the theoretical analyses on hydroxyl-oxo/amino-imino hybrid tautomerism. At a glance, it seems that there are no correlations between the energy gaps obtained by DFT calculations and ∆ET itself. However, one should remember that the C=O double bond is much more stable than the C−O bond, and thus, a calibration factor should be added to the calculated Hückel energies. One of the reasonable calibrations is to add the perturbation with respect to resonance integral β. The formulation of such a perturbation has been summarized by early workers at the first- and second-order levels.23,24 In this study, however, a more intuitive and simple method is employed. We simply considered the bond energy difference and added it to the Hückel results. If hyperconjugation does not occur, this is a very reasonable method to estimate the tautomeric

energetics.

The

C−O/C=O

bond

energy

difference

has

been

estimated

thermodynamically to be 13 kcal/mol per grouping.2,13 Supposing that the empirical resonance integral β for benzenoids (not corresponding to the vertical resonance energy) is ca. −1 eV,24 it becomes 0.56β. This value is also obtained by try-and-error fitting of the present data. That is, bond-energy calibration of the oxo form is: 15



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δEbond (δβ C =O ) oxo ≅ +0.56β

Page 16 of 38

(per carbonyl group),

(11)

and the expression of the energy gap (Eoxo−Ehydroxyl) in tautomerism with n active carbonyl groups is given by: active

∆ET =

∑ qr {(δα r ) b − (δα r ) a } + r

active

1 ∑ 2 π {(δα r ,r

r

}

) 2 b − (δα r ) 2 a + 0.56 β ⋅ n.

(12)

r

Again, the summation is taken over all the active sites, and subscripts a and b correspond to forms a and b in Figures 1 and 2.

16


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Table 1. Summary of amino-imino tautomeric energies for 1-16. Eb−Ea Eb−Ea Eb−Ea Preference a) b) a) 1st-order ∆ET 2nd-order ∆ET ∆EDFT Hückel DFTb) Experiments (in unit of |β|) (in unit of |β|) (kcal/mol) (form) (form) (form) biguanide 1 0.125 0.156 +6.87 1a 1a 1ac) amidinourea 2 0.125 0.156 +6.36 2a 2a 2ad) 2-aminopyridine 3 0.418 0.361 +13.8 3a 3a 3ae) 3-aminopyridine 4 0.571 0.589 +29.4 4a 4a 4af) 4-aminopyridine 5 0.418 0.400 +16.4 5a 5a 5ag) guanamine 6 0.500 0.410 +24.0 6a 6a 6ah) melamine 7 0.600 0.583 +32.5 7a 7a 7ai) 3-aminopyrazole 8 0.109 0.093 +2.59 8a 8a 8aj) 7-azaindole 9 0.217 0.233 +12.4 9a 9a 9ak) 2-aminoquinoline 10 0.294 0.283 +11.5 10a 10a 10al) 3-aminoquinoline 11 0.529 0.600 +32.1 11a 11a 11am) 4-aminoquinoline 12 0.250 0.381 +11.9 12a 12a 12an) 5-aminoquinoline 13 0.400 0.533 +25.4 13a 13a 13ao) 6-aminoquinoline 14 0.529 0.593 +35.2 14a 14a 14ap) 7-aminoquinoline 15 0.470 0.505 +24.8 15a 15a 15aq) 8-aminoquinoline 16 0.450 0.615 +27.9 16a 16a 16ar) (a) Based on the sum of the first- and second-order perturbation terms. (b) B3LYP/6-311+G(d,p)// B3LYP/6-311+G(d,p). (c) X-ray diffraction, Ref. 35. (d) X-ray, Ref. 36. (e) X-ray, Ref. 37. (f) X-ray, Ref. 38 (g) X-ray, Ref. 39. (h) X-ray, Ref. 40. (i) X-ray, Ref. 41, 42; Neutron diffraction, Ref. 42, 43. (j) See reviews in Ref. 1 and Ref. 44. (k) X-ray, Ref. 45. §All the aminoquinolines are detected by fluorescence to be amino-type, not imino type. (l) Ref. 46,48. Speculation on imino form in Ref. 47 is probably incorrect. (m) Ref. 49. (n) Ref. 50. (o) Ref. 51. (p) Ref. 52, 53. (q) Ref. 53. (r) Ref. 51, 54. §All the enol and keto types of aminoquinoline are also distinguished by low pKa (

Role of Topological Charge Stabilization in Protomeric Tautomerism

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