Accepted Manuscript

On relation between prototropy and electron delocalization for neutral and redox

adenine – DFT studies

Ewa D. Raczyńska, Katarzyna Kolczyńska, Tomasz M. Stępniewski, Beata

Kamińska

PII: S2210-271X(13)00351-4

DOI: http://dx.doi.org/10.1016/j.comptc.2013.08.009

Reference: COMPTC 1224

To appear in: Computational & Theoretical Chemistry

Received Date: 3 July 2013

Revised Date: 12 August 2013

Accepted Date: 13 August 2013

Please cite this article as: E.D. Raczyńska, K. Kolczyńska, T.M. Stępniewski, B. Kamińska, On relation between

prototropy and electron delocalization for neutral and redox adenine – DFT studies, Computational & Theoretical

Chemistry (2013), doi: http://dx.doi.org/10.1016/j.comptc.2013.08.009

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On relation between prototropy and electron delocalization for

neutral and redox adenine – DFT studies

Ewa D. Raczyńska,1* Katarzyna Kolczyńska,2 Tomasz M. Stępniewski,2 Beata Kamińska1

1Department of Chemistry,Warsaw University of Life Sciences (SGGW), 02-776 Warszawa, Poland

2Interdisciplinary Department of Biotechnology, SGGW, 02-776 Warszawa, Poland

ABSTRACT

Electron delocalization, which plays a principal role for the tautomeric adenine system, was studied

for all possible major, minor, and rare tautomers of neutral, oxidized, and reduced adenine. The

recently extended geometry-based HOMED (harmonic oscillator model of electron delocalization)

index, which measures any type of resonance conjugation (π-π, n-π, and σ-π), was applied to the

geometries of adenine isomers optimized at the DFT(B3LYP)/6-311+G(d,p) level. For neutral

adenine, variations of the HOMED indices estimated for the whole tautomeric systems (eleven bonds)

are almost parallel to those of the relative Gibbs energies (ΔG), which measure the thermodynamic

stabilities of individual isomers. Some subtle effects, being a consequence of intramolecular

interactions of neighboring groups and variability of electron delocalization for the imidazole and

pyrimidine fragments, perturb this relation. One-electron oxidation has slight effect on the general

HOMED/ΔG relation. The favored canonical NH-NH tautomer is well delocalized for both neutral

and oxidized adenine. One-electron reduction dramatically changes electron delocalization and

thermodynamic stability of individual tautomers that two subfamilies can be distinguished on the

HOMED vs ΔG plot, one for the NH-NH tautomers and the other one for the NH-CH isomers. The

reduced canonical NH-NH-tautomer (although well delocalized) is not the favored one. The non-

aromatic NH-CH tautomer predominates in the tautomeric mixture, indicating that aromaticity is not

the main factor that dictates the tautomeric preference for reduced adenine.

Keywords: Adenine, Neutral and redox tautomeric forms, Electron delocalization, Internal effects,

HOMED/ΔG relation, DFT

________________________________________________________________________ *Corresponding Author; Tel.: +48 225937623; Fax: +48 225937635 E-mail: ewa_raczynska@sggw.pl

1. Introduction

Prototropic tautomerism, also called prototropy, and electron delocalization, also

called resonance, are two phenomena that occur very frequently for natural products [1-5].

Electron delocalization applies to a single arrangement of atoms, characterized by two or

more resonance structures, which differ only by the π- and/or n-π electron and charge

arrangements, whereas prototropic tautomerism refers to an equilibrium between two or more

independent isomers (tautomers), which differ by positions of bond(s) and proton(s), and

which can be represented by a hybrid of various resonance structures. A relation between

prototropy and electron delocalization has been signaled more than fifty years ago by Pauling

in his famous book on 'The Nature of the Chemical Bonds' [6]. This relation seems to be very

simple, because prototropy by definition is associated with changes in π-electron

delocalization [2-5]. However, many other factors influence also tautomeric equilibria such as

stability of functionalities, acid-bases properties, intra- and intermolecular interactions, excess

electron, ion, solvent, light, etc. that it is not always evident that electron delocalization

dictates the tautomeric preferences [2,5].

Nucleobase adenine (A) is a bicyclic heterocompound consisting of imidazole fused

with 4-aminopyrimidine. It displays prototropic tautomerism similar to other nucleobases,

uracil, thymine, cytosine, and guanine [1-5,7-14]. Two H atoms can move as protons for

adenine between five N and/or five C atoms. Each intramolecular proton-transfer is

accompanied by migration of one or more double bonds. Twenty-three tautomers, nine forms

containing the exo −NH2 group (A1-A9 in Fig. 1) and fourteen forms containing the exo =NH

group (A10-A23 in Fig. 2) are possible for adenine. When geometric isomerism of the imine

forms is taken into account, thirty-seven isomers can be considered [7]. The amine forms A1-

A9 are analogous to those for unsubstituted purine. They contain one labile proton at the exo

N atom and the other one at the endo N (NH-NH forms: A1, A3, A7, and A9) or C atom (NH-

CH forms: A2, A4, A5, A6, and A8). They are a consequence of amine-imine and imine-

enamine tautomerism, respectively. The imine forms A10-A23 are typical for adenine. Some

of them are analogous to those for 4-aminopyrimidine. The NH-NH tautomers (A13, A15,

A18, and A20) possess two labile protons at the endo N atoms and result from amine-imine

tautomerism. The NH-CH isomers (A10-A12, A14, A16, A17, A19, and A21-A23) have one

labile proton at the endo N atom and the other one at the endo C atom and result from imine-

enamine tautomerism. Depending on the position of the labile protons, one tautomeric

function may favorably or unfavorably interact with the other one. Possible favorable

intramolecular interactions are shown in Fig. 1 and 2.

10

9 876

5432

1N

N

N

N

N

H

HH

N

N

N

N

N

H

H

HH

N

N

N

N

N

H

HH

A1 A2 A3

N

N

N

N

N

H

HH

N

N

N

N

NH

HH

N

N

N

N

NH2H

A4 A5 A6

N

N

N

N

N HHH

N

N

N

N

N

H

H

HH

N

N

N

N

N

H

HH

A7 A8 A9

Fig. 1. Amine tautomers for adenine and possible favorable intramolecular interactions

Adenine contains eight π- and ten n-electrons which participate in electron

delocalization during tautomerization. Various types of π-π and n-π resonance conjugations

are possible for the NH-NH tautomers and additionally σ-π hyperconjugations for the NH-CH

isomers. These different types of resonance conjugations lead to different electron

delocalization for individual tautomers which can be represented by different hybrids of

resonance structures [7]. The number of resonance structures strongly depends on the

positions of the labile protons and on the positions of the double bonds in the Lewis

structures. The number of resonance structures affects the stability of the tautomeric form and

its contribution in the tautomeric mixture. Consequently, prototropy and electron

delocalization influence the structure of adenine, its physicochemical, chemical, and

biochemical properties.

N

N

N

N

N

H

H

H

H

N

N

N

N

N

H

H

H

H

N

N

N

N

N

H

H

H

N

N

N

N

N

H

H

H

A10a A10b A11a A11b

N

N

N

N

NH

H

H

N

N

N

N

NHH

H

N

N

N

N

N HH

H

N

N

N

N

N HH

H

A12a A12b A13a A13b

N

N

N

N

N

H

H

H

H

N

N

N

N

N

H

H

H

H

N

N

N

N

N

H

H

H

N

N

N

N

N

H

H

H

A14a A14b A15a A15b

N

N

N

N

N

H

H

H

N

N

N

N

N

HH

H

N

N

N

N

NH

H

H

N

N

N

N

NH

H

H

A16a A16b A17a A17b

N

N

N

N

N

H

HH

N

N

N

N

N

H

HH

N

N

N

N

N

H

H

H

H

N

N

N

N

N

H

H

H

H

A18a A18b A19a A19b

N

N

N

N

N

H

H

H

N

N

N

N

N

HH

H

N

N

N

N

NH

HH

N

N

N

N

NH

HH

A20a A20b A21a A21b

N

N

N

N

NH

H

H

N

N

N

N

NH

H

H

N

N

N

N

N

H

H

H

H

N

N

N

N

N

H

H

H

H

A22a A22b A23a A23b

Fig. 2. Imine tautomers for adenine and possible favorable intramolecular interactions

Although one can find numerous experimental and theoretical reports on the structure

of neutral adenine, there are only a few articles in which prototropy has been examined in

details for maximum twelve isomers, four amine (A1, A3, A7, and A9) and eight imine forms

(A13, A15, A18, and A20, including isomers a and b) [8-12]. In some papers, the zwitterionic

forms have been also taken into account, however, they cannot be considered as tautomers.

One exception is the anionic state of adenine, for which the NH-CH isomers, neglected for

neutral adenine, have been considered, and surprisingly, they have been found as the favored

forms in the gas phase [13,14]. This exception shows evidently that in particular conditions,

which may occur in living organisms, the NH-CH isomers as dominant forms may influence

the products formation in proton-transfer, electron-transfer, and/or ion-radical reactions,

leading to DNA and RNA mutations. For this reason, we investigated in our previous work

[7] all possible thirty-seven isomers for adenine, and we analyzed in details the amine-imine

conversions between the N atoms for the NH-NH forms and also the enamine-imine

conversions between the N and C atoms for the NH-CH isomers. The complete studies for all

possible tautomers of adenine gave the possibilities to examine the variations of the

composition of the tautomeric mixture when proceeding from the neutral to redox forms, and

also from the isolated (gas phase) to solvated (water) molecules. To our knowledge, electron

delocalization has been solely discussed for one neutral canonical structure A9 [15-19] and

for N-benzyl derivatives of three amine tautomers of neutral adenine (A3, A7, and A9) [20].

The aim of this paper was to study the relation between prototropy and electron

delocalization for all possible thirty-seven isomers of neutral adenine (A) and for its charged

radicals, the radical cation (A+•) and the radical anion (A-•). The charged radicals can be

formed in the presence of oxidizing or reducing agents. They may be also generated

electrochemically, photochemically, or in mass spectrometers during positive (A → A+• + e)

or negative ionization (A + e → A-•). For investigations, the density functional theory (DFT)

[21] with the Becke three-parameter hybrid exchange functional and the non-local correlation

functional of Lee, Young, and Parr (B3LYP) [22,23] and the 6-311+G(d,p) basis set with the

diffuse and polarization functions [24] were employed as previously described [7]. The DFT

method has been recommended in the literature to study the geometry of π-electron systems

in which various phenomena, such as protobranching, hyperconjugation, conjugation,

aromaticity, tautomerism, proton-transfer, and/or hydrogen bonding may take place [25-30].

To well determine the distribution of π- and n-electrons for all individual tautomers of

neutral and redox adenine, and to well describe the relation between prototropy and electron

delocalization, the recently extended geometry-based HOMED (harmonic oscillator model of

electron delocalization) procedure [31,32] was applied to the geometries of the adenine

isomers optimized at the B3LYP/6-311+G(d,p) level. The HOMED index is based on the

original HOMA (harmonic oscillator model of aromaticity) idea [33,34]. An abbreviation

HOMED was proposed in 2006 for the modified index [31], but it may be also abbreviated as

moHOMA (modified original HOMA) or simply HOMA. Unfortunately, the HOMA index,

reformulated by Krygowski in 1993 (rHOMA) [35] and applied to heterocycles [36,37]

including the canonical structures of nucleobases [15], seems to be inappropriate for π-

electron compounds containing heteroatoms because different measures of π-electron

delocalization were employed for the reference CC, CX, and XY bonds [32]. For this reason,

the rHOMA index was not applied here for the adenine tautomers.

Since there is one concept of resonance for neutrals, ions, and radicals [6], the

HOMED (modified oHOMA) indices were estimated for all possible neutral, oxidized, and

reduced adenine tautomers. Next, they were compared with the previously reported relative

Gibbs energies (ΔG) [7]. The comparison of these data gives the possibilities to analyze

different factors, such as intramolecular interactions between the −NH2/=NH and =N/NH

groups, one-electron loss, and one electron gain, which may influence tautomeric equilibria

and electron delocalization. It should be mentioned here that one can find in the literature

many other indices of aromaticity which can be classified as energetic and magnetic ones

[26,37]. For simple five-membered rings, good correlations occur between the geometry-

based, energetic, and magnetic indices [26]. However, for polycyclic systems, situation is

more complex, because the magnetic indices are local descriptors and cannot be applied to the

whole molecule, whereas the energetic indices are rather global ones, and cannot be used for

the fragments [26,37]. Solely the geometry-based indices can be applied for the whole

molecule as well as for its fragments [5,32,36]. They can measure local and global electron

delocalization for polycyclic systems. The geometry-based indices can be also applied to

ionic species (cations and anions) as well as to open-shell radicals (neutrals, cations, and

anions) for which electrons are delocalized by various resonance conjugations

[5,32,36,38,39]. For example, the application to the arene cation- and anion-radicals (reactive

and kinetically unstable products of one-electron oxidation and one-electron reduction of

aromatic hydrocarbons) has led recently to interesting conclusion on aromaticity of radical

ions [39]. For simple acetaldehyde/vinyl alcohol tautomeric system, it has been noted that

removing an electron from the n orbital of the carbonyl oxygen in the keto tautomer has no

important effect on the location of the π-electrons, whereas removing an electron from the π

orbital of the enol tautomer causes strong electron delocalization [40]. This trend is well

described by the geometry based indices [5].

2. Methods

Geometries of all possible neutral and charged amine (A1-9 in Fig. 1) and imine (A10-

23 in Fig. 2) isomers of adenine in their ground states were fully optimized without symmetry

constraints using the DFT(B3LYP) method [21-23] and the 6-311+G(d,p) basis set [24] using

the Gaussian 03 program [41] as previously described [7]. The HOMED (modified oHOMA)

indices, described previously in details [32], were estimated on the basis of the theoretically

derived bond lengths according to equation (1) [33-35]. In this equation, α are normalization

constants, Ro are the optimum bond lengths (assumed to be realized for fully delocalized

homo- and hetero-systems), Ri are the running bond lengths in the investigated system, and n

is the number of bonds taken into account. For the system containing the even number of

bonds (2i), the normalization α constants were calculated from equation (2), where Rs and Rd

are the reference single and double bonds, respectively. For the system containing the odd

number of bonds (2i + 1), i.e., (i + 1) single bonds and (i) double bonds, the normalization α

constants were calculated from equation (3).

HOMED = 1 − {α(CC) ⋅ Σ[Ro(CC) − Ri(CC)]2] + α(CX) ⋅ Σ[Ro(CX) − Ri(CX)]2]}/n (1)

α = 2 ⋅ {(Ro − Rs)2 + (Ro − Rd)2}-1 ⋅ (2)

α = (2i + 1) ⋅ {(i + 1) ⋅ (Ro − Rs)2 + i ⋅ (Ro − Rd)2}-1 (3)

Ro = (Rs + ω ⋅ Rd)/(1 + ω) (4)

The following Rs, Rd, and Ro values (in Å), calculated at the B3LYP/6-311+G(d,p)

level, were taken here: 1.530 (ethane), 1.329 (ethene), and 1.394 (benzene) for the CC bonds,

and 1.466 (methylamine), 1.267 (methylimine), and 1.334 (1,3,5-triazine) for CN bonds [32].

The Ro bond lengths, computed for the reference aromatic systems (benzene and 1,3,5-

triazine), are in accord with the harmonic oscillator method of optimization {equation (4)}

[33-35], where ω (close to 2 for the CC and CN bonds) is the ratio of the stretching force

constants for the pure double and pure single bonds. The use of the same level of theory for

the reference molecules and for π-electron heteroatomic adenine system has this advantage

that computational errors cancel out in the procedure of the HOMED estimation. This

cancellation was confirmed for simple molecules using different quantum-chemical methods

and different basis sets [32]. Similarly as in the case of adenine building blocks [42-45] and

other heteroaromatic compounds containing the N atoms [32], the normalization α constants

calculated according to equation (2) and equal to 88.09 (CC) and 91.60 (CN) were used for

the systems containing the even number of bonds, i.e., pyrimidine ring (six bonds) and purine

system (ten bonds). For the systems with the odd number of bonds, the normalization α

constants calculated according to equation (3) were applied: 78.34 (CC) and 81.98 (CN) for

the imidazole fragment (five bonds), 80.90 (CC) and 84.52 (CN) for the 4-aminopyrimidine

fragment (seven bonds), and 83.37 (CC) and 86.96 (CN) for the whole tautomeric system of

adenine (eleven bonds).

3. Results and discussion

3.1. HOMED procedure

Electron delocalization is a phenomenon that occurs for various neutral and charges

molecules (cations and anions) such as homo- and hetero-aromatics, π-π and n-π conjugated

cyclic and acyclic systems as well as σ-π hyperconjugated compounds [6,46-48]. The same

phenomenon of electron delocalization takes place for neutral, cationic, and anionic radicals

conjugated by resonance [6,46-48]. An equalization of single and double bonds is possible for

well delocalized symmetric species [5,6,32-36]. When resonance conjugation decreases,

localization of double and single bonds appears. The double bonds shorten and the single

bonds lengthen in comparison to those for well delocalized systems. Situation is reverse,

when resonance conjugation increases due to internal or external factors. The double bonds

lengthen and the single bonds shorten. The relation between changes of bond lengths and

changes of electron delocalization has been described by the geometry-based indices,

oHOMA, rHOMA, and moHOMA (HOMED), all based on the same harmonic oscillator

method of optimization [31-36].

From the mathematical point of view, the procedure of the HOMED index [31,32] is

the same as that of the original HOMA index proposed in 1972 by Kruszewski and

Krygowski [33] to describe quantitatively π-electron delocalization for aromatic systems. The

HOMED index describes the same phenomenon - shortening of the single bond(s) and

lengthening of the double bond(s) due to the resonance conjugation(s) in the system. The

HOMED index can be estimated according to equation (1), which is the same as that proposed

for the original HOMA index for homo- and hetero-aromatics [33,34]. For its parametrization,

the simplest acyclic compounds of similar electron delocalization are employed for the

reference molecules. They are the same as those for the original HOMA index. For example,

the C−C single bond in ethane and the C=C double bond in ethene, the C−N single bond in

methylamine and the C=N double bond in methylimine, the C−O single bond in methanol and

the C=O double bond in formaldehyde, etc. are used for the reference Rs and Rd bonds,

respectively [31,32]. The choice of the simplest acyclic compounds for the reference

molecules has this advantage that the HOMED index can measure the strength of any

resonance conjugation, weak σ-π hyperconjugation, medium n-π and π-π conjugations, and

also strong aromaticity for any type of π-electron heteroatomic systems, for acyclic and cyclic

neutral molecules, ions, and radicals. According to the definition, HOMED = 1 for aromatic

benzene similarly as oHOMA [32]. It is also equal to 1 for 1,3,5-triazine. The HOMED

indices are equal to zero for the systems with the localized single and double bonds equal to

those for the reference molecules. To minimize errors of the HOMED estimations, the

reference bond lengths determined by the same method as those for investigated compounds

are applied [32].

One difference between the original HOMA and the modified HOMED index is the

normalization constants α. In the original HOMA procedure, the factor of 98.89 was used for

the CC bond [33]. The same normalization constant α (98.89) was employed for the CX and

XY bonds for heterocycles containing the odd and even number of bonds [34]. In the

HOMED procedure, two equations (2) and (3) were applied for estimation of the

normalization constants α, one (2) for the system containing the even number of bonds, which

is similar to that proposed for the reformulated HOMA index [35], and the other one (3) for

the system containing the odd number of bonds [32]. In this way, the HOMED indices are

close to unity for aromatic systems. For weakly delocalized σ-π hyperconjugated systems,

they are considerably lower or close to zero.

For the reformulated HOMA index (rHOMA), in 1993 Krygowski proposed to use the

reference molecules of different electron delocalization [35]. For example, 1,3-butadiene for

the CC bonds and formic acid for the CO bonds were applied, for which π-electrons are

moderately delocalized by π-π and n-π conjugation, respectively, However, the reference

molecules of slight electron delocalization (methylamine and methylimine) were used for the

CN bonds as those for the original HOMA index. This reformulation involved a necessity of

application of completely different normalization constants α for different bonds, e.g., 257.7

(CC), 93.52 (CN), and 157.38 (CO). Consequently, applications of the rHOMA index to

heteroatomic systems have led to artificial results [5,31,32,36,37,42,45]. For example, the

rHOMA indices are strongly negative for the imidazole and purine CH tautomers, which are

delocalized by a mixture of σ-π hyperconjugation and π-π conjugation [42,45]. The rHOMA

index is also close to zero for furan (0.298), whereas it is close to unity for pyrrole (0.876)

[37]. When the CH groups are replaced in the ring by the N-aza groups, the rHOMA values

increase (to 0.332, 0.527, 0.586, for 3-aza-, 2-aza-, and 2,3,5-triazafuran, and to 0.908, 0.926,

and 0.960 for 3-aza, 2-aza, and 2,3,5-triazapyrrole, respectively [37]). These variations of the

rHOMA index are only numerical and have nothing common with real π-electron

delocalization in heteroaromatic systems. It should be mentioned here that the original

HOMA values are close to unity for aromatic furan and pyrrole [34]. For the neutral non-

aromatic CH tautomers of imidazole and purine (models for adenine), the modified oHOMA

(HOMED) values are positive or close to zero [42,45]. The artificial rHOMA values are a

consequence of the use of different measures of electron delocalization for the CC and CX

bonds. For this reason, the rHOMA index cannot be employed for the systems containing

heteroatoms, i.e., adenine. It may be solely used for compounds containing the same type of

bonds, e.g., neutral hydrocarbons and their radical ions [39,49]. On the other hand, the

HOMHED (harmonic oscillator model of heterocyclic electron delocalization) index,

proposed in 2012 by Frizzo and Martins [50], is based on the hypotheses of the HOMED

index [32]. The principal difference is an application of the statistical reference bond lengths

in the HOMHED procedure. The use of statistical reference CC, CX, and XY bond lengths

leads to some kind of the statistical HOMHED values which do not describe well the real

electron delocalization in heteroatomic systems. For this reason, the HOMHED index was not

applied here for the DFT-computed structures of adenine tautomers.

To quantitatively measure variations of electron delocalization for the favored and rare

tautomers of adenine when proceeding from its neutral to oxidized and reduced forms, the

geometry-based HOMED index was applied to the DFT-calculated bond lengths listed in

Tables S1-S3 (Supplementary material). For all neutral isomers of adenine (A1-A23), their

oxidized (A1+•-A23+•) and reduced forms (A1-•-A23-•), the HOMED indices were

estimated for the imidazole (five bonds), pyrimidine (six bonds), 4-aminopyrimidine (seven

bonds), and purine fragment (ten bonds) and also for the whole tautomeric system including

the exo −NH2/=NH group (eleven bonds). They are summarized in Tables S4-S6

(Supplementary material). The relative Gibbs energies (ΔG), estimated for individual isomers

at the same level of theory [7], are also included in these Tables. First perusal of the HOMED

values indicates strong dependence of electron delocalization on position of the labile protons.

The HOMED values are very low or close to zero for weak delocalized fragments containing

the C-sp3 atom in the non-aromatic NH-CH tautomers with one labile proton at the C atom,

and they are close to unity for well delocalized aromatic fragments with the labile protons at

the N atoms. Comparison of the HOMED values estimated for the structural fragments of the

adenine tautomers with those for the building blocks (imidazole, 4-aminopyrimidine, and

purine) [42-45] gives the possibilities to distinguish additionally the effects of the structural

fussion of the imidazole and 4-aminopyrimidine fragments and the effects of the exo

−NH2/=NH group. On the other hand, comparison of the HOMED values for the neutral and

redox forms makes possible to analyze the effects of one-electron oxidation and one-electron

reduction.

3.2. Canonical and favored tautomers

As it could be expected [15-19], the canonical tautomer A9 of neutral adenine,

possessing the lowest Gibbs energy, is aromatic. The HOMED values estimated for the

imidazole, pyrimidine, 4-aminopyrimidine, and purine fragments, and also for the whole

adenine tautomeric system are as follows (Chart 1a): 0.883, 0.995, 0.992, 0.931, and 0.938,

respectively. They are slightly larger than the HOMED5, HOMED6, and HOMED10 values

for the favored tautomer of purine (0.872, 0.994, and 0.927, respectively), confirming that the

electron-donating resonance effect for the exo −NH2 group is stronger than its electron-

accepting inductive effect for the conjugated aromatic adenine system. The structural fusion

of the favored tautomers of the building blocks, imidazole and 4-aminopyrimidine, slightly

decreases the HOMED5 value in A9 for the imidazole fragment (from 0.902 to 0.883) and

slightly increases the HOMED6 and HOMED7 values for the 4-aminopyrimidine fragments

(from 0.991 to 0.995 and from 0.981 to 0.992, respectively).

When proceeding from neutral A9 (Chart 1a) to oxidized A9+• (Chart 1b), the

HOMED5 value increases (from 0.883 to 0.926), whereas the HOMED6 value strongly

decreases (from 0.995 to 0.890). This decrease changes the other HOMED values which also

decrease: HOMED7 for the 4-aminopyrimidine fragment (from 0.992 to 0.911), HOMED10

for the purine fragment (from 0.931 to 0.904), and HOMED11 for the whole tautomeric

adenine system (from 0.938 to 0.916). In the case of the building blocks, imidazole and 4-

aminopyrimidine, one-electron oxidation also influences electron delocalization, but in

different way than for adenine. The HOMED indices decrease for both building blocks,

imidazole (from 0.902 to 0.877) and 4-aminopyrimidine (from 0.991 to 0.950 and from 0.981

to 0.960 for the six and seven bonds, respectively). On the other hand, the structural fusion of

the favored radical cations of imidazole and 4-aminopyrimidine increases the HOMED5 value

(from 0.877 to 0.926), and decreases the HOMED6 and HOMED7 values (from 0.950 to

0.890 and from 0.960 to 0.911, respectively). Similar effects occur when going from the

favored radical cation of purine to A9+•. The HOMED5 value increases (from 0.903 to

0.926), whereas the HOMED6 value decreases (from 0.965 to 0.890). All these variations

suggest that the exo NH2 group, rather than the endo NH group, loses one electron from its n-

orbital in A9+•. Indeed, the most important amount of the spin density exists on the N10 atom

[7]. This may explain why one-electron oxidation reduces n-π conjugation of this group with

the pyrimidine ring in the oxidized adenine tautomer and decreases the HOMED6 and

HOMED7 values.

a) neutral

N

N

N

N

H

NH2

N

N

N

N

H

N

N

H

N

N

NH20.981

0.991 0.902

0.927

0.994 0.872

0.992

0.995

0.931

0.883

0.938

b) oxidized

0.916

0.926

0.904

0.890

0.911

0.9030.965

0.938

0.8770.950

0.960

N

N

NH2

N

N

H

N

N

N

N

H

N

N

N

N

H

NH2 +.

.+

c) reduced

_ .

._

N

N

N

N

H

NH2

N

N

N

N

H

N

N

H

N

N

NH20.843

0.904 0.937

0.892

0.923 0.885

0.989

0.966

0.867

0.791

0.839

Chart 1. Variations of the HOMED indices when going from the favored tautomers of the building blocks to the canonical tautomer of adenine for neutral (a), oxidized (b), and reduced (c) form

One-electron reduction of A9 decreases all partial HOMED values (Chart 1c), in

higher degree for the imidazole fragment (from 0.883 to 0.791) than for the pyrimidine one

(from 0.995 to 0.966). Consequently, the HOMED7, HOMED10, and HOMED11 values also

decrease (from 0.992 to 0.989, from 0.931 to 0.867, and from 0.938 to 0.839, respectively).

On the other hand, the structural fusion of the respective radical anions of imidazole and 4-

aminopyrimidine leads to the decrease of HOMED5 (from 0.937 to 0.791) and to the increase

of HOMED6 and HOMED7 (from 0.904 to 0.966 and from 0.843 to 0.989, respectively).

Similar effects take place when going from the respective radical anion of purine to A9-•. The

HOMED5 value decreases (from 0.885 to 0.791) and the HOMED6 value increases (from

0.923 to 0.966). These changes compared to those for the neutral tautomers may suggest that

the purine system takes one excess electron during the reduction process of adenine. For A9-

•, most of spin density is carried by the C2, C6, and C8 atoms [7].

0.638

0.342

0.614

0.906

0.881

0.3390.881

0.614

0.4060.904

0.843

N

N

NH2

N

N H

H

N

N

N

N

H

H

H

N

N

N

N

H

NH2

H

H

_.

._

Chart 2. Variations of the HOMED indices when going from the reduced building blocks to the favored reduced adenine tautomer

Although A9-• is the most aromatic tautomer, it is not the favored one for reduced

adenine. This means that aromaticity is not the main factor that dictates the tautomeric

preference for reduced adenine. The lowest G value in the family of the reduced adenine

isomers has been found for A8-• which has considerably weaker electron delocalization than

A9-• due to the presence of the C8-sp3 atom. The HOMED values for the five, six, seven,

ten, and eleven bonds of A8-• are as follows (Chart 2): 0.342, 0.906, 0.881, 0.614, and 0.638,

respectively. The structural fusion of the respective radical anions of imidazole and 4-

aminopyrimidine leads to similar effects as those for A9-•, i.e., the HOMED5 value decreases

(from 0.406 to 0.342), and the HOMED6 and HOMED7 values increase (from 0.904 to 0.906

and from 0.843 to 0.881, respectively). The exo NH2 group in A8-•, when compared to the

respective radical anion of purine, slightly increases both the HOMED5 (from 0.339 to 0.342)

and HOMED6 values (from 0.881 to 0.906).

3.3. Effects of the exo −NH2/=NH group

For all individual amine tautomers of neutral (A1-A9), oxidized (A1+•-A9+•), and

reduced adenine (A1-•-A9-•), the total effect of the exo −NH2 group on delocalization of π-

and n-electrons can be analyzed by direct comparison of their HOMED indices estimated for

five, six, and ten bonds with those for the corresponding tautomers of purine (P1-P9 -

analogous to A1-A9, P1+•-P9+• - analogous to A1+•-A9+•, and P1-•-P9-• - analogous to

A1-•-A9-• [45]). This effect {δHOMED = HOMED(adenine form) − HOMED(purine form)

given in Table S7, Supplementary material} is a sum of the inductive and resonance effects of

the exo NH2 group and also of the internal favorable and unfavorable effects resulting from

specific interactions of this group with the endo neighboring N1/N1H and N7/N7H groups

(Fig. 1).

In the case of neutral adenine, the lowest δHOMED5, δHOMED6, and δHOMED10

values (< 0.01) occur for the aromatic A7 and A9 tautomers (Fig. 3). This suggests that the

NH2 group has a slight effect on already well delocalized aromatic purine system. For less

aromatic A1 and A3 tautomers, larger δHOMED values are for the five-membered ring (0.05-

0.06) than for the six-membered one (0.01-0.02) possessing the labile proton. For the non-

aromatic A2 and A8 tautomers, the absolute δHOMED values are not larger than 0.07 units.

The largest δHOMED values occur for the non-aromatic A4 (0.07-0.18) and A5 (0.04-0.15)

tautomers, for which the NH2 group increases π-electron delocalization in both rings and in

the whole purine system. This effect may explain an exceptional increase of the

thermodynamic stability of the adenine tautomers A4 and A5 in comparison to the purine

ones [7]. Some exception is A6 − the non-aromatic tautomer possessing the largest Gibbs

energy value. For this isomer, the lone electron pair of the NH2 group cannot participate in

the delocalization of π-electrons in the ring due to the sp3-hybridization of the C6 atom which

takes the labile proton. Moreover, this group cannot intramolecularly interact with the

neighboring groups. The NH2 group acts solely by its electron-accepting inductive effect.

Hence, the partial HOMED indices decrease for A6 in comparison to the corresponding

purine tautomer (by 0.02-0.04 units).

a) neutral adenine

-0,2

0

0,2

0,4

1 2 3 4 5 6 7 8 9

Number of tautomer

HO

ME

Dne

utra

l

b) oxidized adenine

-0,2

0

0,2

0,4

1 2 3 4 5 6 7 8 9

Number of tautomer

HO

ME

Dox

idiz

ed

c) reduced adenine

-0,2

0

0,2

1 2 3 4 5 6 7 8 9

Number of tautomer

HO

ME

Dre

duce

d

Fig. 3. Variations of the total effect of the NH2 group (δHOMED) for the neutral (a), oxidized (b) and reduced (c) adenine tautomers (for five, six and ten bonds). Numbers of tautomers 1-9 correspond to the amine tautomers A1-A9 (a), A1+•-A9+• (b), and A1-•-A9-• (c), respectively

For the oxidized and reduced amine tautomers of adenine, the variations of the total

effects of the exo NH2 group are completely different than those for the neutral ones. For the

oxidized forms, the partial δHOMED values vary from -0.17 to 0.34. Generally, they are

close to zero or negative for the aromatic NH-NH tautomers, and they are close to zero or

positive for the nonaromatic NH-CH ones. For the reduced forms, the δHOMED values are

close to zero, except those for A7-• and A9-•, which are negative for the imidazole fragment

containing the labile proton, and consequently for the whole tautomeric system.

a) neutral adenine

-0,3

0

0,3

1 3 5 7 9 11 13

Number of isomer

HO

ME

Dne

utra

l

b) oxidized adenine

-0,6

-0,3

0

0,3

1 3 5 7 9 11 13

Number of isomer

HO

ME

Dox

idiz

ed

c) reduced adenine

-0,3

0

0,3

1 3 5 7 9 11 13

Number of isomer

HO

ME

Dre

duce

d

Fig. 4. Variations of the subtle effect of the =NH group (δHOMED) for the neutral (a), oxidized (b), and reduced (c) adenine tautomers (for five and six bonds). Numbers of isomers 1-14 correspond to the imine isomers A10-A23 (a), A10+•-A23+• (b), and A10-•-A23-• (c), respectively

Intramolecular interactions between the exo =NH group and the endo N1/N1H and

N7/N7H groups possible for the imine tautomers of adenine (Fig. 2) influence also electron

delocalization, and consequently the HOMED indices for the imine NH-NH and NH-CH

tautomers of neutral (A10-A23), oxidized (A10+•-A23+•), and reduced adenine (A10-•-A23-

•). Direct comparison of the HOMED indices for the structures a and b gives the possibilities

to estimate the subtle intramolecular interactions of the exo =NH group (Table S8,

Supplementary material). Depending on the positions of the labile protons, the =NH group

may favorably or unfavorably interact with the neighboring functional groups. These effects

change the HOMED values when going from a to b {δHOMED = HOMED(b) −

HOMED(a)} in higher degree for the oxidized than reduced and neutral forms. Fig. 4 shows

the variations of the δHOMED values for the imidazole (five bonds) and pyrimidine (six

bonds) fragments of neutral, oxidized, and reduced adenine. The subtle effects of the exo

=NH group influence also the relative Gibbs energies [7]. Unfortunately, the variations of the

δHOMED values (< 0.5) are not in line with the variations of the corresponding δG values (<

10 kcal mol-1). Similar trend occurs for 4-aminopyrimidine. These subtle effects of the exo

=NH group perturb the general HOMED/ΔG relation for the adenine tautomers.

3.4. HOMED/ΔG relation for neutral adenine

Interesting information on general relation between π-electron delocalization and

prototropy can be derived from a direct comparison of the partial HOMED indices and the

relative Gibbs energies (ΔG) calculated for the individual tautomers of adenine at the same

level of theory. Fig. 5 shows the effect of prototropy on electron delocalization for the

fragments of the neutral adenine system, imidazole, pyrimidine, 4-aminopyrimidine, and

purine. The most important conclusion is that the variations of π-electron delocalization for

the imidazole fragment (Fig. 5a) are not similar to those for the 4-aminopyrimidine fragment

(Fig. 5c). For the aromatic NH-NH tautomers, for which the relative Gibbs energies vary from

zero to 31 kcal mol-1, the HOMED5 values vary solely from 0.87 to 0.95, whereas the

HOMED6 values vary from 0.68 to 0.99. In the case of the non-aromatic NH-CH tautomers,

for which the ΔG values vary from 34 to 64 kcal mol-1, the variations of the HOMED5 (from

0.27 to 0.62) and HOMED6 values (from 0.25 to 0.76) are considerably larger. These

differences influence the HOMED/ΔG relation for the purine fragment (Fig. 5d), and also for

the whole tautomeric system (Fig. 6d).

The HOMED5 values are close to 0.95 for the imidazole fragment of the NH-NH

tautomers having both labile protons in the 4-aminopyrimidine fragment (A1 and A3),

whereas they are close to 0.9±0.3 for the tautomers containing the labile proton at the N7 (A7,

A13, and A18) or N9 atom (A9, A15, and A20). In the case of the NH-CH tautomers, the

largest HOMED5 values occur for those forms which possess the labile proton at the

pyrimidine C atom (A2, A6, and A10), and the lowest HOMED5 values are for those forms

with the labile proton at the imidazole C atom (A8, A14, A19, and A23). Generally, the

variations of the HOMED5 indices for the imidazole ring do not follow well the variations of

the ΔG values, and a scatter plot is observed in Fig. 5a. This trend influences the deviations of

points from linear relation for the purine fragment (Fig. 5d), and also for the whole adenine

tautomeric system (Fig. 6d). The HOMED6 (Fig. 5b) and HOMED7 (Fig. 5c) values for the

pyrimidine and 4-aminopyrimidine fragments, respectively, seem to be almost parallel to the

ΔG values. Some subtle internal effects of the exo −NH2/=NH group and resonance

conjugations (n-π and π-π) of the pyrimidine and imidazole rings cause smaller or greater

deviations for particular points from the HOMED/ΔG relation. These subtle effects influence

also the deviations of points from the HOMED/ΔG relation for the whole adenine tautomeric

system (Fig. 6d).

Quite a good linear relation (Fig. 6d) between the HOMED11 indices, which measure

electron delocalization for individual isomers, and the relative Gibbs energies, which measure

their thermodynamic stability, suggests that electron delocalization (aromaticity) is one of the

main factors that dictate the tautomeric preferences for neutral adenine, similarly as it takes

place for its neutral building blocks, imidazole (Fig. 6a), 4-aminopyrimidine (Fig. 6b), and

purine (Fig. 6c). Interestingly, imidazole and purine do not contain the exo substituent which

could additionally affect the relative stability and electron delocalization of individual

tautomers by intramolecular favorable or unfavorable interactions, and thus the HOMED/ΔG

linear relations are better for imidazole and purine (Fig. 6a and 6c, correlation coefficient, r ≥

0.99) than those for 4-aminopyrimidine (Fig. 6b, r = 0.98) and adenine (Fig. 6d, r = 0.94),

where the exo −NH2/=NH group can intramolecularly interact with the endo N/NH groups.

a) imidazole fragment

0

0,5

1

0 20 40 60 80

ΔG

HO

ME

D5

b) pyrimidine fragment

0

0,5

1

0 20 40 60 80

ΔG

HO

ME

D6

c) 4-aminopyrimidine fragment

0

0,5

1

0 20 40 60 80

ΔG

HO

ME

D7

d) purine fragment

0

0,5

1

0 20 40 60 80

ΔG

HO

ME

D10

Fig. 5. Plots between the HOMED indices and the ΔG values (in kcal mol-1) estimated for the imidazole (a), pyrimidine (b), 4-aminopyrimidine (c), and purine fragments (d) of adenine isomers

a) neutral imidazole

0

0,5

1

0 5 10 15 20

ΔG

HO

ME

D5

b) neutral 4-aminopyrimidine

0

0,5

1

0 10 20 30 40

ΔG

HO

ME

D7

c) neutral purine

0

0,5

1

0 20 40 60

ΔG

HO

ME

D10

d) neutral adenine

0

0,5

1

0 20 40 60 80

ΔG

HO

ME

D11

Fig. 6. Plots between the HOMED indices and the ΔG values (in kcal mol-1) estimated for the whole tautomeric system of neutral imidazole (a) [42], 4-aminopyrimidine (b) [43], purine (c) [45], and adenine (d) isomers

3.5. Effects of one-electron oxidation and one-electron reduction

The comparison of the HOMED values estimated for the oxidized and reduced forms

of adenine (Table S5 and S6, respectively, Supplementary material) with those for the neutral

ones (Table S4) shows evidently that internal resonance conjugations and internal specific

interactions possible for the individual isomers are very sensitive to electron-transfer. One-

electron detachment (oxidation) involves changes in the HOMED values which are

completely different from those caused by one-electron attachment (reduction). When

proceeding from the neutral to oxidized isomers, the HOMED11 values (Table 1) decrease for

the amine NH-NH tautomers (A1+•, A3+•, A7+•, and A9+•), whereas they increase for both

structures a and b of the imine NH-NH ones (A13+•, A15+•, A18+•, and A20+•). Hence,

two subfamilies may be distinguished on the HOMED(A+•) vs HOMED(A) plot for the

oxidized NH-NH family. For the family of the oxidized NH-CH isomers, the HOMED11

values decrease for A2+•, A4+•, A6+•, A11a+•, A11b+•, A21b+•, and A22b+•, whereas

they increase for A10a+•, A19a+•, A19b+•, A22a+•, A23a+•, and A23b+• in higher degree

than for the other ones. In this case, at least three subfamiles can be distinguished. For this

reason, there is not good linear relation between the HOMED11 values of the oxidized and

neutral forms of adenine (Fig. S1a, Supplementary material). Quite a different situation takes

place for the reduced adenine isomers (Table 1). One-electron reduction decreases the

HOMED11 values for the NH-NH tautomers (except A20a-• and A20b-•), whereas it

augments them for the NH-CH isomers, in considerably higher degree for A6-•, A10a-•, and

A10b-• than for the other ones (except A4-•). These changes, however, do not perturb quite a

good linear relation between the HOMED11 values of the reduced and neutral forms (Fig.

S1b, Supplementary material).

Important differences of the electron-transfer effects can be distinguished from the

general HOMED/ΔG relations for the redox forms of adenine (Fig. 7). For the oxidized

isomers, the HOMED11 values are in quite good line with the ΔG values (r = 0.93). The

correlation is only slightly worsen than that for the neutral tautomers. The HOMED11 values

for the aromatic NH-NH tautomers do not change very much (from 0.84 to 0.92), whereas

their ΔG values vary from 0 to 21 kcal mol-1. On the other hand, variations of the HOMED11

values for the non-aromatic NH-CH tautomers are relatively greater (from 0.24 to 0.65), and

their ΔG values vary from 47 to 83 kcal mol-1. Despite of these different changes for the NH-

NH and NH-CH tautomers, electron delocalization seems to be one of the most important

factors that determine the tautomeric preferences for oxidized adenine. In the case of reduced

adenine, the tautomeric preferences depend on the electron affinity of the individual

tautomers [7]. The non-aromatic NH-CH tautomers take easier one excess electron than the

aromatic NH-NH ones [7,13,14]. However, the favored non-aromatic tautomer A8-• is less

delocalized than the canonical aromatic minor form A9-•. An interesting separation of the

NH-NH and NH-CH subfamilies can be distinguished on the plot of the HOMED11 vs ΔG

values. Two almost parallel linear relations exist for the reduced adenine isomers, one for the

NH-NH tautomers, and the other one for the NH-CH forms. For both subfamilies, variations

of electron delocalization is not very large in comparison to those of their thermodynamic

stability.

a) oxidized adenine

0

0,5

1

0 20 40 60 80 100

ΔG

HO

ME

Dox

idiz

ed

b) reduced adenine

0

0,5

1

0 10 20 30 40

ΔG

HO

ME

Dre

duce

d

Fig. 7. Plots between the HOMED indices and the ΔG values (in kcal mol-1) estimated for the

whole tautomeric system of the oxidized (a) and reduced (b) adenine isomers

Table 1. Variations of the HOMED11 indices for the whole tautomeric system when going

from the neutral to redox forms of adenine

Isomer Neutral Oxidized Δa Reduced Δa

A1 0.906 0.841 -0.065 0.777 -0.129 A2 0.560 0.418 -0.142 0.646 0.086 A3 0.944 0.878 -0.066 0.818 -0.126 A4 0.578 0.450 -0.128 0.560 -0.018 A5 0.606 0.652 0.046 0.610 0.004 A6 0.364 0.244 -0.120 0.545 0.181 A7 0.922 0.845 -0.077 0.763 -0.159 A8 0.606 0.645 0.039 0.638 0.032 A9 0.938 0.916 -0.022 0.839 -0.099 A10a 0.425 0.560 0.135 0.619 0.194 A10b 0.448 0.509 0.061 0.639 0.191 A11a 0.345 0.245 -0.100 0.417 0.072 A11b 0.378 0.306 -0.072 0.453 0.075 A12a 0.475 0.496 0.021 0.523 0.048 A12b 0.487 0.519 0.032 0.554 0.067 A13a 0.837 0.874 0.037 0.713 -0.124 A13b 0.847 0.878 0.031 0.710 -0.137 A14a 0.479 0.512 0.033 0.556 0.078 A14b 0.488 0.545 0.057 0.576 0.088 A15a 0.800 0.870 0.070 0.736 -0.064 A15b 0.826 0.896 0.070 0.764 -0.062 A16a 0.403 0.496 0.093 0.508 0.105 A16b 0.414 0.485 0.071 0.527 0.113 A17a 0.415 0.491 0.076 0.515 0.100 A17b 0.370 0.461 0.091 0.512 0.142 A18a 0.840 0.917 0.077 0.775 -0.065 A18b 0.825 0.912 0.087 0.710 -0.115 A19a 0.453 0.631 0.178 0.543 0.090 A19b 0.457 0.609 0.152 0.542 0.085 A20a 0.747 0.858 0.111 0.814 0.067 A20b 0.752 0.867 0.115 0.822 0.070 A21a 0.554 0.563 0.009 0.569 0.015 A21b 0.458 0.421 -0.037 0.527 0.069 A22a 0.413 0.556 0.143 0.447 0.034 A22b 0.406 0.339 -0.067 0.454 0.048 A23a 0.507 0.651 0.144 0.598 0.091 A23b 0.498 0.641 0.143 0.594 0.096 a Difference between the HOMED11 values of the redox and neutral forms.

4. Conclusions

Quantum-chemical calculations performed for all possible favored and rare tautomers

of adenine gave the possibilities to study the relation between prototropy and electron

delocalization, and to analyze the effects of intramolecular interactions of the exo −NH2/=NH

group, and the effects of one-electron oxidation and one-electron reduction. To quantitatively

measure electron delocalization which is a consequence of different types of resonance

conjugations (π-π, n-π, and σ-π) possible for the adenine tautomers, the HOMED procedure

was applied to the geometries of neutral (A), oxidized (A+•), and reduced adenine (A-•)

optimized at the DFT(B3LYP)/6-311+G(d,p) level. Generally, the mixture of π-π and n-π

conjugations possible for the NH-NH tautomers lead to stronger electron delocalization than

the mixture of σ-π hyperconjugation with π-π and n-π conjugations possible for the NH-CH

tautomers. The HOMED indices estimated for the whole tautomeric system of the neutral and

redox NH-NH tautomers (HOMED11 > 0.7) are larger than those of the NH-CH ones

(HOMED11 < 0.7). For the neutral and oxidized adenine isomers, the variations of the

HOMED11 indices are almost parallel to those of the relative Gibbs energies. Some

deviations from these relations are a consequence of subtle internal effects. For the reduced

adenine isomers, the HOMED/ΔG relation seems to be more complex probably due to

differences in the reduction energies [7].

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Highlights

• Structural and energetic parameters are achieved for 37 isomers of neutral and redox adenine. • Good relation between prototropy and electron delocalization exists for neutral adenine. • One-electron oxidation has slight effect on the general HOMED/ΔG relation. • Except reduced adenine, aromaticity is the main factor that dictates the tautomeric preferences. • The reduced NHNH and NHCH subfamilies are separated in the HOMED vs ΔG plot.

Graphical abstract

Neutral adenine (37 isomers)

0

0,5

1

0 20 40 60 80

ΔG (in kcal/mol)

HO

ME

D11