Rethinking Aromaticity in H-Bonded Systems. Caveats for Transition

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Rethinking Aromaticity in H-Bonded Systems. Caveats for Transition Structures Involving Hydrogen Transfer and #-Delocalization María Pilar Romero-Fernández, Martin Avalos, Reyes Babiano, Pedro Cintas, Jose L. Jimenez, and Juan C. Palacios J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp5113735 • Publication Date (Web): 22 Dec 2014 Downloaded from http://pubs.acs.org on December 29, 2014

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The Journal of Physical Chemistry

Rethinking Aromaticity in H-Bonded Systems. Caveats for Transition Structures Involving Hydrogen Transfer and π-Delocalization† María P. Romero-Fernández,* Martín Ávalos, Reyes Babiano, Pedro Cintas,* José L. Jiménez, and Juan C. Palacios Departamento de Química Orgánica e Inorgánica, QUOREX Research Group, Facultad de Ciencias-UEX, Avda. de Elvas s/n E-06006 Badajoz, Spain

ABSTRACT: Monoaza- and diaza-derivatives of malondialdehydes, in short aminoacroleins and vinamidines, are prototypical examples of open-chain structures prone to π-electron delocalization, for which intramolecular hydrogen bonding enhances (or diminishes) their pseudo-aromaticity depending on the substitution pattern. This interplay is illustrated herein by DFT-based calculations of aromaticity indices in the gas phase and polar solvents. Elucidation of transition structures involved in tautomeric conversions helps to solve how the intramolecular hydrogen transfer occurs. While TSs exhibit a high degree of aromaticity, the dichotomy between forward and backward pathways point to a complex trajectory. Addition of thermal corrections to the electronic energy decreases both the enthalpy and free energy leading to negative ∆H‡ and ∆G‡ values. This variational effect accounts for the otherwise elusive distinction between transition structures and saddle points (usually overlooked for high electronic barriers). Also, this rationale fits well within the framework of Marcus’ theory.

INTRODUCTION

It is unnecessary to underline that the hydrogen bond constitutes a dominant weak interaction that plays a pivotal role in numerous chemical, biochemical, and physical processes, ranging from crystal packing to the stabilization of α-helices or β-sheets in proteins.1-5 Considerable research has also been focused on very strong hydrogen bonds involved in the transition structures of enzymatic processes.6-12 Among all the types of H-bonding interactions, the strongest ones are those assisted by additional effects, such as the so-called resonanceassisted or charge-assisted hydrogen bonds.13 In a nutshell, given a system H-X-(CH=CH)nCH=Y, the intramolecular resonance-assisted hydrogen-bond (RAHB),14,15 is identified as the relationship between the hydrogen bond strength (measured by the X⋅⋅⋅⋅Y distance, the X-H bond stretching frequency, or the X-H proton chemical shift) and the π-delocalization of the

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conjugated chain connecting the hydrogen bond donor (X) and acceptor (Y) atoms (measured by delocalization parameters).16 Moreover, the RAHB can be interpreted in terms of the minimum difference between X and Y proton affinities [∆PA = PA(X–) – PA(Y)] or, alternatively the minimum difference between their pKa values [∆pKa = pKa (X-H) – pKa (H-Y+)] as measured in a specific solvent.17,18 In any case, the RAHB concept is controversial as some authors consider that stabilization is largely provided by the σ-skeleton, rather than π-effects, even if some correlation between the delocalized π-electron structure and RAHB parameters has also been found.19-26 This context brings us to mind the fact that H-bonding interactions that increase cyclic πelectron delocalization also enhances both the aromaticity of such H-bonded compounds and their association energy. Conversely, H-bonding leading to greater π-electron localization decreases the aromatic character and association energies.27 In a recent study, Wu et al. have also computed H-bonding interaction energies (at the PBE0/6-311++G(3df,3pd) level without zeropoint energy corrections) and dissected nucleus-independent chemical shifts (NICS) at the PW91/Def2-TZVPP level, both accounting for the enhancement (or reduction) of aromaticity.28 Along with inherently aromatic compounds, the concept of aromaticity can be extended to pseudo-aromatic rings (or quasi-aromatic as often denoted), for which π-electron delocalization mediated by hydrogen bonding can be evaluated through indices based on geometrical considerations.16 Recently, we have studied in detail the tautomeric and conformational equilibria of mono- [Ar1-NH-CH=CAr2-CH=O] and di-azaderivatives [Ar1-NHCH=CAr2-CH=N-Ar1] of malondialdehydes, namely acrolein and vinamidines structures with extended conjugation.29 The tautomeric preferences for these substances could be rationalized by dissecting and quantifying contributions arising from structural fragments and intramolecular interactions (at the M06-2X/6-311++G(d,p) level and including solvent effects via the SMD model). The major stabilizing effect responsible for a favored tautomer or conformer is provided by intramolecular hydrogen bonding (O-H····N and N-H····N bonds), which contributes to further electron delocalization. Our theoretical modeling showed that H-bonded structures were largely favored in CDCl3, while fully extended (E-configured, s-trans conformers) enamine derivatives became prevalent as solvent polarity increased (DMSO or ethanol). The latter fully agreed with experimental observations of the corresponding tautomeric and/or conformational equilibria as inferred from NMR monitoring in DMSO-d6.29


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We now present a further computational estimation of the intramolecular hydrogen bond that characterizes the pseudo-heterocyclic structure of 2-arylmalondialdehydes and their monoand di-azaderivatives. The delocalization degree in both the gas phase and standard polar solvents (chloroform, dimethyl sulfoxide, and ethanol) for tautomers a and b of 2-aryl-3methyl(aryl)aminoacroleins (1-9), as well as the chelated forms of 2-arylmalondialdehydes 1012, and 2-arylvinamidines 13-21 (Figure 1) have been thoroughly quantified by geometry-based aromaticity indices.

O

H

N

R2

d1

d4

H

H

d2

1 2 3 4 5 6 7 8 9

d3

O

H

H

N

R2 H

R1

R1

a

b

O

H

H

R2

O H

10 R1 = H 11 R1 = OCH3 12 R1 = NO2

H

H

R1

R1 = H; R2 = CH3 R1 = CH3O; R2 = CH3 R1 = NO2; R2 = CH3 R1 = CH3O; R2 = C6H5 R1 = NO2; R2 = C6H5 R1 = CH3O; R2 = 4-CH3OC6H4 R1 = CH3O; R2 = 4-NO2C6H4 R1 = NO2; R2 = 4-CH3OC6H4 R1 = NO2; R2 = 4-NO2C6H4

N

N

R2 H

R1

13 14 15 16 17 18 19 20 21

R1 = H; R2 = CH3 R1 = OCH3; R2 = CH3 R1 = NO2; R2 = CH3 R1 = CH3O; R2 = C6H5 R1 = NO2; R2 = C6H5 R1 = CH3O; R2 = 4-CH3OC6H4 R1 = CH3O; R2 = 4-NO2C6H4 R1 = NO2; R2 = 4-CH3OC6H4 R1 = NO2; R2 = 4-NO2C6H4

Figure 1

Moreover, this study focuses on the location of transition structures accounting for the hydrogen transfer process. In doing so, some pitfalls and inconsistencies emerge, as documented in previous literature. The apparent dead end has now been satisfactorily settled by detours involving an analysis of variational effects with inclusion of zero-point energy (ZPE) corrections.


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RESULTS AND DISCUSSION

Computational Details. The computational DFT study has been performed using the M06-2X30 hybrid density functional in conjunction with the 6-311++G(d,p) basis set31-35 as implemented in the Gaussian09 package.36 The M06-2X method was chosen on the basis of previous studies showing its accuracy in estimating conformational energies related to noncovalent interactions;37 while energy re-assessments using other functionals and basis sets lie beyond the scope of this work. In all cases, frequency calculations were also carried out to confirm the existence of true stationary points on the potential energy surface. All thermal corrections were calculated at the standard values of 1 atm at 298.15K. Solvent effects were modeled through the method of density-based, self-consistent reaction field (SCRF) theory of bulk electrostatics, namely, the solvation model density (SMD) method38-42 as implemented in the Gaussian09 suite of programs. This solvation method accounts for long-range electrostatic polarization (bulk solvent)43 as well as for short-range effects associated with cavitation, dispersion, and solvent structural effects.44 Pseudo-aromaticity and Molecular Geometry Indices. As mentioned above, the aromatic character of planar pseudo-heterocycles can adequately be interrogated through a series of indices developed since the early 1970s, all possessing pros and cons, although as a whole they provide a valuable description of cyclic π-electron delocalization. For structures 1-21, Table 1 displays the values of the sum of the bond orders differences, Σ∆N,45 the Bird’s aromaticity index, I,46-48 the Kotelevskii and Prezhdo modification, APoz,KP,49 of the Pozharskii structural index, APoz,50,51 the Gilli parameters, Q and λ,52,53 the harmonic oscillator model of aromaticity, HOMA,54,55 the harmonic oscillator model of electron delocalization, HOMED,56-58 and the new HOMA index parametrization for π-electron heterocycles, HOMHED.59 A complete description of the above-mentioned indices together with specific parameters employed for the calculation of HOMA, HOMED, and HOMHED indices have been included with the SI (Appendix 1).


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Table 1. Aromaticity indices: Σ∆N, I, APoz,KP, Q, λ, HOMA, HOMED, and HOMHED, calculated at the M06-2X/6-311++G(d,p) level for structures 1-21 in the gas-phase. Entry 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

Structure 1a 2a 3a 4a 5a 6a 7a 8a 9a 1b 2b 3b 4b 5b 6b 7b 8b 9b 10 11 12 13 14 15 16 17 18 19 20 21

Σ∆N 55.77 54.94 57.84 44.27 48.64 48.68 35.59 52.31 39.40 23.40 21.62 25.33 31.05 33.20 29.49 35.10 31.27 35.69 26.01 25.16 26.60 29.41 27.05 33.84 29.34 33.71 31.64 25.71 37.02 29.73

I 67.08 66.96 66.05 61.99 62.88 64.30 57.27 64.31 58.45 48.03 46.84 48.70 53.30 54.29 52.32 56.03 53.16 56.11 52.51 52.08 52.55 44.50 43.87 44.57 47.66 48.10 49.09 46.30 49.60 47.29

APoz,KP 64.64 63.98 66.34 55.11 58.74 58.68 47.82 61.70 51.07 37.90 36.45 39.64 43.84 45.78 42.59 47.16 44.10 47.85 37.16 36.45 37.74 48.15 46.37 51.46 47.64 51.02 49.37 44.77 53.49 47.98

Q 0.174 0.176 0.169 0.204 0.193 0.193 0.226 0.184 0.216 -0.134 -0.139 -0.128 -0.115 -0.108 -0.119 -0.105 -0.113 -0.102 0.180 0.182 0.178 0.139 0.144 0.130 0.140 0.131 0.135 0.148 0.124 0.139

λ 47.27 46.67 48.79 38.18 41.52 41.52 31.52 44.24 34.55 44.17 42.08 46.67 52.08 55.00 50.42 56.25 52.92 57.50 43.75 43.13 44.38 44.40 42.40 48.00 44.00 47.60 46.00 40.80 50.40 44.40

HOMA 0.93 0.93 0.92 0.89 0.90 0.91 0.85 0.91 0.86 0.57 0.55 0.60 0.62 0.66 0.60 0.64 0.64 0.67 0.65 0.64 0.67 0.85 0.84 0.85 0.86 0.87 0.87 0.86 0.88 0.86

HOMED 0.89 0.89 0.88 0.85 0.86 0.87 0.81 0.87 0.82 0.80 0.79 0.80 0.84 0.85 0.83 0.86 0.84 0.86 0.82 0.82 0.82 0.86 0.85 0.86 0.87 0.88 0.88 0.87 0.88 0.87

HOMHED 0.88 0.88 0.87 0.85 0.85 0.86 0.82 0.86 0.82 0.79 0.78 0.80 0.83 0.84 0.83 0.85 0.83 0.85 0.82 0.82 0.82 0.84 0.84 0.84 0.87 0.86 0.87 0.86 0.87 0.86

Some conclusions can be extracted from data gathered in Table 1. Thus, a) the HOMED and HOMHED indices underestimate the differences in pseudo-cyclic electron delocalization showing in all cases values between 0.80 and 0.89, which shadow the tautomeric structural features. The substituent effect is also underestimated by the HOMA index within each structural family. b) Parameters based on bond orders (Σ∆N, I, and APoz,KP,) as well as the HOMA index do not afford clear-cut aromaticity relationships. While 3-aminoacroleins (structures 1a-9a) exhibit a greater pseudo-aromaticity than other series, small variations and divergences are observed for vinamidines (structures 13-21), malondialdehydes (structures 10-11), or iminoenols (structures 1b-9b). However, parameters based on bond lengths, such as Q and, as a result λ, lead to other


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conclusive statement. Thus, c) within each of these structural families, the π-electron delocalization is slightly enhanced as the electron-withdrawing character of R1 increases (see for example, entries 4 and 5, 6 and 8, and 7 and 9). d) Disparate results are instead obtained for the effect caused by R2 substituents, which varies in each group of structures. While for 3aminoacroleins (1a-9a) electron delocalization decreases as the electron-withdrawing character of R2 increases (compare entries 2, 4, 6, and 7 or entries 3, 5, 8, and 9), for iminoenols 1b-9b the π-delocalization increases as the electron-withdrawing character of R2 increases too (compare entries 11, 13, 15, and 16 or entries 12, 14, 17, and 18). For vinamidines 13-21, electron delocalization decreases as the electron-withdrawing character of R2 increases, regardless of the electronic effect of R1. The scarce influence observed for substituents on the pseudo-aromaticity of aminoacroleins and vinamidines can reasonably be ascribed to the lack of coplanarity between the conjugated unit and its aromatic substituents (Figure 2). Thus, for aminoacroleins (1a-9a) the dihedral angle ϕ varies from 34º to 48º while the dihedral angle ψ ranges from 3º to 31º, with lower values measured in structures where R2 is an electron-withdrawing group (Table S1). On the contrary, enolimine tautomers 1b-9b show similar ϕ and ψ angles (35º-46º), irrespective of the electronic nature of R1 and R2 groups. For vinamidines 13-21, the calculated dihedral angles ϕ, ψ, and ω show the following variations: 30º < ϕ < 47º, 1º < ψ < 29º, and 35º < ϕ < 43º (Tabla S2). Once again, the presence of electron-withdrawing groups at R2 gives rise to lower ψ angles. Figure 2 depicts optimized structures for aminoacrolein 9a and vinamidine 21, showing for the sake of clarity the above-mentioned dihedral angles.

O

H

N

H

R2

R2

ψ

ω

H

N

H

H

H

φ

R1

R2 N ψ

φ

R1

Figure 2. Optimized geometries at the M06-2X/6-311++G(d,p) level for aminoacrolein 9a (ϕ = 36.7º y ψ = 16.5º) and vinamidine 21 (ϕ = 36.4º, ψ = 1.6º, y ω = 37.4º) in ethanol.


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It has been demonstrated that on decreasing the X····X(Y) distance, the intramolecular hydrogen bonding becomes stronger.52 Table S3 collects all distances calculated for the fragment X····H-X(Y) in compounds 1-21, both in the gas-phase and polar solvents: chloroform, dimethyl sulfoxide, and ethanol. Such data show that regardless of the medium, the distances X····H and X····X(Y) decrease as the electron-withdrawing character of R1 increases. As expected, the effect of R2 is noteworthy in H-bonded structures 1b-9b, for which the intramolecular hydrogen bonds weaken in all media when R2 = 4-NO2C6H4. The influence of these three solvents on the π-delocalization has further been assessed by optimizing structures 1-21 at the M06-2X/6-311++G(d,p) level with the SMD model,38-42 and then re-calculating the parameters collected in Table 1 from the new bond lengths d1-d4. These results recorded in Tables S4-S6 (Supporting Information) show that solvent replacement does not result in a significant alteration of the delocalization indices, a fact particularly noticeable when comparing the results obtained in liquids of different solvation abilities, i.e. chloroform (ε = 4.71) and dimethyl sulfoxide (ε = 46.83). For instance, Figure 3 shows a comparative picture of the sum of the bond order differences (Σ∆N) for structures 1a-9a in chloroform, dimethyl sulfoxide, and ethanol. Data collected in Table S7 enable an additional inspection of the pseudoaromatic stabilization linked to solvent effects. 75.00 70.00 65.00 Σ∆ Σ∆N

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


60.00 chloroform 55.00

dmso

50.00

ethanol

45.00 40.00 1a

2a

3a

4a

5a

6a

7a

8a

9a

Structure

Figure 3. Sum of the bond order differences (Σ∆N) for structures 1a-9a in chloroform, dimethyl sulfoxide, and ethanol.


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Transition Structures. The location and identification of transition structures (TSs) corresponding to the intramolecular hydrogen transfer provide further insights into the πdelocalization and pseudo-aromaticity of these chelated open-chain molecules. Tables 2-4 show the relative electronic energies, enthalpies, and free energies in the gas phase and polar solvents (chloroform, dimethyl sulfoxide, and ethanol as above) for transition structures accounting for the interconversion of tautomers a and b in 2-aryl-3-methylaminoacroleins 1-9, as well as the interconversion of two equivalent forms in malondialdehydes 10-11 and vinamidines 13-21 (Figure 4). Furthermore, Table S8 lists X····H-X(Y) distances involved in the hydrogen transfer, whilst Table 5 displays the values of Σ∆N, I, APoz,KP, Q, λ, HOMA, HOMED, and HOMHED, calculated at the M06-2X/6-311++G(d,p) level for transition structures TS1a/1b-TS9a/9b and TS1021

in the gas phase, all serving to characterize the delocalization degree. Data obtained for the

same transition structures in chloroform, dimethyl sulfoxide and ethanol have been included in the SI (see Tables S9-S11).

O

H

H

R2 H

R1 TS1a/1b TS2a/2b TS3a/3b TS4a/4b TS5a/5b TS6a/6b TS7a/7b TS8a/8b TS9a/9b

N

O

H

H

R2 O

H

H

H

N

R2 H

R1

R1

TS10 R1 = H R1 = H; R2 = CH3 1 2 TS11 R1 = OCH3 R = CH3O; R = CH3 TS12 R1 = NO2 R1 = NO2; R2 = CH3 1 2 R = CH3O; R = C6H5 R1 = NO2; R2 = C6H5 R1 = CH3O; R2 = 4-CH3OC6H4 R1 = CH3O; R2 = 4-NO2C6H4 R1 = NO2; R2 = 4-CH3OC6H4 R1 = NO2; R2 = 4-NO2C6H4

N

TS13 TS14 TS15 TS16 TS17 TS18 TS19 TS20 TS21

R1 = H; R2 = CH3 R1 = OCH3; R2 = CH3 R1 = NO2; R2 = CH3 R1 = CH3O; R2 = C6H5 R1 = NO2; R2 = C6H5 R1 = CH3O; R2 = 4-CH3OC6H4 R1 = CH3O; R2 = 4-NO2C6H4 R1 = NO2; R2 = 4-CH3OC6H4 R1 = NO2; R2 = 4-NO2C6H4

Figure 4


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Table 2. Relative electronic energies (∆E), entalphies (∆H), and free energies (∆G) (kcal/mol) for transition structures TS1a/1b-TS9a/9b relative to the most stable isomer (1a-9a). Gas phase Struct. TS1a/1b TS2a/2b TS3a/3b TS4a/4b TS5a/5b TS6a/6b TS7a/7b TS8a/8b TS9a/9b

∆E 7.48 7.52 7.60 7.70 7.46 7.26 8.11 7.12 7.56

‡

‡

Chloroform ‡

∆H 4.43 4.35 4.45 4.78 4.64 4.20 5.14 3.95 4.48

∆G 5.69 5.10 5.37 5.77 5.84 4.82 6.10 4.59 5.54

∆E 8.73 8.70 9.03 8.58 8.45 7.97 9.10 7.99 8.53

‡

‡

Dimethyl sulfoxide ‡

∆H 5.68 5.47 5.79 5.60 5.58 4.82 6.03 4.75 5.14

∆G 6.86 6.06 6.35 6.37 7.06 4.90 6.74 5.55 6.00

∆E 9.14 9.12 9.56 8.87 8.80 8.33 9.55 8.38 9.19

‡

‡

Ethanol ‡

∆H 5.93 5.89 6.24 5.60 5.75 5.43 6.30 5.18 5.96

∆G 7.19 6.56 6.67 6.37 7.69 6.33 6.85 5.99 6.66

∆E 8.98 9.71 10.17 9.29 9.19 8.72 9.88 8.84 9.40

‡

‡

‡

∆H 6.03 6.43 6.82 6.07 5.87 5.70 6.74 5.71 6.08

∆G 7.32 7.04 7.12 6.67 7.18 6.57 7.47 7.53 7.23

Table 3. Relative electronic energies (∆E), entalphies (∆H), and free energies (∆G) (kcal/mol) for transition structures TS1a/1b-TS9a/9b relative to the less stable isomer (1b-9b). Gas phase Struct. TS1a/1b TS2a/2b TS3a/3b TS4a/4b TS5a/5b TS6a/6b TS7a/7b TS8a/8b TS9a/9b

∆E 2.37 2.54 1.95 2.50 2.01 2.57 2.71 2.00 2.34

‡

‡

Chloroform ‡

∆H -0.31 -0.23 -0.84 -0.26 -0.70 -0.14 -0.01 -0.54 -0.47

∆G 0.06 -0.12 -0.51 0.33 -0.06 0.53 0.47 -0.05 0.13

‡

‡

∆E 1.51 1.70 1.08 2.05 1.51 1.97 2.01 1.39 1.62

∆H -0.91 -1.02 -1.55 -0.77 -1.25 -0.50 -0.54 -1.00 -0.98


∆G 0.17 -0.95 -1.32 -0.56 -0.50 -0.33 -0.37 -0.82 -0.84

‡

‡

∆E 1.22 1.46 0.85 1.84 1.28 1.86 1.71 1.18 1.27

Ethanol ‡

∆H -1.36 -1.27 -1.79 -1.19 -1.69 -0.50 -0.85 -1.15 -1.21

∆G -0.46 -1.07 -1.71 -1.14 -1.23 0.28 -0.28 -0.39 -0.55

‡

‡

∆E 0.36 1.30 0.78 1.79 1.28 1.68 1.78 1.16 1.37

‡

∆H -1.90 -1.33 -1.83 -1.14 -1.69 -0.62 -0.74 -1.17 -1.19

∆G -0.87 -1.10 -1.95 -0.96 -1.56 0.25 -0.38 -0.56 -0.56

Table 4. Relative electronic energies (∆E), entalphies (∆H), and free energies (∆G) (kcal/mol) for transition structures TS10-21 relative to their corresponding tautomers (10-21). Gas phase Structure TS10 TS11 TS12 TS13 TS14 TS15 TS16 TS17 TS18 TS19 TS20 TS21

∆E 3.14 3.21 3.00 6.98 7.11 6.54 6.89 6.41 6.60 7.20 6.24 6.73

‡

‡

∆H 0.37 0.40 0.26 3.68 4.14 3.08 3.63 2.92 3.48 4.27 2.79 3.05

Chloroform ‡

∆G 0.97 0.87 0.88 3.94 4.98 3.61 4.70 3.28 4.72 5.45 3.03 3.81

∆E 2.93 3.00 2.80 7.47 7.60 6.86 7.24 6.71 6.90 7.45 6.35 7.01

‡

‡

∆H 0.21 0.26 0.00 3.98 4.44 3.43 3.74 3.17 3.64 3.90 3.10 3.92


∆G 0.88 1.06 0.42 3.94 4.82 4.05 3.95 2.80 4.35 4.09 3.20 4.51

∆E 2.75 2.79 2.57 7.65 7.79 6.99 7.46 6.86 7.13 7.30 6.62 7.01

‡

‡

∆H 0.05 0.15 -0.20 4.00 4.54 3.70 3.93 3.53 3.59 3.94 3.20 3.90

Ethanol ‡

∆G 0.65 1.09 0.52 3.89 4.91 4.01 4.80 3.99 4.08 5.84 3.24 5.68

∆E 3.19 3.28 3.02 7.81 7.96 7.04 7.29 6.90 7.21 7.71 6.59 7.26

‡

‡

∆H 0.43 0.45 0.20 4.25 4.67 3.78 3.87 3.44 3.95 4.41 3.16 4.11

‡

∆G 1.10 0.94 1.23 4.55 4.91 4.23 4.49 3.46 5.19 5.92 3.09 5.78


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The computational results gathered in Table 4 suggest that intramolecular hydrogen transfer in 2-arylmalondialdehydes 10-12 is faster (∆G‡ < 1.25 kcal/mol) than for 2arylvinamidines 13-21 (3.0 kcal/mol < ∆G‡ < 6.0 kcal/mol), whose barriers are somewhat lower than those found for the conversion of 3-alkyl(aryl)-2-arylaminoacroleins 1a-9a into their tautomers 1b-9b (4.5 kcal/mol < ∆G‡ < 7.7 kcal/mol) (Table 2). However, like in other intramolecular hydrogen transfers occurring on unsymmetrical systems,60 the energy barriers (∆H‡ and ∆G‡) found for the opposite process, i.e., for the conversion of 1b-9b into 1a-9a, are < 0 kcal/mol (Table 3), which deserves an explanation (see below). The computed distances between all atoms involved in the intramolecular hydrogen transfer for compounds 1-21 (Table S8) not only unravel the transfer evolution, which takes place primarily through the N···H distance leading to an increase in symmetry for transition stuctures TS1a/1b-TS9a/9b and TS10-TS21, but also a shortening of the distance X···X(Y) by 0.20.3 Å with respect to the corresponding tautomers. The latter results in an increase of the πdelocalization along the unsaturated spacer. In order to confirm these conclusions, Tables 5 and S9-S11 (Supporting Information) show the Σ∆N, I, APoz,KP, Q, λ, HOMA, HOMED, and HOMHED indices, calculated at the aforementioned M06-2X/6-311++G(d,p) level for transition structures TS1a/1b-TS9a/9b and TS10-21 in the gas phase and polar solvents. An analysis of such data evidence that all parameters show an increase of π-electron delocalization in the transition structures relative to the parent tautomers (see Tables 1 and S4-S6).


10

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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


Table 5. Aromaticity indices: Σ∆N, I, APoz,KP, Q, λ, HOMA, HOMED, and HOMHED, calculated at the M06-2X/6-311++G(d,p) level for structures TS1a/1b-TS9a/9b and TS10-21 in the gas phase Entry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21

Structure TS1a/1b TS2a/2b TS3a/3b TS4a/4b TS5a/5b TS6a/6b TS7a/7b TS8a/8b TS9a/9b TS10 TS11 TS12 TS13 TS14 TS15 TS16 TS17 TS18 TS19 TS20 TS21

Σ∆N 67.76 68.31 66.44 79.10 75.90 76.26 87.96 73.36 84.48 93.19 94.02 90.45 70.55 71.89 65.15 78.18 72.82 78.18 81.92 71.49 76.84

I 73.00 73.59 70.72 80.84 77.17 79.01 85.52 75.78 81.69 93.51 94.31 90.92 70.00 71.36 64.55 77.56 72.08 77.56 81.67 70.71 76.19

APoz,KP 74.06 74.48 72.99 83.10 80.54 80.79 89.86 78.46 85.84 94.23 94.94 91.92 78.40 79.38 74.47 83.84 79.89 83.84 86.58 78.91 82.85

Q -0.019 -0.018 -0.022 0.009 0.002 0.002 0.031 -0.004 0.023 0.001 0.000 0.001 0.000 0.000 0.000 0.000 0.000 0.000 -0.002 0.000 0.000

λ 94.24 94.55 93.33 97.27 99.39 99.39 90.61 98.79 93.03 99.69 100 99.69 100 100 100 100 100 100 99.20 100 100

HOMA 0.88 0.88 0.88 0.92 0.91 0.91 0.94 0.91 0.94 0.93 0.93 0.94 0.97 0.97 0.95 0.98 0.97 0.98 0.99 0.97 0.98

HOMED 0.91 0.91 0.90 0.96 0.95 0.96 0.98 0.95 0.97 0.99 0.99 0.99 0.96 0.96 0.93 0.98 0.97 0.98 0.99 0.96 0.98

HOMHED 0.90 0.90 0.88 0.95 0.94 0.94 0.97 0.93 0.96 0.99 0.99 0.98 0.93 0.94 0.90 0.97 0.94 0.96 0.97 0.94 0.96

A plot of the electronic energy profiles extracted from Tables 2 and 3, as shown in Figure 5, reveals the lack of symmetry in the tautomerization of 3-alkylaminoacroleins; the energy barrier that separates the transition structure from tautomers a and b is greater than 7 kcal/mol and less than 3 kcal/mol, respectively. This accounts for the distinctive bond lengths calculated at the saddle point for the O-H (< 1.20 Å) and N-H (> 1.27 Å) bonds. Figure 6 shows a similar picture for the intramolecular hydrogen transfer between the tautomers a and b of 3-alkyl(aryl)-2-arylaminoacroleins 1-9 based on the ∆G‡ values calculated (Tables 2 and 3), which might suggest a more complex reaction path involving at least another relative local minimum and an additional saddle point sandwiched between the transition structure drawn and tautomer b.


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Figure 5. Schematic diagram showing the different stability of tautomers a and b for 2-aryl-3methylaminoacroleins 1-9.

Figure 6. Schematic diagram showing the relative free energy of tautomers a and b for 2-aryl-3methylaminoacroleins 1-9.


12

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In the search for a plausible rationale, we computed the internal reaction coordinate (IRC) for TS3a/3b in ethanol (∆E‡ = 0.78, ∆H‡ = –1.83, ∆G‡ = –1.95 kcal/mol), the transition structure corresponding to the tautomerization of one 3-alkyl-2-arylaminoacrolein derivative. Figure 7 shows the electronic energy variation along the reaction pathway as plotted for the equilibrium between 3a and 3b. The IRC calculation indicated that TS3a/3b is actually the true saddle point for that prototropy characterized by both a low energy barrier (0.78 kcal/mol) and a high imaginary frecuency (–933.62 cm-1), which cause a sharp drop in the zero point energy (ZPE) as shown in Figure 8, constructed from thermochemical data of each structure in the reaction path.

0.3 0.2 Energy (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


0.0 -0.2 -0.3 -0.5 -0.6 -0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

Reaction coordinate (Bohr)

Figure 7. Tautomeric equilibrium between 3a and 3b in ethanol. The curve shows the variation of the electronic energy (kcal/mol) along the reaction pathway.


13



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-0.5 -1.0 E

-1.5

ZPE -2.0 H -2.5 -3.0 -0.15

G -0.10

-0.05

0.00

0.05

0.10

0.15


Figure 8. Variations of electronic energy (E), zero point energy (ZPE), as well as enthalpy (H298.15) and free energy (G298.15) calculated at 298.15 K (in kcal/mol) near the saddle point.

Addition of thermal corrections, including the ZPE correction, to the electronic energy does justify a marked decrease in the internal energy and hence, of the enthalpy and free energy at the saddle point, thus leading to negative values for ∆H‡ and ∆G‡. This fact shifts the maximum values of ∆H‡ and ∆G‡ (variational effect) with respect to the saddle point, which is not particularly evident in the presence of high electronic energy barriers. Similar results are obtained when this methodology is applied to the tautomeric interconversion between forms a and b of another 3-arylaminoacrolein such as 4. The internal reaction coordinate (IRC) for TS4a/4b in chloroform (∆E‡ = 2.05, ∆H‡ = –0.77, ∆G‡ = –0.56 kcal/mol) shows that TS4a/4b is the real saddle point for the tautomerization reaction and exhibits a low energy barrier (2.05 kcal/mol) plus an imaginary frecuency (–466.83 cm-1), which cause a drop in the zero point energy (ZPE) (Figures 9 and 10). A variational effect can newly be invoked as the inclusion of thermal corrections, including the ZPE correction, to the electronic energy decreases the internal energy and accordingly both the enthalpy and free energy at the saddle point.


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1.0 0.0 -1.0 -2.0 -3.0 -4.0 -5.0 -6.0 -2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5


Figure 9. Variation of the electronic energy (kcal/mol) along the reaction coordinate for the tautomeric equilibrium between 4a and 4b in chloroform. 3.0 1.5 Energy (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


0.0

E ZPE

-1.5

H -3.0

G

-4.5 -6.0 -1.5

-1

-0.5

0

0.5

1

1.5


Figure 10. Variations of electronic energy (E), zero point energy (ZPE), and enthalpy (H298.15) and free energy (G298.15) near the saddle point.

Finally, it should be emphasized that if the intramolecular hydrogen transfer occurs on a symmetrical substrate, i.e., malondialdehydes like 10-12 or vinamidines like 13-21, the calculate barriers (∆E‡, ∆H‡ and ∆G‡) are low, yet positive (see Table 4), whereas for substrates lacking symmetry such as aminoacroleins 1a-9a, their transformation into the corresponding tautomers 1b-9b, requires more energy and tends to make equal the reaction energy (∆Eº, ∆Hº, and ∆Gº ) to


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Page 16 of 27

the activation energy (∆E‡, ∆H‡ and ∆G‡). This thermodynamic contribution to the reaction barrier, also responsible for the negative values of ∆H‡ and ∆G‡ as found for the inverse transformation (1b-9b → 1a-9a), does not exist when ∆Eº, ∆Hº and ∆Gº are equal to 0. The necessary correction could then be formulated in terms of the Marcus theory,61 by expressing the reaction barrier for proton transfers, ∆X‡, as function of ∆Xº and ∆‡ , the latter being the value of ∆X‡ when ∆Xº = 0, or “intrinsic kinetic barrier” (X = E, H or G).

‡

∆ =

∆‡

∆ ∆ + + 2 16∆‡

Given the different nature of the atoms involved in proton transfer (N and O), the set of ‡ ) were calculated as the arithmetic mean of the ∆‡ data for aminoacroleins (∆, ‡ ‡ corresponding ∆‡ values for malondialdehydes (∆, ) and vinamidines (∆, ).

Accordingly, the preceding expression should be written as follows: ∆ 1 ∆ ‡ ‡ ∆ = ∆, + ∆, + + ‡ ‡ 2 2 8 ∆, + ∆,

‡

Tables 6 and 7 depict the new values for ∆E‡, ∆H‡, and ∆G‡ calculated for the transformation 1a-9a ⇄ 1b-9b by applying the Marcus theory, and Figures 11 and 12 show, as representative examples, the variations in electronic energy and free energy along the reaction pathway for the intramolecular proton transfer from the iminoenol donor 3b to the acceptor molecule, aminoacrolein 3a, in ethanol. In these plots, the reaction coordinate (RC) is defined as the difference between the distances of the O-H and N-H bonds (RC = dO-H – dN-H). Then, the total reaction pathway length (d) can be estimated as d = RC3a – RC3b, while the introduction of the relative reaction coordinate, r = RC – RC3b, allow us to obtain r values between 0 and d.62 In the framework of Marcus’ theory, the reactant and the product of the hydrogen transfer process are regarded as simple harmonic oscillators with identical force constant, k, though shifted by the pathway length (d), and whose energies can be calculated according to:


16

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1 2 1 = ∆ + 2 =

being ∆ the reaction energy and the force constant of the oscillator (k) calculated as: 8∆‡ = The graphical representations of the above functions give rise to two parabolas crossing at the point that determines the energy and position of the transition structure along the reaction coordinate (Figures 11 and 12).

Figure 11. Marcus plot of the electronic energy data for the N---H-O → N-H---O proton transfer for 3b ⇄ 3a calculated at the M06-2X/6-311++G(d,p) level versus the relative reaction coordinate (r). [k = 17.07 kcal mol-1 Å-2; d = 1.536 Å; ∆Er = -9.39 kcal mol-1; ∆E‡N---H-O → N--H--O = 1.43 kcal mol-1; ∆E‡N-H---O → N--H--O = 10.83 kcal mol-1]


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Figure 12. Marcus plot of the free energy data for the N---H-O → N-H---O proton transfer for 3b ⇄ 3a calculated at M06-2X/6-311++G(d,p) level versus the relative reaction coordinate (r). [k = 9.25 kcal mol-1 Å-2; d = 1.536 Å; ∆Gr = -9.08 kcal mol-1; ∆G‡N---H-O → N--H--O = 0.08 kcal mol-1; ∆G‡N-H---O → N--H--O = 9.15 kcal mol-1]

Data shown in Tables 6 and 7 indicate that the hypothetical equilibrium is completely shifted to the left, being 3-alkyl(aryl)-2-arylaminoacroleins (1a-9a) the only species present in solution, particularly in polar solvents, as it has been experimentally confirmed through 1H and 13

C NMR experiments.29 It should finally be pointed out in context that correlations between

aromatic stabilization and reactivity in some pericyclic transformations have been discussed in the light of Marcus theory.63,64 Table 6. Relative electronic energies (∆E‡), entalphies (∆H‡), and free energies (∆G‡) (kcal/mol) for transition structures TS1a/1b-TS9a/9b relative to the most stable isomer (1a-9a) obtained by application of the Marcus equation. Gas phase Struct. TS1a/1b TS2a/2b TS3a/3b TS4a/4b TS5a/5b TS6a/6b TS7a/7b TS8a/8b TS9a/9b

∆E 7.94 7.95 8.02 7.99 7.83 7.53 8.26 7.54 7.82

‡

‡

∆H 5.08 5.14 5.37 5.33 5.38 4.72 5.62 4.60 5.06

Chloroform ‡

∆G 6.07 6.11 6.14 6.17 6.08 5.35 6.60 4.97 5.83

∆E 9.44 9.37 9.63 8.91 8.86 8.41 9.37 8.46 8.97

‡

‡

∆H 6.69 7.28 7.34 6.46 6.84 5.52 6.66 5.75 6.22


∆G 6.92 7.38 7.71 7.17 7.60 5.95 7.35 6.40 7.07

∆E 9.91 9.81 10.13 9.17 9.22 8.72 9.73 8.90 9.57

‡

‡

∆H 7.92 7.29 8.06 6.96 7.46 6.01 7.18 6.34 7.17

Ethanol ‡

∆G 7.39 8.03 8.39 7.81 8.92 6.50 7.95 6.43 7.75

∆E 10.66 10.61 10.83 9.77 9.70 9.36 10.29 9.42 9.94

‡

‡

∆H 7.99 7.91 8.6 7.28 7.56 6.50 7.61 6.88 7.32

‡

∆G 8.41 8.41 9.15 7.95 8.75 7.04 8.47 8.10 8.48


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Tables S12 and S13 show the dihedral angles ϕ, ψ, and ω computed for transition structures TS1a/1b-TS9a/9b and TS10-TS21. Like in their corresponding tautomers, the ψ angle decreases as the electron-withdrawing character of the R2 substituents increases, although a narrower variation could be observed (14º < ψ < 35º in TS1a/1b-TS9a/9b and 21º < ψ < 32º for TS10-TS21). Likewise, the values for ϕ oscillate between 32º and 45º for structures TS1a/1b-TS9a/9b and between 25º and 43º for TS10-TS21. Table 7. Relative electronic energies (∆E‡), entalphies (∆H‡), and free energies (∆G‡) (kcal/mol) for transition structures TS1a/1b-TS9a/9b relative to the less stable isomer (1b-9b) obtained by application of the Marcus equation. Gas phase Struct. TS1a/1b TS2a/2b TS3a/3b TS4a/4b TS5a/5b TS6a/6b TS7a/7b TS8a/8b TS9a/9b

∆E 2.83 2.97 2.37 2.78 2.38 2.84 2.86 2.42 2.61

‡

‡

∆H 0.35 0.56 0.07 0.28 0.04 0.38 0.47 0.11 0.11

Chloroform ‡

∆G 0.45 0.89 0.27 0.73 0.18 1.06 0.97 0.32 0.42

∆E 2.22 2.38 1.67 2.38 1.91 2.41 2.28 1.87 2.06

‡

‡

∆H 0.10 0.14 0.01 0.08 0.01 0.20 0.09 0.01 0.09


∆G 0.23 0.51 0.05 0.24 0.05 0.72 0.25 0.03 0.23

∆E 1.99 2.16 1.42 2.14 1.71 2.25 1.89 1.70 1.65

‡

‡

∆H 0.00 0.13 0.04 0.04 0.02 0.08 0.03 0.00 0.00

Ethanol ‡

∆G 0.09 0.40 0.01 0.30 0.00 0.44 0.82 0.04 0.54

∆E 2.04 2.20 1.43 2.27 1.79 2.32 2.19 1.73 1.91

‡

‡

∆H 0.06 0.15 0.02 0.07 0.00 0.17 0.13 0.00 0.05

‡

∆G 0.21 0.27 0.08 0.32 0.01 0.72 0.63 0.01 0.69

CONCLUSIONS

A series of well-established aromaticity indices, namely Σ∆N, I, APoz,KP, Q, λ, HOMA, HOMED, and HOMHED, provide insightful correlations to evaluate the

electronic

delocalization of pseudo-heterocyclic tautomers of 2-aryl-substituted alkyl(aryl)aminoacroleins and 3-aryl-substituted 1,5-dialkyl(aryl)vinamidines, as well as their transition structures corresponding to the intramolecular proton transfer. Our DFT-based study (M06-2X/6311++G(d,p) conducted in both the gas phase and polar solvents allowed us to estimate the influence of substituents on the conjugated backbone. No appreciable solvent effect could be detected from this computation. The striking fact that negative ∆G‡ values were found for the proton transfer between iminoenol and aminoketone tautomers of 3-aminoacroleins, characterized by low energy barriers


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Page 20 of 27

and large imaginary frecuencies, can be attributed to variational effects, which are usually overlooked for processes involving higher energy barriers (as the proton transfer from aminoketone to iminoenol tautomers in the aforementioned 3-aminoacroleins). These negative ∆G‡ values can however be easily corrected by applying the Marcus theory.

ASSOCIATED CONTENT Supporting Information Mathematical description of aromaticity indices (appendix 1), additional data from theoretical calculations and Cartesian coordinates for all structures, as well as full Reference 19 (Gaussian package). This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author [email protected] Notes †

In memoriam Paul von Ragué Schleyer.

The authors declare no competing financial interest.

ACKNOWLEDGMETNS This work was supported b the Spanish Ministry of Science and Innovation (CTQ201018938/BQU) and the Autonomous Government of Extremadura (Ayudas a Grupos Consolidados, Grant GRU10049). We thank the Centro de Investigación, Innovación Tecnológica y Supercomputación de Extremadura (CenitS) for allowing us the use of supercomputer LUSITANIA.


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(22) Dobosz, R.; Gawinecki, R. DFT Studies on Tautomeric Preferences: Proton Transfer in 1,5-Bis(pyridin-2-yl)-

and

1,5-Bis(quinolin-2-yl)pentane-2,4-diones.

J.

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Rethinking Aromaticity in H-Bonded Systems. Caveats for Transition

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