Correlation between Hydrogen Bonding Association Constants in

Article pubs.acs.org/JPCA

Correlation between Hydrogen Bonding Association Constants in Solution with Quantum Chemistry Indexes: The Case of Successive Association between Reduced Species of Quinones and Methanol Annia Galano,*,† Martín Gómez,‡ Felipe J. González,§ and Ignacio González*,† †

Departamento de Química de la Universidad Autónoma Metropolitana-Iztapalapa, San Rafael Atlixco 186, Col. Vicentina, Iztapalapa, C.P. 09340, México D.F., México ‡ Departamento de Sistemas Biológicos, Universidad Autónoma Metropolitana-Xochimilco, Calzada del Hueso 1100, Col. Villa Quietud, Coyoacán, C.P. 04960, México D.F., México § Departamento de Química, Centro de Investigación y de Estudios Avanzados del IPN, Av. IPN 2508, Col. San Pedro Zacatenco, C.P. 07360, México D.F., México S Supporting Information *

ABSTRACT: The functional M05-2X together with the SMD solvent model have been used to calculate hydrogen bonding association constants in dimethylsulfoxide (DMSO) solution. Data of equilibrium constants in DMSO for the case of electrochemically generated dianions interacting with methanol have been considered to test the reliability of the chemistry theoretical approach. From this approach, it was found that the successive association constants involved in the formation of the complexes depend on a linear combination of three quantum chemistry indexes which are the ionization energy, the electron affinity, and the charge on the oxygen atom receiving the methanol molecule. Under this perspective, the stoichiometry of all the dianion−methanol complexes was explained on the basis of the relative strength of the hydrogen bonding interaction compared to that of the methanol−DMSO and methanol dimer complexes. This linear combination seems to be valid regardless of the nature of the dianion structure and the number of methanol molecules in the complex, which is a relevant finding to generalize the applicability of both the functional M05-2X and the SMD solvent model, to calculate association constants for any other neutral or anionic molecules interacting by hydrogen bonding with proton donors.

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INTRODUCTION Even though the nature of hydrogen bonding (HB) is still the subject of many discussions,1 there are no doubts on the importance of this kind of interactions in biochemical, chemical, and physical processes.2 In the particular case of quinones, HB has been described to play important roles regarding their structures in biological systems and their functions as the active site of quinoenzymes.3−5 It has been established that HB and protonation are fundamental processes that affect the potentials and mechanisms involved in the reduction of quinones.6 This is particularly important since quinone-based redox couples have a key role as electron and proton carriers in biological systems.7−11 In addition, quinone− hydroquinone pairs have been the focus of attention over many decades since they are considered prototypical examples of organic redox systems.12−17 Quinones are widespread in nature, where they play a large variety of functions. 18 They also have pharmaceutical applications, due to their anticancer, antibacterial, and fungicide activities.18,19 The biological activity of quinones have been associated to their redox and acid−base properties,10,18,20−26 © XXXX American Chemical Society

which have motivated a great number of electrochemical studies in different solvents.27,28 In nonaqueous media, quinone derivatives without acidic moieties (Q) undergo two successive reduction processes yielding two stable anionic intermediates. The first one involves the formation of the semiquinone radical (Q•−), and the second one yields the quinone dianion (Q2−). Due to the fact that the semiquinone radicals are paramagnetic high energy species, they can disproportionate into the corresponding quinone and dianion.14,29 In this framework, stabilization of neutral quinones and the reduced species has been achieved by employing hydrogen bonding (HB) donors, which results in the regulation of the redox potential of both quinones−semiquinone and semiquinone−dianion redox couples.30,31 The presence of HB agents can stabilize the semiquinone radical and the dianion,18 shifting the two reduction potentials toward more positive values.32−34 This behavior is in agreement with the fact that the influence of HB Received: September 13, 2012 Revised: October 11, 2012

A

dx.doi.org/10.1021/jp309085g | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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in biological functions of quinones is well recognized.35,36 Particularly, it has also been established that studies on HB processes involving Q•− and Q2− are relevant to the understanding of electron and proton transfers in energytransducing membranes for respiration and photosynthesis.37−39 Therefore, it is not surprising that the quinone HB processes is an active field of research.33,34,40−48 It has been recently found that the HB processes between the quinone system and alcohols depend on the concentration of the HB agents.34 In the same work, it was proposed that the mechanism consists in consecutive association steps, with their strength depending on the quinone basicity. The equilibrium constants were estimated for a set of seven different quinones, as well as the maximum number of alcohol molecules forming the association complexes. The latter was found to be different depending on the particular quinone involved in the process. For example, for the interaction between Q2− and methanol, it varies from 3 when the process involves tetrachloro-1,4benzoquinone to 6 for 1,4-benzoquinone; tetramethyl-1,4benzoquinone; and 2-phenyl-1,4-benzoquinone. For 9,10anthraquinone and 5,12-naphthacenequinone, the maximum methanol−dianion ratio (CH3OH−Q2−) was found to be 4:1; and for 1,4-naphthoquinone, it was 5:1. All these experiments were carried out in dimethylsulfoxide (DMSO) solution. Despite of all the experimental investigations conducted so far on the HB processes involving quinones, and the importance of such processes, to our best knowledge, there are only a few theoretical studies dealing with their physical chemistry insights.49,50 Therefore, it is the main goal of the present work to perform a systematic study on a series of quinones and their HB interactions with methanol. Equilibrium constants are estimated and compared with the experimental data available. Chemical descriptors have been investigated and related with the strength of the interactions. Geometrical parameters are reported for the formed complexes. An explanation to the variation on the maximum (CH3OH)− Q2− ratio, depending on the quinone, is provided. The agreement with the available experimental data supports the presented results. In addition, accurate computation of free energy changes, and thus of equilibrium constants, for chemical processes in solution has been proven to be particularly challenging. Accordingly, finding computational strategies able of producing reliable values of such equilibrium constants would be an important milestone in the search for computational methods reliable enough to quantitatively reproduce experimental results in solution. Therefore another important goal of the present work is testing the efficiency of the used methodology to that purpose, in particular for predicting the equilibrium constants associated with the formation of complexes between reduced quinones and HB donors.

and ionic species, in aqueous and also in nonaqueous solvents, is better than that achieved with other solvent models. In addition, the solvent relevant to the present study (DMSO) was included in the parametrization of SMD.52 Geometries were fully optimized without imposing any restriction. Local minima were confirmed by the absence of imaginary frequencies. All the electronic calculations were performed with the Gaussian09 package of programs.53 Thermodynamic corrections at 298.15 K were included in the calculation of relative energies. To characterize the HB interactions between quinones and methanol, Bader topological analysis54 of the wave functions were performed. The electronic spectra have been computed using the time-dependent density functional theory (TD-DFT), based on vertical excitations involving the 6 lowest lying excited states.

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RESULTS AND DISCUSSION The electrochemical reduction of quinones in aprotic medium gives rise to semiquinones and dianions, whose stabilization can be favored by hydrogen bonding (HB) interactions with weak proton donors such as alcohols. In this framework, previous voltammetric studies on the reduction of several quinones in the presence of methanol allowed establishing successive association steps and their respective equilibrium constants.33,34 From these studies, it was demonstrated that experimental values of the association constants for the semiquinones are significantly smaller and less precise than in the case of dianions.34 Therefore, the HB association processes involving the dianions of six different quinones and up to four molecules of methanol, in DMSO solution, have been considered to test the performance of the functional used in this work to predict the equilibrium constants of the association steps. The studied quinones are 1,4-benzoquinone (BQ), tetrachloro-1,4-benzoquinone (TCBQ), tetramethyl-1,4-benzoquinone (TMBQ), 2phenyl-1,4-benzoquinone (2PBQ), 1,4-naphthoquinone (NQ), and 9,10-anthraquinone (AQ) (Figure 1).

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Figure 1. Quinones studied in this work.

COMPUTATIONAL DETAILS Geometry optimizations and frequency calculations have been carried out using the M05-2X functional51 and the 6-311+G(d) basis set. They have been carried out in solution, using the SMD continuum model52 and DMSO as solvent. The M05-2X functional has been chosen for the task at hand because it has been proven to be among the functionals with the best performance for calculating binding energies in hydrogenbonded complexes and in weak-interaction complexes in general.51 The SMD solvent model has been chosen since its performance for describing solvation in energies of both neutral

Before the test of functional M05-2X for the estimation of equilibrium hydrogen bonding constants, selected geometrical parameters of the fully optimized geometries of these quinones, as well as those of the corresponding semiquinone radicals and dianions are reported in Table 1. According to these data, as the reduction proceeds (Q→Q•− → Q2−), the CO distances increase, while the CC distances become larger and the C−C distance shorter. This is in agreement with previous descriptions of gradual geometrical change from quinonoid to benzenoid form, as quinones are successively reduced.55 B



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1S). The first one (a) corresponds to a conventional HB between the H atom in the OH moiety of methanol and one of the O atoms in BQ2−, while the second one (b) corresponds to a nonconventional HB between the same H atom in methanol and the π orbitals in the quinone ring. It was found that the Gibbs free energy of structure (a) is lower than that of structure (b) by 6.56 kcal/mol. For the 1:2 BQ2−−CH3OH cluster, five configurations were tested (Supplementary Figure 2S), three of them (c, d, and e) involving only conventional HB and two of them (f and g) including one nonconventional HB. On the basis of the findings for the 1:1 cluster, structure (a) was taken as a starting point, and a second methanol molecule was added at different locations. As it was the case for the clusters with only one methanol molecule, the clusters involving nonconventional HB have significantly higher Gibbs free energies than those formed only by conventional HB. Among the latter ones (c, d, and e), the difference in Gibbs free energies are very small and below the currently accepted accuracy of theoretical calculations. It means that any of them could be used to model the 1:2 BQ2−− CH3OH cluster. For the 1:3 and 1:4 BQ2−−methanol clusters, two orientations were tested in each case (Supplementary Figures 3S and 4S). As for the other cases, one of them corresponds to conventional HB and the other one not. The complexes formed through the conventional HB were found to be those with lower Gibbs free energies, by 5.93 and 6.49 kcal/ mol, for the 1:3 and 1:4 complexes, respectively. According to the information gathered from the conformations tested for the BQ2−−CH3OH clusters, the more energetically favored interactions are conventional HB involving the H atom in the OH moiety of methanol and one of the O atoms in BQ2−. Therefore, for all of the other quinones studied in this work, these are the only interactions that have been taken into account. Moreover, their starting geometries have been constructed based on the conformations that were found to have the lowest Gibbs free energy for the BQ2−−CH3OH system. In order to calculate the equilibrium constants of the different successive association steps, the number of equivalent configurations, i.e., with similar energies, has been included. To that purpose, we have considered the two p orbitals of each oxygen atom in the quinone that can be involved in the HB with every methanol molecule. This means that the degeneracy number (σ) is equal to 4, 3, 2, and 1 for the formation of clusters 1:1, 1:2, 1:3, and 1:4, respectively, when computed according to the successive association steps mechanism:

Table 1. Bond Distances (Å) of the Quinones (Q), Semiquinones (Q•−), and Dianions (Q2−); Obtained from Full Geometry Optimizations at the M05-2X/6-311+G(d) Level of Theory BQ BQ•− BQ2− TMBQ TMBQ•− TMBQ2− TCBQ TCBQ•− TCBQ2− 2PBQ 2PBQ•− 2PBQ2− NQ NQ•− NQ2− AQ AQ•− AQ2−

CO

C−C

CC

C−Xa

1.215 1.261 1.302 1.217 1.264 1.309 1.200 1.241 1.277 1.213 1.258 1.296 1.215 1.257 1.297 1.214 1.253 1.290

1.482 1.445 1.423 1.491 1.452 1.428 1.494 1.452 1.426 1.500 1.459 1.436 1.481 1.472 1.457 1.488 1.457 1.433

1.333 1.365 1.400 1.342 1.373 1.406 1.337 1.364 1.396 1.341 1.373 1.415 1.400 1.412 1.432 1.400 1.417 1.444

1.082 1.084 1.088 1.497 1.505 1.510 1.707 1.730 1.753 1.477 1.482 1.480 1.391 1.405 1.416 1.393 1.411 1.424

a C−X represents single bonds between the C atoms in the quinone and the substituent (X = H for BQ, 2PBQ, NQ and AQ; X = C for TMBQ; and X = Cl for TCBQ).

There are no experimental data reported for the geometries of the reduced species, but there are for some of the studied neutral quinones (Table 2). By comparing the values in Tables Table 2. Experimental Bond Distances (Å) of the Studied Quinones (Q) BQ

TCBQ NQ AQ

CO

C−C

1.230 1.150 1.225 1.222 1.211 1.216 1.215 1.220 1.150

1.490 1.520 1.470 1.489 1.492 1.430 1.499 1.500

CC

1.322 1.344 1.344 1.353 1.390 1.400 1.390

C−X

ref

1.089 1.700 1.701

57 58 59 60 61 62 63 64 65

1 and 2, it can be observed that the calculated geometries are in excellent agreement with the experimental data, which supports the reliability of the geometries obtained with the M05-2X functional. The mean unsigned error was found to be only 0.012 Å. The maximum absolute error was 0.05 Å and corresponds to the C−C distance in NQ. The geometrical parameters presented in this work are also in good agreement with those values obtained from theoretical calculations at different levels of theory not only for quinones but also for their first reduced species (Q•−).56 Because of the large amount of calculations involved in the present work, it was unfeasible to perform exhaustive conformational analyses for all the quinone−methanol clusters. Alternatively, we used BQ2− as reference molecule and tested different conformations in DMSO as solvent. For the complex with BQ2−−CH3OH ratio 1:1, where two different orientations of the methanol molecule were tested (Supplementary Figure

Q2 − + CH3OH ↔ [Q···CH3OH]2 −

(step 1)

[Q···CH3OH]2 − + CH3OH ↔ [Q···(CH3OH)2 ]2 − (step 2) 2−

+ CH3OH ↔ [Q···(CH3OH)3 ]2 −

2−

2−

[Q···(CH3OH)2 ]

(step 3)

[Q···(CH3OH)3 ]

+ CH3OH ↔ [Q···(CH3OH)4 ]

(step 4)

Each of the successive equilibrium constants (Ki), conditioned here to DMSO as solvent, has then been calculated with eq 1, while the global equilibrium constants (βn) have been obtained, from the values of Ki, according to eq 2. K i = σ e−ΔGi / RT C

(1)



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Table 3. Global Equilibrium Constants (βn), in M−n, for the Hydrogen Bonded Complexes Formed between the Dianions of Studied Quinones and n Molecules of Methanol in DMSO66 β1 BQ TMBQ TCBQ 2PBQ NQ AQ a

calcd exptla calcd exptla calcd exptla calcd exptla calcd exptla calcd exptla

β2

4.03 × 10 2.90 × 102 6.78 × 103 3.50 × 102 3.92 1.71 × 101 1.46 × 102 2.10 × 102 2.93 × 102 1.25 × 102 1.87 × 102 8.30 × 101 2

5.96 4.83 7.65 1.50 1.15 2.20 7.53 1.70 4.37 4.70 2.53 1.44

× × × × × × × × × × × ×

β3 4

10 104 104 104 101 101 103 104 103 103 103 103

β4

1.34 × 10 3.80 × 105 5.60 × 105 4.20 × 105 2.66 8.00 × 101 4.95 × 105 9.90 × 104 1.79 × 104 5.25 × 104 3.83 × 102 2.30 × 102 6

1.24 × 107 5.80 × 106 4.39 × 107 1.03 × 107 1.55 × 10−1 NA 5.74 × 105 1.50 × 106 8.96 × 103 4.10 × 103 5.76 × 103 1.02 × 104

From ref 34. n

βn =

∏ Ki i=1

Because of the fact that the experimental successive association constants have been properly reproduced, we have calculated also the equilibrium constants related with the formation of the methanol dimer and the methanol−DMSO complex to explain why the maximum number of methanol molecules forming the association complexes is not the same for different quinones, Their values were found to be 2.37 × 10−3 and 5.63 × 10−2 M−1, respectively. Therefore, complexation processes with values of Ki lower than 5.63 × 10−2 M−1 are less favored than the formation of the methanol−DMSO complex, and the corresponding complexes are not expected to be observed. That might explain why the TCBQ2−−(CH3OH)3 complex was not detected in the experiments. Other linear correlation involving the experimental global equilibrium constants has been obtained from the geometries of optimized quinone dianion−(CH3OH)i complexes (Figures 3−8). Among the 1:1 complexes, the shortest interaction

(2)

The calculated values of βn are reported in Table 3, together with the experimental values obtained in DMSO. The agreement is very good with the largest discrepancy corresponding to the TCBQ2−−(CH3OH)3 and TCBQ2−− (CH3OH)1 complexes. In these cases, the calculated values were found to be 4.5 and 2.1 times lower than the experimental one. For all the other βn values, this factor was lower than 1.5 times. The correlation between calculated and experimental βn values is shown in Figure 2. The linear correlation has an r2

Figure 2. Calculated (calcd) vs experimental (exptl) global equilibrium constants (βn) in DMSO.

value of 0.92, a slope close to one (∼1.1), and an intercept close to zero (∼−0.2). Accordingly, it can be stated that the presented calculations properly reproduce the experimental behavior of the successive association phenomenon. The relevance of this finding arises from the fact that association equilibrium constants for different quinones structure were reproduced with the same functional. At our knowledge, this is a first example of electronic structure calculations in which the HB association phenomena has been described for electrochemically generated species. Although this functional was used for a particular set of quinones, this work opens the possibility to predict single or successive association constants for other systems.

Figure 3. Structures of the BQ2−−(CH3OH)n clusters.

distance was found for TMBQ and the longest one for TCBQ. Moreover, a linear correlation between the experimental β1 values and the HB distance in these complexes was found with r2 = 0.996 (Figure 9, n = 1). Similar correlations were tested for the complexes with more than one methanol molecules, using the average HB distance. As the number of methanol molecules increases, the correlation decreases. While for the 1:2 complexes r2 is still quite good (r2 = 0.982), for the 1:3 and D



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Figure 6. Structures of the 2PBQ2−−(CH3OH)n clusters.

Figure 4. Structures of the TMBQ2−−(CH3OH)n clusters.

Figure 7. Structures of the NQ2−−(CH3OH)n clusters.

Figure 5. Structures of the TCBQ2−−(CH3OH)n clusters.

Despite the fact that the relationships involving the average HB distance or involving the sum of the electronic charge density at the BCPs weakens as the number of methanol molecules increases, they seem to be good descriptors of the strength of the HB interactions leading to the complex formation, at least qualitatively. The decreasing of r2 with the number of methanol molecules can be attributed to the way used to consider more than one interaction at the same time. Averaging the HB distances or summing the ρ(r) values might not be as accurate as desired. However, we did not find another way of considering all the interactions together. Searching for alternative indexes that provide a better quantitative description of the complex formation, we have also calculated several global reactivity indexes. They were calculated according to the Perdew−Levy approximation, which is the analogue to Koopmans theorem approximation67 for DFT framework. Perdew et al.68,69demonstrated that, in exact DFT, the ionization energy (IE) is

1:4 complexes, r2 is significantly lower (r2 = 0.853 and 0.771, respectively). In order to confirm the interactions leading to the complex formation, Bader topological analyses were performed, and several critical points were identified. The electronic charge density ρ(r) and its Laplacian,∇2ρ(r), are reported in Supplementary Table 1S. For all the complexes, at least one bond critical point (BCP) was found between the dianion of the quinone and every methanol molecule involved, confirming the existence of the intermolecular interaction for each pair of fragments. Correlations between the experimental βn values and the electronic charge density, at the BCP, were also investigated (Figure 10). For the complexes with more than one methanol molecule, the ρ(r) was taken as the sum of all the individual values. Clear trends were found in all the cases. However, as the number of methanol molecules increases, the correlation worsens.

IE = −E HOMO(gN ) E

(3)



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where EHOMO(gN) represents the energy of the highest occupied molecular orbital (HOMO) of the N-electron system, from which an electron is removed. Similarly the electron affinity (EA) was calculated as EA = −E LUMO(gN )

(3)

where ELUMO(gN) represents the energy of the lowest unoccupied molecular orbital (LUMO) of the N-electron system. The absolute hardness (η), defined by Parr and Pearson as the second derivative of the electronic energy of the system with respect to the number of electrons at a constant external potential,70 η=

1 ⎛ ∂ 2E ⎞ ⎜ ⎟ 2 ⎝ ∂N 2 ⎠ν(r)

(4)

was evaluated based on the commonly used finite difference approximation, leading to Figure 8. Structures of the AQ2−−(CH3OH)n clusters.

η=

IE − EA 2

(5) 71

The electronegativity (χ) of Pauling and Mülliken was calculated according to the Mülliken formula72 as

χ=

IE + EA 2

(6)

The electrophilicity (ω) has been calculated as proposed by Parr et al.73 for the ground-state parabola mode as ω=

(IE + EA)2 8(IE − EA)

(7) +

The electroaccepting power (ω ) and the electrodonanting power (ω−) indexes, which have been recently presented by Gazquez et al.,74 have been calculated as

ω+ =

Figure 9. Relationship between the experimental global equilibrium constants (βn) in DMSO and average HB distance in the complexes.

(IE + 3EA)2 16(IE − EA)

(8)

(3IE + EA)2 16(IE − EA)

(9)

and ω− =

IE, EA, and the reactivity indexes were calculated for the system receiving the next methanol molecule (CH3OH = M), i.e., they were calculated for Q2−−Mi−1 for the formation of each Q2−−Mi complex. The obtained values for the mentioned indexes are reported in Supplementary Tables 2S and 3S, together with the partial charge on the O atom (qO) in Q2− involved in the formation of the Q2−−Mi complex. No direct relationship was found for any of these descriptors alone. However, multiple linear regressions were tested, and it was found that only a linear combination of IE, EA, and qO correctly describes the formation of the complexes, regardless of the number of methanol molecules involved, on the contrary of which was previously described for the HB distance and the electronic charge density at the BCPs. The values of the coefficients are reported in Table 5. Apparently such combination of IE, EA, and qO accounting for the structure−reactivity relationships are relevant for the complexation processes of the quinone dianions with different numbers of methanol molecules. The r2 values were found to

Figure 10. Relationship between the experimental global equilibrium constants (βn) and the sum of the electronic charge density at the BCPs.

F



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Table 5. Coefficients of the Multiple Linear Regressiona

a

n

a

b

c

d

1 2 3 4

−0.72 −1.59 −1.43 4.62

−0.20 −0.13 −0.69 −5.48

−3.61 −9.11 −18.16 57.39

2.70 4.84 −1.17 16.43

molecule. This combination seems to be valid regardless of the number of methanol molecules in the complex. Because of the fact that the parameters before mentioned could be calculated with the M05-2X and SMD approach for any molecule, an interesting perspective of this work could be the use of the coefficients of the linear combination to predict association constants for other HB systems.

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log(βn) = a(IE) + b(EA) + c(qO) + d

ASSOCIATED CONTENT

S Supporting Information *

be 0.967, 0.98, 0.96, and 0.977 for the complexes with 1, 2, 3, and 4 methanol molecules, respectively (Figure 11). The results

Electronic charge density and its Laplacian at the BCP critical points. Ionization energies, electron affinities, and Mulliken charge in the O involved in the HB interaction. Absolute hardness, electronegativity, electrophilicity, electrodonanting power, and electroaccepting power of the H acceptors. Optimized geometries of the complexes. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (A.G.); [email protected] (I.G.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS A.G. acknowledges the Laboratorio de Visualización y Cómputo Paralelo at Universidad Autónoma MetropolitanaIztapalapa for the access to its computer facilities. M.G. acknowledges CONACYT (Project #CB2006-1-62198) for the financial support.

Figure 11. Relationship between the experimental global equilibrium constants (βn) and the linear combinations of IE, EA, and qO.

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obtained with this combination, which can be defined as a descriptor directly related to the formation of HB complex solution, are quite promising. Therefore, this descriptor might be useful for other HB complexation processes, albeit this remains to be tested since such generalization escapes the purposes of the present work. Moreover, the weight of the different coefficients in the multiple linear regressions allows for directly quantifying the relative importance IE, EA, and qO on the complexation process, which can be highly useful to the detailed understanding of such process for different systems.

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(1) Rozas, I. Phys. Chem. Chem. Phys. 2007, 9, 2782−2790. (2) Grabowski, S. J. Chem. Rev. 2011, 111, 2597−2625. (3) Okamura, M. Y.; Feher, G. Annu. Rev. Biochem. 1992, 61, 881− 896. (4) Klinman, J. P.; David, M. Annu. Rev. Biochem. 1994, 63, 299−344. (5) Ding, H.; Moser, C. C.; Robertson, D. E.; Tokito, M. K.; Daldal, F.; Dutton, P. L. Biochemistry 1995, 34, 11606−11616. (6) Gupta, N.; Linschitz, H. J. Am. Chem. Soc. 1997, 119, 6384−6391. (7) Swallow, A. J. In Function of Quinones in Energy ConserVing Systems; Trumpower, B. L., Ed.; Academic Press: New York, 1982; Chapter 3, p 66. (8) Crofts, A. R.; Wraight, C. A. Biochem. Biophys. Acta 1983, 726, 149−185. (9) Rich, P. R. Biochem. Biophys. Acta 1984, 768, 53−79. (10) Trumpower, B. L. J. Biol. Chem. 1990, 265, 11409−11412. (11) Okamura, M. Y.; Feher, G. Annu. Rev. Biochem. 1992, 61, 861− 896. (12) Peover, M. E. J. Chem. Soc. 1962, 4540−4549. (13) Peover, M. E. In Electroanalytical Chemistry; Bard, A. J., Ed.; Dekker: New York, 1967; pp 1−51. (14) Chambers, J. Q. In The Chemistry of the Quinonoid Compounds; Patai, S., Rappoport, Z., Eds.; Wiley: New York, 1988; Vol. II, Chapter 12, pp 719−757; 1974; Vol. I, Chapter 14, pp 737−791. (15) Lehmann, M. W.; Evans, D. H. Anal. Chem. 1999, 71, 1947− 1950. (16) Kim, J.; Chung, T. D.; Kim, H. J. Electroanal. Chem. 2001, 499, 78−84. (17) Lehmann, M. W.; Evans, D. H. J. Phys. Chem. B 2001, 105, 8877−8884. (18) Guin, P. S.; Das, S.; Mandal, P. C. Int. J. Electrochem 2011, 2011, 1−22 and references therein. (19) O’Brien, P. J. Chem.-Biol. Interact. 1991, 80, 1−41.

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CONCLUSIONS The functional M05-2X together with the SMD solvent model have shown to be adequate for describing binding energies and solvation both in neutral and ionic species interacting by hydrogen bonds. The reliability of these calculations was tested in the case of the hydrogen bonding interaction of methanol and a set of quinone dianions. For all the dianion−methanol systems, the number of methanol molecules involved in the observed complexes has been explained based on the relative strength of these complexes compared to that of the methanol−DMSO and methanol dimer complexes, although the last one was found to be the weakest. That is, the electronic stoichiometry of the dianion−methanol complexes is mainly determined by the dianion basicity and the strength of the hydrogen bonding interactions between DMSO and methanol. From this approach, it was found that the successive association constants involved in the formation of the complexes depend on a linear combination of three quantum chemistry indexes which are the ionization energy, the electron affinity, and the charge on the O atom receiving the methanol G



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Correlation between Hydrogen Bonding Association Constants in

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