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Origin of Remarkably Different Acidity of HydroxycoumarinsJoint Experimental and Theoretical Studies Paweł Mateusz Nowak,*,† Filip Sagan,‡ and Mariusz Paweł Mitoraj*,‡ †

Faculty of Chemistry, Department of Analytical Chemistry, Jagiellonian University in Kraków, Ingardena 3, 30-060 Kraków, Poland Faculty of Chemistry, Department of Theoretical Chemistry, Jagiellonian University in Kraków, Ingardena 3, 30-060 Kraków, Poland

‡

S Supporting Information *

ABSTRACT: In the present work the origin of highly varied acidity of hydroxycoumarins (pKa values) has been for the first time investigated by joint experimental and computational studies. The structurally simple regio-isomers differing in the location of hydroxyl group, 3-hydroxycoumarin (3-HC), 4hydroxycoumarin (4-HC), 6-hydroxycoumarin (6-HC), 7hydroxycoumarin (7-HC), as well as 4,7-dihydroxycoumarin (4,7-HC) and the larger 4-hydroxycoumarin-based derivatives: warfarin (WAR), 7-hydroxywarfarin (W7), coumatetralyl (CT), and 10-hydroxywarfarin (W10), have been compared in terms of enthalpy−entropy relationships accounting for the observed pKa values. We have revealed that in the case of large molecules the acidic proton is stabilized by the following noncovalent interactions OH···O (WAR and W7), OH···π (CT), and OH···OH···O (W10), this effect leads to a compensatory enthalpy−entropy relation and yields a moderate pKa increase. On the other hand, different location of the hydroxyl group in the regio-isomers (3-HC, 4-HC, 6-HC, and 7-HC) leads to the massive changes in acidity due to a lack of enthalpy−entropy compensation. Our results suggest that the solvent−solute interactions and electron delocalization degree in anions contribute to the observed behaviors. Such knowledge can be useful in the future to design novel systems exhibiting desired acid−base properties, and to elucidate enthalpy−entropy compensation phenomena.

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INTRODUCTION Acidity, usually expressed by the logarithmic acid dissociation (deprotonation, ionization) constant, pKa, is one of the basic molecular properties of both inorganic and organic molecules. The pKa value determines water solubility, lipophilicity, polarizability, membrane permeability, as well as aptitude for intermolecular interactions which are crucial for maintaining functionality of biomolecules. On that account, modification of acidity is a prospective means for enhancing bioavailability and activity of many biologically important molecules, like drugs, diet supplements, and various endogenic compounds.1−6 Acid− base properties originate directly from the changes of enthalpy and entropy (ΔH and ΔS, respectively) in solution upon deprotonation. Their quantification provides a profound thermodynamic description of a deprotonation process, and facilitates identification of structure−acidity relationships. Despite the fact that dynamical processes in solution have been intensively studied over the recent decades, the role of enthalpy−entropy relations as well as their physical origin are still enigmatic and uncovered for many types of systems.7−9 Hydroxy-coumarins and their derivatives (denoted collectively as HCs) represent a versatile group of phenolic molecules that are known for their fluorescent properties, anticoagulant activity in vivo, and their utilization in the therapy of thrombosis and in the production of rat poisons.10−13 Although each HC © XXXX American Chemical Society

possesses the same structural motif, their structural diversity stems from a variety of substituents and regio-isomeric forms. It is important to emphasize that HCs differ severely in acidity, and remarkably, the largest difference of pKa, in the order of 5 pH units, is observed for the structurally similar regio-isomers: 4-hydroxycoumarin (4-HC, pKa = 4.1) and 6-hydroxycoumarin (6-HC, pKa = 9.0).14 An explanation of these differences with regard to the thermodynamic and electronic effects has never been attempted so far. Their unraveling would be a large step toward better understanding of structure−acidity relationships, and their impact on the functionality of biomolecules, including HCs. This work is aimed at a pioneering investigation of the enthalpy−entropy relations, and their physical origin, underlying the observed variety of pKa values. We have compared the structurally simple HCs, 3-hydroxycoumarin (3-HC), 4-HC, 6HC, 7-hydroxycoumarin (7-HC), and 4,7-dihydroxycoumarin (4,7-dHC), with the larger 4-HC-based derivatives, coumatetralyl (CT), warfarin (WAR), 7-hydroxycoumarin (W7), and 10-hydroxycoumarin (W10) (Figure 1). The experimental values obtained for WAR, W7, and W10 have been taken from Received: February 25, 2017 Revised: April 5, 2017 Published: April 13, 2017 A

DOI: 10.1021/acs.jpcb.7b01849 J. Phys. Chem. B XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry B

information about noncovalent interactions from the plots of sign (λ2)ρ vs s. Molecular Electrostatic Potential (MEP). Maps of molecular electrostatic potential (MEP) have been drawn in ADF2014.04 suite for graphical representation of charge distribution. The potential V(r), interpreted as a force acting on a positive point charge in position r is given by V (r ) =

∑ A

ZA − |RA − r |

∫

ρ(r′)dr′ |r − r′|

(2)

where ZA is the nucleus charge at the position RA, and ρ(r) is the total electronic density. Negative values of V(r) show nucleophilic areas of a molecule and positive values show electrophilic regions. Materials and Instrumentation. All HCs were supplied by Sigma-Aldrich (St. Louis, MO, USA), except with W7 and W10, which were supplied by LGC Standards (Teddington, UK). Dimethyl sulfoxide (DMSO) was used as the EOF marker (Sigma-Aldrich). The experiments were performed with a P/ ACE MDQ Capillary Electrophoresis (CE) System (Beckman Coulter, Brea, CA, USA) equipped with a diode array detector. A bare silica capillary was used, it was of 60 cm total length, 50 cm effective length, and 50 μm internal diameter. The UV−vis absorption spectra were collected between 200 and 600 nm. The 200 nm was the analytical wavelength for measuring electrophoretic mobility. The sample trays and capillaries were conditioned at various temperatures, between 15−55 °C. All aqueous solutions were prepared using a deionized water (Milli-Q, Merck-Millipore Billerica, MA, USA), filtered through a 0.45 μm regenerated cellulose membrane and then degassed by sonication and centrifugation. The rinsing of capillaries between the runs was done by applying a pressure of 137.9 kPa (20 psi). The capillary, between the runs, was rinsed with 0.1 M NaOH for 2 min and with the background electrolyte (BGE) for 4 min. Prior the first use of the capillary on a working day a rinse with deionized water for 5 min, 0.1 M NaOH for 10 min, and BGE for 10 min was applied. For a fresh capillary conditioning, the same rinsing sequence was used but the duration of each step was doubled. All BGE solutions were of a 50 mM ionic strength. The buffer ingredients and the pH values are presented in Table 1.

Figure 1. DFT/BLYP-D3/TZP optimized structures of the hydroxycoumarins (HCs) studied in the present work.

our recent work.15 For determination of the standard dissociation (deprotonation) enthalpy ΔH° and entropy ΔS° we used a modern and accurate analytical technique, the capillary electrophoresis (CE), and we supported our investigation with the density functional theory (DFT) calculations.

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MATERIALS AND METHODS DFT Calculations. Theoretical calculations were performed at DFT/BLYP-D3 level of theory. TZP basis set as available in the ADF 2014.0416,17 suite was used in bond order analysis and COSMO-RS18 calculations. CPCM19,20 calculations used for determination of pKa from the thermodynamic cycles (Supporting Information, Figure.S1) were performed in Gaussian09 rev. E.0121 program in 6-31+G* basis set. Such protocol was demonstrated to perform adequately in the past.22,23 All geometries were reoptimized prior to computational runs with different basis sets. The optimized structures of WAR molecule appeared to be similar to ones found by Regalado et al.24 Noncovalent Index (NCI). In order to shed some light on noncovalent interactions, the NCI (noncovalent index) method25 implemented in NCIPLOT26 program was used. The method is based on the interpretation of the reduced density gradient: |∇ρ| 1 s= 2(3π 2)1/3 ρ 4/3 (1)

Table 1. Composition of Buffering Solutions Used in pKa Determinationa pH

buffer type

3.5, 4.5, 5.5 6.5, 8.0 9.5, 11.0

acetic buffer phosphate buffer borate buffer

buffer ingredients CH3COOH NaH2PO4 Na2B4O7·10H2O

CH3COONa Na2HPO4 HCl/NaOH

a

The amounts of the given ingredients were calculated to ensure the constant ionic strength of 50 mM. The pH values presented in the table are the nominal values, their variation was measured prior to the CE analysis.

Sample injection was done hydrodynamically, applying forward pressure of 3.45 kPa (0.5 psi) for 5 s. All analytes were used in a final concentration of 0.1 mg/mL, and DMSO 0.2% (v/v), all dissolved in BGE. Electrophoretic analysis was performed with a separation voltage of 30 kV, using a normal polarity (anode at inlet). All measurements were done in triplicate. Determination of pKa . CE is broadly utilized in determination of pKa values.27 The procedure is based on plotting the relation between electrophoretic mobility, depend-

plotted against the molecular density ρ. To distinguish between attractive and repulsive interactions, the eigenvalues (λi) of the second derivative of density (Hessian, ∇2ρ) are used, ∇2ρ = λ1 + λ2 + λ3. Namely, bonding interactions are characterized by λ2 < 0, whereas λ2 > 0 indicates that atoms are in a nonbonded contact. Therefore, within the NCI technique, one can draw B


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Table 2. Comparison of the pKa Values Determined Experimentally (CE), the DFT/BLYP-D3/TZP/COSMO-RS Estimations, Enthalpic and Entropic Factors, and Relative Molecular Size (in Relation to 4-HC) compound

pKa (CE)

pKa (DFT)

ΔH° (kJ·mol−1)

−TΔS° (kJ·mol−1)

size (relative)

3-HC 4-HC 4.7-dHC 6-HC 7-HC CT WAR W7 W10

6.81 (0.05) 4.06 (0.04) 4.43 (0.06) 8.98 (0.07) 7.54 (0.05) 4.36 (0.03) 4.87a 5.05a 6.01a

7.8 6.0 6.6 8.2 8.6 6.5 6.9 7.3 8.7

13.37 7.38 7.12 9.32 16.01 21.61 16.90a 18.40a 34.30a

3.07 1.90 2.18 5.05 3.25 0.37 1.31a 1.25a 0a

1.10 1.00 (reference) 1.03 1.21 1.04 1.54 1.60 no data 1.41

a

Denotes the values taken from our recent work.15 The pKa values refer to the temperature of 298 K. The standard errors are presented in the brackets.

Figure 2. Contours describing the reduced density gradient at the isovalue of 0.5 au for CT, WAR, W7, and W10. The surfaces are colored in a bluegreen-red scale according to the values of sign(λ2)ρ, ranging from −0.07 to 0.01 au.

ent on ionization degree, and pH, and finding pKa as the inflection point of the obtained sigmoidal curve. Electrophoretic mobility can be calculated as μep =

L totLeff ⎛ 1 1 ⎞ ·⎜ − ⎟ Unom ⎝ t tot teof ⎠

where μA− is the electrophoretic mobility of the anion created upon deprotonation, and pKa is a fitting parameter (pH at the inflection point). Calculation of ΔH° and ΔS°. The values of the standard dissociation (deprotonation) enthalpy (ΔH°) and entropy (ΔS°) were calculated from the Van’t Hoff model describing the relation between pKa and temperature:

(3)

where μep is the electrophoretic mobility of analyte, Ltot and Leff are the total and effective capillary lengths (m), Unom is the nominal (programmed) separation voltage (kV), ttot is the total (observed) migration time of analyte (min), while teof is the time measured for the neutral marker of electroosmotic flow (EOF). For a monoprotic acid pKa can be obtained from the following equation: ⎤ ⎡ 10−pKa μep = ⎢ −pK ⎥ ·μ A− − pH ⎦ ⎣ 10 a + 10

pK a =

ΔH ° ΔS° − 2.303RT 2.303R

where R is the gas constant (8.3145 J·mol−1·K−1). Accordingly, the pKa values determined at various temperatures were plotted against the inverse absolute temperature (1/T) and fitted by the linear function. Subsequently the enthalpic and entropic terms were calculated from the slope and intercept, respectively. The same method was used in our recent work.15 Hydrodynamic Radius. The CE technique, besides determination of thermodynamic parameters, may also be used to compare molecular size of molecules. Provided that temperature and ionic strength are the same and that all

(4) C


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The Journal of Physical Chemistry B compounds are totally ionized, there is a strict proportionality between the difference in electrophoretic mobility and the difference in hydrodynamic radius. In this study the relative molecular size was estimated by measuring and comparing electrophoretic mobilities at the highest pH value −11.0, when all molecules except with W7 occur as the singly ionized anions.14

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RESULTS AND DISCUSSION It is seen from Table 2 that the calculated pKa values (based on the COSMO-RS solvation model) follow qualitatively the experimental trend, however quite notable discrepancies in the absolute values are noted (from 0.78 for 6-HC up to 2.69 for W10). Despite a lack of quantitative agreement, the qualitative picture is nicely maintained, i.e., the lowest pKa are consistently noted for 4-HC, 4,7-HC, and CT, whereas the least acidic species are 6-HC, 7-HC, and W10. The similar trends in pKa values are obtained when considering the proton exchange and direct schemes with the CPCM solvation model, Table S1 in the Supporting Information. These computational results obtained from the different schemes demonstrate that the optimized structures are reliable for further discussion. The experimentally determined pKa value of 4-HC (4.06) is in accordance with the potentiometric estimation, ca. 4.10, by Georgievskii28 and others.29 The other values agree well with our previous study.14 However, one must admit that the accuracy of all thermodynamic parameters determined by CE using electrophoretic mobilities may be burdened with some systematic errors, related to the excessive Joule heating generation upon voltage application and axial electric field distortion along the capillary.30,31 Nevertheless, all the analytes were tested in the same experimental setup and thus some effects compensated for each other, and moreover, the observed differences are very large. Therefore, one shall state that all trends and behaviors discussed in the next section are trustworthy. An inspection of the calculated structures leads to the conclusion that CT, WAR, W7, and W10 are characterized by the presence of close intramolecular contacts, Figure 1. We have calculated the noncovalent index (NCI) based on the reduced density gradient, which is well suited for the visualization of weak interactions,25,26 Figure 2. It is clearly seen that CT displays the OH···π interaction, WAR and W7 the primarily single OH···O stabilization, whereas W10 the specific OH···OH···O hydrogen bonds, Figures 1 and 2. Additionally, we have found out for the first time that WAR, W7, and W10 are also stabilized by the secondary CH···O interactions, Figure 2. All these noncovalent intramolecular contacts stabilize the nondissociated form, however, the increase in the experimentally determined pKa in regard to 4-HC is quite moderate, up to 1.95 for W10. By contrast, the variation of the pKa values seen for the smaller regio-isomers (3-HC, 4-HC, 6-HC, and 7-HC) is much more significant, up to 4.92 pKa units between 4-HC and 6-HC (Table 2). In order to get some hints on the physical origin of the mentioned outcomes, the enthalpic (ΔH°) and entropic (−TΔS°) terms have been determined from the Van’t Hoff plots (Figure 3) and are gathered in Table 2. To facilitate analysis, the values of the ΔH° and −TΔS° terms have been plotted against each other and are presented in Figure 4. Taking into account the relative contribution of the enthalpic and entropic terms, HCs can be arbitrarily divided into two groups. The entropic group comprises molecules for which, in general, the −TΔS° to ΔH° ratio is relatively high

Figure 3. Van’t Hoff plots obtained for 4-HC, 3-HC, 7-HC, 6-HC, 4,7dHC, and CT, with an indication of the selected temperature values.

Figure 4. Enthalpy−entropy plot for nine structurally different HCs. To facilitate interpretation the structures of 6-HC and W10 have been shown as the inset graphics, these molecules exhibit the highest (6HC) and lowest (W10) contribution of entropy. Note that 4-HC has the hydroxyl group located at the same carbon atom as WAR, W7, W10, and CT.

(the green rectangle, Figure 4), while in the enthalpic group it is much lower (the red rectangle, Figure 4). Interestingly, the compounds assigned to both groups differ noticeably in a molecular structure and size. The entropic group contains small molecules exhibiting no intramolecular hydrogen bonds (see the structures in Figure 1), whereas all molecules in the enthalpic group are larger, their hydrodynamic radius differ by 30−50% (Table 2), and they display various intramolecular noncovalent interactions. This suggests that there is a strict link between molecular geometry/structure and the observed enthalpy−entropy relation. The structures of CT, WAR, W7, and W10 are characterized by the same OH position as 4-HC, thus we will first discuss the enthalpy−entropy relations in these systems. It is seen that 4HC, without the presence of any intramolecular contact, is characterized by the lowest pKa (4.06), whereas the pKas are higher for the systems in which the acidic protons are stabilized by noncovalent interactions, CT (4.36), WAR (4.87), W7 (5.05), and W10 (6.01) (Table 2). We observe concurrently that the ΔH° term increases gradually in the order 4-HC (no intramolecular interaction) < WAR and W7 (OH···O D


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and accordingly, a rise of heat capacity as compared with the breaking of the single OH···O connection observed for WAR and W7. We have also suggested that this effect is accompanied by a larger increase in molecular disorder (entropy) in the case of W10. However, for all molecules dissociation entails also an entropically unfavorable organization of water dipoles around the created ions, irrespective of a type of intramolecular bond. In consequence, the final entropy change shall be seen as a sum (compensation) of both effects.15 The data obtained in this work shed additional light on these issues. Namely, the enthalpic and entropic factors change in the order, 4-HC < WAR/W7/CT < W10 and 4-HC > WAR/W7/CT > W10, respectively. This nicely correlates with the fact that 4-HC displays no intramolecular contact, whereas CT forms the single intramolecular connection OH···π, analogously as WAR and W7, but both these noncovalent interactions are weaker than the hydrogen bonding OH···OH···O observed for W10. Please note, the reduced density gradient areas are clearly similarly green for CT, WAR, and W7, whereas the bluecolored region (indicating stronger intramolecular interactions) is noted for W10 (Figure 2). It is consistent with the shortest H···O distance (1.65 Å) noted for W10 (Figure 1). Therefore, due to a simpler structure and the lack of intramolecular hydrogen bond, the deprotonation of 4-HC may entail a much lower release of molecular strain and rise of heat capacity (ΔH°). Concomitantly, the unspecific entropically unfavorable water organization-related effect may be responsible for the higher −TΔS° value of 4-HC than for WAR, W7, CT, and W10 due to a lack of compensation specific for the intramolecular interactions. Since 3-HC, 6-HC, and 7-HC also do not form intramolecular interactions, this argumentation (the presence or lack of intramolecular interactions with the resulting thermodynamic consequences) explains a clear division between the enthalpic and entropic groups. It is worth highlighting that the presence of intramolecular hydrogen bonding appeared also to influence the absorption and NMR spectra of HCs.32 Another issue is the huge variation of the deprotonation entropy observed if one compares 4-HC to 3-HC, 6-HC, and 7HC. It is noticeable that despite the same molecular mass, the estimated hydrodynamic radius of the deprotonated 6-HC is by 20% larger than for 4-HC, see Table 2. This difference is comparable to that one seen between 6-HC and W10, though in that case the difference in molecular mass is significant. This suggests that the size of solvation shell may play a crucial role in the observed deprotonation thermodynamics, especially taking into account the fact that the larger is degree of water organization around the anion, the larger is the unfavorable impact of entropy which hampers deprotonation. It could be added that in the case of 6-HC the corresponding anion is characterized by the presence of the two negatively charged basins (stemming from the carbonyl units) which are geometrically located at the opposite sites of the molecule (hence, the largest distance between can be present as compared to other isomers), Figure S2 in the Supporting Information. By assuming that solvent species will be mostly distributed around these poles, it seems qualitatively understandable that the largest hydrodynamic radius is determined for 6-HC (Table 2). As far as the strongest acidity (and the lowest deprotonation enthalpy) of 4-HC is concerned, it is necessary to point out that the stability of the anionic form is also an important factor. Namely, we have figured out that 4-HC is characterized by the

interaction) < CT (OH···π interaction) < W10 (OH···OH···O interaction) (Table 2 and Figure 4). The entropic −TΔS° term, in turn, decreases concomitantly exactly in the same order to reach zero in the case of W10 exhibiting the highest pKa. This observation reveals a compensatory enthalpy−entropy relationship. Therefore, despite the massive differences in the magnitude of particular factors, the pKa values differ to a relatively small degree. To illustrate this, ΔH° noted for W10 is almost five times as high as for 4-HC (the difference reaches 27 kJ/mol) but the corresponding difference in pKa is only 1.95 pH units. This compensatory relation has also been illustrated in Figure 5.

Figure 5. Enthalpy−entropy compensation plot with an indication (red squares) of the three HCs (3-HC, 6-HC, 7-HC) that disobey the compensation rule.

The second issue is a transition between the regio-isomeric structures, i.e., different localization of the hydroxyl group with the maintenance of the same atomic composition. We observe a drastic rise of the pKa in the order 4-HC (4.06), 3-HC (6.81), 7-HC (7.54), 6-HC (8.98). However, in contrast to the former effect (the presence of intramolecular noncovalent interactions), the increase in pKa is accompanied not by a drop, but by the appreciable increase in the entropic −TΔS° term, from 1.90 kJ/mol (4-HC) up to 5.05 kJ/mol (for 6-HC). Concurrently, the ΔH° values observed for 3-HC, 7-HC, and 6-HC are also higher (by around 1.9−8.7 kJ/mol depending on a system) than that for 4-HC (7.38 kJ/mol), hence, enthalpy and entropy display no compensatory behavior. This explains why the pKa of 6-HC (8.98) is higher nearly by 5 units in comparison to 4HC (4.06), although, the dissociation enthalpy differ barely by 1.94 kJ/mol. This peculiar enthalpy−entropy relation is seen in Figure 5 as a deviation of 6-HC, 3-HC, and 7-HC from the enthalpy−entropy compensation plot. It is noticeable that the pKa of 4,7-HC differs only subtly (by 0.36 unit) with respect to 4-HC, and the ΔH° and −TΔS° terms are also basically comparable (Table 2). It shows that, in this case, the presence of two phenolic groups has a mere impact on the deprotonation thermodynamics. In our recent work we have discussed the differences in the ΔH° and −TΔS° terms between WAR/W7 and W10.15 We have postulated that the loss of the double OH···OH···O interaction, observed for W10 upon dissociation (deprotonation), may impose a much bigger release of molecular strain E


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Figure 6. Molecular electrostatic potentials (0.005a.u.) of the anions (in water) formed due to deprotonation of 3-HC, 4-HC, 6-HC, and 7-HC, as well as their relative free energies. Additionally, the Nalewajski-Mrozek bond orders are depicted together with the related schematic drawings of the partially double bonds (---). The arbitrary threshold for the existence of partially double bond (X) has been chosen as 1.100 < X < 1.600, whereas the single bonds (Y) are those exhibiting the values in the range 0.900 < Y < 1.100.

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CONCLUSIONS In the present work the physical origin of the remarkable differences in acidity of various HCs has been for the first time discussed based on the experimental and theoretical investigations. It has been shown that the presence or lack of the intramolecular hydrogen bonds stabilizing the acidic proton accounts for the enthalpy−entropy relations and the final change of the free energy. Contribution of the energetically unfavorable enthalpic effect (positive ΔH°) is larger for the compounds displaying intramolecular interactions, like WAR, W7, CT, W10, however, the final pKa difference is relatively low (up to 1.95) due to the enthalpy−entropy compensation. On the other hand, the regio-isomers, 3-HC, 4-HC, 6-HC, and 7HC, differ pronouncedly in the acidity even by 5 pH units due to the lack of enthalpy−entropy compensation. The distinct entropy behavior can be explained on a ground of the solute− solvent interactions and the resulting stability of anions. Different localization of the −OH group in the regio-isomers may induce a remarkably different size of solvation shell and different degree of water dipoles organization around ions. This hypothesis is supported by the significant rise in the −TΔS° contributions (from 1.9 kJ/mol for 4-HC up to 5.05 kJ/mol for 6-HC) and by the assessments of the hydrodynamic radius (larger by ∼20% for 6-HC than 4-HC). Another crucial factor leading to the strongest acidity of 4-HC (and the lowest enthalpy of deprotonation) is the most pronounced stability of the anionic form due to effective delocalization of the negative charge. Breaking/formation of an intramolecular hydrogen bonding engages additional factors, like release/gain of molecular strain, and rise/drop of heat capacity and molecular disorder. The outcomes presented herein provide a novel physical insight into the relation between the geometries, electronic structures of various HCs, and their highly varied

lowest anionic energy from among all regio-isomers (Figure 6, Table S2 and Table S3). It is valid both in the gas phase as well as in the water solvent, and this implies that a facile deprotonation of 4-HC is related to the electron density distribution in the anion 4-O−. In order to better understand the origin of this outcome, we have calculated the Nalewjski− Mrozek bond orders33,34 shown in Figure 6. It is clearly seen that the ionized 4-HC exhibits the most efficient delocalization of the negative charge which is reflected in the partial double character of C−C bonds (ca. 1.338 and 1.364) that connect the carbonyl (CO) fragments (Figure 6). At the same time, the bond orders of the carbonyl units are lowered and amount to ca. 1.87 and 1.95, respectively. The molecular electrostatic potentials (MEP) consistently point at a significant delocalization of the negative charge in 4-O− as indicated clearly by the orange color around the carbonyl units (weakly negative MEP values) and the connecting carbon-skeleton, as compared to the more localized picture (red color showing the most negative MEP values) noted for the remaining anions (Figure 6). It is finally worth mentioning that the family of 3-HC, 4-HC, 6-HC, and 7-HC is a good example of structurally similar molecules that in the evident way disobey the enthalpy− entropy compensation rule (see Figure 5), and this notion may be used as an argument in the still alive debates about its validity and universality.7,8 On the other hand, the obtained results may indicate that in a “thermodynamic” sense these molecules differ considerably, and this rule, by definition, does not apply for them. It seems understandable if one considers different structure of solvation shells, discussed previously, which may make these molecules far less similar as it follows from the structures valid for the gas-phase. F


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acidity (pKa values). Such knowledge can be useful in the future design of novel systems exhibiting desired physicochemical properties.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.7b01849.

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Details and the results of theoretical calculations (PDF)

AUTHOR INFORMATION

Corresponding Authors

*Tel./Fax +48 12 663 2257; E-mail: [email protected]. *Tel./Fax +48 12 663 2042; E-mail: [email protected]. ORCID

Filip Sagan: 0000-0001-5375-8868 Mariusz Paweł Mitoraj: 0000-0001-5359-9107 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Paweł Nowak acknowledges the financial support from the National Science Centre, Poland (Preludium, 2016-2019, grant no. 2015/17/N/ST4/03792). The study was carried out with equipment purchased thanks to the European Regional Development Fund within framework of the Polish Innovation Economy Operational Program (contract no. POIG.0 2.01.0012-0 23/08). DFT calculations were performed using PL-Grid Infrastructure and resources provided by ACC Cyfronet AGH (Cracow, Poland). Filip Sagan acknowledges the financial support from Krakowskie Konsorcjum “Materia-EnergiaPrzyszłośc”́ within the KNOW subsidy as well as from the Polish Ministry of Science and Education “T-subsidy” for young researchers.

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REFERENCES

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