Investigation on Intramolecular Hydrogen Bond and Some

Article pubs.acs.org/jced

Investigation on Intramolecular Hydrogen Bond and Some Thermodynamic Properties of Polyhydroxylated Anthraquinones Ruijuan Qu,† Hongxia Liu,‡ Mingbao Feng,† Xi Yang,† and Zunyao Wang*,† †

State Key Laboratory of Pollution Control and Resources Reuse, School of the Environment, Nanjing University, Nanjing 210046, P. R. China ‡ College of Biological, Chemical Science and Engineering, Jiaxing University, Zhejiang Jiaxing, 314001, P. R. China ABSTRACT: Anthraquinone and polyhydroxylated anthroquinones (PHOAQs) have been studied at the B3LYP/6-311G** level using the Gaussian 09 program. The isodesmic reactions were designed to calculate the standard enthalpy of formation (ΔfHθ) and standard Gibbs energy of formation (ΔfGθ) for PHOAQ congeners. Two kinds of intramolecular hydrogen bonds exist in PHOAQs, and the isodesmic reactions of isomerization were used to determine the intramolecular hydrogen bond energy. The Atoms in Molecules (AIM) 2000 program (version 1.0) was used to study the characteristics of the hydrogen bonds. Relations of Sθ, ΔfHθ, and ΔfGθ with the number and position of hydroxyl substitution (NPHOS) were also discussed. How the intramolecular hydrogen bond influences ionization was investigated, and the first-order ionization constant for the most likely ionization path of the most stable conformations in each group of isomers was obtained with the self-consistent reaction field (SCRF) method.

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INTRODUCTION Anthraquinone derivatives constitute the largest group of naturally occurring quinines and historically are the most important.1 They are of considerable practical application in various areas of pharmacology, chemistry, biochemistry, and industry.1−3 Anthraquinone dyes have been widely used for the coloration of cotton and cellulose fibers in recent years. In particular, the hydroxyl derivatives of 9,10-anthraquinone provide dyes that are mostly of a red hue.4 Synthetic derivatives of anthraquinone as well as the natural ones are also used for medical purposes. For instance, the hydroxylated 9,10anthraquinones which exist widely in nature are known to show various pharmacological activities,5 and β hydroxysubstituted derivatives are the components of pharmaceuticals and physiologically active substances.6,7 Several families of antitumor natural products, involving the pluramycins (e.g., sapurimycin8), the anthracyclines (e.g., doxorubicin and daunorubicin9), and some of the enediyne antibiotics (such as dynemycin A and deoxydynemycin A10) contain a 9,10anthraquinone substructure. Furthermore, glycoside derivatives of hydroxyanthraquinone are potentially effective for kidney stone therapy because they could inhibit the formation and increase the solubility of kidney stones.11 Thus, studies on properties of polyhydroxylated anthraquinones (PHOAQs) are very important. Some research has already been conducted on anthraquinone derivatives. For example, Tabaraki et al.12 developed a wavelet neural network (WNN) model for predicting solubility of 25 anthraquinone dyes in supercritical carbon dioxide. Comini et al.13 studied some photophysical, photochemical and photobiological properties of photosensitizing anthraquinones. With regard to PHOAQs, Khan et al.14 reported an efficient and convenient methodology for the synthesis of naturally occurring hydroxyl substituted anthraquinones. Fain et al.15 © 2012 American Chemical Society

used the semiempirical quantum-chemical Pariser−Parr−Pople (PPP) method to calculate their electron absorption spectra and compared them with experimental results. However, there is little research concerning the hydrophobicity and thermodynamic properties of PHOAQs, both of which are important to study their environmental behavior, potential environmental risk, and medicinal property. To study the properties of molecules, density functional theory (DFT) is one of the most frequently used computational methods.16−18 In a previous report,19 thermodynamic parameters of polychlorinated anthraquinones (PCAQs) were calculated with DFT, and it was found that thermodynamic properties of PCAQs have close relationships with the number and position of chlorine substitution. Similar conclusions have also been reached for halogenated dioxin-like chemicals.20−22 The intramolecular hydrogen bond often has significant influence on crystal packing and engineering, conformational preferences, chemical reactions, ionization of protons, and a host of other important phenomena. Extensive research has been conducted on the nature of the hydrogen bond for nearly a century. As the most important concept for the description of the hydrogen bond, the hydrogen bond strength is known to be given by a measurable quantity such as hydrogen bond energy. However, in contrast to the case of intermolecular hydrogen bonds, there is no practical method for calculating the intramolecular hydrogen bond energy. For this reason, computational approaches are of particular importance. Various computational methods for estimating intramolecular hydrogen bond energy have been proposed, but none of them is accurate.23−25 To the best of our knowledge, the most Received: April 6, 2012 Accepted: July 26, 2012 Published: August 21, 2012 2442

dx.doi.org/10.1021/je300407g | J. Chem. Eng. Data 2012, 57, 2442−2455

Journal of Chemical & Engineering Data

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frequently adopted methods are as follows:26 cis/trans analysis, isodesmic reactions, local potential energy density, conformational analysis, and empirical energy-geometry correlations. The parent molecule 9,10-anthraquinone and 75 PHOAQs were fully optimized at the B3LYP/6-311G** level using the DFT method. To verify the calculation accuracy for the intramolecular hydrogen bond energy by isodesmic reactions of isomerization, a method for the measurement of the reaction heat was developed. The Atoms in Molecules (AIM) 2000 program (version 1.0)27 was used to study the characteristic of the hydrogen bonds. By designing isodesmic reactions, the standard enthalpies of formation (ΔfHθ) and the standard Gibbs energies of formation (ΔfGθ) for all PHOAQs were obtained. Based on the relative magnitude of their ΔfGθ values, the relative stability order of PHOAQ isomers in each isomer group was theoretically proposed. The correlations of these properties with the number and position of hydroxyl (HO) substitution (NPHOS) were also derived. The influence of the intramolecular hydrogen bonds on ionization was examined, and the first-order ionization constants (pKa1) for the most likely ionization path of the most stable conformations in each group of isomers were also acquired.

accuracy of the experiment. The measured heat of reaction was denoted by ΔHo and ΔHp. Combined with the difference between the calculated total energy of the hydrated ions (ΔE), the intramolecular hydrogen bond energy EHB,exp is available: E HB,exp = ΔHo − ΔHp + ΔE

(1)

The formula for calculating the reaction heat ΔHo(p) is: m

ΔHo(p) =

(∑i = 1 (Cp ,i·n i) ·Δt n

(2)

where the values of Cp,i, the heat capacity at constant pressure for acetonitrile and water, are 21.86 kcal·mol−1 and 17.995 kcal·mol−1,28 respectively, ni is the moles of acetonitrile and water in the reaction system, n is the moles of ohydroxybenzaldehyde added, and Δt is the difference between the temperature change of the control experiment and that of the sample test. Calculation Method. The numbering system for C atoms in anthraquinone (AQ) is illustrated in Figure 2. In this study,

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EXPERIMENTAL AND COMPUTATIONAL METHODS Experimental Section. We developed a method of measuring the reaction heat to examine the calculation results for the intramolecular hydrogen bond energy with isodesmic reactions of isomerization. Take o-hydroxybenzaldehyde and phydroxybenzaldehyde, for example; the schematic diagram for determining the experimental hydrogen bond energy (EHB,exp) is shown in Figure 1, and the experimental procedure was

Figure 2. Numbering system for C atoms in anthraquinone.

the molecules are named according to the spatial position of hydroxyl. AQ was supposed to be planar, and two oxygen atoms were defined as a and b, respectively. The orientations where the hydrogen atom of the hydroxyl faces oxygen-a or faces away from oxygen-b were considered positive, defined as 1-, 2-, 3-, 4-, 5-, 6-, 7-, and 8-, respectively. Accordingly, the orientations where the hydrogen atom of the hydroxyl faces oxygen-b or faces away from oxygen-a were considered negative, defined as 1′-, 2′-, 3′-, 4′-, 5′-, 6′-, 7′-, and 8′-, respectively. PHOAQ isomers with one to eight hydroxyls are represented by the notations MHOAQ, DHOAQ, tri-HOAQ, THOAQ, penta-HOAQ, hexa-HOAQ, hepta-HOAQ, and OHOAQ, respectively. All theoretical calculations on thermodynamic properties of AQ and 75 PHOAQs in the standard state were carried out at the B3LYP/6-311G** level using a Gaussian 09 program.29 The term “Opt Freq” refers to the optimization of the molecular structure (Opt) followed by frequency calculations (Freq) performed at the stationary points on the potential energy surface. The calculations were all scaled by 0.967 so that known systematic errors in calculating thermodynamic parameters might be eliminated. The calculation results of vibration analysis had no negative frequencies. Thermodynamic parameters including the standard state entropy (Sθ), the absolute enthalpy (Hθ), and Gibbs free energies (Gθ) can be obtained directly from Gaussian 09 output files. In this paper, the number of HOs at positions 1, 4, 5, and 8 is defined as Nα, while the number at positions 2, 3, 6, and 7 is defined as Nβ. In addition, the pair number of HOs at ortho, meta, and para positions on one benzene ring is symbolized as No, Nm, and Np. Futhermore, the above-mentioned parameters are defined as a general designation NPHOS. Take OHOAQ, for example; its Nα and Nβ are both 4, meanwhile, its No, Nm, and Np are respectively 6, 4, and 2, as can be seen from Figure 3.

Figure 1. Schematic diagram for determining E HB,exp in ohydroxybenzaldehyde.

adopted. The compounds were dissolved in acetonitrile at a low concentration respectively, with the existence of intramolecular hydrogen bond in o-hydroxybenzaldehyde and the elimination of intermolecular hydrogen bonds in p-hydroxybenzaldehyde. Then, a certain amount of NaOH aqueous solution was added to produce a ralization reaction, generating hydrated ions. The reason why we choose acetonitrile as solvent is that: (1) there is no intermolecular hydrogen bond between it and the solute molecule, (2) it is miscible with water, favorable to the conduction of the reaction, (3) for the neutralization reaction involving a particular sample, the temperature of the system slightly increases, while in the blank experiment, the temperature of the system slightly declines when water is added. The overall result is that the heat exchange between the system and the environment is reduced, improving the measurement 2443



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(SMD)30 of the self-consistent reaction field (SCRF) method, the total free energy in water (Gθwater) was obtained on a 6311G** level. Then, ΔGθwater was achieved by eq 8. The computational formula of pKa31 was shown as eq 9. HA + OH− → A− + H 2O ΔG θ water = G θ water(A−) + G θ water(H 2O) − G θ water(HA) − G θ water(OH−) (8) θ

pK a(HA) =

Figure 3. No, Nm, and Np of OHOAQ.

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In this study, the following isodesmic reaction was designed to calculate the ΔfHθ and ΔfGθ of PHOAQs.

ΔG water + 15.74 2.303RT

(9)

RESULTS AND DISCUSSION Calculation of Intramolecular Hydrogen Bond in Aromatic Compounds. The calculation method for the intramolecular hydrogen bond energy with isodesmic reactions is relatively simple and has been successfully applied. Take catechol, for example; the two kinds of isodesmic reactions for the determination of the intramolecular hydrogen bond energy (EHB) are presented in Figure 4. However, based on the

Equations 4 and 5 could be obtained. Δr H θ = [H θ(PHOAQs) + nH θ(benzene)] − [H θ(AQ) + nH θ(phenol)]

(4)

Δr H θ = [Δf H θ(PHOAQs) + nΔf H θ(benzene)] − [Δf H θ(AQ) + nΔf H θ(phenol)]

(5)

θ

wherein ΔrH is the standard enthalpy change of the reaction. Therefore, eq 6 is obtained. Δf H θ(PHOAQs) = H θ(PHOAQs) + nH θ(benzene) − nH θ(phenol) − H θ(AQ) − nΔf H θ(benzene) + nΔf H θ(phenol) + Δf H θ(AQ) (6) θ

Similarly, ΔfG of PHOAQs could be obtained by eq 7: Δf G θ (PHOAQs) = G θ (PHOAQs) + nG θ (benzene) − nG θ (phenol) − G θ (AQ) − nΔf G θ (benzene) + nΔf G θ (phenol) + Δf G θ (AQ)

(7) θ

Figure 4. Two kinds of isodesmic reactions for the determination of EHB.

θ

The data used for calculating the ΔfH and ΔfG of PHOAQs are listed in Table 1. According to a continuum solvation model, which is based on the quantum mechanical charge density of a solute molecule interacting with a continuum description of the solvent

isodesmic reaction (a), the EHB value in catechol obtained at the B3LYP/6-31+G** level is 1.89 kJ·mol−1,32 and it is calculated to be 1.81 kJ·mol−1 at the B3LYP/6-311G** level.

Table 1. Thermodynamic Data (Standard Enthalpy of Formation (ΔfHθ), the Standard Gibbs Energy of Formation (ΔfGθ), the Absolute Enthalpy (Hθ), and the Gibbs Free Energies (Gθ)) Used for Calculating ΔfHθ and ΔfGθ of PHOAQsa number 1 2 3 a

name benzene phenol AQN

ΔfHθ

ΔfGθ b

b

82.89 −96.31b −119.40b

129.66 −32.87b −6.26c

Hθ

Gθ

−609657.46 −807195.17 −1808335.27

−609737.89 −807288.99 −1808463.64

All values are in kJ·mol−1. bData from ref 28. cData from ref 19. Other data from Gaussian 09 output files at the B3LYP/6-311G** level. 2444



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Table 2. Total Energy (E/kJ·mol−1) and Hydrogen Bond Energy (EHB/kJ·mol−1) of the Molecules Calculated at the B3LYP/6311G** Level molecule

E in the pure gas state

E in acetonitrile

hydroquinone catechol p-hydroxybenzaldehyde o-hydroxybenzaldehyde p-hydroxyacetophenone o-hydroxyacetophenone

−1005020.28 −1005030.54 −1105095.54 −1105123.91 −1208362.94 −1208393.31

−1005024.05 −1005034.07 −1105106.79 −1105128.55 −1208371.34 −1208397.72

EHB,cal in the pure gas state

EHB,cal in acetonitrile

EHB,exp in acetonitrile

10.26

10.02

13.24

28.37

21.76

21.19

30.37

26.38

24.27

kJ·mol−1, 3.80 kJ·mol−1, 25.60 kJ·mol−1, and 11.10 kJ·mol−1, respectively. The ions formed in the neutralization reaction do not exist in the form of single ion but combine with water molecules originally in the sodium hydroxide solution and generated in the reaction to produce hydrated ions which are more stable. The total energy of the single o-hydroxybenzaldehyde anion and the anion hydrated with four water molecules is calculated at the B3LYP/6-311G** level in the medium acetonitrile using the SCRF method and listed in Table 3. The corresponding

Clearly, these two values are much lower than the strength of a conventional intramolecular hydrogen bond. For this reason, the isodesmic reaction is improved, that is, isodesmic reactions between isomers (b) are adopted to calculate EHB in catechol, o-hydroxybenzaldehyde, and o-hydroxyacetophenone. The hydrogen bond energy in catechol at the B3LYP/6-311G** level is calculated, EHB = 10.26 kJ·mol−1. Similarly, the EHB value in o-hydroxybenzaldehyde and o-hydroxyacetophenone is computed to be 28.37 kJ·mol−1 and 30.37 kJ·mol−1, respectively (see Table 2). Comparing the two isodesmic reaction a and b(1), we can see that the conjugated system of the hydroxyls in the molecules on both sides of (b(1) are more similar to each other, more consistent with the requirements of isodesmic reaction. For the reaction a, the conjugated system of the hydroxyl in phenol Π78 is less than the conjugated system Π810 in catechol. Therefore, the calculated EHB value is smaller, with some error. There exists a solvation effect when these molecules are soluble in acetonitrile. Of SCRF, the Onsager model, which places the solute in a spherical cavity within the solvent reaction field, is employed to calculate the total energy of the molecules at the B3LYP/6-311G** level, and the specific values are listed in Table 2. The calculated hydrogen bond energy (EHB,cal) of catechol in acetonitrile is 10.02 kJ·mol−1. Likewise, the EHB,cal value in o-hydroxybenzaldehyde and o-hydroxyacetophenone is ascertained to be 21.76 kJ·mol−1 and 26.38 kJ·mol−1, respectively. Apparently, these values are smaller than those corresponding values in the pure gas state. By comparion, the appropriate reaction conditions, including the amount of the certain sample added, the concentration and dosage of NaOH aqueous solution and so forth for measuring the reaction heat ΔHo and ΔHp are obtained. Take ohydroxybenzaldehyde, for example; the specific measurement steps are as follows: 1.2414 g (0.01 mol) of o-hydroxybenzaldehyde and 40.00 mL of CH3CN added to an adiabatic reactor of 100 mL. At the stirring speed of about 420 r·min−1, the Apresys 179A-T1 high-precision temperature recorder is inserted into the mixture. When the temperature of the solution becomes constant, 3.50 mL of NaOH solution with concentration 5.00 mol·L−1 is added, and the real-time temperature of the reaction mixture is recorded until it begins to rise. The temperature change turns out to be −2.81 °C. The corresponding value for the control experiment, that is, the reaction of adding the same volume of NaOH solution to pure acetonitrile, is −3.69 °C. Thus, the actual temperature change caused by the neutralization reaction with o-hydroxybenzaldehyde and NaOH is 0.88 °C. According to the formula 2, the reaction heat for ohydroxybenzaldehyde is calculated, ΔHo = 12.89 kJ·mol−1. Similarly, the reaction heat for p-hydroxybenzaldehyde ΔHp is 33.26 kJ·mol−1. The reaction heat for p-hydroxyacetophenone, o-hydroxyacetophenone, hydroquinone, and catechol is 23.59

Table 3. Total Energy (E/kJ·mol−1) of the Ions and the Corresponding Energy Difference (ΔE/kJ·mol−1) Calculated at the B3LYP/6-311G** Level with the SCRF Method no. water molecules

0 4

0 4 0 4

ΔE

E p-Hydroxybenzaldehyde Ion −1103664.86 −1906762.59 p-Hydroxyacetophenone Ion −1206930.33 −1906763.41 Hydroquinone Ion −1001563.73 −1804879.03

o-Hydroxybenzaldehyde Ion −1103635.36 −1906763.41 o-Hydroxyacetophenone Ion −1206883.08 −1906767.89 Catechol Ion −1001546.22 −1804877.77

−29.50 0.82

−47.24 4.48 −17.51 −1.26

values for p-hydroxybenzaldehyde anions are also given. It can be seen from Table 3 that the total energy difference between the single ions is great (−29.497 kJ·mol−1), mainly due to the large repulsion between the negative oxygen ion and the carbonyl group in the o-hydroxybenzaldehyde anion. When they are respectively combined with four water molecules, the total energy difference is just 0.82 kJ·mol−1. Similarly, the total energy difference in the two ion pairs “the p-hydroxyacetophenone ion and the o-hydroxyacetophenone ion” and “the hydroquinone ion and the catechol ion”, of which each ion is hydrated with four water molecules, is also calculated, and the value is 4.48 kJ·mol−1 and −1.26 kJ·mol−1, respectively. Concerning the computation of the total energy of the hydrated ions, there has the problem of complex conformations. Generally, different conformation has different total energy value. In our calculation system, the interaction between the water molecule and the oxygen anion group or the carbonyl group is the most obvious, while it is relatively weak between the water molecule and the water molecule, as well as the other groups. Figure 5 shows the configuration of p-hydroxyacetophenone and o-hydroxyacetophenone ions respectively hydrated with four water molecules. It can be seen from Figure 5 that, for the two hydrated ions, each oxygen anion group is hydrated with two water molecules, which is also the case of 2445



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Figure 5. Configuration of p-hydroxyacetophenone and o-hydroxyacetophenone ions respectively hydrated with four water molecules.

bonds and the corresponding Sθ and ΔfGθ values are listed in Table 4. As is shown in Table 4, an Type I intramolecular hydrogen bond exists in 1-MHODD, so its standard Gibbs free energy (ΔfGθ) is 51.344 kJ·mol−1 smaller than that of 1′-MHODD, which contains no intramolecular hydrogen bond. Similarly, ΔfGθ of 1,3-DHODD is 51.192 kJ·mol−1 smaller than that of 1′,3′-DHODD, and ΔfGθ of 1,4′-DHODD is 51.964 kJ·mol−1 smaller than that of 1,4-DHODD. Thus, the energy of the Type I hydrogen bond is thought to be about 51.5 kJ·mol−1. As can also be seen from Table 4, ΔfGθ of 2′-MHODD (−170.208 kJ·mol−1) is 2.896 kJ·mol−1 smaller than that of 2-MHODD (−173.104 kJ·mol−1), which means that the hydrogen atom of the hydroxyl located at position 2 is so far away from oxygen-a that it is impossible to form a Type I hydrogen bond. When there exists a hydrogen bond of Type II in one molecule of the isomers and other hydrogen bonds are similar, the difference of ΔfGθ is approximately 14−21 kJ·mol−1. For example, ΔfGθ of 2,3-DHODD, 1,2,3-tri-HOAQ, and 1,2,4′-triHOAQ is 15.871 kJ·mol−1,14.543 kJ·mol−1, and 20.891 kJ·mol−1 smaller, respectively, compared with 2,3′-DHODD, 1,2,3′-tri-HOAQ, and 1,2′,4′-tri-HOAQ. Consequently, the Type I intramolecular hydrogen bonds are much stronger than the Type II hydrogen bonds. Concerning Sθ values of these isomers, it can be concluded from Table 4 that Sθ values increase with the number of substituent groups, which is different from ΔfGθ values. There is no distinctive relationship between Sθ values and ΔfGθ values; as a result, Sθ values might not be considered as the criterion of determining stability. According to the thermodynamic principle, the congener possessing smaller ΔfGθ value is more stable than those with larger ΔfGθ values and is easier to form, in general. In this paper, the 75 most stable conformations in each group of isomers are listed in Table 5. They are determined in the light of the following principles: the molecules should possess as many hydrogen bonds as possible, and the priority is given to the hydrogen bonds of Type I, followed by the hydrogen bonds of Type II. Atoms in Molecules Analysis. To clarify the nature of the hydrogen bonds, the electron density topological analysis of

carbonyl. A further increase in the number of water molecules primarily leads to the interaction among water molecules, which has a small impact on the total energy. The EHB,exp values for the three kinds of molecules calculated according to formula 1 are listed in Table 2. The differences between them and the corresponding calculation values obtained with the isodesmic reaction of isomerization (EHB,cal) are 3.22 kJ·mol−1, −0.57 kJ·mol−1, and −2.11 kJ·mol−1, respectively, indicating that it is reliable to calculate the energy of the intramolecular hydrogen bond by designing appropriate isodesmic reactions of isomerization; that is, isodesmic reactions of isomerization can be used to predict the intramolecular hydrogen bond energy, with an error of about 3 kJ·mol−1. When using isodesmic reactions of isomerization to calculate the intramolecular hydrogen bond energy, we may replace the total energy change with the Gibbs free energy change despite that the derived values have some differences, since G = E + RT − TS. Take catechol, for example; EHB is 10.26 kJ·mol−1 when E is adopted for the calculation, while it is 9.22 kJ·mol−1 in the case of G, so the difference is only 1.04 kJ·mol−1. Therefore, to be consistent with the reaction heat, we use E in the above method of examining the calculation accuracy for the intramolecular hydrogen bond via the determination of the reaction heat. Combined with the stability order of the isomers, the standard Gibbs energy of formation (ΔfGθ) is employed to calculate the EHB values in the following computations. PHOAQs Owning Minimum Gibbs Free Energy. As is mentioned previously, intramolecular hydrogen bonds will greatly affect the energy of the molecule. In this study, ΔfGθ of PHOAQs with hydroxyls substituted at the same benzene ring were calculated and compared. There are two kinds of intramolecular hydrogen bonds in PHOAQs. The following definitions are adopted: the hydrogen bonds between oxygen-a (or oxygen-b) and the hydrogen atoms of hydroxyls are the first type of hydrogen bond (Type I), and the ones between the oxygen atom of a hydroxyl and the hydrogen atom of another hydroxyl at an ortho position are the second type of hydrogen bond (Type II). The molecules in which hydroxyls are located at only one benzene ring as well as their number of hydrogen 2446



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Table 4. Configuration of the Molecules in Which Hydroxyls Are Located at Only One Benzene Ring, with Their Number of Hydrogen Bonds and the Values of the Standard State Entropy (Sθ/J·mol−1·K−1) and the Standard Gibbs Energy of Formation (ΔfGθ/kJ·mol−1)

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Table 4. continued

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Table 4. continued

atoms of the two hydroxyls. Both of ρ(r) values are 0.0485, and ∇2ρ(r) values are 0.0373, which indicate that the two hydrogen bonds are equal. Thus, G(rCP) and V(rCP) is 0.0247 and −0.0401, respectively. Hence, the EHB is calculated to be 52.672 kJ·mol−1. For 2,3-DHOAQ, a BCP exists between two ortho hydroxyl groups; ρ(r) is 0.0186, and ∇2ρ(r) is 0.0230. Thus, G(rCP) and V(rCP) is 0.0076 and −0.0094, respectively. Hence, the EHB is calculated to be 12.353 kJ·mol−1. The values of ∇2ρ(r) do fall within the proposed typical range of the hydrogen bonds. While the ρ(r) value of 1-MHOAQ and 1,8DHOAQ is larger than the upper limit value of 0.034 au, suggesting that the type I hydrogen bond is stronger than the conventional hydrogen bond. Obviously, these EHB values for the two kinds of intramolecular hydrogen bonds are in good agreement with those obtained from comparisons of ΔfGθ values. Moreover, the H bonds in the three molecules are found to be partly covalent (0.5 < −G(rCP)/V(rCP) < 1). Relations of Thermodynamic Parameters and NPHOS. The values of ΔfHθ and ΔfGθ of PHOAQs were obtained with the design of isodesmic reactions. They are available in Table 5. The multiple linear regression method of the SPSS for Windows program (version 12.0)43 was used to obtain the relationship between thermodynamic parameters and NPHOS. The results are presented in Table 6. There exist close relationships between Sθ, ΔfHθ, ΔfGθ, and NPHOS, as shown in eqs 12 to 14. The following conclusions could be obtained: (1) The number of substituents is the main factor influencing the thermodynamic parameters. ΔfHθ and ΔfGθ decrease with the number of hydroxyls, while the value of Sθ increases with the number of hydroxyls. The change of Sθ value caused by Nβ is slightly larger than that resulted from Nα, which is different from the variation of the other two thermodynamic parameters. When Nα or Nβ increases by 1, the value of ΔfHθ decreases by 214.245 kJ·mol−1 and 188.525 kJ·mol−1, respectively. (2) The relative position of hydroxyls (No, Nm, Np) also has a small influence to these values. When Np adds 1, the value of Sθ decreases by 1.974 J·mol−1·K−1, and ΔfHθ and ΔfGθ increase by 5.084 kJ·mol−1 and 5.673 kJ·mol−1, respectively. So hydroxyls located at para positions do have an effect on the thermodynamic properties of the congeners. This also applies to hydroxyls located at ortho positions. Nm does not enter the regression equation for the three parameters, which indicates that the effect of Nm is negligible. (3) The squared correlation coefficients R2 of eqs 12 to 14 are all greater than 0.98. Therefore, NPHOS of PHOAQs can be used to predict the values of Sθ, ΔfHθ, and ΔfGθ. Figure 7 shows plots of the values obtained from the correlations versus the corresponding DFT results or isodesmic reactions.

four congeners was performed with the atoms in molecules (AIM) method. According to the AIM theory of Bader,33,34 the molecular graph is directly correlated with the topological property of electron density, which can also display the structure of bonds in a system. Electron density ρ(r) is used to describe the strength of a bond, and the Laplacian of the electron density ∇2ρ(r) reflects the characteristics of the bond. Generally, the larger the value of ρ(r) is, the stronger the bond is. When ∇2ρ(r) 0, the bond possesses ionic features. The bond critical point (BCP) or (3, −1) means that it holds a bond action between the corresponding atoms, and the ring critical point (RCP) or (3, +1) indicates that a ring structure exists. Figure 6 illustrates the molecular graphs of several congeners, which indicate that there exist BCP and RCP in each molecule. Popelier et al.35 proposed a set of criteria to judge the existence of hydrogen bonds, among which three were the most fundamental and often applied: (1) the existence of BCP between the two interacting atoms; (2) the ρ(r) value at the BCP should be in the range of (0.002 to 0.034) au; (3) the ∇2ρ(r) value at the BCP should be within the range (0.02 to 0.14) au. Besides the electron densities and Laplacians, the kinetic energy density G(rCP) and the potential energy density V(rCP) at the hydrogen bond critical point are often used to gain additional insights into the strength and nature of a given H bond.36−38 G(rCP) can be calculated from the values of ρ(r) and ∇2ρ(r) as G(rCP) =

3 1 (3π 2)2/3 ρ(r )5/3 + ∇2 ρ(r ) 10 6

(10)

Whereas V(rCP) can be obtained from the viral equation V (rCP) =

1 2 ∇ ρ(r ) − 2G(rCP) 4

(11)

Additionally, the hydrogen bond energy can be estimated using V(rCP) according to the empirical relationship as EHB = 0.5 V(rCP).39 Previous studies have established that the nature, noncovalent or partly covalent, of a hydrogen bond can be assessed by the ratio −G(rCP)/ V(rCP).40−42 To be specific, the hydrogen bond is noncovalent if −G(rCP)/ V(rCP) > 1 while the interaction is partly covalent if 0.5 < −G(rCP)/ V(rCP) < 1. The AIM 2000 program (version 1.0) is used to study the characteristic of the hydrogen bonds. In 1-MHOAQ, there is a BCP between a-O (or b-O) and the hydrogen atom of hydroxyl; ρ(r) is 0.0496, and ∇2ρ(r) is 0.0364. Thus, G(rCP) and V(rCP) are 0.0253 and −0.0415, respectively. Hence, the EHB is calculated to be 54.424 kJ·mol−1. While in 2-MHOAQ, no BCP exists between a-O (or b-O) and hydroxyl. That is to say, no hydrogen bonds form. In addition, for 1,8-DHOAQ, two BCPs appear between a-O (or b-O) and the hydrogen 2449



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Table 5. Standard State Entropy (Sθ, J·mol−1·K−1), the Standard Enthalpy of Formation (ΔfHθ, kJ·mol−1), the Standard Gibbs Energy of Formation (ΔfGθ, kJ·mol−1), the Relative Standard Gibbs Energy of Each Isomer (ΔfGθR, kJ·mol−1), and the FirstOrder Ionization Constant (pKa1)) of PHOAQs Owing Minimum Gibbs Free Energy Calculated at the B3LYP/6-311G** Level Sθ no.

molecule

1

AQN MHOAQ 1 2 1,4′-DHOAQ 1,2 1,3′ 1,4′ 1,5′ 1,6′ 1,7 1,8 2,3 2,6′ 2,7 Tri-HOAQ 1,2,3 1,2,4′ 1,2,5′ 1,2,6′ 1,2,7 1,2,8 1,3′,5′ 1,3′,6′ 1,3′,7 1,3′,8 1,4′,5′ 1,4′,6′ 2,3,5′ 2,3,6′ THOAQ 1,2,3′,4′ 1,2,3,5′ 1,2,3,6′ 1,2,3,7 1,2,3,8 1,2,4′,5′ 1,2,4′,6′ 1,2,4′,7 1,2,4′,8 1,2,5′,6′ 1,2,5′,7 1,2,5′,8 1,2,6′,7′ 1,2,6′,8 1,2,7,8 1,3′,5′,7 1,3′,5′,8 1,3′,6,7 1,3′,6′,8 1,4′,5′,8 1,4′,6,7 2,3,6′,7′ Penta-HOAQ 1,2,3′,4′,5′ 1,2,3′,4′,6′ 1,2,3,5′,6′

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

−1

ΔfHθ −1

J·mol ·K

−1

kJ·mol

ΔfGθ kJ·mol

−1

ΔfGθR kJ·mol−1

pKa1a

430.357

−119.400

−6.260

456.214 464.917

−331.910 −305.994

−196.426 −173.104

0.000 23.322

8.137 4.354

476.882 479.190 463.140 464.741 478.843 478.789 465.377 487.487 481.536 481.223

−522.804 −520.292 −541.424 −535.160 −519.278 −518.039 −541.031 −491.078 −492.987 −491.768

−363.423 −361.601 −377.944 −372.158 −360.482 −359.227 −378.220 −334.860 −334.994 −333.681

14.797 16.619 0.276 6.062 17.738 18.993 0.000 43.360 43.226 44.539

3.382(2) 3.309(3′) 8.191 7.898 3.627(6′) 4.012(7) 7.385 1.474(2) 4.197 4.601

500.364 489.997 491.264 499.398 499.996 491.640 493.141 502.237 501.999 494.752 484.765 491.636 502.442 511.459

−708.960 −736.065 −737.097 −711.028 −707.799 −731.408 −733.072 −706.702 −707.017 −729.893 −751.375 −728.089 −704.066 −677.482

−526.523 −550.536 −551.946 −528.306 −525.252 −546.369 −548.482 −524.824 −525.068 −545.781 −564.285 −543.050 −522.249 −498.356

37.762 13.749 12.339 35.979 39.033 17.916 15.803 39.461 39.217 18.504 0.000 21.235 42.036 65.929

1.835(2) 1.861(2) 3.063(2) 3.620(6′) 3.944(2) 3.052(1) 3.053(3′) 3.769(3′) 3.624(3′) 3.143(3′) 6.362(4′) 3.899(6′) 1.480(2) 1.731(2)

507.293 514.436 524.072 524.155 516.510 505.621 513.299 513.583 505.905 505.223 513.934 505.324 523.189 514.637 512.002 509.803 508.117 525.544 511.329 487.621 515.933 528.634

−911.960 −922.864 −896.194 −894.332 −917.762 −946.898 −923.888 −921.538 −945.275 −930.714 −923.646 −942.397 −894.981 −921.254 −902.574 −921.454 −939.691 −891.904 −917.770 −957.901 −913.352 −862.133

−701.530 −714.565 −690.768 −688.932 −710.083 −735.968 −715.250 −712.987 −734.432 −719.667 −715.198 −731.381 −689.295 −713.016 −693.548 −711.774 −729.507 −686.919 −708.548 −741.603 −705.499 −658.070

40.073 27.038 50.835 52.671 31.520 5.635 26.353 28.616 7.171 21.936 26.405 10.222 52.308 28.587 48.055 29.829 12.096 54.684 33.055 0.000 36.104 83.533

2.845(2) 1.260(2) 1.833(2) 2.424(2) 2.174(2) 1.519(2) 2.570(2) 2.380(2) 1.624(2) 3.126(2) 3.047(2) 3.012(1) 1.434(6′) 2.930(6′) 3.439(1) 3.095(3′) 3.081(3′) 1.239(7) 3.490(3′) 7.191(1) 1.059(6) 1.812(2)

528.722 536.095 535.861

−1122.076 −1098.415 −1115.029

−887.978 −866.515 −883.061

27.930 49.393 32.847

2.347(3) 3.121(2) 1.469(2)

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Table 5. continued no.

molecule Penta-HOAQ 1,2,3,5′,7 1,2,3,5′,8 1,2,3,6′,7′ 1,2,3,6′,8 1,2,3,7,8 1,2,4′,5′,6′ 1,2,4′,5′,7 1,2,4′,5′,8 1,2,4′,6′,7′ 1,2,4′,6′,8 1,2,4′,7,8 Hexa-HOAQ 1,2,3′,4′,5′,6′ 1,2,3′,4′,5′,7 1,2,3′,4′,5′,8 1,2,3′,4′,6,7 1,2,3,5′,6′,7′ 1,2,3,5′,6′,8 1,2,3,5′,7,8 1,2,3,6,7,8 1,2,4′,5′,6′,8 1,2,4′,5′,7,8 Hepta-HOAQ 1,2,3′,4′,5′,6′,7′ 1,2,3′,4′,5′,6′,8 OHOAQ 1,2,3′,4′,5′,6′,7,8

53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 a

Sθ

ΔfHθ

ΔfGθ

ΔfGθR

J·mol−1·K−1

kJ·mol−1

kJ·mol−1

kJ·mol−1

pKa1a

538.897 529.868 547.453 539.616 537.533 526.798 529.441 520.697 536.321 528.973 527.283

−1109.681 −1128.403 −1080.574 −1106.732 −1107.583 −1139.719 −1133.743 −1152.400 −1108.153 −1134.767 −1134.423

−878.618 −894.647 −852.064 −875.885 −876.114 −905.047 −899.859 −915.908 −876.321 −900.743 −899.898

37.290 21.261 63.844 40.023 39.794 10.861 16.049 0.000 39.587 15.165 16.010

1.746(2) 1.331(2) 1.585(6′) 1.649(2) 2.687(2) 1.675(2) 1.817(2) 1.423(2) 1.206(6′) 1.764(2) 2.140(2)

550.736 552.664 538.064 560.907 563.767 550.757 551.485 556.302 537.906 538.027

−1312.910 −1309.733 −1328.132 −1283.383 −1283.801 −1324.575 −1321.487 −1293.704 −1336.904 −1334.147

−1055.319 −1052.717 −1066.763 −1028.825 −1030.095 −1066.991 −1064.119 −1037.772 −1075.488 −1072.765

20.169 22.771 8.725 46.663 45.393 8.497 11.369 37.716 0.000 2.723

3.082(6′) 2.977(2) 2.551(2) 1.377(7) 1.536(6′) 1.089(2) 1.939(2) 2.122(2) 1.372(6′) 2.264(7)

575.192 566.096

−1498.506 −1522.482

−1218.151 −1239.415

21.264 0.000

1.685(6′) 1.945(6′)

577.467

−1697.849

−1388.111

3.119(2)

The first-order ionization constant for the most likely ionization path, which is indicated in the bracket.

Relative Stability of Most Stable Isomers of Each Isomer Group. Isomers having the same number of hydroxyls are defined as an isomer group, and there exist eight isomer groups altogether. To study the relative standard Gibbs energy of each isomer (ΔfGθR), the lowest ΔfGθ value of each isomer group was set to be zero, and then ΔfGθR was obtained by taking the lowest ΔfGθ value from ΔfGθ of the isomer in a group. These ΔfGθR values are also represented in Table 5. As what has been mentioned above, ΔfGθ reflects the stability of congeners. Thus, for each group of isomers, the most and least stable isomers are obtained and listed in Table 7. As is shown in Table 7, in MHOAQs, 1-MHOAQ is more stable than 2-MHOAQ due to the effect of hydrogen bonds. The most stable isomers of DHOAQs, Tri-HOAQs, THOAQs, penta-HOAQs, hexa-HOAQs, and hepta-HOAQs are those with hydroxyls located at position 1, 4, 5, and 8, where the Type I hydrogen bonds forms. In contrast, the least stable isomers are those with hydroxyls substituted at position 2, 3, 6, and 7, where no hydrogen bonds form or the Type II hydrogen

Figure 6. Molecular graphs of selected congeners (the yellow point represents the ring critical point, while the red point the bond critical point).

Table 6. Correlation of Partial Thermodynamic Parameters with the Number and the Relative Position of HO Substitution (NPHOS)a eq 12 13 14 a

descriptor θ

−1

−1

S /J·mol ·K ΔfHθ/kJ·mol−1 ΔfGθ/kJ·mol−1

constant

Nα

Nβ

No

437.211 −117.357 −6.262

15.221 −214.245 −188.726

24.375 −188.525 −165.736

−1.162 1.860 2.207

Nm

Np

R2

SE

−1.974 5.084 5.673

0.990 1.000 1.000

2.941 5.096 5.211

Note: R2, squared correlation coefficient; SE, standard error. 2451



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Figure 7. (a) Plots of Sθ obtained from the correlations versus the corresponding DFT results. (b) Plots of ΔfHθ obtained from the correlations versus the corresponding isodesmic reactions. (c) Plots of ΔfGθ obtained from the correlations versus the corresponding isodesmic reactions.

bonds form first. This is consistent with the previous conclusions; that is, the most stable conformations in each group of isomers should possess as many hydrogen bonds as possible, and the priority is given to the hydrogen bonds of Type I. Ionization of PHOAQs. The pKa of 1-MHOAQ is 8.137, 3.783 larger than that of 2-MHOAQ, which is 4.354. Thus, 1MHOAQ is more difficult to ionize, resulting from the intramolecular hydrogen bond in 1-MHOAQ. The pKa1 and pKa2 values for DHOAQs along different ionization paths are listed in Table 8. With 1,2-DHOAQ as an example, the possible ionization ways are shown in Figure 8. Two types of hydrogen bonds (Type I and Type II) exist in 1,2-DHOAQ. The hydrogen bond energy of Type I is larger than that of Type II; it is difficult for the Type I hydrogen bond to break, and the ionization intermediate product (1) is less stable than (2). As a result, the proton at position 2 of 1,2DHOAQ is easier to ionize, and pKa1 (2) is smaller than pKa1 (1). Similarly, pKa2 of the intermediate (1) is smaller than that

of (2). In short, the proton of the hydroxyl at position 2 tends to ionize first for 1,2-DHOAQ. With regard to 1,3′-, 1,6′-, and 1,7-DHOAQ, there exists the Type I hydrogen bond, making the ionization of hydroxyl at position 1 more difficult. The Type II hydrogen bond exists in 2,3-DHOAQ. When the proton of the hydroxyl at position 2 dissociates first, compared with the attraction between the hydrogen atom of the hydroxyl at position 3 and the oxygen atom of the hydroxyl at position 2, there is enhanced attraction between the hydrogen atom at position 3 and the resulting oxygen anion at position 2, generating the stable ionization intermediate. Concerning the first-order ionization of the hydroxyl at position 3, there is a hydrogen bond to break, and the ionization intermediate product is less stable, due to the repulsion between the oxygen atom of the hydroxyl at position 2 and the resulting oxygen ion at position 3. Thus, the ionization for the hydroxyl at position 3 of 2,3-DHOAQ is restrained. While for 1,4′-, 1,5′-, 1,8-, 2,6′-, and 2,7-DHOAQ, the corresponding first-order ionization path is identical. 2452



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Table 7. The Most and Least Stable Isomers in Different Isomer Groups for PHOAQs

Table 8. pKa1 and pKa2 Values for DHOAQs along Different Ionization Pathsa DHOAQs

pKa1

pKa2

1,2

3.518(1) 3.382(2) 8.732(1) 3.309(3′) 8.191 7.898 8.257(1) 3.627(6′) 8.412(1) 4.012(7) 7.385 1.474(2) 4.547(3) 4.197 4.601

11.074 11.210 9.574 14.997 12.413 10.996 7.638 12.268 6.238 10.638 14.025 13.766 10.693 5.914 6.678

1,3′ 1,4′ 1,5′ 1,6′ 1,7 1,8 2,3 2,6′ 2,7

Figure 8. Possible ionization pathways of 1,2-DHOAQ.

corresponding pKa1 values are computed and summarized in Table 5. Table 5 shows that the congeners having the largest pKa1 are 1-MHOAQ and 1,4′-DHOAQ, and the specific value is 8.137 and 8.191, respectively. The congeners with the smallest pKa1 are 1,4′,6,7-THOAQ and 1,2,3,5′,6′,8-hexaHOAQ, and the specific value is 1.059 and 1.089, respectively. The variation trend of pKa1 with the symbolic number of PHOAQs (refer to Table 5) is presented in Figure 9. We can see from Figure 9 that the pKa1 value generally decreases with the number of the hydroxyl substituent; that is, the first-order ionization of the congener possessing more hydroxyls is easier to occur, attributing to the effect of the hydrogen bond. pKa plays an important part on the migration, transformation, and distribution of compounds in the environment. Obviously, the isomer with a smaller pKa value is easier to migrate in aqueous solution.

a

The number in the bracket indicates the ionization path; i.e., the hydroxyl at this position ionizes first.

Generally, the sole presence of the Type II hydrogen bond facilitates the ionization of the proton which is not directly involved in the hydrogen bonding effect. For compounds containing these two types of hydrogen bonds, the Type I hydrogen bond inhibits the ionization of hydroxyl at a greater degree than Type II hydrogen bond does; that is, it is more difficult for the proton involving in the Type I hydrogen bond to ionize. According to this finding, the most likely ionization paths of the other most stable conformations in each group of isomers are determined. Especially, for the isomers, the ionization order of which cannot be ascertained, the relevant calculations have been carried out and compared. The 2453



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Figure 9. Relationship between pKa1 and the symbolic number of PHOAQs.

■

Funding

CONCLUSION By comparing the EHB,exp values and the corresponding calculation results obtained with the isodesmic reaction of isomerization for the three kinds of molecules, we found that the appropriate isodesmic reactions of isomerization can be used to accurately predict the intramolecular hydrogen bond energy with an error of about 3 kJ·mol−1. There are two types of intramolecular hydrogen bonds in PHOAQ molecules, and both of them could affect the hydrophobicity and stability of these molecules. The energy of the first and second kinds of hydrogen bond is about (51 to 52) kJ·mol−1 and (14 to 21) kJ·mol−1, respectively. The characteristic of the hydrogen bonds was studied with the AIM 2000 program (version 1.0), and it was found that the first type of hydrogen bond is stronger than the conventional hydrogen bond. Taking into account the impact of spatial orientation on molecular stability, fully optimized calculations of 75 PHOAQs owning minimum energy were carried out at the B3LYP/6-311G** level using the Gaussian 09 program. These thermodynamic parameters (Sθ, Hθ, and Gθ) were directly obtained from Gaussian output files. In addition, with the design of isodesmic reactions, ΔfHθ and ΔfGθ values of each PHOAQ molecule were calculated. Then, the multiple linear regression method of the SPSS for Windows program (version 12.0) was used to obtain the correlations between thermodynamic parameters (Sθ, ΔfHθ, and ΔfGθ) and NPHOS. The results show that each of these parameters has a close relationship with NPHOS, indicating these parameters can be predicted from NPHOS. The number of substitutents is the main factor influencing all the parameters. Based on the relative magnitude of their ΔfGθ values, the relative stability order of PHOAQ isomers in each isomer group is also theoretically proposed in this paper. The most stable isomers are usually those with as many Type I hydrogen bonds as possible; that is, hydroxyls should primarily substitute at position 1, 4, 5, and 8. It is found that intramolecular hydrogen bond sometimes facilitates and sometimes restrains the ionization of the proton, depending on the location of the hydroxyl.

■

This work was financially supported by the National Natural Science Foundation of China (41071319, 20977046, 20737001) and the Fundamental Research Funds for the Central Universities of China (1112021101). Notes

The authors declare no competing financial interest.

■

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AUTHOR INFORMATION

Corresponding Author

*Address: State Key Laboratory of Pollution Control and Resources Reuse, School of the Environment, Xianlin Campus, Nanjing University, Jiangsu Nanjing 210046, P. R. China. Tel.: +86-25-89680358. Fax: +86-25-89680358. E-mail address: [email protected]. 2454



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Investigation on Intramolecular Hydrogen Bond and Some

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