J. Phys. Chem. A 2010, 114, 7417–7422
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Molecular Electrostatic Potential as a tool for Evaluating the Etherification Rate Constant Mojtaba Alipour* and Afshan Mohajeri* Department of Chemistry, College of Sciences, Shiraz UniVersity, Shiraz, 71454, Iran ReceiVed: May 3, 2010; ReVised Manuscript ReceiVed: May 28, 2010
In this work the molecular electrostatic potential (MEP) is proposed as an effective approach in describing the influence of substituent on the rate constant of etherification reaction. A relationship on the basis of density functional theory has been established to show that the etherification rate constant should be proportional to the electrostatic potential on the atomic sites. Indeed, we employed the MEP at the atomic sites as a local quantum descriptor to estimate the reaction rate constant variation caused by substituent effect. Taking the experimental rate constants of 30 substituted phenols, the validity of the proposed method has been verified. Moreover, the atoms-in-molecules (AIM) charge scheme as another local descriptor was tested for its ability to represent variations in the kinetic data for etherification reaction of phenols. It was shown that the changes in these two descriptors were strongly correlated with the variation of experimental rate constant data. The outcome of good correlations in this study offers a relatively simple and effective method to compute the rate constant for etherification reaction of substituted phenols based on MEP and AIM charge. I. Introduction Quantum chemists and experimentalists are living in two different worlds. Nowadays, computational chemistry has reached an accuracy to bring both worlds together. It provides the powerful possibilities of a multidisciplinary approach to study subtle details of experimental methods for small and medium sized molecules. Conceptual density functional theory (CDFT)1,2 is a computationally less demanding method that uses the reactivity descriptors and is found to be a very befitting approach to describe chemical process. CDFT has been successfully used to study generalized acid/base reactions, including most of the organic reactions3 and the inorganic complexation reactions, and recently also redox reactions4 and pericyclic reactions.5 In this article, we show that the CDFT framework can give an extra dimension to the rate constant variation of etherification reaction caused by substituent effect. Among reactivity descriptors, the molecular electrostatic potential (MEP) is a real physical property that can be determined either computationally or experimentally by diffraction methods.6 The MEP at a given point in the vicinity of the molecule can be interpreted as the interaction energy of a positive test charge located at this point and the electrical charge cloud generated by the electrons and nuclei of the molecule. The MEP that the electrons and nuclei of a molecule create in the surrounding space is given by the following equation
Φ(r) )
Z
dr' ∑ |RR -R r| - ∫ |r'F(r') - r|
(1)
R
in which ZR is the charge on nucleus R, located at RR, and F(r) is the electronic density. The first term in the above equation refers to the bare nuclear potential and the second * To whom correspondence should be addressed. E-mail: amohajeri@ shirazu.ac.ir (A.M.),
[email protected] (M.A.).
to the electronic contribution. The MEP can be also interpreted from the classical electrostatics point of view; the molecule provides a potential around itself that is seen by a point like positive probe charge approaching or avoiding regions where the MEP is negative or positive, respectively. Despite the fact that the molecular charge distribution remains unperturbed through the external test charge (no polarization occurs), the electrostatic potential of a molecule is still a good guide in assessing the molecules reactivity toward positively or negatively charged reactants. It is not surprising that the MEP plays an increasingly important role in theoretical chemistry, and since the pioneering work on MEP, 7-13 this quantity has been widely used in many different areas. For example, electrostatic potential has been applied in analyzing noncovalent interactions14-20 and also in study of the hydrogen bonding, and electrophilic and nucleophilic processes.21-28 The MEP and average local ionization energy have also been used to predict pKa values and other properties for different compounds.29-32 In our previous work, regioselectivity of the complete series of dichloropyridines as ambiphilic molecules have been investigated in terms of electrostatic potential and various chemical reactivity descriptors.33 More recently, Liu and co-workers employed the MEP as a measure for estimation of molecular acidity in different compounds.34,35 However, no study has been reported on the use of MEP at the nucleus for estimation of the reaction rate constant. Actually, there is an urgent need for reliable and low cost methods for predicting rate constants of organic compounds.36 Not only is this a prerequisite for environmental exposure and risk analysis, but such rate constants are also important to industries that try to improve specialty chemical materials.37,38 In this context, predicting the rate constants of phenolic compounds by computational methods is important not only from chemical aspects but also for environmental, biological, and industrial applications. Accordingly, in the present work as our main goal we focus on the MEP at the hydrogen and oxygen nuclei of the hydroxyl group to predict the etherifi-
10.1021/jp104000c 2010 American Chemical Society Published on Web 06/17/2010
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SCHEME 1
cation rate constant of phenolic compounds. In the recent years, phenolic hydroxyl group has received major attention because of its wide range of activity.39-41 On one hand, it represents antioxidant activity, whereas on the other hand it exhibits significant toxicity. Quantum topological molecular similarity (QTMS) indices have been previously used by Popelier and co-workers to assess the toxicity of chlorophenols as well as the cytotoxicity of ortho alkyl-substituted phenols.42-44 The substituent effect on the charge density of phenolic oxygen and consequently on the rate constant of O-methylation reaction was studied by Cork and Hayashi.45 In a recent study, we have provided evidence that supports the application of the different chemometrics methods including principal component analysis (PCA), partial least-squares (PLS), and genetic algorithms (GA) in analysis of the O-methylation reaction of some substituted phenols.46 It is obvious that such studies are much more complicated than the used method in this work. In other words, one of the noteworthy points of the present study is the simplicity of the proposed approach based on MEP at the nucleus to estimate reaction rate constant. Finally, since the atomic charges are known to be the key concept in understanding various phenomena such as dipole moment, quantitative structure property/activity relationships (QSPR/QSAR) studies, and particularly in chemical reactions, we will investigate the ability of this local property for the purpose. We used the charge on the oxygen and dissociating proton of the phenolic hydroxyl group for predicting the etherification reaction rate constant of phenol derivatives. To the best of our knowledge, however, this is the first time that the MEP at the nucleus and atomic charge scheme are introduced as local descriptors in prediction of the rate constant for a reaction.
TABLE 1: Chemical Structure of Phenol Derivatives and Their Corresponding Experimental Rate Constant Data No.
X2
X3
X4
X5
X6
log (kX/kH)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
H H H H H H H H H H H H H H H H Me F Cl COMe CONH2 CN H H H H H Cl NO2 CONH2
H H H H H H H H H Me OMe F Cl COMe CN NO2 H H H H H H Me OMe OMe Cl Me H H H
H Me OMe F Cl COMe CONH2 CN NO2 H H H H H H H H H H H H H H H H H NO2 Cl NO2 Cl
H H H H H H H H H H H H H H H H H H H H H H Me OMe Cl Cl H H H H
H H H H H H H H H H H H H H H H H H H H H H H H H H H H H H
0.000 0.216 0.226 -0.001 -0.111 -1.246 -1.629 -1.578 -2.687 0.412 0.160 -0.663 -0.518 -0.426 -0.956 -0.996 0.164 -0.396 -0.611 -1.863 -1.629 -1.687 0.200 0.267 -0.420 -1.164 -2.518 -1.196 -5.189 -2.231
can be perturbed by changing N and/or υ(r) as ∆N and/or∆υ(r). With the Taylor expansion up to the second order, the subsequent change in the total energy reads
II. Theoretical Aspect Scheme 1 shows a schematic representation for the etherification reaction mechanism of phenols, where RY is an alkyl halide and Xi are substituents and their positions according to Table 1. In their recent papers, Liu and co-workers suggested that the molecular acidity is a property localized to the particular acidic atom and the impact of environment is reflected through the change to that atom.34,35 They proposed MEP at acidic atom to quantitatively estimate molecular acidity. As the above mechanism shows, the first step corresponds to the proton dissociation of phenol, thus we can use similar justification for the etherification reaction. Here, we consider the oxygen of phenol as acidic atom that is also the reaction center and pursue the substituent effect on the rate constant through the nuclear MEP at oxygen. In addition, the dependency of the MEP at oxygen and MEP at hydrogen prompts us to investigate whether the MEP at dissociating proton can be used as a quantum descriptor for etherification reaction of phenols or not. According to the DFT framework, the total energy of a given system is a functional of the number of electrons,N, and of the external potential, υ (r), that is, E ) E [N, υ(r)]. The energy
∆E ) +
∂E ) [( ∂N
υ(r) 2
δE ∫ ( δυ(r) )N∆υ(r)dr]
∆N +
[( )
1 ∂E 2! ∂N2 +
(∆N)2 + 2∆N υ(r)
A
(
)
δ∂E ∫ ( δυ(r)∂N )∆υ(r)dr
]
δ2E ∆υ(r)∆υ(r')dr dr' δυ(r')δυ(r) N
(2)
We consider proton dissociation of phenol as a special case of the general consideration in eq 2 leading to the change in external potential ∆υ(r) but the number of electrons remains unchanged (∆N ) 0). Hence, eq 2 can be rewritten as follows
∆E )
δE ∫ ( δυ(r) )N∆υ(r)dr +
1 2
A
(
)
δ2E ∆υ(r)∆υ(r')dr dr' (3) δυ(r')δυ(r) N
Taking F(r) ) (δE/δυ(r))N and considering only the first term, the simplest form of the above equation becomes
Evaluating the Etherification Rate Constant
∆E )
∫ F(r)∆υ(r)dr
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(4)
Considering the reaction mechanism the change in the external potential, ∆υ(r), resulted from the dissociation of a proton from phenol, can be explicitly given by
Z
∑ |Ri -i RH| - |r -1 RH|
∆υ(r) )
(5)
i*H
where the first term is the nuclear-nuclear repulsion potential between the dissociating proton and the other nuclei in the phenol molecule, and the second term is the attraction potential between an electron at position r and the leaving proton at RH. Thus, eq 5 reflects both the electronic and nuclear contributions caused by various substituents on the dissociating proton. In this equation RH is the coordinate of the leaving proton, and {Ri} are the coordinates of the other nuclei in the phenol molecule. Substitution of eq 5 into eq 4 leads to
∆E )
Z
dτ ∑ |Ri -i RH| - ∫ |r F(r) - RH |
(6)
i*H
Comparing the right side of this formula with eq 1 indicates that the change in the total electronic energy of the phenol molecule when it undergoes etherification reaction is well proportional to the electrostatic potential on the hydrogen of the phenolic hydroxyl group. On the other hand, ∆E can be considered as a measure of reaction activation energy, which suggests that the MEP value of dissociating proton can serve as a descriptor to show the rate constant variation caused by substituent effect,
log kX /kH ∝
Z
dτ ∑ |Ri -i RH| - ∫ |r F(r) - RH |
(7)
i*H
where kX is the first-order rate constant of substituted phenol and kH is the corresponding value for phenol. Several assumptions have been used to obtain eq 7: (i) neglecting thermodynamic contribution from solvent and temperature effects, (ii) approximating the reaction activation energy by the total electronic energy difference in eq 6, (iii) omitting third and higher order terms in the Taylor expansion of eq 2 since these terms are usually assumed to be qualitatively unimportant, and (iv) being undetectable structure relaxation in the phenolate ion so the only change in the external potential is due to removal of the proton from the phenol. In the present work, as an illustration of etherification reaction, the experimental rate constant data for O-methylation of substituted phenols were used to verify the validity of eq 7 for the assessment of rate constant variation resulted from substituent effect through the nuclear MEP at hydrogen and oxygen of hydroxyl moiety. III. Computational Procedures Thirty mono- and disubstituted phenol derivatives including electron-donating and electron-withdrawing substituents have been investigated. All molecular structures were fully optimized in the gas phase at the density functional theory with B3LYP functional47,48 employing standard split valence basis set with inclusion of polarization and diffuse functions, namely, 6-311++G(d,p). All geometries are confirmed to be the genuine
minima by the harmonic vibrational frequency calculation (i.e., with no imaginary frequency). After structure optimization, single-point calculations are performed to obtain the MEP on each of the oxygen and hydrogen nuclei of phenolic hydroxyl group for all phenol derivatives. All calculations have been performed with the Gaussian 03 suite of programs.49 In continuation, based on Bader’s “atoms in molecules” (AIM) quantum theory,50 the derived wave functions at the same level of theory have been used to compute the charge on the oxygen and dissociation proton of the phenolic hydroxyl group using the AIM2000 program.51 IV. Results and Discussion Table 1 shows the chemical structure of the phenol derivatives as well as their corresponding experimental rate constant data for O-methylation reaction.45 The data were transferred to the logarithmic scale as log(kX/kH). The rate constant data manifest the considerable changes by changing substituent from electrondonating to electron-withdrawing groups. For example, the value of log(kX/kH) is 0.226 for 4-methoxyphenol with an electrondonating substituent, whereas it is -2.687 for 4-nitrophenol, which includes nitro group as an electron-withdrawing substituent. These changes in the rate constant data suggest that the electronic features of the phenol derivatives play an important role in the mechanism of the etherification reaction of phenols. Indeed, the effect of the substituents causes change in the electron density at the hydroxyl group, which in turn is reflected in the rate of etherification reaction. As it is well-known that the electron-withdrawing substituents, particularly those para to the hydroxyl moiety, tend to decrease the atomic charge at the phenolic oxygen on the basis of standard resonance arguments. Likewise, electron-donating groups should produce an opposite effect. Under the hypothesis that oxygen is the center of reaction, we noticed that the change in the electronic feature of the phenol derivatives through the substituent influence can be well reflected by the local property of either oxygen or hydrogen of phenolic hydroxyl group. In the present study, by focusing on the hydroxyl moiety we have computed the MEP values at the hydrogen and oxygen nuclei to quantitatively predict rate constant of the etherification reaction of some substituted phenols. Computational data for the MEP at the oxygen, MEP@O, and at the hydrogen, MEP@H, of phenolic hydroxyl group for 30 mono- and disubstituted phenols are reported in Table 2. Figures 1 and 2 present the experimental rate constant data versus MEP at oxygen and hydrogen nuclei, respectively. For the compounds studied, the MEP at the oxygen worked quite well as an indicator of the etherification rate constant:
log(kX /kH) ) -72.9((8.3) × MEP@O - 1628.7((186.4) n ) 30
R2 ) 0.920
MAD ) 0.26
F ) 320 (8)
Here, n is the number of compounds, R is the correlation coefficient, MAD shows the mean absolute deviation, and F is the Fisher statistic of the regression. Similar results, although not as good, were obtained for MEP at the hydrogen;
log(kX /kH) ) -81.0((11.4) × MEP@H - 78.5((10.9) n ) 30
R2 ) 0.884
MAD ) 0.32
F ) 212 (9)
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TABLE 2: Computational Data for the MEP (au) and AIM Charge at the Hydrogen and Oxygen Nuclei of the Phenolic Hydroxyl Group No.
MEP@O
MEP@H
Q(H)
Q(O)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
-22.3333 -22.3369 -22.3393 -22.3271 -22.3237 -22.3170 -22.3201 -22.3073 -22.3016 -22.3360 -22.3343 -22.3231 -22.3224 -22.3257 -22.3116 -22.3089 -22.3346 -22.3224 -22.3219 -22.3160 -22.3077 -22.3077 -22.3384 -22.3367 -22.3256 -22.3123 -22.3049 -22.3133 -22.2639 -22.2991
-0.9706 -0.9742 -0.9760 -0.9642 -0.9611 -0.9552 -0.9581 -0.9455 -0.9402 -0.9734 -0.9718 -0.9608 -0.9598 -0.9629 -0.9491 -0.9464 -0.9720 -0.9600 -0.9590 -0.9529 -0.9449 -0.9454 -0.9759 -0.9739 -0.9633 -0.9500 -0.9434 -0.9504 -0.9166 -0.9364
0.5597 0.5591 0.5593 0.5611 0.5657 0.5673 0.5676 0.5683 0.5716 0.5604 0.5620 0.5599 0.5613 0.5594 0.5639 0.5663 0.5615 0.5665 0.5668 0.5675 0.5695 0.5685 0.5591 0.5597 0.5638 0.5688 0.5727 0.5674 0.5807 0.5714
-1.0768 -1.0829 -1.0807 -1.0735 -1.0825 -1.0813 -1.0732 -1.0797 -1.0789 -1.0859 -1.0726 -1.0798 -1.0772 -1.0799 -1.0823 -1.0692 -1.0686 -1.0601 -1.0816 -1.0791 -1.0947 -1.0804 -1.0790 -1.0631 -1.0590 -1.0751 -1.0797 -1.0771 -1.0608 -1.0938
The oxygen atom, however, is in direct contact with the phenolic ring, and consequently it is more influenced by the substituent effect. Therefore, we can deduce that the MEP on the oxygen is a more sensitive descriptor for interpretation the behavior of the hydroxyl group under etherification reaction and also for rate constant prediction. Apart from MEP, it has proven that atomic charges are important descriptors in many chemical reactions. In another approach, we consider the connection between the AIM atomic charge as a local descriptor and rate constant data for the compounds studied. Although the atomic charge is not a proper quantum chemical observable, the idea of assigning charges to atoms has proved an immensely valuable heuristic tool for
Figure 2. Etherification rate constants versus MEP@H (au) for a series of mono- and disubstituted phenols.
Figure 3. Etherification rate constants versus AIM charge on the dissociating proton for a series of mono- and disubstituted phenols.
chemists. Consequently, a great many schemes, both quantum chemical and empirical, have been proposed for partitioning the electronic density distribution among the atoms of a molecule or otherwise assigning charge to these atoms. Among them, AIM charges have been observed to be quite useful and effective measure for predicting pKa variation in substituted phenols.52 Here, AIM charges at the oxygen and hydrogen of the hydroxyl moiety were tested for their ability to represent the variation in rate constant data. In Table 2 the AIM charges on the oxygen, Q(O), and on the hydrogen, Q(H), are collected for all phenol derivatives. For the entire set of 30 phenolic compounds Figure 3 shows the correlation between AIM charges at the hydrogen and rate constant data;
log(kX /kH) ) -216.1((33.4) × Q(H) + 121.2((18.9) n ) 30
Figure 1. Etherification rate constants versus MEP@O (au) for a series of mono- and disubstituted phenols.
R2 ) 0.862
MAD ) 0.34
F ) 175 (10)
Although the AIM charges on the hydrogen exhibit a rather good correlation with log(kX/kH), the use of AIM charge on oxygen makes the correlation worse (R2 < 0.2). The AIM charge at either oxygen or hydrogen atom are obtained from the electron density integration over basins assigned to respective atoms. However, since the substituent effects are directly reflected on the oxygen atom the calculated AIM charge at oxygen shows
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TABLE 3: Cross Correlation Between MEP and AIM Charge at the Hydrogen and Oxygen Nuclei for the Phenol Data Set MEP@O
MEP@H
Q(H)
1
0.980 1
0.862 0.856 1
MEP@O MEP@H Q(H)
grater variation than the corresponding values on hydrogen. Thus, Q(O) cannot provide meaningful regression model for O-methylation reaction when compared to Q(H). The situation is different for the calculation of MEP at oxygen or hydrogen. In eq 7, not only in the first term where the effect of other nuclei is included, but the second term also exhibits the electronic contribution with integration over all electronic density. Thus, both MEP@H and MEP@O may correlate with the rate constant data. In general, the accuracy of predicted rate constant using MEP at the nucleus was found to be rather better than of the rate constant obtained from AIM charge, which is due to different definitions of these two local quantities. Finally, Table 3 shows the interdependency of MEP on the nuclei of the hydroxyl group with AIM charge at hydrogen nucleus. As expected, the descriptors that correlated strongly to the etherification rate constant data also tended to correlate strongly with each other. V. Final Remarks Quantum chemistry, DFT in particular, offers the chemists a variety of techniques to predict properties of chemical reactions. In this way, conceptual DFT plays an emerging role to get a simple picture of chemical phenomena and rationalizing the experimental data. In the present research, an explicit and drastic approach based on MEP at the nucleus and AIM charge scheme was proposed for estimation of etherification reaction rate constant of phenol derivatives. We observed a linear relationship between experimental rate constant data and electrostatic potential on the hydrogen and oxygen of phenolic hydroxyl group. A similar correlation was found for kinetic data and the AIM charge of dissociating proton of the phenolic hydroxyl group, although the correlation observed was not as strong as those found for MEP. The results suggest that these two descriptors can be successfully employed to estimate the variation in the rate constant of the etherification reaction of phenol derivatives due to substituent effect. Overall, the proposed method in this work provides a simple route to predict rate constant of etherification reaction of substituted phenols from a simple density functional calculation. However, the use of MEP and the atomic charge as local descriptors for estimation of etherification rate constant is not limited to DFT and these quantities can be computed by both ab initio as well as DFT methods. References and Notes (1) (a) Parr, R. G.; Yang, W. Density-Functional Theory of Atoms and Molecules; Oxford University Press: New York, 1989. (b) Parr, R. G.; Yang, W. Annu. ReV. Phys. Chem. 1995, 46, 701. (2) Geerlings, P.; De Proft, F. Phys. Chem. Chem. Phys. 2008, 10, 3028. (3) Geerlings, P.; De Proft, F.; Langenaeker, W. Chem. ReV. 2003, 103, 1793. (4) (a) Moens, J.; Roos, G.; Jaque, P.; De Proft, F.; Geerlings, P. Chem.sEur. J. 2007, 13, 9331. (b) Moens, J.; Jaque, P.; De Proft, F.; Geerlings, P. J. Phys. Chem. A 2008, 112, 6023. (5) (a) De Proft, F.; Ayers, P. W.; Fias, S.; Geerlings, P. J. Chem. Phys. 2006, 125, 214101. (b) Ayers, P. W.; De Proft, F.; Geerlings, P. Chem.sEur. J. 2007, 13, 8240. (c) De Proft, F.; Chattaraj, P. K.; Ayers,
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