Computational Analysis of Substituent Effects in Para-Substituted

Hartree-Fock and density functional theory study of remote substituent effects on gas-phase ... International Journal of Molecular Sciences 2002 3 (4)...
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10116

J. Phys. Chem. 1996, 100, 10116-10120

Computational Analysis of Substituent Effects in Para-Substituted Phenoxide Ions Markus Haeberlein and Tore Brinck* Department of Chemistry, Physical Chemistry, Royal Institute of Technology, S-100 44 Stockholm, Sweden ReceiVed: February 8, 1996; In Final Form: April 5, 1996X

Para-substituted phenoxide ions are characterized by a strong resonance interaction between the oxygen and the substituent when the substituent is electron-accepting. We have modeled these interactions by computing the minima of the electrostatic potential, Vmin, and the average local ionization energy, hIS,min, near the unprotonated oxygens of para-substituted phenoxide ions. The calculations of Vmin and hIS,min were carried out at different levels of theory using both ab initio and density functional methods. Vmin and hIS,min have been found to correlate well with the empirical substituent constant, σp-. The calculated energy differences for the acidic dissociation of phenols and the corresponding experimental gas-phase acidities were found to agree very well. A close linear relationship was found between Vmin and the gas-phase acidities. The findings suggest that through-resonance is accounted for in our calculations and that Vmin and hIS,min can be used as tools for predicting σp-.

Introduction Since substituent constants were introduced in the 1930s, they have been widely used for interpreting electronic effects for example in organic reactions and for biological QSAR analysis.1 The original substituent constants of Hammett for describing the effects of substituents in the para-position to a reactive site, σp, are based upon the aqueous acidities of substituted benzoic acids. These substituent constants have been shown to be applicable for estimating the electronic effects of substituents in similar reaction systems. Because of their wide applicability, numerous quantum chemical studies have been devoted to reproducing and/or explaining the values of the σp constants.2-11 These studies have been performed at different levels of theory using both semiempirical and ab initio methods. The approaches employed to correlate quantum chemically derived descriptors with substituent constants for substituents in the para-position may be divided into two different categories. One approach is to correlate σp directly with the computed energy difference between the acid and its conjugate base.2,3 However, this requires that calculations are done on both species for each substituent. An alternative approach is to use a computed property of the reaction site of either the acid or the base as the descriptor in the correlation. Among the properties that have been used are atomic charges,3-8 the electrostatic potential,9 and the average local ionization energy.9-11 In most of the studies the descriptors were calculated on monosubstituted benzoic acids or benzenes. The regular σp substituent constants are not generally applicable to systems with a direct conjugation between the substituent and the reaction center. A different set of substituent constants σp- has been derived for systems where a lone pair or a permanent negative charge on the reaction center can be resonance stabilized by an electron-accepting substituent. The σp- constants have mainly been determined from the aqueous acidities of phenols and from the aqueous basicities of anilines. The through-resonance stabilizations of an electron-accepting substituent (A) on a phenoxide ion (1) and on aniline (2) are depicted as follows: X

Abstract published in AdVance ACS Abstracts, May 15, 1996.

S0022-3654(96)00393-0 CCC: $12.00

For electron-donating substituents the σp- constants are identical to σp. Despite the widespread use of σp- constants, few attempts to model them by computational methods have appeared in the literature. In addition, the overall knowledge of how well strong through-resonance interactions are reproduced by conventional quantum chemical methods seems to be limited. The objective of this work has been to seek correlations between theoretical descriptors and σp-. Such relationships can provide tools for predicting σp- values for substituents for which they are not known. The quality of the relationships may also be of more general interest, since it reveals how well the through-resonance interactions are reproduced by the selected computational methods. We have used the para-substituted phenoxide anion (1) as a model system for correlating σp- values with quantum chemical descriptors. The phenol system was selected for two reasons: firstly, there are strong indices that the effects of the substituents on the acidity of phenols are largely determined by effects in the phenoxide anion and that the effects on the corresponding phenols are of minor importance.3,12,13 Secondly, the geometry of the reaction site of the phenoxide ion is rather insensitive to changes in the substituent. This is in marked contrast to the aniline system where the H-N-H angle of the amino group varies greatly depending upon the substituent.9,14,15 Many theoretical descriptors, such as the electrostatic potential minima, Vmin, and atomic charges, are dependent on the conformation. For example, it has been shown that Vmin is strongly dependent on the H-N-H angle of the amino group.16 In an earlier study we also found that our calculated nitrogen Vmin for a series substituted did not reflect the through-resonance interactions that have been found to exist experimentally.9 We attributed © 1996 American Chemical Society

Calculated Substituent Effects in Phenoxide Ions

J. Phys. Chem., Vol. 100, No. 24, 1996 10117

this to the inability of the STO-3G basis set to reproduce the correct H-N-H angles of the anilines. The descriptors we use are the spatial minima of the electrostatic potential, Vmin, and the surface minima of the average local ionization energy, hIS,min, in the vicinity of the phenoxide oxygen. Both quantities have been used successfully in the past to correlate substituent constants and aqueous basicities.9-11,15,17-20 The electrostatic potential, V(r), that surrounds a molecule has been used extensively as a tool for the analysis of chemical reactions and intermolecular interactions.9,15,20-25 V(r) at point r in the space of a molecule is rigorously defined by

ZA F(r′) dr′ V(r) ) ∑ -∫ |r′ - r| A |RA - r|

(1)

where ZA is the charge on nucleus A, located at RA, and F(r) is the electronic density of the molecule. V(r) gives the interaction energy between a positive point charge of unitary magnitude located at r and the unperturbed charge distribution of the molecule. An approaching electrophile will initially be attracted to the points in space where V(r) has its most negative values (the local minima Vmin). The magnitudes of the Vmin values within families of compounds often reflect aqueous basicities, as has been demonstrated by good correlations with pKa values and with substituent constants derived from aqueous basicities.9,15,20,21 The average local ionization energy, hI(r), is another tool for the analysis of the chemical reactive behavior of molecules which was originally introduced by Sjo¨berg et al.10 hI(r) is defined within the Hartree-Fock theory by

hI(r) ) ∑ i

Fi(r)|i| F(r)

(2)

where Fi(r) is the electronic density of the ith molecular orbital at the point r and i is the orbital energy. Since Koopmans theorem26 justifies regarding the orbital energies as approximations to the ionization energies, hI(r) can be interpreted as the average energy required to remove an electron located at point r from the molecule. Sjo¨berg et al.10 showed for a series of substituted benzenes that the positions on a molecular surface of constant electron density where hI(r) has its lowest values (IhS,min) are indicative of the sites most reactive toward electrophiles. The magnitudes of the values were found to reflect the relative reactivity at these sites. We have found hIS,min to be complementary to Vmin for analysis of electrophilic interactions, since hI(r) reflects charge transfer and polarization while Vmin is a purely electrostatic parameter.21 Several studies have shown that hIS,min is particularly suited for correlating aqueous basicities of anionic and neutral molecules.9,11,17-19,21 These relationships are generally less family dependent than the relationships between aqueous basicities and Vmin. For example, it has been shown for a diverse group of 40 carbon, oxygen and nitrogen acids that a linear relationship exists between the pKa value of the acid and the calculated hIS,min of the anionic conjugate base.18 Methods and Procedures Geometry optimizations and single point calculations for 20 para-substituted phenoxide ions were carried out at different levels of theory using the Gaussian 92/DFT package.27 The substituents were chosen to cover a wide range of σp- values but with a focus on those capable of a strong through-resonance.

No charged substituents, such as NN+, were included since they are not expected to behave like the noncharged substituents.28 For investigation of the basis set dependence of Vmin in the correlation with σp-, the geometry optimizations and the subsequent single point calculations were performed at the ab initio SCF level using two different basis set combinations (HF/ 6-31+G*//HF/6-31G* and HF/3-21G*//HF/3-21G*). The latter was considered the most economical basis set combination that was likely to be capable of reproducing the substituent effects in these systems (the 3-21G* basis set includes a set of polarization functions for atoms Na-Xe but is otherwise identical to 3-21G).29 In order to verify that the optimized structures were true minima, HF/3-21G* frequency calculations were performed at the HF/3-21G* optimized geometries. The HF/6-31+G*//HF/6-31G* level is computationally much more demanding but is expected to give more reliable results. The 6-31G* basis set has been shown to predict accurate geometries, both for neutral and ionic systems.29 Earlier studies have also indicated that the basis set dependence of the electrostatic potential of neutral molecules nearly converges when the 6-31G* basis set is used.30 However, it is generally considered that diffuse functions are necessary to properly describe the electronic structure of anions.29,31-33 The 6-31+G* basis was therefore used for the electrostatic potential computations at the 6-31G* geometries. To investigate whether it is important to include electron correlation in order to model the resonance interactions, the Hartree-Fock calculations were compared with nonlocal density functional computations. Becke’s gradient corrected exchange functional34 and the correlation functional of Lee, Yang, and Parr35 were used with the higher of the HF basis set combinations (BLYP/6-31+G*//BLYP/6-31G*). We also used this method for computations on a number of phenols in order to calculate the gas-phase acidities. hI(r) was calculated at the HF/6-31+G*//HF/6-31G* level on molecular surfaces defined by a contour of constant electron density equal to 0.001 electrons/bohr3. Bader and co-workers have shown that this contour gives a good representation of the van der Waals surface of the molecules.36,37 Earlier work has indicated that the 6-31+G* basis set is well-suited for the calculation of hI(r) for anions.18 Results The results from our calculations of Vmin and hIS,min in the vicinity of the oxygen for 20 para-substituted phenoxide ions are summarized in Table 1. Close linear relationships were found between the Vmin values at different levels of theory. However, the magnitudes of the absolute values of Vmin differed considerably. The least negative values of Vmin were obtained from the BLYP/6-31+G*//BLYP/6-31G* calculations and the most negative Vmin values from the HF/3-21G* computations. The diffuse functions included in the 6-31+G* basis set result in Vmin being further from the nucleus and hence lower than without diffuse functions. Gadre and co-workers have found a similar behavior of Vmin when improving the basis set quality.38 The electron correlation incorporated in the BLYP method pushes the minima of the electrostatic potential even further from the nucleus, and hence Vmin becomes even less negative. For the series of para-substituted phenoxide ions we have found a close linear relationship between hIS,min and Vmin (R ) 0.996). However, it is not a general feature that hIS,min and Vmin correlate.21 Substituent Constants. In Table 2 we have listed σp- values derived from pKa measurements on phenols together with the recommended σp- values from two different compilations by Hansch et al.39 and Exner.40,41 The recommended values have

10118 J. Phys. Chem., Vol. 100, No. 24, 1996

Haeberlein and Brinck

TABLE 1: Calculated Vmin and hIS,min of the Oxygen at the Reaction Site for Some Para-Substituted Phenoxide Ions

TABLE 3: Correlations between Calculated Vmin and hIS,min and Substituent Constants y

Vmin (kcal/mol) substituent

HF/ 3-21G*

HF/ 6-31+G*

BLYP/ 6-31+G*

hIS,min (eV) HF/6-31+G*

NH2 CH3 H F Cl CCH CF3 COOH SO2NH2 CHO CN SO2CH3 SO2CH2F CHdC(CN)2 COCl NO2 SO2F SO2CF3 NO C(CN)dC(CN)2

-207.9 -203.9 -204.1 -200.4 -193.7 -189.5 -185.0 -181.8 -179.1 -180.5 -181.3 -177.4 -170.9 -155.1 -167.5 -166.2 -169.3 -165.6 -171.4 -144.9

-191.6 -188.4 -187.4 -185.7 -179.5 -174.5 -172.6 -167.1 -161.4 -165.1 -165.5 -162.8 -157.4 -139.9 -156.3 -156.2 -155.0 -153.4 -157.4 -129.6

-171.6 -169.4 -169.4 -166.9 -162.4 -156.6 -154.4 -150.7 -145.6 -148.4 -149.6 -148.5 -143.3 -129.2 -139.4 -140.8 -140.1 -140.1 -141.1 -121.1

7.15 7.41 7.48 7.51 7.92 8.20 8.29 8.62 8.92 8.73 8.71 8.86 9.14 10.13 9.21 9.24 9.29 9.38 9.16 10.71

-a

σp σp- a σp- a σp- b σp- a σp c

x

n

least squares eq

R

Vmin HF/3-21G* Vmin HF/6-31+G* Vmin BLYP/6-31+G* Vmin BLYP/6-31+G* hIS,min HF/6-31+G* Vmin BLYP/6-31+G*

11 11 11 20 11 11

y ) 0.0375x + 7.595 y ) 0.0422x + 7.863 y ) 0.0484x + 8.126 y ) 0.0400x + 6.797 y ) 0.749x - 5.637 y ) 0.0321x + 5.375

0.981 0.994 0.994 0.955 0.994 0.953

a Selected values of σ - marked italics in Table 2. b σ - values p p selected according to the following preferences: firstly, we used the σp- which are available from measurements on pKa of phenols40. Secondly, we used the recommended values from Exner,41 and for the substituents which are not listed there we used the recommended values given by Hansch et al.39 c σp values taken from Exner.40,41

TABLE 2: Experimental and Predicted σp- Values substituent constants σpσp(exp) (pred)e substituent NH2 CH3 H F Cl CCH CF COOH SO2NH2f CHO

-0.30a -0.15b -0.17b -0.14a 0.00 -0.03b 0.15a 0.19b 0.24a 0.52a 0.53b 0.62a 0.65b 0.77b 0.78a 0.89a 0.94b 0.94b 1.03a 1.04c

-0.19

substituent CN

-0.08 -0.08 0.04 0.26 0.54

SO2CH3 SO2CH2F CHdC(CN)2 COCl NO2

0.65 SO2F 0.83 SO2CF3 1.07 NO 0.94 C(CN)dC(CN)2

substituent constants σpσp(exp) (pred)e 0.88c 0.99a 1.00b 0.98c 1.05a 1.13b 1.17b 1.20a,b 1.24b 1.24c 1.25a 1.27b 1.32a,d 1.54b 1.36c 1.63b 1.46a 1.63b 1.70a,b

0.88 0.93 1.19 1.87 1.37 1.31 1.34 1.34 1.29 2.26

a Recommended σp- values by Exner.40,41 b Recommended σpvalues by Hansch et al.39 c σp- values determined from pKa measurements on phenols. d Questionable value according to Exner,41 either in experimental determination or in relation to other values. e The predicted σp- values are determined from the correlation between the selected σp- values, marked in italics in the table, and Vmin BLYP/6-31+G*// BLYP-31G*. f For SO2NH2 the only σp- values available were obtained from measurements on anilines. This substituent is, therefore, not included in the correlation, since substituents containing a sulfone group have different σp- depending on if they are determined from aniline systems or from phenol systems. Hydrogen-bonding between the amine in SO2NH2 and water may also affect the σp- value.

predominantly been determined from pKa measurements on anilines. However, a number of other chemical systems have also been used for the σp- derivations. There are, in some cases, rather large discrepancies between σp- values from different sources for a given substituent. These discrepancies can mainly be attributed to a lack of transferability for the parameters between different chemical systems. Therefore, it is very difficult to select the experimental σp- values which are most reliable to use for a correlation. We have preferred to use the σp- values determined from pKa measurements on phenols. However, we have also included substituents which lack a

Figure 1. Correlation between σp- and the charged oxygen Vmin calculated at three different levels (HF/3-21G*//HF/3-21G*, HF/631+G*//HF/6-31G*, and BLYP/6-31+G*//BLYP/6-31G*).

phenol derived σp- value if the recommended values from the two compilations agree to within 0.1 unit. In these cases we consistently used the values recommended by Exner. On the basis of these two criteria we have chosen 11 substituents to include in our correlation. The selected σp- values are marked in italics. In Table 3 the selected σp- values were correlated with the three sets of Vmin values and with the hIS,min values. Very good correlations were found with the calculations that used the 6-31+G* basis set (Vmin, HF/6-31+G*, hIS,min, HF/6-31+G*, Vmin, BLYP/6-31+G*). All three correlations gave a correlation coefficient of 0.994. The correlation between σp- and Vmin HF/ 3-21G* resulted in a slightly lower correlation coefficient (0.981). We have also listed the correlation between σp- and Vmin BLYP/6-31+G* for all 20 substituents (R ) 0.955), where it is mainly the di- and tricyanovinyl groups which deviate from the linear relationship. Figure 1 displays the correlations between Vmin and σp- for the 11 selected substituents. Predictions of σp- made on the basis of the correlation between Vmin from the density functional calculations and the selected σp- values have also been listed (Table 2). The predictions are in good agreement with the recommended values from Hansch et al.39 and Exner40,41 with some exceptions, which will be analyzed in more detail in the Discussion. Table 3 shows also the correlation between the Vmin BLYP/ 6-31+G*//BLYP/6-31G* calculations and σp for the previously 11 selected substituents. σp is identical to σp- for electron

Calculated Substituent Effects in Phenoxide Ions

J. Phys. Chem., Vol. 100, No. 24, 1996 10119

TABLE 4: Substituent Effects on Gas-Phase Acidities and Vmin Calculated in the Vicinity of the Oxygen of Phenols and Phenoxide Ionsa ∆Eb

substituent NH2 CH3 H F CF3 CN NO2 NO

∆G (MS)

δ∆E

Vmin δ∆Gc δ∆Gd (MS) (ICR) phenoxide phenol

351.8 351.1 -4.4 -4.2 -3.1 348.8 348.2 -1.4 -1.3 -1.2 347.4 346.9 0.0 0.0 0.0 344.0 344.3 3.4 2.6 2.1 332.8 14.6 328.8 329.2 18.6 17.7 321.4 (321.1)e 25.9 (25.8)e 320.8 26.6

-171.6 -169.6 -169.6 -166.9 -154.4 -149.6 -140.8 -141.1

-39.02 -36.29 -34.73 -31.64 -25.78 -22.26 -19.52 -19.40

a All computations were performed using BLYP/6-31+G*// BLYP/ 6-31G*. The gas-phase acidities and the electrostatic potentials are given in kcal/mol. b Calculated energy differences for the reaction XC6H4OH f XC6H4O- + H+. c Corresponds to ∆G°(600K) for the isodesmic reaction C6H5OH + XC6H4O- f C6H5O- + XC6H4OH obtained by McMahon and Kebarle.42 d Values for the same reaction obtained from ion cyclotron resonance (ICR) measured by McIver and Silvers43 at 298 K. e Estimated value, see ref 42.

donors but does not include any through-resonance for electronaccepting substituents. The relationship had a significantly lower correlation coefficient (R ) 0.953) compared with the corresponding relationship between σp- and Vmin (R ) 0.994). This shows that Vmin is sensitive to the through-resonance interactions of the electron-withdrawing substituents. Gas-Phase Acidities. Comparative computations between substituted phenols and phenoxide ions are given in Table 4. The first column lists the BLYP/6-31+G* calculated gas-phase acidities (proton affinities), approximated as ∆E ) E(XC6H4OH) - E(XC6H4O-). A decreasing value of ∆E corresponds to an increasing value of the acidity, and hence an increasing value of σp-. Table 4 also gives experimental gas-phase acidities obtained from pulsed electron beam high-pressure mass spectrometry (HPMS)42 and pulsed ion cyclotron resonance (ICR),43 given as ∆G° at 600 and 298 K, respectively. The agreement between the calculated and experimental (HPMS) absolute gas-phase acidities lies within 0.7 kcal/mol. The very good agreement between ∆E and ∆G° is noticeble since the calculated energies are not corrected for temperature dependence and zero-point vibrational energies. The very good agreement between the computed and experimental absolute gas-phase acidities consequently results in a close agreement for the corresponding relative gas-phase acidities. Table 4 also shows Vmin for both phenoxide ions and phenols. For the phenols Vmin is calculated in the vicinity of the hydroxyl oxygen. There is an excellent correlation between ∆E and Vmin for the phenoxide ions, with a correlation coefficient of 0.996. These results show that Vmin reflects the gas-phase acidity very well. The correlation between Vmin for the phenols and δ∆E was also very good, with a correlation coefficient of 0.993, suggesting that there exists a linear relationship between the substituent effects on the phenols and the phenoxide ions. It is, therefore, sufficient to do calculations on either substituted phenols or substituted phenoxide ions. Discussion The very good correlations found between σp- and Vmin (R ) 0.994 for HF/6-31+G* and BLYP/6-31+G*) and between σp- and hIS,min (R ) 0.994) provide evidence that the throughresonance has been accounted for. This is also supported by the excellent agreement between the calculated and experimental gas-phase acidities of substituted phenols. Very good correlations were also found at the HF/3-21G* level (R ) 0.981). The results show that it is not necessary to include electron

correlation to model the substituent effects in these systems. The HF/3-21G*//HF/3-21G* level may be the lower limit for reproducing the through-resonance since an earlier study by us has shown that it is not fully accounted for in para-substituted anilines calculated at the HF/3-21G*//HF/STO-3G and HF/STO5G//HF/STO-3G levels.9 It has also been shown that at least a split valence basis set is required to reproduce relative effects in proton affinities for pyridines.44 Our computations are all gas-phase calculations, while the experimental σp- are determined in aqueous solutions or in an EtOH(aq) mixture. The very good correlations between σpand Vmin, and between δ∆E and Vmin show that the substituent effects in phenoxide ions in solution and gas-phase are linearly related. This is in agreement with earlier studies on substituted phenols42, anilines,45 and benzoic acids,45 which came to the same conclusion based on purely experimental data. Therefore, good results can be expected without using solvent models. The σp- constants were originally derived from the dissociation constants of substituted phenols. However, it has been argued that substituted anilines are preferable for defining σp-.46 Experimental results show that there exists a difference in σpbetween phenols and anilines for some methylsulfone groups (e.g. SO2CH3, SO2CH2F, and SO2CF3), where the values for phenols (here referred to as σp-(P)) are consistently lower than the corresponding values for anilines (here referred to as σp-(A)).47 These substituents are among the strongest neutral electron-withdrawing substituents known, and their throughresonance is considerable. Our predictions of σp- for SO2CH3-nFn (n ) 0-3) agree very well with the experimental σp-(P), indicating that the resonance interactions are accounted for. For SO2NH2 the only σp- values available were obtained from measurements on anilines. The discrepancy between our predicted σp- value and the measured σp- may depend on hydrogen-bonding between the amine in SO2NH2 and the solvent. The predicted σp- for the di- and tricyanovinyl groups are considerably higher than the experimental values obtained from pKa measurements on N,N-dimethylanilines48 and N-phenylpiperidines.49 In a linear relationship between σp- and the secondorder polarizability for para-substituted methoxybenzenes, similar deviations from linearity as ours were found for CHdC(CN)2 and SO2CF3.50 Consequently, the reason for the large discrepancy may also in this case depend on the different behaviors of the phenol and aniline systems, which suggests that there is a stronger through-resonance for cyanovinyl groups in phenol than in anilines. Conclusions The electrostatic potential, Vmin, and the average local ionization energy, hIS,min, calculated on para-substituted phenoxide ions have shown to be good tools in which substituent effects with a considerable through-resonance between the reaction site and the substituent can be studied. The good correlations found between σp- and Vmin together with the good agreement between experimental and calculated ∆E provide evidence that through-resonance is accounted for in our calculations. The method presented can therefore be used for estimating unknown or uncertain σp- values. We have shown that it is sufficient to do calculations on either substituted phenols or substituted phenoxide ions. Our study shows that for a number of substituents there is a lack of transferability of σp- between different systems, for example, between substituted anilines and phenols. Therefore, care should be taken when using σp- on systems very different from those for which it was derived.

10120 J. Phys. Chem., Vol. 100, No. 24, 1996 Acknowledgment. We would like to thank Professor Corwin Hansch for a suggestion that led to this study. Professor Peter Politzer and Professor Jane S. Murray are acknowledged for helpful discussions. T.B. thanks the Swedish Natural Science Research Council (NFR) for support. References and Notes (1) Hansch, C.; Leo, A. Exploring QSAR: Fundamentals and Applications in Chemistry and Biology; American Chemical Society: Washington, DC, 1995. (2) Bo¨hm, S.; Kuthan, J. Int. J. Quantum Chem. 1984, 26, 21. (3) Karaman, R.; Huang, J.-T. L.; Fry, J. L. J. Comput. Chem. 1990, 11, 1009. (4) Gilliom, R. D.; Beck, J.-P.; Purcell, W. P. J. Comput. Chem. 1985, 6, 437. (5) Krygowski, T. M.; Ha¨felinger, G. J. Chem. Res. Synop. 1986, 348. (6) Sotomatsu, T.; Murata, Y.; Fujita, T. J. Comput. Chem. 1989, 10, 94. (7) Krygowski, T. M.; Wozniak, K.; Bock, C. W.; George, P. J. Chem. Res. Synop. 1989, 396. (8) Kim, K. H.; Martin, Y. C. J. Org. Chem. 1991, 56, 2723. (9) Haeberlein, M.; Murray, J. S.; Brinck, T.; Politzer, P. Can. J. Chem. 1992, 70, 2209. (10) Sjoberg, P.; Murray, J. S.; Brinck, T.; Politzer, P. Can. J. Chem. 1990, 68, 1440. (11) Murray, J. S.; Brinck, T.; Politzer, P. J. Mol. Struct. (THEOCHEM) 1992, 255, 271. (12) Pross, A.; Radom, L.; Taft, R. W. J. Org. Chem. 1980, 45, 818. (13) Kemister, G.; Pross, A.; Radom, L.; Taft, R. W. J. Org. Chem. 1980, 45, 1056. (14) Adams, D. B. J. Chem. Soc., Perkin Trans. 2 1993, 567. (15) Murray, J. S.; Politzer, P. Chem. Phys. Lett. 1988, 152, 364. (16) Murray, J. S.; Politzer, P. Chem. Phys. Lett. 1987, 136, 283. (17) Brinck, T.; Murray, J. S.; Politzer, P.; Carter, R. E. J. Org. Chem. 1991, 56, 2934. (18) Brinck, T.; Murray, J. S.; Politzer, P. J. Org. Chem. 1991, 56, 5012. (19) Murray, J. S.; Brinck, T.; Politzer, P. Int. J. Quantum Chem., Quantum Biol. Symp. 1991, 18, 91. (20) Murray, J. S.; Brinck, T.; Grice, M. E.; Politzer, P. J. Mol. Struct. (THEOCHEM) 1992, 256, 29. (21) Brinck, T.; Murray, J. S.; Politzer, P. Int. J. Quantum Chem. 1993, 48, 73. (22) Scrocco, E.; Tomasi, J. Top. Curr. Chem. 1973, 42, 95. (23) Scrocco, E.; Tomasi, J. AdV. Quantum Chem. 1978, 11, 116. (24) Politzer, P.; Murray, J. S. In ReViews in Computational Chemistry; Lipkowitz, K. B.; Boyd, D. B., Eds.; VCH Publishers: New York, 1991. (25) Politzer, P.; Truhlar, D. G., Eds. Chemical Applications of Atomic and Molecular Electrostatic Potentials; Plenum Press: New York, 1981.

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