J. Phys. Chem. 1996, 100, 18725-18730
18725
Systematic Analysis of Substituent Effects: 1. Geminal and Vicinal Interactions in Fluorochloroethanes Jerzy Cioslowski* Department of Chemistry and Supercomputer Computations Research Institute, Florida State UniVersity, Tallahassee, Florida 32306-3006
Tereza Varnali Bogjazici UniVersity, F.E.F. Kimya Bo¨ lujmu¨ , Bebek 80815, Istanbul, Turkey . ReceiVed: June 7, 1996; In Final Form: August 29, 1996X
The contributions of individual substituents to properties of fluorochloroethanes are highly nonadditive. The nonadditivies can be accurately modeled with sums of terms describing geminal, gauche vicinal, and anti vicinal interactions between substituents. Such an approach, which requires 12 parameters per property, produces the total and zero-point energies and the lengths of the C-C bond with rms errors of 0.8 and 0.04 kcal/mol and 0.002 Å, respectively. The inclusion of all three types of interactions is prerequisite to obtaining reasonably accurate estimates of molecular properties, although in the cases of the total and zero-point energies the geminal contributions strongly dominate. The present methodology is very general, making it possible to analyze and predict substituent effects in a systematic manner by summing transferable increments ascribed to individual substituents, substituent pairs, triples, etc., until the desired accuracy is attained. The substituent effects in the molecules under study cannot be attributed solely to the phenomenon of electronegativity equalization.
Introduction Although many methods of pure and applied chemistry have as their objective the prediction of molecular properties, their approaches to attaining it vary widely. Interestingly, the usefulness of these methods is not a simple function of their sophistication. Thus, despite the impressive advances in rigorous electronic structure calculations that employ only the first principles of quantum mechanics, approximate additive schemes have not ceased to play an important role in diverse branches of chemical research. To the contrary, beginning with the early work on the molar volumes of normal hydrocarbons,1 these schemes have been invoked in a steadily increasing number of applications such as the estimation of the standard enthalpies of formation,2-7 other thermodynamic properties,7,8 the zeropoint energies,9,10 and the molar magnetic susceptibilities.11 Today, in addition to furnishing estimates of properties for which measurements are lacking and theoretical predictions would be too expensive, additive schemes serve as tools for the systematization of large databases of experimental results and the detection/elimination of the data that are of substandard accuracy or plainly incorrect. New methodologies that allow the computation of group contributions to various properties directly from electronic wave functions are beginning to emerge.12 Equally useful are the studies of the deviations from simple additivities among contributions of structural fragments, such as atoms, bonds, or functional groups, to various properties of molecules. When present, these nonadditivities usually indicate the importance of nonlocal interactions of greater complexity in the systems under study. For example, the deviations of the actual standard enthalpies of formation from those predicted from group equivalents reflect strain in nonconjugated hydrocarbons and are commonly used to measure its extent.13 Similarly, substantial deviations of molar magnetic susceptibilities from those obtained from the Pascal rules are often associated with ring currents and thus aromaticity.11 * To whom all correspondence should be addressed. X Abstract published in AdVance ACS Abstracts, November 15, 1996.
S0022-3654(96)01684-X CCC: $12.00
The nonadditivities in electronic properties of polysubstituted systems, which reveal the fundamental aspects of interactions between substituents and therefore are of great interest to organic chemistry, have been recently given much attention in chemical literature.14-16 The data required for investigations of these nonadditivities can be nowadays rapidly generated for a large number of molecules with ab initio electronic structure methods.14 The need for a systematic analysis of such data is addressed in the present paper, in which a simple cluster expansion of molecular properties is proposed and employed in a study of geminal and vicinal interactions in fluorochloroethanes. Three properties that are readily computed with good accuracy, namely, the total and zero-point energies and the C-C bond length, are analyzed. One should note that the C-C bond length can be measured directly with X-ray and electron diffraction techniques, whereas the two energies can be retrieved from IR spectra and thermochemical experiments. Systematic Additive Schemes for the Prediction of Molecular Properties Many of the additive schemes employed in the estimation of molecular properties are of the ad hoc type. In such schemes, the property estimates are given by sums of atomic, bond, and/or group contributions (equivalents). In cases where the estimates are deemed to lack sufficient accuracy, the sums are augmented with contributions due to other structural elements, such as rings and conjugated bonds. Schemes of that kind have been used with great success in the prediction of the standard enthalpies of formation of organic compounds.2-7 The estimation of molar magnetic susceptibilities11 constitutes another important application of these approaches. Their practical successes notwithstanding, ad hoc additive schemes are of little value in systematic studies of substituent effects. Conversely, the cluster-expansion schemes described below combine the possibility of open-ended improvements in accuracy with a clear interpretation of the computed fragment contributions. The theoretical formalism upon which these © 1996 American Chemical Society
18726 J. Phys. Chem., Vol. 100, No. 48, 1996
Cioslowski and Varnali
schemes are based invokes only the very elementary concepts of chemistry. Let {Ai} denote a set of chemical systems and {Pi} stand for the set of the corresponding values of the property in question. The understanding of the mapping {Ai} f {Pi} is sought. The fragment that is common to all the elements of the set {Ai} is called the molecular frame. In addition to the molecular frame, each of the members of {Ai} contains one or several disjoint fragments. Each of these variable fragments is called a substituent. For example, in the set of fluorochloroethanes with the general formula C2HKFLClM (K + L + M ) 6), which is the subject of the present study, each molecule consists of the C-C molecular frame and six substituents that come from the members of the set {H, F, Cl}. A given molecule Ai can be divided in many ways into fragments (nondisjoint clusters of atoms), each encompassing at least one substituent. The number of substituents present in a particular fragment is called its rank. Let nki be the number of fragments of the kth type in Ai. The cluster expansion for the property Pi of Ai is given by
Pi ) π0 + ∑nkiπk
(1)
k
where π0 and πk are the contributions due to the molecular frame and the kth fragment type, respectively. Untruncated, the cluster expansion produces exact molecular properties. In practice, however, only the fragments up to a particular rank can be retained in eq 1. The resulting truncation error measures the nonadditivities among the contributions from the included fragments. The advantage of the expansion (1) stems from the fact that it is of a mathematical nature and therefore does not rely upon assumptions about the phenomena responsible for interactions among the substituents, making it universally applicable to any molecular property of any class of compounds. In its simplest form, in which only the rank 1 fragments are included, the expansion becomes equivalent to a simple group additivity scheme. On the other hand, the inclusion of fragments of progressively higher ranks makes it possible to systematically analyze substituent effects without resorting to any preconceived notions of their nature. Thus, for example, the properties of the C2HKFLClM (K + L + M ) 6) molecules can be analyzed in terms of bond contributions and the geminal and vicinal interactions between substituents by simply restricting the expansion to fragments of ranks 1 and 2. Models of substituent interactions such as the gauche effects and hyperconjugation14-16 do not need to be invoked at all in the course of such analysis. To be more specific, for the properties of the C2HKFLClM (K + L + M ) 6) molecules, the above cluster expansion assumes the form
Pi ) πCC + nH,iπH + nF,iπF + nCl,iπCl + nCH,iπCH + nCF,iπCF + nCCl,iπCCl + nHCH,iπHCH + nHCF,iπHCF + nHCCl,iπHCCl + nFCF,iπFCF + nFCCl,iπFCCl + nClCCl,iπClCCl + g g g g g g πHCCH + nHCCF,i πHCCF + nHCCCl,i πHCCCl + nHCCH,i g g g g g g nFCCF,iπFCCF + nFCCCl,iπFCCl + nClCCCl,iπClCCCl + a a a a a a πHCCH + nHCCF,i πHCCF + nHCCCl,i πHCCCl + nHCCH,i a a a a a a nFCCF,iπFCCF + nFCCCl,iπFCCCl + nClCCCl,iπClCCCl + ...
tions due to the bonds between the molecular frame and the substituents. Since the latter contributions are linearly dependent on the former ones, they can be entirely omitted without affecting the accuracy of the expansion. If there were no interactions among the substituents, the first four terms of eq 2 would provide exact values of the properties under study. In other words, the deviations of the actual properties from the predictions of the simple additive formula,
Pi ) πCC + nH,iπH + nF,iπF + nCl,iπCl
(3)
are entirely due to the substituent interactions that can be further divided into those involving pairs, triples, ... of substituents. In its simplest version, the analysis of these interactions takes into account only the substituent pairs. Three distinct classes of such pairs, namely, geminal (those giving rise to the πHCH, πHCF, πHCCl, πFCF, πFCCl, and πClCCl contributions in eq 2), gauche g g g g , πHCCF , πHCCCl , πFCCF , vicinal (giving rise to the πHCCH g g πFCCCl, and πClCCCl contributions; the dihedral X-C-C-Y angle close to 60°), and anti vicinal (giving rise to the a a a a a a , πHCCF , πHCCCl , πFCCF , πFCCCl , and πClCCCl contributions; πHCCH the dihedral X-C-C-Y angle close to 180°), occur in the C2HKFLClM (K + L + M ) 6) molecules. For example, the effects ascribed to the pair interactions of substituents in the CF3CH2Cl molecule at its equilibrium geometry are represented by the sum g g a + 2πFCCCl + 2πHCCF + πHCH + 2πHCCl + 3πFCF + 4πHCCF a (4) πFCCCl
There are 15 pair interactions in each of the molecules under study. The interpretation of the parameters that enter eq 2 may be hindered by their large number. This potential drawback is readily eliminated by analyzing the changes in properties {∆Pi} that accompany the bond combination reaction
(K/6)C2H6 + (L/6)C2F6 + (M/6)C2Cl6 f C2HKFLClM (5) rather than the properties {Pi} themselves (note that the property changes {∆Pi} would vanish if the contributions of clusters with rank 2 and higher were zero). Another advantage of using {∆Pi} instead of {Pi} is the elimination of systematic errors in molecular properties obtained from calculations involving approximate treatment of the electron correlation effects (note that since reaction 5 is isodesmic, the bulk of the residual electron correlation effects are expected to cancel out). The cluster expansion for the property change, given by
j HCF + nHCCl,iπ j HCCl + nFCCl,iπ j FCCl + ∆Pi ) nHCF,iπ g g g g g g π j HCCF + nHCCCl,i π j HCCCl + nFCCCl,i π j FCCCl + nHCCF,i a a a a a a π j HCCF + nHCCCl,i π j HCCCl + nFCCCl,i π j FCCCl + ... (6) nHCCF,i
where
π j HCF ) πHCF - (1/2)(πHCH + πFCF) g g g g ) πHCCF - (1/2)(πHCCH + πFCCF ) π j HCCF
(2)
where only the contributions from the fragments with ranks 1 and 2 are explicitly written. The first four terms represent the contributions due to the molecular frame and the atoms of substituents, whereas the next three terms stand for the contribu-
a a a a ) πHCCF - (1/2)(πHCCH + πFCCF ) etc. π j HCCF
(7)
follows directly from eq 2. The reduction (from 18 to 9) in the number of phenomenological parameters is a consequence of the fact that the quantities defined in eq 7 vanish for pairs involving identical substituents. It should be mentioned that a
Systematic Analysis of Substituent Effects
J. Phys. Chem., Vol. 100, No. 48, 1996 18727
TABLE 1: Changes in Properties of Fluorochloroethanes That Accompany the Bond Combination Reaction (Eq 5)a R1R2R3
R4R5R6
∆ETOT
∆EZPE
∆RCC
R1R2R3
R4R5R6
∆ETOT
∆EZPE
∆RCC
HHH HHH HHH HHH HHH HHF HHF HHF HHF HHF HHF HHF HHF HHF HHCl HHCl HHCl HHCl HHCl HHCl HHCl HFF HFF HFF HFF HFF HFF HFF HFCl HFCl HFCl HFCl HFCl HFCl HFCl HFCl HClCl HClCl HClCl HClCl FFF FFF FFCl FFCl FClCl FClCl
HHH HHCl HFCl FFF FClCl HHF HFH HFCl HClF FFH FFCl FClF ClClH ClClCl HFF HClH HClCl FFF FClH FClCl ClClF HFF HClCl FHCl FFCl ClHF ClFF ClClCl HClF FHCl FFCl FClF ClHCl ClFF ClClH ClClCl FFF FClCl ClFF ClClCl FFCl ClClCl FClF ClClF FClCl ClClCl
0.00 -7.94 -1.48 -13.79 -5.95 25.70 25.25 15.58 16.39 23.15 14.23 14.35 5.22 5.08 1.41 -11.42 -15.47 -10.62 -0.53 -4.88 -4.04 18.54 1.57 16.61 15.69 16.04 14.66 5.77 10.64 11.59 11.00 12.12 -1.71 11.07 -1.31 2.51 -7.45 -0.54 -1.16 -8.61 6.68 -1.31 13.66 13.61 12.54 6.05
0.00 1.65 1.63 0.50 0.82 2.25 2.17 2.40 2.41 2.22 1.34 1.32 2.74 1.79 2.51 2.91 2.96 1.53 2.68 1.64 1.63 2.00 2.39 2.27 1.05 2.24 1.02 1.37 2.26 2.39 1.11 1.11 2.61 1.08 2.59 1.37 1.37 1.28 1.26 1.46 -0.07 0.14 -0.18 -0.17 -0.20 -0.08
0.00 -2.04 -3.24 -3.39 -3.99 -1.65 -2.74 -2.93 -2.53 -2.41 -2.63 -2.50 -3.09 -2.88 -2.85 -3.20 -3.63 -2.87 -3.31 -3.49 -3.28 -1.66 -2.28 -1.94 -1.06 -1.91 -1.18 -1.39 -2.41 -2.59 -1.63 -1.51 -2.94 -1.63 -2.80 -1.88 -1.85 -2.07 -1.98 -2.16 -0.16 -0.46 -0.11 -0.15 -0.26 -0.17
HHH HHH HHH HHH HHH HHF HHF HHF HHF HHF HHF HHF HHF HHCl HHCl HHCl HHCl HHCl HHCl HHCl HHCl HFF HFF HFF HFF HFF HFF HFCl HFCl HFCl HFCl HFCl HFCl HFCl HFCl HClCl HClCl HClCl HClCl FFF FFF FFCl FFCl FFCl FClCl ClClCl
HHF HFF HClCl FFCl ClClCl HHCl HFF HClH HClCl FFF FClH FClCl ClClF HHCl HFCl HClF FFH FFCl FClF ClClH ClClCl HFCl FHF FFF FClCl ClHCl ClFCl HFCl HClCl FFF FClH FClCl ClFH ClFCl ClClF HClCl FFCl ClHCl ClFCl FFF FClCl FFCl FClCl ClClCl ClFCl ClClCl
10.44 2.15 -13.19 -6.36 -12.73 5.80 20.53 6.67 2.97 7.94 18.30 13.34 13.49 -13.80 -3.57 -2.25 3.45 -4.73 -3.72 -12.94 -12.37 14.28 21.28 9.17 15.09 2.69 13.79 9.65 -2.16 5.17 11.79 11.16 11.63 9.71 10.76 -13.38 -0.93 -14.25 -1.74 0.00 6.27 12.40 12.55 5.52 13.08 0.00
1.22 1.35 2.02 0.59 1.20 2.62 2.20 2.56 2.73 1.30 2.42 1.48 1.48 2.95 2.67 2.69 2.51 1.53 1.51 2.97 1.91 2.14 2.12 1.08 1.15 2.51 1.12 2.23 2.46 1.17 2.36 1.16 2.35 1.17 1.16 2.60 1.28 2.81 1.30 0.00 -0.03 -0.17 -0.17 -0.03 -0.20 0.00
-1.78 -2.90 -3.31 -3.77 -4.00 -2.33 -2.33 -2.91 -2.95 -2.25 -2.89 -2.84 -2.64 -3.07 -3.53 -3.18 -2.85 -3.30 -3.11 -3.55 -3.53 -2.03 -1.42 -0.94 -1.20 -2.30 -1.32 -2.48 -2.73 -1.44 -2.49 -1.73 -2.34 -1.81 -1.75 -3.00 -1.96 -3.25 -2.11 0.00 -0.33 -0.24 -0.28 -0.28 -0.18 0.00
a
∆ETOT and ∆EZPE in mhartree, ∆RCC in pm.
similar approach, though put on a less formal footing, has been previously used in the studies of substituent interactions in fluorochloromethanes and fluorochlorosilanes.16 Details of Calculations There are 55 different molecules with the general formula C2HKFLClM (K + L + M ) 6), giving rise to 92 distinct rotamers that are energy minima on the corresponding potential energy hypersurfaces. For each of these rotamers, the total energy ETOT and the length of the C-C bond RCC were calculated at the MP2/6-311G** level of theory. In addition, the zero-point energies (ZPEs) EZPE were computed within the Hartree-Fock approximation using the same basis set. All calculations were carried out with the GAUSSIAN 92/DFT suite of programs.17 The changes in ETOT, EZPE, and RCC that accompany the bond combination reaction (eq 5), which were derived from the computed properties, are listed in Table 1 as ∆ETOT, ∆EZPE, and ∆RCC. The values of ∆ETOT and ∆EZPE are given in mhartree (1 mhartree ) 0.6275 kcal/mol), whereas those of ∆RCC are quoted in pm (1 pm ) 0.01 Å). Each of the rotamers under study is identified in Table 1 by the sequence R1R2R3/ R4R5R6, where the first three symbols stand for the substituents
connected to the first carbon and the last three denote those linked to the second carbon. The R1-C-C-R4, R2-C-C-R5, and R3-C-C-R6 dihedral angles are close to 180°. In light of the trends present in the previously published results for substituted methanes and silanes,16 one expects the computed values of ∆ETOT and ∆RCC to change by insignificant amounts upon the improvement in either the basis set or the electron correlation treatment. Results As already mentioned above, if there were no interactions among the substituents, ∆ETOT, ∆EZPE, and ∆RCC would all equal zero. However, the observed rms deviation of ∆ETOT from zero amounts to 7.0 kcal/mol, indicating substantial nonadditivities among the substituent contributions. The individual values of ∆ETOT range between -9.7 and 16.1 kcal/mol, implying that the substituent interactions can be either stabilizing or destabilizing. In contrast, mostly positive deviations from the simple additivity are exhibited by the computed ZPEs. These deviations are as large as 1.86 kcal/mol (the rms value equaling 1.14 kcal/mol), putting the commonly held assumption of the almost perfect additivity of atomic/bond contributions to
18728 J. Phys. Chem., Vol. 100, No. 48, 1996
Cioslowski and Varnali TABLE 2: Geminal, Gauche Vicinal, and Anti Vicinal Contributions to ∆ETOT, ∆EZPE, and RCC in Fluorochloroethanesa contr. to ∆ETOT (mhartree)
contr. to ∆EZPE (mhartree)
contr. to ∆RCC (pm)
g a g a g a j XCCY π j XCCY π j XCY π j XCCY π j XCCY π j XCY π j XCCY π j XCCY XY π j XCY π
HF 6.97 -1.64 -0.69 0.47 0.05 HCl -1.75 -1.75 -0.91 0.57 0.13 FCl 3.57 -0.40 0.01 -0.07 0.01
0.08 -0.06 -0.36 -0.46 0.15 -0.33 -0.45 -0.46 0.01 -0.02 -0.02 0.01
a The values of E TOT are C2H6, -79.570 889 hartrees; C2F6, -674.044 494 hartrees; C2Cl6, -2833.852 752 hartrees. The values of EZPE are C2H6, 0.078 612 hartree; C2F6, 0.032 869 hartree; C2Cl6, 0.020 533 hartree. The values of RCC are C2H6, 152.8885 pm; C2F6, 153.8127 pm; C2Cl6, 157.9084 pm.
gauche vicinal ones, although only the latter involve closely positioned substituents. The geminal interactions are also the dominant source of the nonadditivities among the substituent contributions to ZPEs. Equation 6 predicts the values of ∆EZPE with the rms error of 0.04 kcal/mol (the individual errors varying between -0.11 and 0.11 kcal/mol. The pair contributions are mostly positive. Again, the gauche and anti vicinal interactions are found to be of equal importance. All three types of pair interactions appear to contribute in similar amounts to the C-C bond lengths in fluorochloroethanes. Overall, the correlation between the computed and the predicted values of ∆RCC is somewhat worse (a rms error of 0.002 Å) than that obtained for either ∆ETOT or ∆EZPE (compare part c of Figure 1 with parts a and b). Only the (small) a contribution is positive, explaining the negative values π j FCCCl of ∆RCC found for all the heterosubstituted species listed in Table 1. It should be emphasized that neither the geminal nor the vicinal interactions can alone account for the observed trends in the three properties under study. This inability is conspicuously exhibited in Figures 2 and 3, which display the results of fittings in which the terms describing different types of interactions were selectively removed from eq 6. Retaining only the geminal interactions increases the rms error from 0.8 to 2.2 kcal/mol for ∆ETOT and from 0.002 to 0.010 Å for ∆RCC, while keeping only the vicinal interactions produces rms errors of 5.7 kcal/mol and 0.004 Å for ∆ETOT and ∆RCC, respectively. Discussion and Conclusions Figure 1. Computed values of ∆ETOT (a, top), ∆EZPE (b, middle), and ∆RCC (c, bottom) vs those predicted from eq 6.
ZPEs9,10 in doubt. The values of ∆RCC, on the other hand, are all nonpositive, the relative shortening of the C-C bonds amounting to as much as 0.040 Å (the RMS deviation being 0.024 Å). The model of pairwise substituent interactions quantitatively accounts for the observed trends in ∆ETOT, ∆EZPE, and ∆RCC (Figure 1). Least-squares fitting of the parameters that enter eq 6 to these properties furnishes the data listed in Table 2. The magnitudes of ∆ETOT, which are reproduced with the rms error of only 0.8 kcal/mol (the errors for individual species ranging from -2.4 for CH3CHF2 to 2.7 kcal/mol for the staggered conformer of CH2FCH2F), are strongly dominated by the geminal contributions. Not surprisingly,15,16 the geminal H-F and F-Cl interactions are strong and destabilizing (in comparison to the respective mean homonuclear interactions; see eq 7). On the other hand, the geminal H-Cl contribution is smaller and of opposite sign. Rather unexpectedly, the anti vicinal interactions turn out to be almost as important as the
The methodology presented in this paper is general enough to be applicable to any property of any set of molecules. The cluster expansion of molecular properties (eq 1) makes it possible to analyze substituent effects in a systematic manner by including contributions due to individual substituents, substituent pairs, triples, etc., until the desired accuracy is attained. No references to specific models of substituent interactions are necessary. The use of bond combination reactions offers both the possibility of employing fewer phenomenological parameters in the cluster expansion and, for properties obtained from electronic structure calculations, an almost complete elimination of errors stemming from the approximate description of electron correlation effects. The substituents in fluorochloroethanes interact strongly with each other, giving rise to large nonadditivities in their contributions to the electronic properties of these systems. The nonadditivities can be accurately modeled with sums of terms describing pair interactions of substituents. The geminal interactions dominate the nonadditivities observed in the calculated total energies and ZPEs, whereas all three types of pair interactions affect the C-C bond lengths to a similar degree.
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J. Phys. Chem., Vol. 100, No. 48, 1996 18729
Figure 2. Computed values of ∆ETOT (a, top), ∆EZPE (b, middle), and ∆RCC (c, bottom) vs those predicted from eq 6 with only the geminal interactions (the terms involving the π j HCF, π j HCCl, and π j FCCl parameters) included.
Figure 3. Computed values of ∆ETOT (a, top), ∆EZPE (b, middle), and ∆RCC (c, bottom) vs those predicted from eq 6 with only the vicinal g g g a interactions (the terms involving the π j HCCF , π j HCCCl , π j FCCCl , π j HCCF , a a , and π j FCCCl parameters) included. π j HCCl
When combined with the properties of the C2H6, C2F6, and C6Cl6 molecules (which are listed in a footnote to Table 2), the computed pair contributions furnish estimates of stabilities and geometries of fluorochloroethanes. For each property, only 12 parameters are required, which compares favorably with the 92 individual values needed for all the structures. Such a comparison would be even more appealing for polysubstituted ethanes with M different types of substituents, for which the present model would require a total of (1/2)M(3M - 1) parameters per property [M parameters for the properties of the homosubstituted molecules and (3/2)M(M - 1) parameters for the geminal and vicinal contributions] as opposed to (1/2)M(19M2 - 46M + 29) distinct property values. The previously published results for fluorochloromethanes15,16 suggest that the residual errors in the property estimates afforded by eq 6 stem mostly from the contributions due to triplets of
geminal substituents. These errors, which are acceptably small for many chemical applications, are nevertheless too large to make the present method accurate enough for the conformational analysis of fluorochloroethanes. Interestingly, equations of the form18,19
ETOT(A-B) ) (1/2)[ETOT(A-A) + ETOT(B-B)] + A|χ(A) - χ(B)|[R(A)+R(B)] (8) where the symbols A and B denote the CR1R2R3 and CR4R5R6 moieties, respectively, produce estimates of ETOT that, despite the much larger number of adjustable parameters χ and R involved, are clearly inferior to those furnished by the present approach. One infers from this observation that the substituent effects in the molecules under study cannot be attributed solely to the phenomenon of electronegativity equalization.
18730 J. Phys. Chem., Vol. 100, No. 48, 1996 Acknowledgment. This work was partially supported by the National Science Foundation under Grant CHE-9224806. One of the authors (T.V.) also thanks TUBITAK and BUVAK for travel funds. References and Notes (1) Koop, H. In Textbook of Physical Chemistry; Glasstone, S., Ed.; Van Nostrand: New York, 1946; p 525. (2) Prosen, E. J.; Johnson, W. H.; Rossini, F. D. J. Res. Natl. Bur. Stand. 1946, 37, 51. (3) Franklin, J. L. Ind. Eng. Chem. 1949, 41, 1070. (4) Pittam, D. A.; Pilcher, G. J. Chem. Soc., Faraday Trans. 1 1972, 68, 2224. (5) Benson, S. W.; Cruickshank, F. R.; Golden, D. M.; Haughen, G. R.; O’Neal, H. E.; Rodgers, A. S.; Shaw, R.; Walsh, R. Chem. ReV. 1969, 69, 279. (6) Pedley, J. B.; Naylor, R. D.; Kirby, S. P. Thermochemical Data of Organic Compounds; Chapman and Hall: London, 1986. (7) Janz, G. J. Estimation of Thermodynamic Properties of Organic Compounds; Academic Press: New York, 1958. (8) Wiberg, K. B. J. Comput. Chem. 1984, 5, 197. (9) Schulman, J. M.; Disch, R. L. Chem. Phys. Lett. 1985, 113, 291. (10) Grice, M. E.; Politzer, P. Chem. Phys. Lett. 1995, 244, 295.
Cioslowski and Varnali (11) Mulay, L. N.; Bordeaux, E. A. Theory and Application of Molecular Diamagnetism; Wiley: New York, 1976. (12) Bader, R. F. W. Atoms in Molecules; Oxford University Press: New York, 1990, pp 209-219, and references cited therein. (13) Wiberg, K. B. Angew. Chem., Int. Ed. Engl. 1986, 25, 312. Halton, B. In Strain in Organic Chemistry: A PerspectiVe in AdVances in Strain in Organic Chemistry; Halton, B., Ed.; JAI Press: London, 1991; Vol. 1, pp 1-18. (14) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986; pp 356-364. (15) See for example: Wiberg, K. B.; Rablen, P. R. J. Am. Chem. Soc. 1993, 115, 614, and references cited therein. (16) Ignacio, E. W.; Schlegel, H. B. J. Phys. Chem. 1992, 96, 5830. (17) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Wong, M. W.; Foresman, J. B.; Robb, M. A.; Head-Gordon, M.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzalez, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. GAUSSIAN 92/DFT; Revision G.3; GAUSSIAN, Inc.: Pittsburgh PA, 1993. (18) Pauling, L. The Nature of the Chemical Bond; Cornell University Press: Ithaca, 1960; eqs 3-12 on p 92. (19) Ochterski, J. W.; Petersson, G. A.; Wiberg, K. B. J. Am. Chem. Soc. 1995, 117, 11299.
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