J. Phys. Chem. 1995,99, 9027-9033
9027
Relationship between Phosphine Proton Affinities and Lone Pair Density Properties S. T. Howard* and J. A. Platts Department of Chemistry, University of Wales, Cardiff. Card@ CFI 3TB, U.K. Received: September 29, 1994; In Final Form: March 28, 1995@
Ab initio calculations on the protonation of substituted phosphines are used to study the relationship between proton affinities and lone pair density properties. It is assumed that these properties are conveniently represented at the point of maximal concentration of non-bonded charge in the phosphorus valence shell of charge concentration, that is, at the (3,-3) critical point in V g . These lone pair properties appear to be an excellent indicator for the proton affinity of alkyl phosphines. However, the same properties fail to recover even the qualitative trend in proton affinities of halo-phosphines. In addition, it is shown that the (3,-3) critical point properties can predict the incorrect site of preferential protonation in halo-substituted phosphines containing distinct trivalent phosphorus atoms. These results are rationalized in terms of Bader’s Atoms-In-Molecules theory. It appears that integrated properties (atomic charges and energies) may give more insight into the mechanism of substituent effects on basicity than V g or the L P properties.
Introduction
This study is motivated by the question “Can one predict the interaction energy of a molecule by determining the details of its charge distribution?’ This is a question of some considerable interest for researchers who determine charge distributions experimentally. The pioneering paper of Bader, MacDougall, and Lau3 first set out the relationship between the Laplacian of the charge density dzg, localized bonded electron pairs (BPs), and lone pairs (LPs). Subsequently there have been a number of applications of @g to predict or interpret various aspects of molecular reactivity and ~tability.~-’~ Most of these studies have utilized ab initio calculations to derive molecular electron densities, but experimental determinations of dzg are also being reported with increasing frequency.I3-l7 Of particular relevance to the present work is the discovery that the properties of the LP can correlate quite closely with basic strength. Tang et al.’* have found that experimentally determined proton affinities (PAS) of amines exhibit a linear relationship with the value of @g at the (3,-3) critical point (CP) in -dze derived from 6-3 lG**//STO-3G calculations. This link between amine PAS and LP properties has also been examined recently in the context of proton sponges by Platts et al.19,20 Related work includes that of Alcam’ et al., who have utilized v g in a study of the PAS and cation basicities of NH3, (Me3)N, PH3 and (Me3)P.I2 Slee and Bader have used @g to study protonation at carbonyl oxygem6 Abboud et aL2I have also utilized LP properties from ab initio calculations to rationalize basic strengths of p-lactams and azetidines and to predict preferred sites of protonation. The enhancement of nitrogen LP electron density due to methyl substitution in amines has also been confirmed experimentally, albeit indirectly, by the new technique of Fourier-transform ion cyclotron resonance (FT-ICR).~~ In much of the research just outlined, it is apparently becoming accepted that the (3,-3) LP (CP) in -dzg provides the key to quantifying basicity in terms of charge density properties. However, the majority of the (theoretical) work has been confined to compounds with only first-row atoms-amines, amides, and carbonyl compounds. This work is an investigation of these properties in phosphines, which extends the previous @
Abstract published in Advance ACS Abstracts, May 1, 1995.
work on alkyl-substituted compounds by looking also at the effect of halogen atom substitution. It will be shown that in alkyl phosphines, LP properties show the same almost-linear relationship with PAS found in amines, but that these trends disappear for fluorophosphines and chlorophosphines, even when some electron correlation effects are taken into account. Furthermore, v g is shown to incorrectly predict the preferred site of protonation in a diphosphine. Given the number of recent studies which have used dzg to predict preferred sites of reactivity, including protonation,6%21 this is an important result. Throughout this paper, for brevity terms like “LP properties” and “LP values” will be taken to mean the values of e and dzg evaluated at the (3,-3) CP in -dzg (these will be denoted gc and dzec)and additionally the distance (re)of this CP from the phosphorus nucleus. Computational Details
Geometry optimizations were performed on DEC Alpha RISC workstations running G A I V ~ E S Susing , ~ ~ Hartree-Fock (HF) Direct SCF techniques. GAUSSIAN9224was also employed, running on a Convex C3800 supercomputer, for performing harmonic frequency calculations on the larger molecules and for all correlated calculations. C, symmetry was applied to H2PMe, HPMe2, H2PEt, HPEt2, H2PF, HPF2, H2PC1, and HPCL, while C3” symmetry was applied to PH3, PMe3, PEt3, PF3, and PCl3. The same symmetry constraints were applied in optimization of the associated cations, although protonation often raises the point-group symmetry. The structures were initially optimized with the 6-31G basis set,25and hannonic frequencies for vibrational zero point energy (ZPE) corrections to the PA were computed at this level. Thus the optimized geometries were characterized as minima, having no imaginary frequencies. Optimization was then carried out with the 6-31G** basis set.26 In the case of the halophosphines it was possible to extend the ZPE correction to the 6-31G** level. Given the counterintuitive relationship found at the HF level for PAS and LP properties in the series PH3-,F,, it was felt necessary to extend at least these results with some limited electron correlation calculations. Thus, second-order MollerPlesset (MP) perturbation corrections were computed at the HF/ 6-31G** geometries by using the same 6-31G** basis set (omitting the contribution of the core orbitals to the correlation
0022-3654/95/2099-9027$09.00/0 0 1995 American Chemical Society
Howard and Platts
9028 J. Phys. Chem., Vol. 99, No. 22, 1995
+
+
H+
I
lm
111.10
r
Me
L
-1
r
l+
l+
Et
J
L
Figure 1. Optimized geometries for methyl- and ethyl-substituted phosphines.
energy) in order to obtain both improved PA estimates and correlated electron densities. The PA calculation for PH3 of Del Bene showed that basis set superposition error (BSSE) can be significant in predicting phosphine PAS with the 6-3 1G** basis set." However, the aim here is to correlate PAS varying over several hundreds of kJmol-' with charge density properties, and since the Boys-Bernardi counterpoise correction2*is only approximate, we have not included these small correction terms. CP analyses of the total density employed the program SADDLE, part of the AIMPAC suite of program^.'^ The CP analyses of V g were carried out by using Laidig's program BUFFALO, a recent addition to this package. The PROAIM programz9was used to compute integrated atomic charges and energies of methyl and fluorophosphines and their protonated counterparts.
Results and Discussion The main structural features resulting from the geometry optimizations are illustrated in Figures 1 and 2 (a complete specificationof the structures may be obtained from the authors). The characteristic structural changes accompanying protonation are shortening of P-C bonds by around 0.05 A; shortening of P-H bonds by around 0.015 A, and shortening of P-F and P-CI bonds by some 0.07-0.08 and ~ 0 . A, 1 respectively. In all compounds, there is an opening of H-P-H, C-P-H, and C-P-C bond angles on protonation by %11". The latter is readily explained in the context of VSEPR theory30 by the replacement of LP-BP repulsions for weaker BP-BP repulsion involving the new o bond to hydrogen. The results of PA calculations at the 6-3 1G**//6-31G** level, which include (ZPE) corrections, are reported in Tables 1 and
Figure 2. Optimized geometries for fluoro- and chloro-substituted phosphines.
TABLE 1: Protonation of Alkylphosphines
PH2 HzPMe HPMez PMe2 HzPEt HPEt2 'I
798.4 868.3 923.7 969.4 880.7 944.1
0.131 0.135 0.138 0.140 0.134 0.137
-0.319 -0.340 -0.357 -0.371 -0.337 -0.352
1.439 1.436 1.434 1.433 1.437 1.436
-8.85 -9.18 -9.46 -9.67 -9.10 -9.30
Including ZPE vibrational corrections at the 6-3 I G level.
TABLE 2: Protonation of Halophosphines
HzPF HPF? PFs HzPCI HPCl? PClS 'I
780.1 744.9 668.5 763.5 735.2 7 10.9
0.144 0.155 0.159 0.138 0.143 0.146
-0.398 -0.465 -0.489 -0.354 -0.380 -0.395
1.419 1.404 1.397 1.426 1.416 1.409
-10.82 -12.57 -13.48 -9.97 -10.90 -11.54
Including ZPE vibrational corrections at the 6-3 IG** level.
2. Also given are the LP properties computed at the same 6-3 1G** level of theory. The relationships between these properties and the calculated PA are illustrated in Figures 3-5. The alkyl phosphine results (Table 1, Figures 3-5) show the same linear relations between LP properties and PAS which have been found in previous studies on amines: successive alkylation enhances the PA and {@c,Iv@cl} values in the same ratio. Thus, in principle, an experimental measurement of Vet for (to give an example) triethylphosphine could utilize Figure 5 to estimate its PA. Unfortunately, as first pointed out by Tang et al., the relationship between VQ and PA is only linear across a
J. Phys. Chem., Vol. 99, No. 22, 1995 9029
Proton Affinities and Lone Pair Density
/
r, a.u.
PHm
1.44
1.43
1.41
PHCl 1.41
800.
750.
860.
900.
950.
10
F?A./kJ.mo14 Figure 3. Relationship between proton affinity and the distance from the phosphorus nucleus to the (3,-3) lone pair CP in -V@.
0.16
0.156
0.15
0.146
0 -14
0.135
-
d
700.
760.
800.
860.
900.
950.
F?A./kJ.mol-I Figure 4. Relationship between proton affinity and
e at the (3,-3)
lone pair CP in -Ve.
particular homologous series of compounds. This is illustrated by the straight line correlations of methyl- and ethylphosphine Vg, LP values with PAS (Figure 5 ) , which give distinct slopes. The same is true for the remaining properties gc and r, in Figures 3 and 4. The enhancement of gc and I Vgcl in the LP is apparently in line with the established notion that alkyl groups donate electron density to the atom with the LP-the so-called “alkyl-inductive effect”. Despite this, there seems no obvious reason to expect such simple linear relationships between PA and the amount of charge in the LP for the free base, since subsequent protonation causes considerable disruption in the valence shell of the
phosphorus (i.e., the LP is replaced by a a-bond to hydrogen). This linear response of phosphine LP properties with respect to interaction energy might be anticipated for weaker types of chemical perturbation, such as formation of hydrogen bonds and complexation with closed-shell metal ions-and this has been verified by ab initio calculation^.^^ The earlier work of Carroll and Bader3* has already shown linear relationships between hydrogen bond energies and bond CP properties. The results in Table 2 for the series PH3-,X, (n = 0-3, X = F or C1) differ markedly from those of the methyl or ethyl series. Despite the overall electron-withdrawing effect of fluorine, as evidenced by the reductions in PA, successive
9030 J. Phys. Chem., Vol. 99, No. 22, 1995
Howard and Platts
‘%/a.u. -0.9
-0.35
-0.4
-0.4t
100.
800.
160.
850.
900.
960.
RA . / k J . ~ l ” Figure 5. Relationship between proton affinity and
v@ at the (3,-3)
TABLE 3: MP2/6-31G**//HF/6-31G**Protonation of Fluorophosphines PA,“ kEmol-’ PH3 H2PF HPF2 PF3
794.3 719.7 746.4 669.0
ec,e ~ B o h r - ~ ve,,e * B ~ h r - ~r,, Bohr 0.128 0.139 0.148 0.150
-0.293 -0.363 -0.417 -0.428
1.444 1.426 1.413 ,1.408
Including ZPE vibrational corrections at the HF/6-3 1G** level.
fluorination of the phosphine leads to substantial enhancement of the LP properties pc, lvp,l. Chlorination gives the same “inverse” trend, only weaker. In fact, phosphine LP enhancements due to fluorination were first noted in the original work of Bader et ~ l . which , ~ included results for PH3 and PF3. We next carried out MP2/6-3 1G**//HF/6-31G** single-point energy calculations on the fluorophosphine series (Table 3) to check that this trend is not an artifact arising from deficiencies in HF level calculations. These correlated calculations give in all cases a slightly more diffuse LP (less charge density and less concentration of charge density at the LP CP). With respect to the HF results, the PA slightly increases in two compounds, and decreases in the remaining two, typically by some 2 kJ-mol-’ (applying the SCF-level ZPE corrections). Trends in PA vs LP properties are unchanged from the HF results, so the HF/6-31G** level of theory is apparently reliable for this purpose. Using a procedure first outlined by Bader et uZ.,~we may gain further insight into the structure of the LP maximum in - p p by looking at the Hessian eigenvalues (pi} of - v p at the (3,-3) CP. The largest and most negative eigenvalue p3 corresponds to the curvature of v p in a direction approximately radially outward, on a line through the phosphorus nucleus and the (3,-3) CP. The magnitude of this curvature therefore effectively measures the radial extent of this concentration in ve. These values are given in the final columns of Tables 1 and 2. Like Bader et al., we find an almost 2-fold increase in p3 for PF3 compared to PH3, verifying that the LP concentration not only increases in height but becomes “sharper”, i.e. thinner
lone pair CP in -VQ.
in radial extent. This “sharpening” of the LP relative to PH3 also occurs to a small extent in the alkyl-substituted phosphines but is significantly more marked for the halo-substituted compounds. Clearly, a rather substantial charge transfer takes place from phosphorus when a hydrogen is replaced by fluorine. The gross effect on the features of V p is similar in chlorination, only less pronounced. It is possible to quantify the electronic population change in phosphorus by carrying out an atoms-inmolecules (AIMS)-type decomposition to give electronic populations and energies.33 This partitioning depends only on p, since it is based on nonoverlapping interatomic surfaces with normal vectors fi placed such that
Vpfi = 0
(1)
So eq 1 defines the shape of each “atomic basin” 52 in coordinate space. These “atoms” individually obey the Virial theorem.35 The electronic population of an atom N ( Q ) is obtained by numerical integration of e over this volume. The atomic energy E(Q) is similarly found by volume integration of the kinetic energy density operator35 and application of the atomic virial theorem. Speers and Laidig have recently applied this form of analysis in a study of the protonatiodlithiation of formaldehyde and thi~formaldehyde.~~ Concentrating on the phosphorus basin, the net charge-withdrawing effect of replacing successive hydrogens by fluorines is clearly illustrated (Table 4),as the electron population decreases by 0.295, 0.251, and 0.211 electrons as one, two, and three hydrogens in PH3 are successively substituted by fluorine atoms. Applying the same analysis to methylphosphines, we might anticipate the opposite effect, namely, successive increases in the phosphorus atomic population due to replacing hydrogens by methyl groups. Yet the results in Table 4 show that the total phosphorus population is barely affected by methylation: it even decreases slightly (relative to P in PH3) in trimethylphosphine. Consequently, whereas we may have attributed a reduction in fluorophosphine PAS to the reduced total electronic population of phosphorus (as opposed to the local
J. Phys. Chem., Vol. 99, No. 22, 1995 9031
Proton Affinities and Lone Pair Density TABLE 4: Phosphorus Electronic Population and Energy in the Free Bases PH3 HzPMe HPMe2 PMe3 HzPF HPF2 PF3 a
population, (e)
energy,“ hartrees
13.158 13.157 13.150 13.132 12.855 12.604 12.393
0.0 -0.003 8 +0.0070 +0.0246 +0.1090 +0.2562 +0.4260
Relative to P in PH3: E = -339.9475 hartrees.
LP effects), the enhanced PAS found in methyl phosphines cannot be explained in this way. The absence of an alkylinductive effect based on AIMS charges was first noted in the study by Stutchbury and Cooper, who looked at substitution effects on basicities and acidities of simple alcohols and amines.37 Substitution effects evidently require a more sophisticated explanation, based on the detailed rearrangement of charge within the phosphorus atomic basin and perhaps also the substituent atoms. According to Bader and M a c D ~ u g a l l , ~ ~ the mapping of reactive sites between molecules is best analyzed in terms of a “transition density” corresponding to the most fascile relaxation of the charge distribution. This is also reminiscent of the “charge sensitivity” approach developed by Nalewajski and c o - w ~ r k e r swhich , ~ ~ invokes normal modes of charge transfer and polarization derived by diagonalizing some representations of hardness and softness tensors. It is the comerstone of Bader’s AIMStheory that the boundary of an atom within a molecule is that surface through which there is no flux of VQ, as implied in eq 1-the so-called zero-flux surface. If a subspace 52 is bounded by a zero-flux surface, Bader and MacDougalP8 showed that, as a consequence of the Virial theorem being obeyed in each basin Q,
+
(fi2/4m)jQV2ed r = V(s2) 2T(Q) = 0
TABLE 5: Atomic Population and Energy Changes on Protonation PH3-P PH3-Hi PH3-Hii HzPF-P HzPF-Hi HZPF-Hii H2PF-F HZPMe-P HZPMe-Hi HzPMe-Hii H2PMe-CH3
A”(),e
AE(Q), hartrees
- 1.325 -0.072 1.542 -1.360 -0.073 1.559 -0.05 1 -1.310 -0.063 +1.568 -0.130
+0.493 +0.007 -0.829 +0.557 +0.009 -0.861 -0.023 f0.473 +0.004 -0.847 +0.021
+ +
11
Hii
1.542
(2)
It follows that, when electron-withdrawing groups such as halogen atoms are substituted for hydrogens, the resulting loss of charge from the phosphorus basin in the vicinity of the withdrawing atom must be accompanied by compensating changes of ve in other areas of the atomic basin, such that “ZQstill integrates to zero. Such a situation was discussed in some detail by Bader and MacDougall in considering the effect of substituting a fluorine for hydrogen in methane.38 So, in fact, the increased concentration of e in the LP region of phosphorus caused by fluorine substitution (and similar increases in the maxima of vQin bonds from phosphorus to the other attached atoms) is readily explained in this context. The AIMS approach may also be used to gain further insight into the changes which occur on protonation. These changes in atomic population and energy for phosphine, methylphosphine, and fluorophosphine are contrasted in Table 5 and illustrated in Figure 6. In Table 5, PH,-P is understood to mean the phosphorus atom in phosphines, the suffix -Hii denotes the hydrogen “atom” added in protonation of fluorophosphine, and H,PMe-CH, refers to the methyl group of methylphosphine. In general, a decrease in electron population is accompanied by destabilization in the same atomic basin-there is only one case in Table 5, where the changes in energy and charge of a fluorine are very small, that this this not realized. It is found that in all cases the stabilization due to protonation is dominated by the stabilization of the added proton (concurring with the findings of Speers and Laidig), which withdraws up to 1.568 e from phosphorus. This loss of charge causes a large destabilization of phosphorus, partially offsetting the stabilization
Figure 6. Electron transfer to and from phosphorus which accompanies protonation of PHj, HzPF, and HZPMe.
of the proton. Across a series such as PH,Me3-, (n = 1-3) the successivedifferences in PA are dominated by small changes in this balance of H-stabilization and P-destabilization. The changes hE(Q) and AN(Q) in the substituents on phosphorus are also revealing. In all compounds, the hydrogens bonded to phosphorus release around 0.07 e on protonation and in doing so are slightly destabilized. Fluorine atoms release even less charge but in doing so are actually slightly stabilized. Treating the methyl group as a single entity, it releases 0.13 e, around twice as much as hydrogen and 2.5 times as much as fluorine. Despite this, the methyl group is only destabilized by a small amount. This, it appears, is the reason for the differences in PAS for these three compounds. Hydrogen can donate a small amount of charge to phosphorus, which acts to stabilize it; fluorine donates even less than hydrogen, so that there is less stabilization of phosphorus, while CH3 is able to donate a much larger amount of charge and hence stabilize P to a greater extent. This provides an alternative insight into the often-postulated electron-donating effects of alkyl groups-the effect is not apparent from the atomic populations of the free bases
9032 J. Phys. Chem., Vol. 99, No. 22, 1995
Howard and Platts
TABLE 6: Protonation of H2P-CH2-PF2 P bearing H P bearing F
PA, kpmol-I
ec,eBohr-’
Vet, ?Bohr+
r,, Bohr
852.7 8 13.4
0.135 0.156
-0.338 -0.467
1.436 1.404
PH3-,Me, series, but it is apparent in the way the alkyl groups have donated charge to the lone pair atom aper protonation. This casts the “donation effect” as a dynamic property, Le., a response function rather than a static property of the free substituted bases. Stutchbury and Cooper3’ looked at the series (NH3, CH3NH2, (CH&N, (CH3)3NH}, and they also concluded that methyl hydrogens act as an important source of stabilizing charge in protonation. As an example where the use of LP properties on such systems could be misleading, we have carried out HF/6-31G** PA calculations with geometry optimization on the diphosphine H2P-CH2-PF2 and its two possible protonation products (Table 6). As was found in the monophosphine cases, the fluorine causes considerable enhancement of the LP on the phosphorus to which it is bonded. Energetically, protonation at the H-bearing phosphorus is ~ 3 Umol-’ 9 more favorable than at the F-bearing phosphorus. This therefore provides a concrete example on how consideration of only the LP properties will lead to the wrong conclusion about the preferential site of protonation. Conclusions
In phosphines, substitution of successive alkyl groups for hydrogen produces regular enhancements in basicity. Across homologous series, increases in PA are accompanied by regular changes in the LP properties: ec and IvQcI are enhanced at the (3,-3) CP, and this CP moves gradually toward the phosphorus nucleus, such that all three properties vary almost linearly with the PA. These simultaneous increases in basicity with increased electron density and increased concentration of electron density on the phosphorus LP are not simply linked with the traditional chemist’s notion of an alkyl-donating effect. The AIMS analysis of the phosphorus electronic population in the free bases reveals that it is virtually unchanged by alkylgroup substitution. These results therefore corroborate and substantially extend the work of Tang et al. on correlating amine basicity with Ve at the (3,-3) CP on nitrogen. The relative slopes of the plots in Figures 3-5 for the differing series of compounds effectively measure the power of these various classes of substituents to alter the basicity of phosphorus. By contrast, substitution of successive halogen atoms for hydrogen does not produce such measured changes in the PA, nor in the LP properties. This is clear when, for example, we consider that the small reduction in PA in going from PH3 to H2PF is accompanied by a large change in Ve,, while the relatively large change in PA in going from HPF2 to PF3 is accompanied by a much smaller change in Ve,. Successive chlorination does not produce such drastic effects, but both types of halogen atom substitution enhance the LP density and concentrattion of density, despite the drop in PA. In the fluorinated (free) bases, analysis of the electron population of phosphorus reveals a clear electron-withdrawing effect (charge transfer from phosphorus to fluorine). We therefore conclude that the (3,-3) CP in -Ve, must be used with some caution in the prediction of relative basicity and in predicting preferred sites of protonation, especially when halogen substituents are present. It may be anticipated that similar effects will be encountered in relative basicities of amines and amides with halo-substituents and in relating other
types of reactivity to Vec. These results are not immediately encouraging, they rather indicate that there is still much work to be done in elucidating the complex relationship between local changes in electron density properties and global changes in energy which determine relative stabilities of products. Integrated atomic properties, on the other hand, are able to give some insight into the relative basicities of phosphines and how the electron-donating effect operates in alkyl-substituted species. Even here, it is necessary to consider the changes in atomic populations and energies on protonation, rather than just the absolute values for the free base. (It’s less clear how to similarly use “changes” in LP properties on protonation, since the LP disappears.) The disadvantage with looking at the integrated properties is that they are relatively time-consuming to compute. With regard to experimental charge-density analysis, it may be more convenient to work with these integrated properties rather than local differential properties such as Ve,, since the former are certainly less sensitive to experimental uncertainty. Finally, since this paper indicates that p e has some shortcomings as a PA indicator, we briefly consider how the molecular electrostatic potential (MEP) would fare in its place. The successive decreases in phosphorus electronic population accompanying reductions in PA for fluorination and chlorination suggest that the MEP, specifically perhaps the potential value at the LP (3,-3) CP in the MEP, would correctly predict the trend in PAS where the Ve model fails. By contrast, the almost constant phosphorus charge which accompanies alkylation suggests that the MEP would vary little (or not at all) across this series and hence fail to predict enhanced PAS,whereas V2Q gives the observed linear trends. Thus it seems that neither of these local indicators derived from the unperturbed density of the free base give a satisfactory description of PA: we should rather concentrate on properties of the “dynamic” type as discussed in the text. Acknowledgment, We thank the U.K. Engineering and Physical Sciences Research Council for an Advanced Fellowship (STH) and a Studentship (JAF’), Dr. Paul Mallinson, for providing access to the University of Glasgow’s DEC Alpha, and the University of London Computer Centre, for computing time on the Convex C3800. Figures 1 and 2 were prepared with the help of David Hibbs. References and Notes (1) Coppens, P. J. Phys. Chem. 1989, 93, 7979. (2) Coppens, P. Annu. Rev. Phys. Chem. 1992, 43, 663. (3) Bader, R. F. W.; MacDougall, P. J.: Lau, C. D. H. J . Am. Chem. Soc. 1984, 106, 1594. (4) Shi, Z.: Boyd, R. J. J . Phys. Chem. 1991, 95, 4698. (5) Laidig, K. E.: Bader, R. F. W. J. Am. Chem. Soc. 1991, 112, 6530. (6) Slee, T.: Bader, R. F. W.J . Mol. Struct. (Theochem) 1992. 87. 173. (7) Aray, Y.: Rodriguez, J.; Murgich, J.: Ruette, F. J . Phys. Chem. 1993, 97, 8393. (8) b g , J. P.: Popelier, P. L. A.: Bader, R. F. W. J . Phys. Chem. 1992, 19, 7604. (9) Dixon, R. E.: Streitwieser, A.: Laidig, K. E.; Bader, R. F. W.: Harder, S. J . Phys. Chem. 1993, 97. 3728. (10) Shi, Z.: Boyd, R. J. J . Am. Chem. Soc. 1993, 115, 9614, (11) Esseffar, M.: Luna, A.: MO, 0.:YQiiez,M. Chem. Phys. Lett. 1994, 223, 240. (12) Alcami, M.: MO, 0.;Yaiiez, M.: Abboud, J.-L. M. J . Phys. Org. Chem. 1991, 4 , 177. (13) Stewart, R. F. In The Application Of Charge Density Research to ChemisQ and Drug Design: Jeffrey, G. A,, Piniella, J. F., Eds.: NATO AS1 Series B: Physics 250: Plenum Press: New York, 1991. (14) Gatti, C.; Bianchi, R.: Destro, R.: Merati, F. J . Mol. Strucr. (Theochem) 1992, 255, 409. (15) Howard, S. T.: Hursthouse, M. B.: Lehmann, C. W.; Mallinson, P. R.: Frampton, C. S . J . Chem. Phys. 1992. 97, 5616.
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