The Quadrupole Moment of Substituted Cyclopentadienyl Anions

Oct 8, 2010 - Furthermore, we show that the quadrupole moments of Cp anions do not behave as ... This was not an unexpected finding given our previous...
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J. Phys. Chem. A 2010, 114, 11708–11713

The Quadrupole Moment of Substituted Cyclopentadienyl Anions Kevin W. Cormier, Michelle Watt, and Michael Lewis* Department of Chemistry, Saint Louis UniVersity, 3501 Laclede AVenue, Saint Louis, Missouri 63103, United States ReceiVed: May 17, 2010; ReVised Manuscript ReceiVed: August 21, 2010

Previous work in our group on the cation binding of substituted cyclopentadienyl anions (Cp) showed the curious result that Cp traceless electric quadrupole moments (Θzz) are almost all positive. Probing this issue further here we show that substituted Cp Θzz values are always significantly more positive than the analogous substituted benzenes. Given the nature of aromatic Θzz values, this is the opposite of what would be predicted. Furthermore, we show that the quadrupole moments of Cp anions do not behave as one would expect based on Cp substitutions. Unlike the quadrupole moments of substituted benzenes, which generally become more negative with the addition of electron-donating groups and more positive with the addition of electronwithdrawing groups, Cp quadrupole moments become more positive when any substituent is added, regardless of the electron-donating/withdrawing nature of the substituent. To explain these results we propose a model where the anionic Cp π-electron density repels the substituent electron density toward the molecular periphery and AIM calculations support this view. Introduction 1

Beginning with the discovery of ferrocene in the 1950s, metal complexes with cyclopentadienyl ligands (Cp) have been widely studied.2 We recently reported a theoretical study investigating the effects of Cp substitution on Cp-Li and Cp-Na complexes3 where we explored the correlation between physical properties of the substituted Cp anions and either the Cp-metal binding energies, the metal-ring centroid distances, or the metal charges in the Cp-metal complexes. One finding was that the traceless zz-component of the molecular electric quadrupole moment (Θzz) of the substituted Cp anions was a good predictor of both the Cp-metal binding energies and the metal-ring centroid distances. This was not an unexpected finding given our previous work on the metal cation binding of substituted benzenes where we found a correlation between the binding energies and the Θzz values of the substituted aromatics.4 A finding that was completely unexpected, however, was that almost all of the substituted Cp anions had a positive Θzz value. Of the 30 substituted Cp anions we investigated, only 4 had negative Θzz values, and 3 of these were between 0 and -1 DÅ. This is in stark contrast to substituted benzenes where one finds an approximately equal distribution of positive and negative Θzz values, ranging from about -15 DÅ to +25 DÅ.4,5 Unlike the dipole moment, which is a simple vector, the traceless aromatic electric quadrupole moment, hereafter referred to as the quadrupole moment, is a 3 × 3 tensor. For planar molecules, like Cp anion and benzene, this leads to off-diagonal tensor components of zero and the only nonzero values are the diagonal tensor components Qxx, Qyy and Qzz. This reduces the quadrupole moment to Θzz ) Qzz - 0.5(Qyy + Qxx) where the Qii terms are a measure of how far negative charge extends from the molecular center of mass with respect to positive charge. A negative Qii term is a result of negative charge extending further from the molecular center of mass than positive charge; a positive Qii term would denote the opposite. Since electrons always extend further from the molecular center of mass than * To whom correspondence should be addressed. E-mail: LewisM5@ slu.edu. Phone: 314-977-2853. Fax: 314-977-2521.

SCHEME 1: The Molecular Axis Used to Define the Traceless Electric Quadrupole Moment of Cyclopentadienyl Anion or Benzene

nuclei, the Qii values for molecules are always negative. Thus, from a chemical standpoint, a negative Θzz means electron density extends more in the direction of the z-axis, as defined in Scheme 1, than in the direction of the x- and y-axes (the xy-plane). A positive Θzz means electron density extends more in the xy-plane than in the direction of the z-axis. Given that the Cp and benzene ring π-clouds extend in the direction of the z-axis, and the hydrocarbon framework occupies the xyplane, one would reasonably expect substituted Cp rings, with their negatively charged π-clouds, to have more negative Θzz values than the corresponding substituted benzenes. Of course, as we have noted, the opposite is true. Ultimately, the significant difference between the quadrupole moments of substituted benzenes and Cp rings must be a result of different substituent effects. Although there has been a wealth of research investigating the effects of Cp substitution on the reactivity6 and catalytic efficiency7 of Cp-metal complexes, there have been relatively few studies systematically investigating Cp substituent effects in terms of structure and physical properties. Recent studies have investigated the effect of substitution on Cp anion aromaticity8 and on the bond localization of annelated Cp radicals.9 Here we report a computational study expanding on the initial insights of our previous work3 regarding the differences between the quadrupole moments of substituted Cp anions and benzenes. We systematically compare the quadrupole moments of identically substituted Cp anions and benzenes and we explain the significant and surprising differences between the two types of aromatics using the Atoms In Molecules (AIM) theory.10 This approach allows for broad

10.1021/jp104499y  2010 American Chemical Society Published on Web 10/08/2010

Cylopentadienyl Quadrupole Moments insights into the nature of the Cp π-electron density and how the anionic Cp π-cloud affects substituents in a very different manner than does the neutral benzene π-cloud. Theoretical Methods The parent and substituted Cp anions and benzenes were optimized and characterized via frequency calculations at the RHF/6-311++G** and RHF/6-311G** levels of theory for the purpose of determining the Θzz values. We had previously determined the Θzz values of many of the Cp anions at the RHF/ 6-311++G** level of theory, and for some of the benzenes at the RHF/6-311G** levels of theory, and we cite them appropriately in the text. We have always employed the RHF/6311G** level of theory for the Θzz calculations of substituted benzenes because it gives excellent agreement between the calculated and experimental Θzz values of benzene (calculated: -8.76 DÅ;4b,11 experimental: -8.7 ( 0.5 DÅ12) and hexafluorobenzene (calculated: +10.06 DÅ;11 experimental: +9.5 ( 0.5 DÅ12). Recent work has shown that the MP2/cc-pVTZ(-f)//HF/ 6-31G* calculated benzene and hexafluorobenzene Θzz values, -8.75 and +10.07 DÅ, respectively, are also in excellent agreement with experiment;13 however, the significant computational cost increase in using the electron-correlated MP2 method with the large cc-pVTZ(-f) basis set precludes justifying this method over the significantly faster, and just as reliable, RHF/6-311G** level of theory. When calculating the Θzz values of substituted Cp anions we have added diffuse functions because they are required for a proper description of the electron density of anions. For completeness, Θzz values were determined for all Cp anions and benzenes at both levels of theory. As described above, the molecular quadrupole moment is a 3 × 3 tensor and the calculations gave the diagonal quadrupole moment tensor components Qii (i ) x, y, or z) and the offdiagonal tensor components Qij (i ) x, y, or z; j ) x, y, z; i * j). The Θzz values were determined from the equation Θzz ) Qzz - 0.5(Qxx + Qyy). For the planar substituted Cp and benzene rings the off-diagonal tensor components are all zero and the equation requires no approximations. For the Cp and benzene rings with substituents that extend above and below the plane of the ring the off-diagonal tensor components are nonzero, however their magnitudes range from 0.1-10% of the value of the diagonal tensor components and therefore the equation is an excellent approximation of the Θzz value. For the purpose of performing atoms in molecules (AIM) calculations, the Cp and benzene molecules were optimized, and the frequency calculations were performed at the B3LYP/ 6-311++G(d,p) level of theory where a set of 6 “d” functions were used for the noncarbon atom polarization. Furthermore, the convergence criteria for these calculations was tightened to: maximum force, 2 × 10-6; rms force, 1 × 10-6; maximum displacement, 6 × 10-6; and rms displacement, 4 × 10-6. The B3LYP/6-311G** level of theory has been shown to perform well in calculating AIM charge densities, as illustrated by the Lyssenko group,14 and this group has also demonstrated the importance of using the very tight convergence criteria employed here.14,15 Diffuse functions were added to account for the anionic nature of the Cp rings. All optimization and frequency calculations were performed using the Gaussian 03 suite of programs16 and the bond critical points were determined using the AIM2000 program.17 Results and Discussion The quadrupole moments of the parent and substituted Cp anions and benzenes, calculated at the RHF/6-311++G** and

J. Phys. Chem. A, Vol. 114, No. 43, 2010 11709 RHF/6-311G** levels of theory, are shown in Table 1. We previously reported the RHF/6-311++G** calculated Θzz values for all substituted Cp anions except the 1,3-difluoro-, 1,2,3trifluoro-, and 1,2,4-trifluoro-substituted analogs (Cp-10b, Cp11a and Cp-11b).3 Also, we reported the RHF/6-311G** calculated Θzz values for the parent, fluoro-, and chloro-benzene (B-1, B-2, and B-3),4b and for perfluoro-, 1,4-difluoro-, and 1,3,5-trifluoro-benzene (B-8, B-10c, and B-11c).4a As explained above, the RHF/6-311++G** calculated Θzz values should be most trusted for the Cp anions and the RHF/6-311G** values for the substituted benzenes. For the purposes of this study, however, we are primarily interested in the relative Θzz values. There are two curious observations to be made from the values in Table 1. First, as noted above, the Θzz values of the Cp anions are more positive than the respective values for the substituted benzenes, independent of the theoretical level. Table 1 includes the four substituted Cp anions that we previously calculated to have negative Θzz values, out of a total of 30 substituted Cp anions:3 the parent Cp (Cp-1), fluoro-Cp (Cp-2), methyl-Cp (Cp-4), and methoxy-Cp (Cp-5). In addition to the RHF/6311++G** Θzz values that we previously reported, Table 1 also includes the RHF/6-311G** Θzz values for the substituted Cp molecules and, for all but the parent, they are positive at this level of theory. Thus, 9 of the 13 substituted Cp anions in Table 1 have positive Θzz values regardless of the level of theory, whereas three of the remaining four substituted Cp anions have negligible Θzz values that are slightly negative at one level of theory and slightly positive at another. In contrast, almost all of the substituted benzenes have negative Θzz values. The only exceptions are perfluorobenzene (B-8), 1,2,4-trifluorobenzene (B-11b) and 1,3,5-trifluorobenzene (B-11c) calculated with both basis sets, and perchlorobenzene (B-9) calculated with the 6-311++G** level of theory. And, even in these cases, the two trifluorobenzenes B-11b and B-11c have barely positive Θzz values and the perchlorobenzene only has a positive Θzz value at the RHF/6-311++G** level of theory. The fact that the substituted Cp Θzz values in Table 1 are almost all positive, while the Θzz values of the substituted benzenes are almost all negative, and the fact that substituted Cp anions always have more positive Θzz values than the corresponding substituted benzenes, leads to the following very peculiar finding. The electron density in substituted Cp anions extends more in the plane of molecular framework, the xy-plane in Scheme 1, than in the direction of the π-cloud region, the z-axis in Scheme 1, while for substituted benzenes electron density extends more in the π-cloud region than in the molecular plane. Given the anionic nature of the Cp π-cloud, this is the opposite of what would be predicted. The second curious observation comes from considering the difference in the Θzz values between the substituted aromatics and the pertinent parent compound, denoted ∆Θzz in Table 1. The ∆Θzz values inform us of the effect of adding substituents to the Cp or benzene rings. The ∆Θzz values for monosubstituted benzenes B-2 to B-7 follow the trend one would predict from simple inductive/resonance electron-withdrawing/electron-donating arguments. Substituting an electron withdrawing fluorine, chlorine, or nitro group on benzene causes the resulting monosubstituted benzenes (B-2, B-3, and B-7) to have a more positive Θzz value. Substituting an electron-donating methoxy or amino group causes the resulting monosubstituted benzenes, B-5 and B-6, to have a more negative Θzz value. The only anomaly is the methyl-substituted benzene (toluene), B-4. Of course, a methyl group is generally regarded as electron donating, yet toluene has a slightly more positive Θzz value than

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Cormier et al.

TABLE 1: Parent and Substituted Cp Anion and Benzene Quadrupole Moments (Θzz)a and the Difference in Quadrupole Moments Upon Substitution (∆Θzz)b

a Quadrupole moments (Θzz) calculated at the RHF/6-311++G** (normal font) and RHF/6-311G** (italicized font) levels of theory. Difference in quadrupole moments (∆Θzz) calculated by subtracting the Θzz value of the parent Cp or benzene from the Θzz value of each respective substituted aromatic. b

benzene. However, since methyl groups are largely seen as weak electron-donating groups, and the ∆Θzz value for B-4 is barely positive, this is a minor anomaly. As we have stated, when discussing benzenes the most reliable numbers in Table 1 are the RHF/6-311G** values, however both theoretical levels reveal the same trends for the benzene ∆Θzz values. In contrast to the ∆Θzz values of the monosubstituted benzenes being easily explained by electron-withdrawing/electron-donating concepts, the ∆Θzz values of the monosubstituted Cp anions are all positive. Thus, adding any substituent to a Cp ring will make the Θzz value more positive. Electron-withdrawing/electrondonating concepts obviously will not work to explain this result. Substituents on Cp rings clearly interact with the anionic Cp π-cloud differently than benzene substituents interact with the neutral π-cloud of benzene. It appears that the anionic π-cloud of the Cp ring is repelling the substituent electron density in the plane of the molecule (xy-plane in Scheme 1), and not allowing the electron density to expand in the direction of the π-cloud (the z-axis in Scheme 1). Scheme 2 illustrates this view and contrasts it with substituted benzenes. The view in Scheme 2 certainly fits the two curious observations described above: (a) substituted Cp anions are

SCHEME 2: Effect of Aromatic π-Electron Density on Substituent Electron Density for (a) Substituted Cyclopentadienyl Anions and (b) Substituted Benzenes

always more positive than the analogous substituted benzenes; (b) adding substituents to Cp anions always makes the Θzz value more positive, regardless of the electron donating/withdrawing ability of the group, while adding substituents to benzenes may make the Θzz value more positive or negative, depending on the electron donating/withdrawing nature of the group. It is worth noting here that although the discussion up to this point has focused on the aromatic Θzz value, the highest order multipole for most of the aromatics in Table 1 is the dipole moment. In fact, only B/Cp-1, B/Cp-8, B/Cp-9, B-10c, and B-11c have a dipole moment of zero, and thus have the quadrupole as the highest order multipole moment. Furthermore,

Cylopentadienyl Quadrupole Moments

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TABLE 2: Difference in AIM Calculated Charge Densitiesa between Benzenes and Cp Anions at the Ring Critical Points (∆qRCP), the Substituted Carbon Atoms (∆qC-ipso), the Bond Critical Points (∆qBCP and ∆qBCP′)b and the Substituents (∆qX and ∆qX′)c aromatics (substituent) ∆qRCP ∆qC-ipso ∆qBCPb B/Cp-1 (-H) B/Cp-2 (-F) B/Cp-3 (-Cl) B/Cp-4 (-CH3) B/Cp-5 (-OCH3)

-0.027 -0.027 -0.027 -0.027 -0.027

+0.062 +0.051 +0.041 +0.081 +0.067

+0.010 +0.029 +0.019 +0.002 +0.032

B/Cp-6 (-NH2) B/Cp-7 (-NO2) B/Cp-8 (-F)6,5 B/Cp-9 (-Cl)6,5 B/Cp-10 (-F)2 B/Cp-11 (-F)3

-0.027 -0.027 -0.026 -0.027 -0.027 -0.026

+0.083 +0.083 +0.090 +0.077 +0.069 +0.091

+0.037 -0.034 +0.032 +0.012 +0.029 +0.029

∆qXc

∆qBCP′b

∆qX′c

+0.000 +0.094 +0.184 -0.009 +0.019 -0.007 +0.018 -0.015d -0.042d +0.016d -0.004d -0.161 +0.011 -0.014 +0.027 +0.074 +0.225 +0.120 +0.219 +0.097 +0.102

SCHEME 3: Positions of the Critical Point Charge Densities for Cp Anions and Benzenes with: (a) Substituents that have One Atom (X ) H, F, Cl); (b) Substituents that have Two Unique Atoms (Methyl (X ) C, Y ) H, n ) 2), Amino (X ) N, Y ) H, n ) 1), Nitro (X ) N, Y ) O, n ) 1)); (c) the Methoxy Substituent

a

All charge densities were determined by optimizing structures at the B3LYP/6-311++G(d,p) level of theory where a set of 6 “d” functions were used for the noncarbon atom polarization, and then performing AIM calculations. Charge density differences (∆q) represent the relevant charge density on a substituted benzene minus the charge density on the analogous substituted Cp anion. b The qBCP and qBCP′ values are the charge densities at the bond critical points defined in the text and in Scheme 3. c The qX and qX′ values are the charge densities at the substituent atoms defined in the text and in Scheme 3. d For B/Cp-5, the top ∆qBCP′ and ∆qX′ values represent the O-Cmethyl bond critical point and the Cmethyl atom, respectively. The bottom ∆qBCP′ and ∆qX′ values represent the Cmethyl-Hmethyl bond critical point and the Hmethyl atoms, respectively.

as recently shown by Lopes and co-workers,13 for the fluorinated benzenes in Table 1 the Θzz value is rarely the quadrupole moment with the largest magnitude. For B-10b, B-10c, B-11a, and B-11b the Θxx and Θyy values are significantly larger than the Θzz value.13 For B-11c the Θzz value is also the smallest in magnitude, however the difference between the three quadrupole moments is quite small and they are all close to zero.13 For B-2 and B-10a the Θzz value is second largest in magnitude, Θxx is the largest in magnitude for the former and Θyy is largest in magnitude for the latter.13 Only for hexafluorobenzene, B-8, is the Θzz value significantly larger than the Θxx and Θyy values among the fluorinated benzenes in Table 1.13 It would not be unreasonable to expect similar trends for the fluorinated Cp rings, Cp-2, Cp-8, Cp-10a, Cp-10b, Cp-11a, and Cp-11b, and perhaps even for other halogenated aromatics like B/Cp-3 and B/Cp-9. Still, although the dipole moments or other quadrupole moments of the molecules in Table 1 may be more appropriate for explaining trends in physical properties such as solubility,13,18 it is the different trends among the substituted benzene and Cp anion Θzz values that allows for the insight in Scheme 2. To offer support for the scenario depicted in Scheme 2, we performed AIM calculations on the substituted Cp and benzene molecules in Table 1 to determine the charge densities at the atoms and relevant critical points (Table 2). As we discuss below, this analysis supports the view in Scheme 2 of the Cp anionic π-density repelling the substituent electron density in the plane of the molecule (xy-plane in Schemes 1 and 2). Table 2 shows the difference in AIM calculated charge densities between the substituted Cp anions and benzenes at the ring critical points (∆qRCP), the substituted carbon atoms (∆qC-ipso), the bond critical points (∆qBCP), and the substituents (∆qX) for all substituted aromatics (absolute charge density values (q) can be found in the Supporting Information). For instance, ∆qC-ipso for the parent benzene and Cp anion, B/Cp-1, is the charge density at a benzene carbon atom minus the charge density at a Cp anion carbon atom. For the parent, fluoro-, and

chloro-substituted benzenes and Cp anions (B/Cp-1 to B/Cp3), the molecular positions for the qRCP, qC-ipso, qBCP, and qX charge densities are shown in Scheme 3a. For the benzenes and Cp anions where the substituent has more than one atom, B/Cp-4 to B/Cp-7 (methyl, methoxy, amino, and nitro groups), besides the ∆qRCP, ∆qC-ipso, ∆qBCP, and ∆qX terms we also report ∆qBCP′ and ∆qX′ terms (Table 2). The molecular positions for the qRCP, qC-ipso, qBCP, qX, qBCP′, and qX′ for B/Cp-4, B/Cp-6, and B/Cp-7 are shown in Scheme 3b. As can be seen in Scheme 3b, the second bond critical point and substituent charge density terms were given because the substituents in B/Cp-4, B/Cp-6, and B/Cp-7 have two unique bonds and two unique substituent atoms. For instance, the methyl group has bond critical points at the Cipso-Cmethyl bond and at the three equivalent Cmethyl-Hmethyl bonds, and we have termed the charge densities at these positions qBCP and qBCP′, respectively. Of course, the methyl group also has one carbon atom and three equivalent hydrogen atoms, and we have denoted the charge densities at these positions qX and qX′, respectively. The same analysis can be applied to the amino and nitro groups. The ∆qBCP′ and ∆qX′ terms for B/Cp-4, B/Cp-6, and B/Cp-7 in Table 2 were calculated using the average qBCP′ and qX′ values for the substituted benzenes and Cp anions. The ∆qBCP′ and ∆qX′ terms for the methoxy substituted aromatics (B/Cp-5) have two entries in Table 2. The top ones are the charge density differences at the O-Cmethyl bond critical points and at the methoxy carbon atoms, while the bottom ones are the charge density differences at the Cmethyl-Hmethyl bond critical points and at the methoxy hydrogen atoms, as shown Scheme 3c. As with B/Cp-4, B/Cp6, and B/Cp-7, the bottom ∆qBCP′ and ∆qX′ terms for B/Cp-5 in Table 2 were calculated from the average qBCP′ and qX′ values, since there are three Cmethyl-Hmethyl bonds and three hydrogen atoms in B/Cp-5. For the multifluorinated and chlorinated aromatics B/Cp-8 to B/Cp-11, the average qC-ipso, qBCP, and qX values were used to determine the ∆qC-ipso, ∆qBCP, and ∆qX values. As stated above, the various ∆q values in Table 2 were determined using the general equation: ∆q ) q(C6H5X) q(C5H4X), where the q values represent AIM calculated electronic charge densities at the molecular positions shown in Scheme 3. Thus, a positive ∆q value means there is more electron density on the substituted benzene and a negative value

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means there is more electron density on the substituted Cp anion. The ∆qRCP values in Table 2 are essentially identical, regardless of substituent. Thus, substituents affect the charge density at Cp anion and benzene ring critical points to the same extent and the Cp π-cloud is more negative than the benzene π-cloud by -0.026 or -0.027. The fact that Cp π-clouds contain more electron density than benzene π-clouds, as measured by qRCP, is certainly to be expected given the anionic nature of Cp rings. Also, although obvious, it is worth noting that this supports the view proposed in Scheme 2, where the substituted Cp anions have greater π-electron density than the substituted benzenes. The ∆qC-ipso values in Table 2 are all positive and the ∆qBCP values are almost all positive, with the only exception being the nitro-substituted aromatics (B/Cp-7). These results are quite surprising considering they clearly indicate that there is more electron density at the ipso-carbon atom and at the bond critical point of a Cipso-substituent bond of a neutral substituted benzene than there is at the same positions of an identically substituted anionic Cp. These two trends certainly fit the view proposed in Scheme 2. The increased electron density of the Cp π-cloud repels electron density away from the ipso-carbon atom and away from the Cipso-substituent bond critical point, toward the periphery of the molecule’s hydrocarbon plane (the xy-plane in Scheme 1). The ∆qX values for the parent and halo-substituted benzenes and Cp anions (B/Cp-1 to B/Cp-3 and B/Cp-8 to B/Cp-11) have the same trend as described above for the ∆qC-ipso and ∆qBCP values. They are all positive, with the exception of the value for the parent aromatics (B/Cp-1), which is ∆qX ) 0, thus there is more electron density at the substituent in the neutral halosubstituted benzenes than in the anionic halo-substituted Cp anions. Again, this fits the view in Scheme 2 of the Cp π-cloud repelling the substituent electron density away from the atomic center and toward the outer perimeter of the molecule. Obviously, the Cp π-cloud does not extend indefinitely, and at some point the effect of repelling Cipso-substituent bond and atom electron density toward the molecular perimeter must abate. Evidence of such abatement is seen with the ∆qX values of the methyl- and amino-substituted benzenes and Cp anions, B/Cp-4 and B/Cp-6, respectively. Note, the ∆qX values are referencing the charge density difference at the methyl C atom in B/Cp-4 and the amino N atom in B/Cp-6, and the values are -0.009 and -0.161, respectively. Thus, for B/Cp-4 and B/Cp-6 the substituted Cp anion has more electron density than the substituted benzene at the atom directly bonded to the ipsocarbon, as would be expected in comparing anions and neutral molecules. Furthermore, the ∆qX values for the methoxy- and nitro-substituted benzenes and Cp anions (B/Cp-5 and B/Cp-7) are only +0.018 and +0.027, respectively. As with B/Cp-4 and B/Cp-6, these values are referencing the charge density differences at the substituent atom directly bonded to the ipso-carbon atom. These values are quite small compared to the ∆qC-ipso values for B/Cp-1 - B/Cp-11, where the range is +0.041 to +0.091 and the average value is +0.072. Thus, for B/Cp-5 and B/Cp-7 there is only slightly more electron density at the substituent for the substituted benzenes than for the substituted Cp anions. The ∆qBCP′ values of B/Cp-4 to B/Cp-7 offer a picture similar to the ∆qX values in terms of the Cp π-cloud lessening its ability to repel substituent electron density toward the molecular periphery. The ∆qBCP′ value of the methoxysubstituted aromatics (B/Cp-5) represents the electron density difference at the O-Cmethyl bond critical point and it is negative. The rest of the ∆qBCP′ values in B/Cp-4 to B/Cp-7, with the exception of the nitro-substituted aromatics (B/Cp-7), are only

Cormier et al. slightly positive. Although the substituent ∆qX and ∆qBCP′ values for B/Cp-4 to B/Cp-7 offer some evidence for abatement of the Cp π-cloud ability to repel substituent electron density, significantly stronger evidence comes from the B/Cp-4 to B/Cp-6 ∆qX′ values. Aromatics B/Cp-4 and B/Cp-6 have methyl and amino substituents and the ∆qX′ values represent the charge density difference at the substituent hydrogen atoms. Aromatics B/Cp-5 have methoxy substituents and the two ∆qX′ values in Table 2 represent the charge density differences at the substituent carbon and hydrogen atoms. All four of the ∆qX′ values for B/Cp-4 to B/Cp-6 are negative, thus the anionic substituted Cp rings have more electron density at these positions than the neutral substituted benzenes, as would be expected. The nitrosubstituted aromatics B/Cp-7 continue to behave very differently than the rest of the aromatics. The ∆qX′ value for B/Cp-7 is very positive, signifying the nitro oxygen atoms have more electron density in the substituted benzene than in the substituted Cp anion. Thus, although the Cp π-electron density seems to no longer be repelling the substituent electron density in aromatics B/Cp-4 to B/Cp-6, the effect depicted in Scheme 2 continues to be strong for the nitrosubstituted Cp anion B/Cp-7. It is worth noting the fact that the chloro- and nitrosubstituted aromatics (B/Cp-3, B/Cp-7, and B/Cp-9) have the largest positive ∆q values in Table 2 toward the molecular periphery, the ∆qX values for the chloro and perchloro aromatics B/Cp-3 and B/Cp-9, and the ∆qBCP′ and ∆qX′ values for the nitro-substituted aromatics B/Cp-7. This suggests that the abatement of the Cp π-cloud’s ability to repel substituent electron density is least effective for the most polarizable substituents. Comparing the ∆qX values of the mono- and per-chloro-substituted B/Cp-3 and B/Cp-9, with the fluoroanalogues B/Cp-2 and B/Cp-8 further clarifies this point. A chlorine atom is more polarizable than a fluorine atom and thus the chloro-substituent should be repelled to a greater extent by the Cp π-cloud than the fluoro-substituent. The larger positive ∆qX values for B/Cp-3 and B/Cp-9 compared to B/Cp-2 and B/Cp-8 are consistent with this view, and this supports the model in Scheme 2. Similarly, substituents that contain π-electron density would be expected to be more polarizable than those that contain only σ-electron density, and comparing the nitro and amino substituents shows this to be true. The ∆qBCP′ and ∆qX′ values for the amino substituted B/Cp-6 are +0.011 and -0.014, respectively, whereas the same values for the nitro substituted B/Cp-7 are +0.074 and +0.225. Again, this supports the model in Scheme 2. Although there are many trends supporting the model in Scheme 2, there is one anomaly to point out. The fact that the ∆qRCP values are almost exactly the same, regardless of substituent, seems very peculiar. This suggests that substituents behave in a similar manner with respect to electron-donating/ withdrawing ability regardless of whether they are bonded to a benzene ring or a Cp anion. This is certainly not in agreement with the rest of the analysis we have presented, where the substituents clearly behave differently depending on whether they are bonded to a benzene or a Cp ring. On the basis of the trends of the other ∆q values one would predict that the ∆qRCP values would vary quite a bit, since there appears to be no such thing as electron-donating substituents with substituted Cp rings. Ongoing and future work in our group will aim to reconcile the ∆qRCP values with the model presented in Scheme 2, which is supported by all of the other ∆q values. Finally, it should be noted that metal-complexed substituted Cp anions may indeed

Cylopentadienyl Quadrupole Moments behave as expected with regard to the electron-donating/electronwithdrawing nature of the substituents. Ongoing work in our group is addressing this issue and preliminary findings suggest the presence of an electron-deficient metal center in Cp-metal complexes provides a destination for the release of electron density from electron-donating groups. Conclusions Our work on the cation binding of substituted Cp anions has led us to probe the nature of the π-electron density in Cp anions in comparison to the analogously substituted benzenes. The comparison of Cp and benzene molecular quadrupole moments clearly demonstrates that substituted Cp rings do not behave like substituted benzenes. As would be expected, adding an electron-donating group to benzene generally makes the Θzz value more negative, while adding an electron-withdrawing group generally makes the Θzz value more positive. In contrast, adding any substituent to a Cp ring makes the Θzz value more positive. Furthermore, almost all substituted Cp anions have a positive Θzz value. To explain this result we propose the model in Scheme 2 where the Cp π-electron density repels the substituent electron density toward the periphery of the molecule, and this hypothesis is supported by the presented AIM calculations. There is more charge density at the ring critical points of the substituted Cp rings than at the ring critical points of the substituted benzene rings. Thus, as expected, the π-cloud of the anionic Cp rings is more negative than the π-cloud of neutral benzenes. However, in general, there is less charge density at the ipso-carbon atoms, the substituent bonded to the ipso-carbon atoms, and the Cispo-substituent bond critical points for the substituted Cp rings than for the substituted benzenes. This signifies that the neutral benzenes have more electron density than the anionic Cp rings at these positions, and this otherwise curious finding fits very well with the model proposed in Scheme 2. With nonpolarizable substituents the AIM calculations suggest the effect of the Cp π-electron density repelling the substituent electron density seems to abate at the second atom of the substituent. For polarizable substituents like chloroand nitro-groups the AIM calculations suggest that the Cp π-cloud repels the substituent electron density to a greater extent, and the effect continues to further reaches of the molecular periphery. While it is worth noting that resonance electron donation to the electron-rich Cp π-cloud would naturally be expected to be unfavorable, the data presented here clearly supports the model proposed in Scheme 2 and shows that, more than simply stopping resonance electron donation, the Cp π-cloud repels the electron density of all substituents, be they electron-accepting or electron-donating. Acknowledgment. This work was partially supported by the American Chemical Society Petroleum Research Fund (47159GB4) and by the National Center for Supercomputing Applications (CHE050039N) through an allocation on the SGI Altix system.

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