ARTICLE pubs.acs.org/JPCA
When Do Molecular Bowls Encapsulate Metal Cations? Jason R. Green†,‡ and Robert C. Dunbar*,‡ † ‡
Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States Department of Chemistry, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, United States
bS Supporting Information ABSTRACT: Curved carbon π surfaces have chemical and physical properties suitable for exploitation for chemical microencapsulation and the self-assembly of nanoscale materials. Advances will greatly benefit from more understanding of their hostguest interactions with guests such as metal cations. Here, quantitative predictions are made for the binding of metal cations to three prototypical surfaces using density functional theory calculations: the buckybowls C20H10, C30H10, and C40H10. The focus was on finding the most favorable binding sites, assessing whether binding is more favorable inside or outside the bowl, and exploring factors influencing the binding site preference. Classes of cations studied included small and large monocations and cations with multiple charges: Naþ, Csþ, NH4þ, Baþ, Ba2þ, and La3þ. Factors found to favor inside binding were large ion size and high ion charge, suggesting that polarization interactions as well as short-range interactions are important in determining the preferred binding sites inside and outside these buckybowls. Unlike monocations, which at best have only a weak tendency toward encapsulation, the multiply charged cations Ba2þ and La3þ were found to have a strong driving force toward containment inside the bowls. Coulomb potentials were found to favor cation binding on the outside surface of the bowls, but cation microsolvation through polarization interactions presents a compensating factor that can tip the balance in favor of encapsulation. Knowledge of these factors will be a valuable tool in the design of nanocontainers and the diverse architecture possible with these structural elements.
’ INTRODUCTION The curved polyhedral carbon networks derived from fullerenes form a variety of bowls and baskets that are intriguing as containers for encapsulating small molecules. Unlike the closed containers formed by fullerenes, the open cages formed by these compounds are leaky, and containment has to rely on host guest interactions that favor the contained configuration in preference both to guest escape and to guest binding on the outside surface. The binding of neutral guests tends to be weak, but cations bind strongly to π surfaces, and it is interesting to think about whether the bowls actually do act as effective containers for cationic guests. Are there circumstances where a guest is convincingly contained within the bowl interior, in preference to sticking to an outside surface or detaching entirely? If so, what are these circumstances? Interest in bowl containment in the context of hostguest chemistry has been stimulated by rapid advances in the synthetic methodology for making bowl-derived hydrocarbons and also by the recent first observation of a metal-ion guest firmly lodged in the interior of a bowl (sumanene).1 Interesting on the theoretical side is recent work of dos Santos et al.2 on the binding of neutral guest molecules (H2, H2O, alanine) to several deep bowls, including the C40H10 bowl studied in the present work. Binding to the mouth of the bowl was quite good, with binding energies up to around 25 kcal mol1. Penetration into the bowl interior was not deep in all cases, but H2 and, particularly, H2O were found to be deeply contained inside the bowl and much more strongly held than by simple van der Waals binding. This work did not address the question of whether the encapsulated r 2011 American Chemical Society
geometries were preferred compared to alternatives with the guest on the outside surface. In another direction, Olson et al.3 explored the self-assembly of structures mimicking viral capsids using pentagonal building blocks derived from corannulene and noted the possible role of encapsulated metal ions in templating such a self-assembly process. Filatov et al.4 have also investigated the organization of the bowls’ crystal stuctures in the bulk solid state. Metal ions offer an interesting class of guests. Coulomb and polarization interactions can lead to much stronger binding than in noncovalent neutralneutral systems. Because the dipole of corannulene and its relatives has its positive pole pointing into the cavity, there is an electrostatic bias toward binding cationic guests on the outside (convex) side of the bowls. In other words, the intrinsic electrostatic properties of the convex C5 ring-based surface lead to a region of relatively negative electric potential outside the bowl.5 However, this tendency is opposed by the enhanced polarization interaction (microsolvation) of the charge with the interior walls of the bowl when the cation is inside. The present work explores the conditions required for this competition to favor encapsulation of metal ions compared with surface binding on the outside and suggests particular cation features that would favor encapsulation within the bowl. At the same time, the Coulomb contribution to cation binding is mapped out, to clarify the degree to which the additional polarization effects Received: December 13, 2010 Revised: March 6, 2011 Published: April 20, 2011 4968
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Figure 1. The three bowls studied in this work.
(charge-induced-dipole forces) are determinative in the ion’s choice of binding sites. Petrukhina et al. have paid substantial attention to the complexes of rhodium ions with bowl-derived hosts and have worked toward finding systems with Rh(I) or Rh(II) contained within bowls.6 The tendency of transition metals such as rhodium or silver7 to bind locally (η2) to CdC bonds often dominates, so that metal ions locally bound to the CdC bonds on the rim of the bowl are common. In one interesting case, a rhodium ion attaches to a hub carbon of a corannulene framework, but on the convex side.8 A striking new development1 was the discovery of the inside (η6) binding of Fe(II) in the bowl of sumanene (C21H12), giving the first solid experimental example of metalion binding on the concave face of a bowl (albeit, a rather shallow bowl). This result is encouraging for experimental manipulation, but in general, a problem with transition-metal guests seems to be a propensity for localized binding (η2) of the ion to double bonds on the rim of the bowl, rather than interaction with the extended π framework inside. The present study looks at main-group metal ions, in the expectation that localized trapping of the guest ion on the rim or the convex surface will be less likely and more central containment inside the bowl will be more favorable compared to transition metals. The set of hosts chosen here to explore this question comprises the three bowls (“buckybowls,” “nanobaskets”) shown in Figure 1 whose carbon skeletons are fragments of buckminsterfullerene C60 and which have a five-membered ring as the apex of the bowl (with essentially C5 symmetry). The smallest is the well-known corannulene molecule; the others appear to have no common names and are referred to here as “bowl-30” and “bowl-40”. Going down this series, the curvature of the surface and the depth of the bowl both increase strongly. If the bowl depth is taken as the distance between the basal C5 plane and the
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outermost plane of carbons, the bowl depths are as follows: corannulene, 0.89 Å; bowl-30, 2.53 Å; bowl-40, 3.78 Å. Paralleling the development of synthetic access to many compounds of this type919 (as well as the related series of bowls having a sixmembered ring at the apex and essentially C3 symmetry20), there has been extended interest in their properties and reactivity,2125 as well as their metal-ion complexes.1,6,20,2632 The C60 fragments with the six-membered ring at the apex (C3) are apparently easier to access synthetically and have been popular study targets, but for consistency with the corannulene analog, the present study addresses the five-membered-ring (C5) series. The intense current interest in carbon nanotubes (notably those with curved end caps) and in single-layer graphitic sheets (graphene, as well as curved graphene sheets33) lends immediate interest to the interactions of charged particles with conjugated carbonsheet surfaces. The two larger bowls have not yet been reported in the laboratory, but pentaindenocorannulene, recently reported in good yield by Jackson et al.,14,19 is a pentabenzo derivative of bowl-30 and probably has a similar bowl geometry. Bowl-40 might be conceptually accessible by construction routes comparable to that used for pentaindenocorannulene or by degradation from larger fullerenes,34 but its preparation still seems distant from actual realization. The degree of curvature of pentaindenocorannulene is higher than that of C60, as pointed out by Jackson et al.,14 and the even greater steric strain of bowl40 will likely make its synthesis difficult. The bowls represent simple models for ions sitting on curved graphitic surfaces. As such, understanding them can elucidate the binding to more extended structures such as fullerenes, carbon nanotubes, and graphitic sheets. The capture and possible encapsulation of ions by these surfaces involves weaker forces than in the much-studied hosts having Lewis-basic-atom sites of attachment to the guest, with these points of attachment usually consisting of oxygen or nitrogen atoms. The attachment principles for the carbon-sheet materials are more diffuse and present different and interesting challenges to understanding and quantitative prediction. The present work aims to extend the base of knowledge about binding to these curved sheets and to elaborate a few principles involved. Because experimental information is scanty, the study is confined to computational methods. Within its limits, quantum chemistry offers a reliable source of binding results for systems of this size. There has also been extensive study of metal ions binding to coronene, the flat analogue of corannulene, as well as other flat polycyclic aromatic hydrocarbons (PAHs) (for example, refs 3547). The comparison of corannulene with coronene will also be considered.
’ COMPUTATIONAL METHODS Calculations were carried out with the Gaussian 98 and Gaussian 03 packages.48,49 The energy results in Tables 13 were obtained by DFT calculations at the B3LYP/6-31þg(d,p) level for C, and H atoms. (In some cases, not all atoms carried diffuse basis functions, but complete consistency was maintained for each given series of complexes.) Naþ also used this same basis, whereas Mg2þ used the 6-311 g(d) basis on the metal. All Csþ, Baþ, Ba2þ, and La3þ calculations used the sdd relativistically corrected pseudopotential included in the Gaussian package on the metal. Geometries were fully optimized at the level of the energy results. Electrostatic potential plots as shown in Figures 4 and 5 below for corannulene and bowl-30 were calculated at the 4969
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same B3LYP/6-31þg(d,p) level, although the results were checked at the B3LYP/6-311 g(d,p) level, and no major differences were found. The potential plot for bowl-40 (Figure 6) used results at the 6-311 g(d,p) level. The electrostatic potentials calculated by Gaussian were contour-plotted using Origin 7.5 and overlaid with molecular structures from GaussView 3.0. Table 1. Inside/Outside Metal-Ion Binding Preferences for Corannulenea corononeb inside binding strength on-axis η5 site η6 site
axial
peripheral
Naþ
28.9
3.1
3.0
3.7
4.5
Csþ Baþ
15.0 22.9
1.8 3.2
0.8 1.1
3.0 6.9
2.9 7.5
NH4þ
21.1
1.3
c
2.7
Mg2þ
150d
10
11
12
15
Ba2þ
87.6
þ3.5
þ5.5
þ1.4
0.5
La3þ
279
þ16
þ18
þ 2.2
2.0
c
Absolute binding energy to the inside site given in the first data column. Second and third columns give the differences between the inside binding site and the two outside binding sites (energy with cation at inside site minus energy with cation at the specified outside site). A negative difference means that the outside site is preferred. Bold entries designate the differences of the most favorable inside and outside sites. b Comparisons of the binding strength to the inside corannulene site with binding to the axial or peripheral η6 sites of coronene. Negative numbers reflect greater binding stability to coronene compared with the corannulene inside binding site. c Converged local minimum not located. d Most stable inside site is the peripheral η6 site, taken as the reference value (see Figure 2). a
Table 2. Inside/Outside Preferences for the Three Outside Binding Sites of Bowl-30a inside binding strength on-axis η5site η6 site peripheral η5 site Naþ
29.8
0.1
2.4
2.2
Csþ
15.2
0.3
1.2
0.6
Mg2þ
(150)
2.8
5.0
10.7
Ba2þ
95.7
þ10.0
þ6.2
þ2.9
La3þ
313
þ36
þ30
þ17
Absolute binding energy to the inside site given in the first data column. The second through fourth columns give the differences between the inside binding site and the outside binding sites (energy with cation at inside site minus energy with cation at the specified outside site). A negative difference means that the outside site is preferred. Bold entries designate the differences of the most favorable inside and outside sites. a
The sp shell constituting the diffuse functions of the 6-31þg(d,p) basis on carbon usually led to a failure of linear independence of the basis, which the Gaussian package resolves by a variable and uncontrolled reduction in the number of basis functions (decreasing the actual basis-set size by as many as 30 for bowl-40 calculations). This basis-set truncation raises the calculated energy by as much as 6 kcal mol1 for bowl-40 complexes, making energy comparisons unreliable. The problem was largely resolved without sacrificing the inclusion of diffuse functions by the expedient of contracting the scale parameter of the diffuse shell on C by a factor of either 1.7 or 1.8. The use of the more compact diffuse functions gave only a small change in calculated energies (less than 1 kcal mol1) while completely or nearly suppressing the basis-set truncation effects. The commonly used B3LYP functional was employed here for consistency with frequent practices, but it has been suggested that the MPW1PW91 functional might give a more realistic metal-ionπ interaction.50 A few unsystematic trials with this functional, compared with B3LYP, gave stronger preference to binding inside the bowls by as much as several kilocalories per mole, suggesting that the B3LYP functional might underestimate the possibilities for encapsulation. It is well-known that DFT without specific corrections does not appropriately treat the weak, long-range dispersion interactions that are responsible for van der Waals complexes of neutral molecules.5153 This shortcoming is probably not important in the present cases, where stronger, shorter-range charge-induced multipole interactions provide the stabilization of the encapsulated metal-ion conformations. DFT/B3LYP with an adequate basis set has been found to give acceptably accurate thermochemical and IR spectroscopic predictions for a variety of metalion complexes (examples of this large literature can be found in refs 5457).
’ RESULTS AND DISCUSSION Quantum Chemical Results. With a few exceptions noted below, cations inside the bowl have only one potential energy minimum on or close to the symmetry axis. However, outsidebound cations have local potential energy minima located on top of each of the ring-centered sites, and the most stable binding site is often not the on-axis site. Accordingly, we investigated binding at all of the possible outside sites. For corannulene, there are two possibilities: the on-axis C5 site, and the five equivalent off-axis C6 sites. Bowl-30 has three possibilities: the on-axis C5 site, the set of central C6 sites, and the set of peripheral C5 sites. Bowl-40 has four possibilities, having all of the sites of bowl-30, plus an additional set of peripheral C6 sites around the edge of the bowl.
Table 3. Inside/Outside Preferences for Bowl-40 for Various Outside Binding Sitesa Inside binding strength
On-axis η5 site
Inner η6 site
Peripheral η5 site
Peripheral η6 site
Naþ
26.0
2.4
3.6
4.1
-5.1
Csþ
12.4
1.3
1.9
-2.4
-2.4
NH4þ
18.9
þ0.1
b
b
1.6
2þ
a
Mg
160
0.8
4.3
11.5
-12.6
Ba2þ La3þ
94 313
þ7.2 þ27
þ6.8 þ21
þ3.7 þ15
þ5.0 þ20
Best inside site is η6 on peripheral 6-membered ring. On-axis C5 site is less favorable by 6.5 kcal mol1. b Not calculated. a Positive value indicates preference for inside binding. Calculations at the B3LYP DZ*þ level. Table format the same as for Table 2. a
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Figure 2. Most favorable inside binding geometries for metal ions in bowl-40.
Figure 3. Differential energy between best outside and best inside binding sites.
Although the most stable binding sites were often located above rings other than the axial C5 ring, there was no tendency to move away from the center of a ring (η5 or η6, as appropriate) toward an off-center η3, η2, or η1 site. This behavior of the maingroup metal ions contrasts with that of transition-metal ions, for which such off-center sites are commonly reported in both experimental and computational structure determinations of bowl complexes. Some calculations with Agþ/corannulene were made in the present study, and it was found that the most stable locations, both inside and outside the bowl, were η2 to the outermost rim double bond. Local potential energy minima were found η5 along the symmetry axis, inside and outside, but they were substantially inferior to the rim sites.58 We have not attempted to compare this silver-ion thermochemistry with the main-group ions forming the subject of the present study. Most of our efforts considered the binding characteristics of small singly charged cations (Naþ) compared with large singly charged cations (Csþ, NH4þ) and with large doubly and triply charged cations (Ba2þ, La3þ). For illustration, Figure 2 shows graphically the calculated packing of the atomic-metal ions inside bowl-40. Tables 13 report these results for the three bowls, including both the absolute binding energy for inside-bound ions and also the differential binding energy between the inside-bound systems and a number of different outside-bound sites. For example, Naþ is bound by 28.9 kcal mol1 to the inside site, by 32.0 kcal mol1 to the most favored axial C5 outside site, and by 31.9 kcal mol1 to the less-favored outside C6 sites. The small-cation (Naþ) results show binding on the order of 30 kcal mol1 for corannulene (as is already well-known). Outside binding of Naþ to corannulene is favored by a significant margin (∼3 kcal mol1). A larger monocation (Csþ or NH4þ) fills the cavity more fully and might be expected to enhance inside binding because of its more intimate contact with the walls of the bowl cavity and more effective microsolvation. It was found that this is generally true, but that the effect is quite small. The large monocations have a somewhat lower preference for outside binding with bowl-30 and bowl-40, but inside binding is not actually favored in any case. The binding strength of these larger monocations to the bowls is low. Stronger effects are seen for the doubly charged Ba2þ cation and even more so for La3þ. The higher charge gives much stronger binding energies and also enhances the microsolvation effects acting to stabilize inside binding. The result is that inside binding is significantly favored for these ions with all three bowls.
It was suggested previously36 that transition-metal ions have unfavorable orbital interactions with the inside of the corannulene bowl, leading to a strong favoring for outside binding. Some calculations were done here for Agþ ion. It was again found that the presence of d electrons enhances the absolute binding strength greatly compared with that of main-group cations of similar size (more than 50 kcal mol1 binding strength to corannulene, inside binding is less favorable than outside binding, and the favored sites are η2 sites inside or outside the rim of the bowl). Bowl-30 introduces the additional complication that the axial outside binding site is not the most favorable point of attachment to the convex face. For the alkali monocations, the C6 rings give the most favorable binding sites. However, the differences among the three site types are small. For Ba2þ and La3þ, the peripheral C5 sites are the most favorable outside sites. It is found, just as for corannulene, that the alkali monocations favor outside binding, but the Ba2þ and La3þ ions prefer inside binding, which is true regardless of whether one is considering axial binding sites or the most favorable off-axis sites. Similar results were found for bowl-40: The best outside binding sites are either the peripheral C5 or peripheral C6 ring sites. Moreover, outside binding is favored for even the largest singly charged cations, but Ba2þ and La3þ favor inside binding. Figure 3 provides a graphical perspective on the inside/outside question, showing the preferences of all of the ions studied for inside versus outside binding to corannulene and bowl-40. Interestingly, corannulene has a slight but consistent tendency toward greater inside preference compared with bowl-40, for all cations regardless of charge. This is contrary to the expectation of better microsolvation of the cations by the deeper and tighterradius bowl-40 cavity. However, it might be explainable in terms of a relatively more favorable Coulomb potential on the outside surface of bowl-40, and this line of argument is explored in the following section. The overall conclusion is that binding is more favorable outside than inside for both small and large monocations and any benefit to inside binding arising from encapsulation and microsolvation of the ion is too small to overcome the intrinsically greater favorability of outside binding. This situation is reversed for the more highly charged Ba2þ and La3þ ions, which favor inside binding to all of the bowls. The fact that only Ba2þ and La3þ show a decisive preference for inside binding reflects the convergence of two factors: first, the large size of the Ba2þ ion allows optimal contact with the inside faces of the bowls, and 4971
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Table 4. MetalRing Distances: Distance between the Ion Center and the Plane of the Closest Aromatic Ringa,b metal ion þ
average outside distance (Å)
Na
2.3
Csþ Mg2þ
3.3 1.8
Ba2þ
2.5
La3þ
2.2
a
Outside bound, averaged over sites and bowls (in Å). b For comparison, the radii of curvature (Å) of the molecular frameworks are as follows: corannulene, 5.0; bowl-30, 3.9; bowl-40, 3.5; C60, 3.4.
second, the dication or trication gains a greater advantage from microsolvation due to the fact that the iondipole interaction (favoring outside binding) increases linearly with ion charge, whereas the polarization interaction (favoring inside binding) increases as the square of the ion charge. Ion size is also a factor, as can be assessed with reference to Table 4, which roughly estimates the relative ion sizes by noting the ion-to-ring distance in the outside-bound geometry averaged over different outside-binding sites. (The difference in binding distance for the different sites for a given metal ion is not large, so that an average gives a useful single-valued estimate.) The radii of curvature of the bowls considered as segments of a sphere are also given, with the idea that ions whose size is similar to the bowl radius will be comfortably packed inside, whereas those with smaller radii will be less efficiently microsolvated by the encapsulating bowl. The Mg2þ ion is evidently too small for effective polarization interaction with the inside surface of the bowls and shows a definite preference for outside binding. The bowl curvature is a further factor determining binding strengths (see curvature values given in Table 4 footnote b). It was suggested early in the study of fullerenes59 that the orbital hybidization at the C60 surface is affected by the surface curvature; the hybridization is such that there is decreased overlap with approaching ligand orbitals and weakened binding, relative to flat surfaces. Experimentally, Buchanan et al.41 reported stronger binding of iron cations to coronene than to C60. In a computational comparison of monocation binding to coronene and corannulene,36 it was found that binding to the outside of corannulene gave similar binding energies to the flat coronene face. Some additional comparisons between corannulene and coronene are indicated here in the last two columns of Table 1. For the mono- and dications, the binding to coronene is seen to be generally stronger by as much as a few kilocalories per mole. It is not possible to tell whether this effect reflects the bond-weakening curvature of corannulene, or the greater polarizability of coronene, or a combination of these two effects. For the La3þ trication, binding to coronene is sharply stronger than to the outside of corannulene, which must be a polarization effect from the higher polarizability of coronene. Perhaps a more informative comparison is that shown in Figure 4, which tracks the binding strength of four cations across the series of bowls. Along this series, the expected curvaturebased bond weakening is counteracted by the increasing polarization attraction as the bowl becomes more massive. The trends displayed in Figure 4 can be understood in these terms. The singly charged alkyl cations, having relatively weak polarization interactions, become somewhat more weakly bound with increasing bowl size and curvature. In contrast, the more highly charged cations, having stronger polarization interactions,
Figure 4. Binding strength relative to corannulene for each of four cations as a function of increasing bowl size. The values shown are for binding to the outside axial site, as derived from the first and second data columns of Tables 13.
increase their binding strength with increasing bowl size. (The trends in Figure 4 are shown for the outside axial C5 binding sites. Roughly similar results are found if the most favorable outside sites are compared, and making the comparison using the inside binding sites gives a similar but even more extreme contrast between cations of different charges.) This plot thus provides a further illustration of the competing effects of electrostatic versus polarization interactions and how these phenomena play out differently depending on the charge of the cation. Electrostatic Coulomb Potentials. Part of the story determining where ions prefer to bind to the bowls is the variation of the electrostatic Coulomb potential over the surface. Because this is the easiest factor to calculate and model, we first look at the expectations coming from this factor in comparison with the actually calculated binding site energetics. In this study, a distinction is drawn between the two types of electrostatic interactions of the ion with the neutral. The energy of the charged particle sitting in the electric field around the molecule is designated as the electrostatic Coulomb energy, Ecoul, whereas the energy gained by polarizing the neutral molecule in the presence of the ionic charge is designated as the polarization energy, Epolz. The present section looks at the correlation between the bowls’ binding characteristics, as described in the preceding section, and the shape of the Coulomb potential Vcoul [which is often referred to (as in ref 5) as the “electrostatic potential surface”]. Maps of these Coulomb potential fields, Vcoul(r), are shown in Figures 57, where the contour plots show the electric potential on a cross-sectional slice through a plane containing the symmetry axis. The electrostatic Coulomb energy is given by Ecoul = qVcoul, where q is the ion charge and Vcoul is the potential plotted in the figures. The present results resolve a puzzling feature of ref 5, which was that the bowls studied there, including corannulene and bowl-30, showed a much more negative electrostatic potential on the inside than the outside when calculated with an earlier DFT methodology (pBP/DN**), although their semiempirical AM1 and HartreeFock calculations gave the expected results of more negative potential on the outside. The present DFT B3LYP results clearly show more negative potentials outside than inside 4972
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Figure 5. Coulomb potential map of corannulene. The electrostatic potential is displayed on a cross-sectional plane containing the symmetry axis (xz plane). Potential contours are labeled in kilocalories per mole.
Figure 6. Coulomb potential map of bowl-30. The electrostatic potential is displayed on a cross-sectional plane containing the symmetry axis (xz plane). Potential contours are labeled in kilocalories per mole.
all three bowls. This is true if we compare inside and outside potentials along the axis, and it is also true if we compare corresponding minimum-potential regions lying above the C5 or C6 rings. For corannulene, the difference is modest, with the potential being on the order of 2 kcal mol1 more negative outside than inside (where the potential energy refers to a monocation). For bowl-30 and bowl-40, the differences are
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Figure 7. Coulomb potential map of bowl-40. The electrostatic potential is displayed on a cross-sectional plane containing the symmetry axis (xz plane). Potential contours are labeled in kilocalories per mole.
larger, with the potentials outside being on the order of 4 kcal mol1 more negative than at corresponding points inside. It seems that the unexpected DFT results in ref 5 must have reflected a problem with the particular DFT methodology used there. Our results confirm that these curved surfaces tend to have more negative electrostatic Coulomb potentials on the convex face than the concave face. For bowl-40, the Coulomb potentials both inside and outside the bowl are subsantially less negative than for the smaller bowls. There is, however, a large accumulation of negative charge outside the peripheral C5 and C6 rings, as shown by the large negatively charged zone in this region appearing in the crosssectional view in Figure 7. This negative potential around the outside periphery of the bowl is reflected in the substantially greater binding energy (Table 3) for the outside peripheral C5 and C6 regions, compared with the on-axis or inner C6 sites. None of the potential maps show regions of minimum Coulomb potential along the axis, either inside or outside. It is curious that the central C5 ring does not display a negative potential corresponding to a negatively charged π cloud sitting above or below it. However, all of the other C5 and C6 rings show regions of minimal (most negative) electrostatic potential above and below these rings, corresponding to the expected accumulation of electron density in the regions occupied by the aromatic π electrons. These features of the potential maps are in agreement with the HartreeFock electrostatic potential surfaces for corannulene and hemifullerene shown in ref 5. For binding on the outside surface of the bowl, the lowpotential sites on the Vcoul maps correlate well with the actual binding sites shown by the quantum calculations. For off-axis binding, the positions of the Coulomb potential wells and the positions of outside cation binding coincide in the regions of πelectron accumulation and negative Coulomb potential above the C5 and C6 rings. On the other hand, for inside binding, the Coulomb potential wells lie off-axis, whereas nearly all metal cations are found to bind most favorably at locations along the 4973
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The Journal of Physical Chemistry A axis. This apparent discrepancy indicates that these are situations where the short-range repulsive interactions cannot be ignored in comparison with the electrostatic forces, because the on-axis sites minimize the repulsive hard-sphere interactions with the interior walls of the bowl. The major discrepancy in this picture is on-axis outside sites. The outside on-axis site for all bowls is a favorable local potential energy minimum from the quantum calculations. However, no corresponding negative Coulomb potential minimum is calculated outside on the axis. It is genuinely surprising that the on-axis binding sites are so favorable, when the Coulomb potential maps would seem to imply spontaneous movement away from the axis out to the sites over the C6 rings. This is a good illustration of the inadequacy of looking at the electrostatic Coulomb forces as the sole determinant of favorable cation binding sites on the π surface.
’ CONCLUSIONS Factors favoring inside binding were found to be large ion size and high ion charge. Inside the bowl, nearly all cations were most favorably attached at the central site along the symmetry axis for all three bowls. Outside the bowl, corannulene favored on-axis binding of nearly all cations, but the larger bowls had various more-favorable off-axis sites located above C5 and C6 rings. Binding of monocations was more favorable outside than inside the bowls, although, for large monocations such as Csþ, the preference for the outside was low. Most striking is the strong preference for inside binding of the multiply charged ions Ba2þ and particularly La3þ. In contrast to some earlier findings with other theoretical methods, the hybrid B3LYP functional found the electrostatic Coulomb potential to be more negative on the convex face than the concave face for all three bowls. However, consideration of the electrostatic potential wells alone was not sufficient for correct prediction of the favored binding sites, emphasizing the fact that polarization interactions as well as Coulomb effects and short-range repulsions are also highly important. There is a real possibility of preparing some of these complexes as isolated gas-phase species using electrospray or matrix-assisted laser desorption/ionization (MALDI) mass spectrometry, assuming that the host bowl molecules will become available with the advancing successes of synthesis. A strong attraction of studying cationic guests as opposed to neutralneutral complexes is that, given a means of creating the complexes, there are then powerful tools for characterizing the structures of gas-phase ionic complexes, notably optical-spectroscopic approaches in both the infrared and the visible/UV spectral regions60,61 and also ion mobility spectrometry.62 The latter technique is particularly sensitive to structure distinctions such as the comparison of inside versus outside binding of a guest ion to a host bowl. Our findings have broader implications for biology, where functionalized forms of these building blocks have informed understanding of virus capsids, and for chemistry, where they expose contributions to basic interactions in hostguest complexes. The results here should also serve to guide future experimental and synthetic work. ’ ASSOCIATED CONTENT
bS
Supporting Information. Complete author lists for refs 48 and 49. Atomic coordinates and absolute energies for stationary states included in Tables 13. This material is available free of charge via the Internet at http://pubs.acs.org.
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’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
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