All-Carbon, Neutral Analogue of ExBox4+: A DFT Study of Polycyclic

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The all-Carbon, Neutral Analogue of ExBox : A DFT Study of Polycyclic Aromatic Hydrocarbon Binding Steven M. Bachrach, and Ann E. Andrews J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 16 Jul 2014 Downloaded from http://pubs.acs.org on July 16, 2014

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The Journal of Physical Chemistry

The all-Carbon, Neutral Analogue of ExBox4+: A DFT Study of Polycyclic Aromatic Hydrocarbon Binding Steven M. Bachrach* and Ann E. Andrews Department of Chemistry, Trinity University, 1 Trinity Place, San Antonio Texas 78212 Revised Manuscript ID: jp-2014-04408u

Abstract To assess the role that electrostatic interactions play in the binding of polycyclic aromatic hydrocarbons within ExBox4+ 1, we report ωB97X-D/6-311G(d,p) computations of the binding of five small linear acenes with the hydrocarbon neutral analogue 5 in both the gas phase and acetonitrile solution. The terphenyl units of 5 are less bowed outward than are the ExBIPY units of 5, due to the lack of charge repulsion. This manifests in a much smaller ring strain energy in 5 than 1. The acenes bind to both 1 and 5 with increasing affinity as the size of the guest increases. The affinity of the PAHs to 1 is greater than the affinity to 5, though the difference in the binding enthapies to 1 and 5 is relatively small, ranging from 2.4 to 9.8 kcal mol-1. Electrostatics account for only 10-20% of the total binding energy.

Keywords: Acene binding, Dispersion, Electrostatics, PAH, DFT, ExBox4+

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Molecular recognition plays a critical role in most biochemical processes. Chemists are now actively seeking ways of exploiting this concept of host-guest chemistry to prepare novel catalysts and materials.1-4 Synthetic hosts come in many shapes and sizes, and an intriguing new entry is the so-called ExnBox4+ series developed by Stoddart’s group. ExBox4+ 1,5 with a cavity of 3.5 Å x 11.2 Å using van der Waals radii, binds a variety of polycyclic aromatic hydrocarbons (PAHs) such as anthracene entirely within the interior. Tetracene, being too long to fit along the major axis, lies along a diagonal with its head and tail poking outside the host. The larger analogue Ex2Box4+ 2,6 with a cavity of 6.8 Å x 18.9 Å, can readily accommodate tetracene wholly inside its interior, and can also simultaneously bind two substituted benzenes. An interesting application is the binding of the non-planar PAH corranulene to the interior of 1.7 Since 1 preferentially binds planar species, it acts to appreciably lower the bowl inversion barrier of corranulene, a fantastic model of transition state stabilization afforded by a catalyst (or enzyme).

N

N

N

+

N

+

N

1

+

N

+

+

+

N

+

N

+

2

The tetrapositive charge on these hosts is dictated by the synthetic approach in their preparation; the macrocycle is constructed by using pyridine as a nucleophile toward attack at benzyllic


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halide positions. Use of TBAI as a catalyst dramatically improves the yield of these ExnBox4+ macrocycles.8 The tetrapositive ExBox4+ hosts should likely bind anionic species. The PAH compounds that bind to 1 and 2 have no charge, but potentially can bind electrostatically though their quadrupole moments. In addition, a PAH guest can interact through dispersion, including van der Waals interactions. The Goddard and Stoddart groups assessed the role of electrostatic interactions in the PAH binding to Ex2Box4+ through spectroscopy and computations.6 The complex of 2 with anthracene was computed at M06-2x/6-311G (with the Poisson-Boltzman solvation model for acetonitrile) to have a minimum energy structure with the anthracene positioned off of the center but aligned with the major axis, able to interact with two pyridinium rings. This suggests that a π-electron rich ring will favorably interact via electrostatics with the electron-poor pyridinium ring. Weak charge transfer bands are seen in the absorbance spectra of anthracene within 2. Similarly, the complex of 2 with 9,10-anthraquinone 3 is optimal when the guest is also displaced from the center of the host, able to interact with two pyridinium rings. However, in this case, no charge transfer bands are observed in the absorption spectra. This result conforms to the large computed HOMO-LUMO gap for this complex. Lastly, the complex of 2 with 1,4-anthraquionone 4 involves the interaction of the dipole of this guest. The most favorable complex has the electron-poor end of 4 near the middle of 2, to minimize its unfavorable interaction with the electron poor pyridinium rings. Both 3 and 4 bind more tightly to 2 than does anthracene, suggesting that in addition to an electrostatic component, van der Waals interactions and dispersion forces play an important role in the binding process.

3

4 3

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We present here an alternative means towards assessing the roles that dispersion and electrostatics may play in this type of complex. Specifically, we examine the exBox4+ analogue 5 which replaces the four pyridinium rings with four phenyl rings. This removes all of the positive charges from the macrocycle, making it neutral. The binding between 5 and a PAH should have negligible electrostatic interactions, with dispersion, in this case π-π stacking, playing the dominant role. We compare the results of computed binding energies of five small PAHs with 5 with our previous results9 for binding to 1.

5 Computational Methods In our previous study of the binding of 1 with the small PAHs benzene 6, naphthalene 7, anthracene 8, and tetracene 9 we found that experimental x-ray structures are well reproduced by computations performed at ωB97X-D/6-311G(d,p).9 In addition trends in binding energies for both the gas- and solution phase (using C-PCM and modeling for acetonitrile) are qualitatively in agreement with experiment. We have therefore used this method (ωB97X-D/6-311G(d,p))10 to examine the binding of the neutral analogue 5 with the PAHs 6-9. We also examined the complex of pentacene 10 with both hosts. A number of different conformations of 5 and configurations its complexes with the PAHs were fully optimized within the constraints of various point groups. All structures were determined to be local energy minima by computing the analytical frequencies and confirming that they possess only real vibrational frequencies. Highly symmetric structures of the complexes often possessed one or more imaginary frequencies. These structures were distorted along the direction of the vector associated with


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the imaginary frequency and reoptimized. Select complexes were also examined at B3LYP11-14-D315/6311G(d,p), using Becke-Johnson16-19 damping. To assess the role of solvent, the structures were completely reoptimized using the conductor-like polarizable continuum model (C-PCM)20 with ωB97XD/6-311G(d,p). The unscaled zero-point vibrational frequencies were utilized in computing enthalpy and free energies, incorporating the quasiharmonic approximation of Truhlar and Cramer21 whereby lowfrequency modes (less than 100 cm-1) were raised to 100 cm-1 for the computation of the vibrational partition functions. We report here enthalpies and free energies evaluated at 25 °C and 1 atm. All of the computations were performed using Gaussian-09, rev. A.02 or rev.D.01.22

Results Structure of 5. The triphenyl components of 5 can be found in two conformations that minimize the ortho-ortho’ interactions, having an alternating orientation 11a or helical orientation 11b.23 The difference in enthaply of these two conformations at ωB97X-D/6-311G(d,p) is less than 0.01 kcal mol-1. Thus, the five generic structures of 5 composed of two alternative triphenyl units (with nominal C2v or C2h symmetry) or two helical triphenyl units (with nominal D2 or C2h symmetry) or with one alternating and one helical triphenyl unit (with C1 symmetry) are likely to have similar energies.

11a

11b

The five identified different conformations of 5 agree with this expectation. Their structures are shown in Figure 1. Unlike the optimized structures of 1 which conform precisely with the expected symmetries, the conformations with two helical triphenyl units optimize to lower point groups (the D2 structure reduces to C2 and the C2h structure reduces to Ci) and the C2h structure with alternating triphenyl units reduces to Cs. The relative energies of these conformations are listed in Figure 1. As expected the range in energy is very small; only 1.20 kcal mol-1 separate the five conformations. The



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conformations with alternating triphenyl units are slightly favored in energy. This is also true with 1, though (a) the energy range of the conformations of 1 is twice as large as with 5 and (b) the C2v structure is the lowest energy form of 1 while it is the C2h-derived structure that is the lowest conformation of 5. A key feature of 5 is its cavity. A measure of the size of the cavity is the distance between the centroids of the middle phenyl ring of each terphenyl unit. This distance is 7.38 Å in 5. The analogous distance is much larger in 1: 8.56 Å. The formal positive charges on each of the pyridinyl rings acts to push the ExBIPY units farther apart in 1, while this electrostatic repulsion is absent in 5.


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5b, C2v 0.10 0.70

5a, Cs 0.0 0.0

5d, Ci 0.74 0.04

5c, C1 0.41 -0.60

5e, C2 1.20 1.38 Figure 1. ωB97X-D/6-311G(d,p) optimized conformations of 5. Relative enthalpies (kcal mol-1) and free energies (italics).



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The outward bowing of the terphenyl units of 5 reflects some strain. A sense of this can be gained by examining the angle formed from the centroids of each of the three phenyl rings in a terphenyl unit. This angle would be 180° in an unstrained terphenyl moiety. The angle is 173.6° and 172.1° for the two triphenyl units of 5a. (The analogous angle in 1 is 166.0°.) To evaluate the ring strain energy of 5 we employ the group equivalent reaction24 shown in Scheme 1. This is analogous to the reaction used to evaluate the ring strain energy of 1.9 Fully optimizing all of the molecules of Reaction 1 at ωB97X-D/6-311G(d,p) and using their enthalpies, we arrive at a ring strain enthalpy of 5 of 5.2 kcal mol-1. The ExBox4+ analogue 5 is clearly not very strained. Scheme 1.

2

+ 4

+ 2

+ 8

5 Comparison to the ring strain energy of 1 is complicated by the fact that 1 is a tetracation. With our approximate treatment to remove the effects of electrostatic repulsion, we estimated the strain energy of 1 to be about 20 kcal mol-1.9 The greater strain energy of 1 than 5 is seen in the greater outward bowing of the ExBIPY units due to electrostatic repulsion by the four positive charges of 1. Assessing the computed binding enthalpy and free energy. The binding free energy (in acetonitrile solution) of the PAHs 6-9 to 1 we previously calculated range from -3.9 to -21.8 kcal mol-1.9 The experimental value for the binding free energy of 8 with 5 is only -4 kcal mol-1.5 Similarly the experimental binding enthalpy of phenanthrene and pyrene to 1 is about 6 kcal mol-1, much smaller than 8 ACS Paragon Plus Environment

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the computed binding enthalpies of the 6-9 with 1. This raises a concern regarding the appropriateness of the computational methodology. To address this concern, we computed the gas an solution phase binding of anthracene and tetracene with both 1 and 5 at B3LYP-D3/6-311G(d,p). This method, which has an explicit dispersion correction, has been shown to adequately treat a variety of complexes where dispersion is the key to the binding.25-27 The values of the enthalpy and free energy of binding computed at both B3LYP-D3 and ωB97X-D are presented in Table 1. The difference in the binding enthalpy between the two methods is less than 2.5 kcal mol-1 and the difference in the binding free energy is even less in both gas and solution phases. This agreement suggests that the difference in the experimental and computational binding energy values is not due to a methodological failure.

Table 1. Comparsion of Computed Enthalpy and Free energy of Bonding (kcal mol-1) of hosts 1 and 5 with PAHs 8 and 9. Gas ωB97X-D

Solution B3LYP-D3

ωB97X-D

B3LYP-D3

ΔH

ΔG

ΔH

ΔG

ΔH

ΔG

ΔH

ΔG

1:8

-38.48

-22.85

-36.56

-21.11

-35.11

-18.84

-32.72

-17.08

1:9

-45.57

-29.33

-43.53

-27.69

-38.17

-21.80

-37.96

-22.16

Rather, the difficulty lies in considering what is measured in the experiments and what is measured in the computations. The computations measure the energy associated with the binding of a PAH with 1 to form the host:guest complex: the energy of the reaction 1 + PAH → 1:PAH. This is not what is being measured in solution. The host 1 is a tetracation and the solution contains counterions, in this case four PF6- molecules. The x-ray structure of the 14+.4PF6- crystal shows one anion within the 9 ACS Paragon Plus Environment


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interior of the host.5 We computed both the gas and solution phase complex of 1 with one PF6molecule, and the anion is located in the center of the host (see Supporting Materials). Therefore, the experiment measures the competition of the host for PAH vs. PF6-. Assuming that only one PF6- molecule needs to be displaced, the experiment measures the equilibrium of the reaction 14+:PF6- + PAH ↔ 14+:PAH + PF6-. Since the computed binding enthalpy of 1 with PF6- is -16.2 kcal mol-1 (the binding free energy is -4.2 kcal mol-1), this value need to be subtracted from the computed binding energies of the PAHs in order to compare with experiment. This gives binding enthalpies and free energies that are much closer to experiment, but one must consider that this approach assumes only one counterion is displaced when a PAH binds to 5; if on average more than one counterion is displaced, the agreement between experiment and computation will improve. We therefore believe that our computations do present an appropriate treatment of the complexes of PAHs with these hosts.

Gas-Phase Complexes of 5 with PAHs 6-10. The search for configurations of the complexes of 5 with the five small PAHs 6-10 began by placing the guest in the center of the host with maximal symmetry. If the optimization ended with a structure possessing one or more imaginary frequencies, the structure was distorted in the direction of the motion corresponding to one the imaginary frequencies. Multiple different conformations of the host 5 were also examined. We discuss here only the lowest energy configuration. Other optimized configurations are presented in the Supporting Materials. The lowest energy configuration of the 5:6 complex positions the benzene guest well off-center, near one side of the host. This structure is shown in Figure 2. This asymmetrical structure is similar to the complex formed of 1 with 6. Naphthalene 7 positions itself just slightly off of the center of the host 5, much nearer the center of the host than in the 1:7 complex.


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5:6

5:7

5:8 (top) 5:8 (side)

5:9 (side)

5:10 (side)

5:9 (top)

5:10 (top)

Figure 2. Optimized geometries of the clusters between host 5 and guest PAHs 6-10. 11 ACS Paragon Plus Environment


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The lowest energy cluster formed of 5 and anthracene 8 has Ci symmetry. The view from the top, shown in Figure 2, shows the molecules entirely within the host, positioned in the center of the host. The 1.8 complex has C2v symmetry, with the guest nicely housed within the macrocycle cavity. The 5.8 complex with C2v symmetry has two imaginary frequencies. The complex between 5 and tetracene 9 also has an overall structure quite similar to that of the ExBox4+ analogue 1:9. Tetracene is too long to fit within the cavity of either host, and so it twists, no longer aligning with the major axis, and the terminal phenyl groups poke outside the confines of the macrocycle. This can be readily observed in the top view of the 5:9 complex in Figure 2. The complex between pentacene 10 and both host 1 or 5 are similar to the 1:9 and 5:9 complexes. These guests are too long to fit within the interior of either host, and so they twist and the termini extend outside the hosts (see Figure 2). The cavity of 5 is narrower than that of 1; the distance between the centroid of the central phenyl ring of the two triaryl units is 1.17 Å smaller in 5 than in 1. The two hosts respond differently when a PAH is placed inside. As listed in Table 2, the triaryl units, referred to as ExBIPY, of 1 move closer to each other, creating a smaller cavity when the PAH is placed inside, and this distance decreases in the series 6 to 9, but then increases with 10. On the other hand, the distance between the centroids of the middle phenyl ring of the ExBIPY units of 5 increases when 6, 7, or 8 is bound by as much as 0.18 Å. However, when tetracene 9 is bound, the cavity shrinks to 7.22 Å, 0.16 Å smaller than in the free host 5, but then increases with the binding of 10. Similar behavior is seen in the major axis. With host 1, the major axis increases in the series 6 to 9, while with host 5, the major axis is essentially unchanged with 6-8 as guests, but with 9, the major axis increases by over 0.1 Å. Binding of 10 leads to a reduction in the major axis for both hosts.


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Table 2. Distances (Å) of the Major and Minor axis of the host.a 5 Gas

a

1 Solution

Gas

Solution

Guest

major

minor

major

minor

major

minor

major

minor

none

14.667

7.385

14.692

7.317

13.961

8.557

14.427

7.463

6

14.612

7.511

14.625

7.490

14.139

8.001

14.421

7.350

7

14.600

7.564

14.599

7.564

14.259

7.689

14.396

7.322

8

14.611

7.557

14.580

7.622

14.366

7.569

14.482

7.355

9

14.730

7.225

14.732

7.250

14.403

7.335

14.523

7.075

10

14.661

7.428

14.668

7.479

14.338

7.517

14.416

7.274

Minor axis: the distance between the centroids of the central phenyl ring of the triaryl units; and Major

axis: the distance between the centroids of the phenyl ring in the monophenyl units.

The binding energy for the formation of the cluster between 5 and the PAHs are listed in Table 3. As might be expected, the binding enthalpy increases with the size of the guest. Benzene is bound by nearly 16 kcal mol-1 and this increases to 41 kcal mol-1 for pentacene. The free energy of binding is less than the binding enthalpy, principally due the loss of entropy upon binding. Nonetheless, the bindings of all five PAHs are predicted to be exoergonic, ranging from -5 (for benzene) to -24 kcal mol-1 (for tetracene).



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Table 3. Gas and Solution Phase (Acetonitrile) Binding Enthalpies and Free Energies (kcal mol−1) for the Reaction 5 + X → 5·X and 1 + X → 1·X 5 + X → 5·X Gas

1 + X → 1·X Solution

Gas

Solution

Guest

ΔH

ΔG

ΔH

ΔG

ΔH

ΔG

ΔH

ΔG

6

-15.86

-10.00

-13.79

-8.22

-18.24

-6.68

-15.64

-3.89

7

-23.75

-16.03

-22.43

-5.82

-26.25

-12.50

-24.42

-10.36

8

-33.48

-17.35

-29.46

-13.33

-38.48

-22.85

-35.11

-18.84

9

-37.14

-19.92

-33.03

-16.55

-45.57

-29.33

-38.17

-21.80

10

-41.13

-24.28

-35.44

-18.43

-50.91

-33.03

-38.25

-21.29

Solution-Phase Complexes of 5 with PAHs 6-10. The geometries of 5 and the complexes formed with 5 as the host and the PAHs 6-9 as guests were reoptimized using the C-PCM method modeling acetonitrile as the solvent. The geometry of 5 is little changed when placed into solution (see Table 1). This is quite different than the changes seen in the geometries of 1 in gas and solution phase. In solution, the minor axis of 1 is considerably smaller than in the gas phase. This can be understood in terms of the solvent screening the electrostatic repulsions between the positive charges on the two ExBIPY units, allowing them to come closer and relieve some of the geometric strain. The optimized solution-phase structures of the complexes with host 5 differ only modestly from their gas phase analogues. Again much larger geometric differences are observed in the gas vs. solution phases of the complexes with the tetrapositive host 1. The solution-phase binding energetics of 5 with the PAHs are listed in Table 3. As expected, the binding is both less exothermic and less exoergonic in solution than in the gas phase. The binding enthalpy is about 3-4 kcal mol-1 less exothermic in solution than in the gas phase, while the binding is 212 kcal mol-1 less exoergonic in solution. This was previously observed for the binding of 1 with the 14 ACS Paragon Plus Environment

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PAHs.9 However, the notable difference is that in general the effect of moving from gas to solution phase results in a larger change for PAH binding to 1 than to 5.

Discussion Replacement of the four nitrogen atoms in ExBox4+ 1 to form the neutral analogue 5 results in some structural and energetic changes. The size of a pyridinyl ring is essentially the same as a phenyl ring (the N-C4 distance is 2.79 Å in pyridine vs. the C1-C4 distance of 2.78 Å in benzene, computed at ωB97X-D/6-311G(d,p)) and so one might expect the major and minor axes to have similar sizes. However, the geometries of 5 and 1 differ: the major axis is about 0.7 Å shorter in 1 than in 5, while the minor axis is almost 1.2 Å longer in 1 than in 5. The large outward bowing of the ExBIPY fragment of 1 compared to the far less bowed terphenyl fragment of 5 can be attributed to the electrostatic repulsion between the positive charges carried by these fragments in 1. This repulsion is somewhat reduced in solution, where the solvent partially screens the repulsion. The minor axis of 1 in acetonitrile solution is predicted to be about 1.1 Å shorter than in the gas phase. In contrast, 5, which by being neutral suffers little from self-electrostatic repulsions, is only 0.06 Å shorter in solution than in the gas phase. The significant outward bowing of the ExBIPY groups in 1 manifests in a strain energy that we estimated to be about 20 kcal mol-1.9 Our estimate of the strain energy of 5, using the group equivalent reaction shown in Scheme 1, is only 5.2 kcal mol-1. Though the two hosts do differ somewhat in their geometries, when a guest is present, their structures are remarkably similar. When 1:9 and 5:9 are aligned, their structures nearly coincide, as seen in Figure S2. The largest difference in the position of analogous atoms is 0.29 Å (for atoms in the phenyl rings at the sides), with an average difference in position of the hosts of 0.11 Å. A PAH guest within 1 screens the repulsion between the formal charges on the host, allowing the ExBIPY fragments to move inward, similar to the effect of solvent on the structure of 5.



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The key question here is whether 1 and 5 bind PAHs with differing affinity. Though the size of the cavities of the two hosts are similar, the binding of PAHs might reflect not just the affinity for the host but also an energetic contribution associated with a change in the geometry of the host upon binding the guest. One might thus consider the binding energy to be the sum of the distortion energy of the host and the interaction energy between the distorted host and the PAH guest. To assess this distortion energy contribution, we have computed the energy of 1 and 5 in the geometry found within the complexes with the PAHs. These distortion energies are listed in Table 4.

Table 4. Distortion energy (kcal mol-1) of the hosts 1 and 5 PAH

1

5

difference

6

1.42

0.74

0.68

7

1.78

0.79

0.99

8

2.26

1.16

1.10

9

3.86

1.69

2.17

10

5.04

2.67

2.37

For both hosts, the distortion energy increases with the size of the guest. For all PAH guests, the distortion energy is larger for 1 than for 5, but in all cases it is less than 5 kcal mol-1. Most importantly, the difference in the distortion energy of the two hosts with any given PAH is small, ranging from 0.7 kcal mol-1 with benzene to 2.4 kcal mol-1 with pentacene. The contribution of the distortion energy to the overall binding is thus only slightly larger (no greater than 2.5 kcal mol-1) for the complexes involving 1 than for 5. So, the major difference in any binding affinity between these two hosts should be attributable to the tetrapositive charge on 1 and the absence of any charge on 5. In other words, the relative binding affinities of 1 vs. 5 should be a measure of the role of electrostatics in the binding of PAHs.


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Inspection of Table 3 reveals a number of important trends and differences between the binding affinities of these two hosts. These trends are also displayed in the plots of enthalpy or free energy of binding involving the two hosts (see Figure 3). A few trends are in common for the two hosts. In the gas phase (Figure 3a), the binding enthalpy and free energy involving 1 increases with the number of π electrons in the guest, this despite the fact that tetracene and pentacene do not entirely fit inside the host cavity. The trend is nearly linear for the first four PAHs, but the curve flattens out with pentacene. While the binding of the PAHs to 5 does also increase with the number of π electrons in the guest, the binding enthalpy and free energy curves flatten with 9 and 10. In solution (Figure 3b), the binding enthalpies and free energies to both hosts increases with the size of the PAH, but the relationship is decidedly non-linear. The binding of tetracene and pentacene in both hosts in solution appear to be near an asymptote in both the binding enthalpy and free energy.

(a) Gas

0 -10

ΔH or ΔG (kcal/mol)

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Number of π e in acene (guest) (b) Solution 17 ACS Paragon Plus Environment


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Number of π e in acene (guest) Figure 3. Computed gas- (a) and solution phase (b) binding enthalpy (red) and free energy (green) vs. number π electrons in the guest acene. Squares indicate binding with host 1 and diamonds indicate binding with host 5. As expected for both hosts, the binding enthalpy is more negative than is the binding free energy. This results from the loss of entropy upon binding. Nonetheless, the binding of all of the PAHs to both hosts is predicted to be exergonic in both gas and solution phases. In all cases – for all PAHs and in gas and solution phases – the binding enthalpy is always more negative (i.e. stronger) with the tetrapositive 1 than with the neutral host 1. The free energy of binding is also more negative with 1 than with 5, with the exception of benzene and naphthalene (gas only). These exceptions include the complexes that have a large number of very low frequency vibrations, which can lead to some errors in computing their entropy contributions. The key element here is that the differences in binding energies to the two hosts is not uniform across the PAH series. In the gas phase, the binding energies of either host with benzene or naphthalene are similar, differing by less than 3 kcal mol-1. For the larger PAHs, 8-10, the binding to 1 is preferential by at 5 to 10 kcal mol-1. Both 9 and 10 prefer to bind to 1 over 5, though that preference is similar: 8.4 kcal mol-1 for 9 18 ACS Paragon Plus Environment

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and 9.8 kcal mol-1 for 10. In solution, the differential preference for binding to 5 over 1 is much smaller than in the gas phase, ranging from 2 to 6 kcal mol-1. The largest difference occurs with anthracene, whose binding enthalpy towards 1 by 5.6 kcal mol-1 greater than towards 5. In fact, the difference in the binding enthalpy of pentacene towards the two hosts is only 2.8 kcal mol-1. The binding of a neutral PAH to the interior of both 1 and 5 will involve dispersion and van der Waals interactions. Since the major difference in the two hosts is the tetrapositive charge on 1 vs. the neutral charge on 5, the stronger binding with 1 must reflect an electrostatic component of the interaction of the PAH with this charged host, an interaction not present with the neutral host 5. The electrostatic component is a monopole (1)—quadrupole (PAH) interaction. Maximizing this interaction requires the PAH to position itself near the pyridinyl rings where the formal charge is located. This is clearly seen in the structures of 1:6 and 1:7, where the guests are located far off center. The major electrostatic benefit comes, however, when the host can interact with all four pyridinyl cations, and this occurs with the larger PAHs anthracene and tetracene. The closest approach of a carbon and hydrogen of anthracene to a nitrogen atom of 1 in 1:8 is 3.852 and 3.456 Å, respectively. In the 1:9 complex, the closest approach of a carbon on tetracene to a nitrogen is about the same as in 1:8, namely 3.889 Å, but a hydrogen gets much closer in 1:9 than in 1:8: 3.173 Å. This close approach of the tetracene to the (formally) positive charged nitrogen atoms, even though parts of the terminal rings poke outside the confines of the host, manifests in its strong binding to 1. Pentacene binds to 1 more strongly than tetracene does, despite the fact that it is not as close to the formal positive charges on nitrogen; the closest approach of a carbon and hydrogen of 10 to nitrogen is 4.115 and 3.363 Å, respectively. The 5:9 and 5:10 complexes also have the guests extending outside the host, but without the electrostatic component, this means that only increasing dispersion interactions account for the increasing binding enthaplies. The increasing surface area of the guest that extends outside of the host in the series 8 to 9 to 10 leads to the tailing off in the increase in binding enthalpy, especially in solution (see Figure 3b).



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The reduction in the PAH binding energy difference between 1 and 5 in solution relative to the gas phase results from preferential solvation of the charged species. Solvation stabilizes 1, due to its tetrapositive charges, significantly more than it stabilizes neutral 1. This leads to a greater reduction in binding energies associated with 1 than 5. The most important trend in the binding energies is that binding to 1 is greater than binding to 5. This implicates an electrostatic component to the binding of neutral PAHs to the charged ExBox4+ 1. However, it is critical to note that the enhancement of binding due to this electrostatic contribution is relatively small. The differences in the PAH enthalpy of binding in the gas phase of the two hosts ranges from 2.4 (with benzene) to 9.8 kcal mol-1 (with pentacene). On a percentage basis of the total gas phase binding enthalpy, the electrostatic contribution extends from 9.5% (naphthalene) to 19.2% (pentacene). The increasing electrostatic contribution with guest size does correlate with the increasing size of the quadrupole moment of the guest. Nonetheless, non-electrostatic (i.e., interactions other than monopolar-quadrupolar) account for the majority of the binding to 1.

Conclusions The recently reported macrocycle host ExBox4+ 1 binds polycyclic aromatic hydrocarbons.5 In order to assess the role of electrostatic interaction in this binding, we have computed the binding of four small linear acenes with the all-carbon neutral analogue 5. Since the geometry of a pyridinyl ring and phenyl ring are very similar, these two hosts should have similar physical dimensions, and so any differences in their binding affinities would reflect the electrostatic component of binding. The two hosts 1 and 5 do differ somewhat in geometry. The tetrapositive 1 has a larger minor axis and shorter major axis than 5. This distortion, primarily the large outward bowing of the ExBIPY units of 1, results from the repulsions between the positive charges. This manifests in substantially more ring strain energy in 1 (20 kcal mol-1) than in 5 (5 kcal mol-1).


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The four linear acene guests 6-9 bind to the interior of 1 and 5, with increasing affinity with increasing size of the guest. Binding affinity is greater in the gas phase than in acetonitrile solution. The most significant result is that the binding enthalpy to 1 is only 2.4 to 9.8 kcal mol-1 greater than the binding to 5. This implicates an electrostatic component in the binding of PAHs to ExBox4+ 1, however it amounts to only 9.5% to 19.2% of the total binding enthalpy. Thus, non-electrostatic contributions dominate the binding of PAHs to neutral and even charged hosts.

Supporting Material

Full citation for Ref. 22, Figures S1 and S2, and coordinates and absolute energies of 1:PF6, 5 and the 5:PAH complexes. This material is available free of charge via the Internet at http://pubs.acs.org.

Author Information Corresponding Author: E-mail: [email protected]. Notes: The authors declare no competing financial interest.

Acknowledgment The authors thank Trinity University for the computational resources utilized in this project and the suggestions of two referees that strengthened the logic behind this study. We thank Prof. Chris Cramer and Will Isley for a script to perform the quasiharmonic approximation.



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References (1) Beer, P. D.; Gale, P. A.; Smith, D. K. Supramolecular Chemistry; Oxford University Press: Oxford, UK, 1999. (2) Lehn, J.-M. Supramolecular Chemistry: Concepts and Perspectives; VCH: Weinheim, 1995. (3) Steed, J. W.; Atwood, J. L. Supramolecular Chemistry; Wiley-VCH: Weinheim, Germany, 2009. (4) Supramolecular Chemistry: From Molecules to Nanomaterials; Steed, J. W.; Gale, P. A., Eds.; WileyBlackwell: Oxford, UK, 2012. (5) Barnes, J. C.; Juríček, M.; Strutt, N. L.; Frasconi, M.; Sampath, S.; Giesener, M. A.; McGrier, P. L.; Bruns, C. J.; Stern, C. L.; Sarjeant, A. A.; Stoddart, J. F. ExBox: A Polycyclic Aromatic Hydrocarbon Scavenger. J. Am. Chem. Soc. 2013, 135, 183-192. (6) Juricek, M.; Barnes, J. C.; Dale, E. J.; Liu, W.-G.; Strutt, N. L.; Bruns, C. J.; Vermeulen, N. A.; Ghooray, K.; Sarjeant, A. A.; Stern, C. L.; Botros, Y. Y.; Goddard, W. A.; Stoddart, J. F. Ex2Box: Interdependent Modes of Binding in a Two-Nanometer-Long Synthetic Receptor. J. Am. Chem. Soc. 2013, 135, 12736– 12746. (7) Juríček, M.; Strutt, N. L.; Barnes, J. C.; Butterfield, A. M.; Dale, E. J.; Baldridge, K. K.; Stoddart, J. F.; Siegel, J. S. Induced-Fit Catalysis of Corannulene Bowl-To-Bowl Inversion. Nat. Chem. 2014, 6, 222-228. (8) Barnes, J. C.; Juríček, M.; Vermeulen, N. A.; Dale, E. J.; Stoddart, J. F. Synthesis of ExnBox Cyclophanes. J. Org. Chem. 2013, 78, 11962-11969. (9) Bachrach, S. M. DFT Study of the ExBox·Aromatic Hydrocarbon Host–Guest Complex. J. Phys. Chem. A 2013, 117, 8484-8491. (10) Chai, J.-D.; Head-Gordon, M. Long-Range Corrected Hybrid Density Functionals with Damped AtomAtom Dispersion Corrections. Phys. Chem. Chem. Phys. 2008, 10, 6615-6620. (11) Becke, A. D. Density Functional Thermochemistry. III. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648-5650.


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(12) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. Rev. B 1988, 37, 785-789. (13) Vosko, S. H.; Wilk, L.; Nusair, M. Accurate Spin-Dependent Electron Liquid Correlation Energies for Local Spin Density Calculations: A Critical Analysis. Can. J. Phys. 1980, 58, 1200-1211. (14) Stephens, P. J.; Devlin, F. J.; Chabalowski, C. F.; Frisch, M. J. Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields. J. Phys. Chem. 1994, 98, 11623-11627. (15) Grimme, S.; Antony, J.; Ehrlich, S.; Krieg, H. A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu. J. Chem. Phys. 2010, 132, 154104-154119. (16) Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456-1465. (17) Becke, A. D.; Johnson, E. R. A Density-Functional Model of the Dispersion Interaction. J. Chem. Phys. 2005, 123, 154101. (18) Johnson, E. R.; Becke, A. D. A Post-Hartree–Fock Model of Intermolecular Interactions. J. Chem. Phys. 2005, 123, 024101. (19) Johnson, E. R.; Becke, A. D. A Post-Hartree-Fock model of Intermolecular Interactions: Inclusion of Higher-Order Corrections. J. Chem. Phys. 2006, 124, 174104. (20) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. Energies, Structures, and Electronic Properties of Molecules in Solution with the C-PCM Solvation Model. J. Comput. Chem. 2003, 24, 669-681. (21) Ribeiro, R. F.; Marenich, A. V.; Cramer, C. J.; Truhlar, D. G. Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation. J. Phys. Chem B 2011, 115, 1455614562.



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Inc.: Wallingford CT, 2009. (23) Bachrach, S. M.; Stück, D. DFT Study of Cycloparaphenylenes and Heteroatom-Substituted Nanohoops. J. Org. Chem. 2010, 75, 6595-6604. (24) Bachrach, S. M. The Group Equivalent Reaction: An Improved Method for Determining Ring Strain Energy. J. Chem. Ed. 1990, 67, 907-908. (25) Hujo, W.; Grimme, S. Performance of Non-Local and Atom-Pairwise Dispersion Corrections to DFT for Structural Parameters of Molecules with Noncovalent Interactions. J. Chem. Theor. Comput. 2013, 9, 308-315. (26) Grimme, S. Density Functional Theory with London Dispersion Corrections. WIREs Comput. Mol. Sci. 2011, 1, 211-228. (27) Grimme, S. Supramolecular Binding Thermodynamics by Dispersion-Corrected Density Functional Theory. Chem. Eur. J. 2012, 18, 9955-9964.


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All-Carbon, Neutral Analogue of ExBox4+: A DFT Study of Polycyclic

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