Unexpected Nonadditivity Effects in Anion−π Complexes - The Journal

ARTICLE pubs.acs.org/JPCA

Unexpected Nonadditivity Effects in Anion
π Complexes Carolina Estarellas, Antonio Frontera,* David Qui~nonero, and Pere M. Deya Departament de Quimica, Universitat de les Illes Balears, 07122 Palma de Mallorca, Spain

bS Supporting Information ABSTRACT: Several complexes of fluorine-substituted ethyne, ethene, butadiene, benzene, and [n]radialenes (n = 3
5) with two anions have been optimized at the RI-MP2/aug-cc-pVTZ level of theory. The additivity of the anion
π interaction was studied depending on the number of double bonds and fluorine atoms. Interesting nonadditivity effects were observed in the aromatic and antiaromatic complexes, which were analyzed by partitioning the total interaction energy into individual components, using Bader’s theory of “atoms in molecules” and changes in the aromatic character of the ring upon complexation.

’ INTRODUCTION In many fields, weak noncovalent interactions have a essential role, because the chemical and biological mechanisms derived from noncovalent binding represent intelligent and elegant utilization of the interactions between molecules.1 In biology, these interactions are the origin of a large number of processes with impressive efficiencies. In chemistry, interactions between predesigned binding centers are able to achieve complex functions in highly organized molecular systems. This is one fundamental aspect of research into supramolecular chemistry, which is often inspired by biological systems and mechanisms.2,3 A deep understanding and accurate description of interactions between organic molecules even in the condensed phase is needed, including the mechanisms of molecular recognition. In particular, interactions involving aromatic rings play an essential role in chemistry and biology.2c The role of aromatic interactions becomes prominent in drug
receptor interactions, crystal engineering, and protein folding, among other applications.4 Actually, it has been estimated that around 60% of aromatic side chains (histidine, phenylalanine, tyrosine, tryptophan) participate in π
π stacking interactions in proteins.5 Finally, a newer and consequently less studied aromatic interaction is the anion
π interaction. However, the importance of this interaction (a noncovalent force between an electron-deficient aromatic system and an anion) has been widely demonstrated by a great deal of theoretical6 and experimental7
9 investigations. Several pioneering theoretical studies revealed that these interactions are energetically favorable.6 Anion
π interactions are gaining significant recognition, and their pivotal role in many key chemical and biological processes is being increasingly recognized.10 The design of highly selective anion receptors and channels11
13 represents significant progress in this nascent field of supramolecular chemistry. The additivity of the anion
π interaction has been studied using s-triazine and trifluoro-s-triazine as electron-deficient aromatic r 2011 American Chemical Society

rings by computing the energy of anion
πn complexes where n varies from 1 to 3.14 In this work, we studied the additivity from a completely different point of view. Instead of varying the number of aromatic rings, here, we studied the influence of the number of double bonds and fluorine substituents on the anion
π interaction while keeping the stoichiometry of the complex the same. This procedure allowed effects such as conjugation, aromaticity, and number of substituents to be taken into account. We used ab initio calculations at the RI-MP2/aug-cc-pVTZ level of theory to compute the interaction energies of complexes of halides and fluorinated derivatives of ethyne, ethene, butadiene, benzene, and [n]radialenes (n = 1
3) (see Figure 1). Nonadditivity effects were analyzed in terms of energetic, geometric, and chargetransfer properties and Bader’s theory of atoms-in-molecules depending on the numbers of double bonds and fluorine atoms in the π system.

’ THEORETICAL METHODS The geometries of all complexes included in this study were optimized at the RI-MP2(fc)/aug-cc-pVTZ level of theory using the program TURBOMOLE, version 5.10.15 (See the Supporting Information.) The RI-MP2 method16,17 applied to the study of cation
π and anion
π interactions (among others) is considerably faster than the MP2 method, and the interaction energies and equilibrium distances are almost identical for the two methods.18,19 The binding energies were calculated with corrections for basis set superposition error (BSSE) using the Boys
Bernardi counterpoise technique.20 Charge-transfer effects were studied using Merz
Kollman population analysis21 for deriving atomic charges. In the optimization of the complexes, we imposed the highest possible abelian symmetry group. Received: April 25, 2011 Revised: May 24, 2011 Published: May 27, 2011 7849

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Table 1. Interaction Energies at the RI-MP2/aug-cc-pVTZ Level of Theory with the BSSE Corrections (EBSSE, kcal/mol), Equilibrium Distances from the Anion to the Mean Plane (Re, Å) for Complexes 16
45, and Computed Merz
Kollman Charge of the Anion

Figure 1. Fluorinated π systems 1
15.

In butadiene complexes, the geometry of the π systems was forced to be planar for comparison purposes. In addition, in the complexes of 6, the global minimum corresponds to the hydrogen-bonded complex where the anion is coplanar with respect to the molecular plane. In this case, the anion was forced to be over the molecular plane. Furthermore, in the hexafluorofulvene complexes, the global minimum corresponds to the nucleophilic attack of the anion on the exocyclic carbon atom, because this yields the aromatic cyclopentadiene anion. In the optimization of these complexes, the anion was forced to be over the molecular plane. The partition of the interaction energies into individual electrostatic, polarization, dispersion, and repulsion components was carried out by performing molecular interaction potential with polarization (MIPp)22 calculations, which is an improved generalization of the molecular electrostatic potential (MEP) in which three terms contribute to the interaction energy: (i) an electrostatic term identical to the MEP,23 (ii) a classical dispersion
repulsion term, and (iii) a polarization term derived from perturbation theory.24 This method was modified, as previously described,25 to separate the classical dispersion
repulsion term into a quantum-mechanical computed dispersion term and a classical repulsion term. The MIPp calculations were performed using the MOPETE-98 program.26 The ionic van de Waals parameters for Cl
were taken from the literature.27 The topological analysis of the electron charge density was performed using Bader’s theory of AIM.28 The electronic density was analyzed using the AIM2000 program29 at the MP2/aug-ccpVTZ level of theory. The molecular polarizabilities of compounds 1
15 were computed using the Gaussian 09 program30 at the MP2/6-31þþG** level of theory. The quadrupole moments were computed using the Molpro31 program at the BP86/ 6-31þþG** level of theory. We used the nucleus-independent chemical shift (NICS)32 criterion to evaluate the aromaticity of several compounds upon complexation. This method is based on the negative of the magnetic shielding computed at the center of the ring. Significant negative values imply aromaticity (diatropic ring current), and positive values correspond to antiaromaticity (paratropic ring current). NICS at the geometrical center of the ring is influenced by the local (paratropic) effects arising mainly from the σ bonds. NICS(1) (1 Å above the plane of the ring) essentially reflects π effects, and it is a better indicator of the ring

compound

nF

EBSSE

EBSSE/nF

Re

q (e)

16 (1 þ Cl
)

2


3.13


1.57

3.370


0.94

17 (1 þ Br
) 18 (2 þ Cl
)

2 2


2.80
3.02


1.40
1.51

3.555 3.405


0.96
0.93

19 (2 þ Br
)

2


2.64


1.32

3.605


0.95

20 (3 þ Cl
)

2


2.84


1.42

3.409


0.93

21 (3 þ Br
)

2


2.60


1.30

3.606


0.95

22 (4 þ Cl
)

4


7.63


1.91

3.131


0.91

23 (4 þ Br
)

4


6.70


1.67

3.322


0.93

24 (5 þ Cl
)

4


6.68


1.67

3.055


0.88

25 (5 þ Br
) 26 (6 þ Cl
)

4 4


5.76
8.68


1.44
2.17

3.299 3.147


0.91
0.87

27 (6 þ Br
)

4


7.81


1.95

3.339


0.90

28 (7 þ Cl
)

6


11.91


1.98

2.968


0.87

29 (7 þ Br
)

6


10.70


1.78

3.162


0.90

30 (8 þ Cl
)

4


9.52


2.38

3.173


0.87

31 (8 þ Br
)

4


8.79


2.20

3.345


0.90

32 (9 þ Cl
)

4


9.47


2.37

3.180


0.87

33 (9 þ Br
) 34 (10 þ Cl
)

4 4


8.74
9.40


2.18
2.35

3.345 3.185


0.90
0.86

35 (10 þ Br
)

4


8.69


2.17

3.348


0.89

36 (11 þ Cl
)

5


12.12


2.42

3.127


0.85

37 (11 þ Br
)

5


11.18


2.24

3.289


0.88

38 (12 þ Cl
)

6


14.83


2.47

3.074


0.84

39 (12 þ Br
)

6


13.69


2.28

3.242


0.87

40 (13 þ Cl
)

6


11.16


1.86

3.134


0.87

41 (13 þ Br
) 42 (14 þ Cl
)

6 8


10.28
13.47


1.71
1.68

3.316 3.027


0.89
0.83

43 (14 þ Br
)

8


12.41


1.55

3.216


0.86

44 (15 þ Cl
)

10


16.83


1.68

2.902


0.79

45 (15 þ Br
)

10


15.45


1.54

3.097


0.82

current than the value at the center. NICS values were computed at the GIAO-HF/6-31þþG**33 level of theory using the MP2optimized structures, because previous studies have demonstrated that reliable results are obtained at this level of theory.34

’ RESULTS AND DISCUSSION Energetic and Geometric Details. Table 1 reports the energies and equilibrium distances corresponding to the interaction of compounds 1
15 with two halides (Cl
and Br
), forming complexes 16
45 (see Figure 2). From the inspection of the results, several interesting points emerge. First, despite the fact that complexes with two fluorine substituents, nF = 2 (16
21) have similar interaction energies, there are some interesting differences. The anion
π interaction is slightly stronger in difluoroethyne complexes (16 and 17) than in either cis- or transdifluoroethene complexes (18
21). Curiously, the interaction energies of the trans-1,2-difluoroethene complexes (18 and 19) are slightly more favorable than those of the cis-1,2-difluoroethene complexes (20 and 21), in agreement with the equilibrium distances. This issue is further analyzed in the discussion of partition 7850

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Figure 2. Anion
π complexes 16
45 studied in this work.

energy (vide infra). Second, from the complexes with nF = 4, several remarkable issues can be extracted. The interaction energies of the complexes of tetrafluoroethene (22 and 23) are more favorable than those of the complexes of 1,2,3,4-tetrafluorobutadiene (24 and 25), indicating that the same number of fluorine substituents distributed in two conjugated double bonds instead of one isolated double bond does not favor the anion
π interaction in the trans
trans isomer (5). However, when the two double bonds are cis (complexes 26 and 27), the interaction energies are more favorable than for tetrafluoroethene complexes 22 and 24. This aspect is further analyzed below, in the discussion of partition energy. Moreover, the interaction energies of complexes 30
35 (several isomers of tetrafluorobenzene) are more favorable than those of complexes 24
27. This result indicates that the aromaticity of the ring plays an important role in the anion
π binding. In fact, the equilibrium distances of complexes 24
27 are shorter than those computed for complexes 30
35, in disagreement with the interaction energies, which further supports the suggestion that the aromaticity is important in the complexation. For complexes with nF = 6, the results are comparable to those for nF = 4 in terms of aromaticity; that is, the interaction energies of the complexes of perfluorobutadiene (28 and 29) are considerably less favorable than those computed for hexafluorobenzene complexes 38 and 39, even though the former have shorter equilibrium distances. In addition, the interaction energies computed for the complexes of [3]radialene 40 and 41 are similar to the interaction energies computed for complexes 28 and 29 (perfluorobutadiene) and noticeably lower than those determined for the hexafluorobenzene complexes, again in agreement with the suggestion that the aromaticity of the ring affects the interaction energy. The interaction energies computed for the complexes of perfluoro[4]radialene 42 and 43 are more favorable than those computed for perfluoro[3]radialene. However, the former complexes are less favorable than the complexes of hexafluorobenzene even though they have shorter equilibrium distances and more fluorine substituents

Table 2. Contributions to the Total Interaction Energy (kcal/mol) for Compounds 1
15 Interacting with Cl
and Molecular Polarizabilities (R, au) of Compounds 1
15 Computed Orthogonal to the Molecular Plane complex

Eele

Epol

Edis

Erep

Etot

R




1 þ Cl (16)


0.94


2.02


1.40

1.23


3.13

12.6

2 þ Cl
(18)

0.20


3.12


1.40

1.30


3.02

17.6

3 þ Cl
(20)

0.48


3.21


1.42

1.29


2.84

18.0

4 þ Cl
(22)


4.45


3.00


2.21

2.03


7.63

17.5

5 þ Cl
(24)


0.44


5.93


3.39

3.08


6.68

30.9

6 þ Cl
(26)


3.96


4.49


2.04

1.81


8.68

30.3

7 þ Cl
(28)


6.52


5.05


3.50

3.16


11.91

30.5

8 þ Cl
(30) 9 þ Cl
(32)


3.40
3.37


6.67
6.64


3.35
3.30

3.90 3.84


9.52
9.47

38.0 38.2

10 þ Cl
(34)


3.29


6.64


3.32

3.86


9.4

38.3

11 þ Cl
(36)


6.35


7.40


3.56

5.18


12.12

37.8

12 þ Cl
(38)


9.07


7.35


3.80

5.40


14.83

37.6

13 þ Cl
(40)


4.31


7.74


3.67

4.57


11.16

40.3

14 þ Cl
(42)


6.69


8.84


5.34

7.40


13.47

52.0

15 þ Cl
(44)


6.21


11.20


4.51

5.09


16.83

63.8

(nF = 8). The complexes of perfluoro[5]radialene 44 and 45 (nF = 10) are the most favorable ones and also present the shortest distances. An interesting parameter that it is very useful in analyzing the additivity/nonadditivity effects is the interaction energy divided by the number of fluorine substituents of the π system (EBSSE/ nF). This parameter can be understood as the contribution of each fluorine atom to the interaction energy. Curiously, this value is smaller than
2.17 kcal/mol for all nonaromatic Cl
complexes, and it is greater than
2.35 kcal/mol in all aromatic Cl
complexes. A similar result was observed for bromide complexes, where EBSSE/nF is smaller than
1.95 kcal/mol for all nonaromatic complexes and greater than
2.17 kcal/mol in all aromatic 7851

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The Journal of Physical Chemistry A complexes. These results confirm that the aromaticity of the ring plays a role in the stabilization of the anion
π complexes. In Table 1, we also include the charges of Cl
and Br
in the complexes in order to study charge-transfer effects. We used the Merz
Kollman scheme for deriving atomic charges because it has been reported that this method provides high-quality charges.35 In general, the charge transfer is modest (6
13%) for the complexes where the π system has one or two π bonds (16
29) and higher (10
21%) in the rest of the complexes (30
45) because the equilibrium distances are shorter. In fact, the complex with the shortest equilibrium distance (44) presents the highest charge transfer (0.21 e), and it is also the most favorable complex (
16.83 kcal/mol). Partition Energy. With the purpose of analyzing the nature of the anion
π interaction in the complexes and, in particular, understanding the nonadditivity effects observed in the aromatic compounds, where the effect of each fluorine substituent on the total interaction energy is higher than in the nonaromatic compounds, we partitioned the energy into electrostatic (Eele), ioninduced polarization (Epol), dispersion (Edis), and repulsion (Erep) terms for chloride complexes (see Table 2). Interestingly, the difluoroethyne complex has a negative electrostatic term, whereas either cis- or trans-difluoroethene complexes have positive electrostatic contributions. It has been demonstrated that the electrostatic term in anion
π interactions depends on the magnitude of the quadrupole moment (Qzz).36 We computed the Qzz value of difluoroethyne, which is positive (0.24 B), and the quadrupole moments of trans- and cis-difluoroethene are
0.15 and
0.42 B, respectively. These Qzz values explain the different electrostatic contributions of the 1 3 3 3 Cl
complex compared to the 2 3 3 3 Cl
and 3 3 3 3 Cl
complexes. In complexes 2 3 3 3 Cl
and 3 3 3 3 Cl
, the interaction is dominated by ion-induced polarization and, to a lesser extent, by the dispersion contribution (see Table 2). The total interaction energies of the complexes of 1
3 with Cl
is very similar because the polarization term compensates the electrostatic term. This is due to the molecular polarizability (R, see Table 2), which is higher in ethene compounds (17.5
18.0 au) than in ethyne (12.6 au). In the complex of perfluoroethene (4 3 3 3 Cl
), the polarization term is similar to that in complexes 2 3 3 3 Cl
and 3 3 3 3 Cl
, and the electrostatic term is more negative because the number of electron-withdrawing fluorine atoms is four; consequently, Qzz is more positive (2.8 B). In complex 5 3 3 3 Cl
, the electrostatic term is very small, and the interaction is dominated by the polarization contribution. Curiously, when the π system is substituted by an equal number of hydrogen and fluorine atoms, the quadrupole moment is almost negligible. As previously mentioned, compounds 2 and 3 have Qzz values of
0.15 and
0.42 B, respectively. Moreover, compound 5 has a Qzz value of þ0.47 B, and the value for 1,3,5-trifluorobenzene is þ0.9 B.37 Therefore, these compounds are expected to have the dual ability to interact favorably with anions and cations, because the interaction would be dominated by polarization effects that are always favorable.36 This fact has already been demonstrated for 1,3,5-trifluorobenzene and other aromatic rings with negligible Qzz values such as s-triazine and 2,5-dichloropyrazine.34a Another interesting point is that the polarization contribution is almost twice as great in butadiene complexes as in ethyne or ethene complexes, in agreement with the molecular polarizability (R). Therefore, the conjugation of two double bonds has a favorable effect on the polarizability of the molecules and, consequently, on the interaction energy. It is worth noting the different behaviors

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of compounds 5 and 6. In the 5 3 3 3 Cl
complex, the electrostatic term is almost negligible, and conversely, in the 6 3 3 3 Cl
complex, Eele is
3.96 kcal/mol, indicating that the relative positions of the substituents in butadiene have a strong influence on the electrostatic term. In contrast, the polarization term is almost the same in both compounds (see Table 2). The analysis of the partition energy of the complexes of compounds 8
12 with Cl
provides hints about the importance of the aromaticity of the ring. For instance, the electrostatic contributions for the complexes of aromatic compounds 8
10 (four F atoms) are lower than those computed for the complexes of tetrafluoroethene (4 3 3 3 Cl
) and tetrafluorobutediene (6 3 3 3 Cl
); however, the total interaction energy is larger. The main difference is the polarization term, which is significantly more negative in the complexes of compounds 8
11 with Cl
than in the complexes of 4 and 6 with Cl
. Moreover, the dispersion term is slightly more favorable in the complexes of the aromatic compounds. It should be noted that only the complex of hexafluorobenzene (12) with Cl
is characterized by having an electrostatic term that is more negative than the polarization term. This result is important because the scientific community tends to rationalize ion
π interactions exclusively using electrostatic arguments, when the polarization is more important for the majority of complexes. Therefore, it should be taken into account that only in the highly π-acidic aromatic rings (ca. Qzz > 9 B) do electrostatic effects dominate the interaction. For the complex of [3]radialene (13), which includes six fluorine substituents in the structure, the interaction energy is less favorable than for hexafluorobenzene because of the electrostatic term, even though the Epol value for the former is slightly more favorable. Even the complex of [4]radialene (14) has a worse interaction energy than hexafluorobenzene, which is also because of electrostatic effects. A likely explanation is that the withdrawing effect of the fluorine atoms on the ring is attenuated by the double bond. The same behavior was observed for the complex of [5]radialene (15), where the electrostatic term is not very high and the interaction is dominated by ion-induced polarization effects, in agreement with its high polarizability (63.8 au). At this point, it is interesting to analyze our results by taking into account the recent work published by Wheeler and Houk38 regarding the nature of anion
π interactions involving benzene rings. They proposed that substituent effects in these systems can be attributed mainly to direct interactions between the anion and local C
X dipoles. Specifically, interaction energies for Cl
3 3 3 C6H6
nXn complexes could be matched using a model system in which the substituents are isolated from the aromatic ring and π-resonance effects are impossible. Wheeler and Houk demonstrated38 that the interaction energy for Cl
3 3 3 C6H6
nXn complexes follows a linear relationship with the electrostatic potential evaluated at the position of Cl
. The resulting equation has a scaling factor between the interaction energy and Eele close to 1 (E = 0.98Eele
7.27). Therefore, the differences in the interaction energies of the complexes reflect the differences in the electrostatic contributions to the total interaction energy. It is also worth noting that the y intercept of the equation reported by Wheeler and Houk is
7.3 kcal/mol. This value corresponds to the sum of all other energy components apart from the electrostatic term. Examining the values collected in Table 2 for the aromatic complexes, it is clear that the main source of this energy is polarization, because the Epol values vary from
6.6 to
7.4 kcal/ mol. Therefore, polarization is roughly constant for the different fluorobenzene complexes considered here (compounds 8
13), 7852

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Figure 3. Regression plot of the polarization term (Epol) versus the molecular polarizability for compounds of 1
15 interacting with Cl
.

and the differences in interaction energy mainly reflect the differences in the electrostatic term, in agreement with the results reported by Wheeler and Houk. Regarding the additivity of the interactions, we demonstrated that EBSSE/nF values are different in aromatic compounds compared to the rest of the acyclic or cyclic π-conjugated compounds. Interestingly, Wheeler and Houk also proposed that the interaction energy in anion
π complexes can be approximately expressed by an additive interaction model (E = 0.73Eadd þ 0.41). However, the scaling factor here is significantly different from 1, indicating that there is some combination between the contributions due to the different substituents. The additive model overestimates the interaction energy if this coupling is neglected. A likely explanation is that the relative differences in the interaction energies of anion
arene complexes mostly reflect relative differences in the interactions with the substituents. However, it is clear that a non-negligible fraction of the total interaction energy comes from other nonadditive effects, which necessarily have to be contained in the polarization term, as demonstrated by the energy results summarized in Tables 1 and 2. The nonaromatic complexes 18, 20, 22, 24, 26, and 28 can be also analyzed using Wheeler and Houk's point of view. The two former complexes contain two fluorine atoms, and the electrostatic energies are similar (0.20 and 0.48 kcal/mol), as are the polarization energies (
3.1 and
3.2 kcal/mol). Adding two other fluorine atoms (complex 22) has little effect on polarization (
3.0 kcal/mol) but leads to a more stabilizing electrostatic energy (
4.5 kcal/mol), which can be attributed to additional interactions with the C
F dipoles. In addition, notwithstanding the fact that the total interaction energies of complexes 22 and 24 are similar (
7.6 and
6.7 kcal/mol), the origins are completely different as the Eele value in complex 24 is
0.4 kcal/mol, whereas Epol amounts to
5.9 kcal/mol (likely reflecting the extension from one double bond in 22 to two double bonds in complex 24). Finally, by comparing complexes 24 and 28, it can be observed that Epol is similar in the two compounds, which have two double bonds, but electrostatics are very different (
0.4 kcal/mol in complex 24 versus
6.5 kcal/mol in complex 28) because of the addition of two extra fluorine atoms. Moreover, in complex 24, there are two C
F bonds (those corresponding

to positions 1 and 4) where fluorine substituents are closer to the anion, thus possibly making an unfavorable electrostatic interaction with the anion. The addition of two extra fluorine atoms in 28 counterbalances this effect. In fact, in complex 26, where the four fluorine atoms are arranged in a cis orientation, the electrostatic term makes a significant stabilizing contribution (
3.96 kcal/mol). An interesting finding that supports the reliability of the partition scheme used in this work is that the Epol values reported in Table 2 for chloride complexes are consistent with the molecular polarizabilities of the π systems studied in this work. We plotted the molecular polarizabilities of compounds 1
14 versus the polarization contribution to the total interaction energy in their complexes with Cl
and obtained a strong correlation, R2 = 0.978 (see Figure 3). AIM Analysis. Topological analysis of the charge density distribution, F(r), and properties of critical points (CPs) were determined for chloride complexes using Bader’s theory of “atoms in molecules”, which provides an unambiguous definition of chemical bonding,39 using the MP2/aug-cc-pVTZ wave function. AIM theory has been successfully used to characterize anion
π interactions.6c,36 For complexes with only one π bond, the exploration of the CPs revealed the presence of one bond CP that connects the anion with the middle of the C—C bond. In Figure 4, we present the distribution of CPs that is generated upon complexation of the anion in the complexes. For the complexes with two π bonds, the distribution of the CPs is different depending on the number of fluorine atoms. For nF = 4 trans (complex 24), the interaction of the anion with the π system is with the central C—C bond because one bond (3,
1) CP that connects the anion with the middle of that bond is obtained (see Figure 4). For nF = 4 cis (complex 26), the interaction of the anion with the π system is also with the central C—C bond; however, the distribution of CPs is different, because two bond (3,
1) CPs that connect the anion with the carbon atoms of the central bond and a ring (3, þ1) CPs that connect the anion with the middle of the central C—C bond are obtained (see Figure 4). For nF = 6 (complex 28), the anion interacts with both CdC bonds, and the exploration of the CPs revealed the presence of two bond CPs that connect the anion 7853

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Figure 4. Schematic representation of the critical points that emerge upon complexation of Cl
to compounds 1
15.

with the middle of the CdC bonds. In addition, a ring (3, þ1) CP connects the anion with the middle of the central C—C bond (see Figure 4). For the aromatic complexes, the distribution of the CPs is different depending on the number of fluorine atoms (see Figure 4). A common feature is the presence of a cage critical point, as is common in anion
π complexes involving aromatic rings. In fact, it has been demonstrated that quantitative values for F(r) and r2F(r) at the cage CP provide hints about the character and strength of the interaction. For the [n]radialene complexes, the distribution of CPs depends on the size of the ring. In the three-membered ring, only one bond CP connects the ring with the anion. In contrast, in perfluoro[4]radialene and [5]radialene complexes, the interaction is characterized by the presence of four and five bond and ring CPs, respectively (see bottom of Figure 4). For both complexes, the interaction is also characterized by the presence of a cage CP. The Laplacian at the (3,
1) CPs is positive in all complexes, indicating a depletion of the electron density, as is common in closed-shell interactions. For the complexes in which the interaction is characterized by the presence of one bond critical point (compounds 1
6), the interaction energy strongly correlates with the values of F(r) at the bond CPs (see Figure 5, top); in fact, we found a good (R2 = 0.991) relationship between the two parameters. This relationship indicates that the value of the charge density at the bond CP can be used as a measure of bond order in this interaction. One should note the relevance of this relationship, because it allows for dealing simultaneously with compounds with one triple, one double, or two double bonds. A similar relationship was found for the complexes of aromatic compounds 8
12 (see Figure 5, bottom), where we represent EBSSE versus F(r) at the cage CPs. In this plot, we have also included two new Cl

π complexes not present in Table 1 (1,3,5-trifluorobenzene and 1,4-difluorobenzene, red dots) in order to include

additional points in the graph and thus provide more reliable results. This analysis allows the further study of the importance of the aromaticity in anion
π binding. Similarly to the rest of aromatic complexes, the complexes of [4]- and [5]radialene are also characterized by the presence of a cage critical point. However, they do not follow the general trend (blue points in the graphic), in agreement with the assumption that aromaticity plays a role in the anion
π interaction, in agreement with the energy- (EBSSE/nF) and geometry-related results. Some Additional Aromatic/Antiaromatic Aspects. Because the previously discussed results regarding energy, geometry, and nonadditivity aspects of the anion
π interaction point out that aromaticity is important, we further studied and extended this topic in this work. We computed two additional compounds and their complexes, as shown in Figure 6. The compounds are perfluoro derivatives of cyclobutadiene (46), which is antiaromatic, and fulvene (47), which is nonaromatic.40 The energyand geometry-related results are gathered in Table 3, where we have also included the hexafluorobenzene complexes 38 and 39 for comparison purposes. From the results, it can be deduced that the antiaromaticity effects also favor the anion
π interaction because the EBSSE/nF values of complexes 48 and 49 are similar to those observed for hexafluorobenzene complexes and considerably more negative than those observed for nonaromatic hexafluorofulvene complexes 50 and 51. In fact, the computed values of EBSSE/nF for complexes 50 and 51 (
2.02 and
1.87, respectively) are similar to those observed for the nonaro matic complexes 28 and 29 (
1.98 and
1.78 kcal/mol, respectively); see Table 1. Using the nucleus-independent chemical shift (NICS) magnetic criterion, we measured the aromaticity of tetrafluorocyclobutadiene before and after complexation of Cl
. We measured the NICS at 1.0 Å in order to minimize paratropic effects of the σ bonds. The NICS(1) value of 7854

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The Journal of Physical Chemistry A

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Figure 5. Top: Regression plot between the charge density F at the bond critical point and the interaction energies (EBSSE, kcal/mol) of the Cl

π complexes of nonaromatic compounds 1
6. Bottom: Regression plot between the charge density F at the cage critical point and the interaction energies (EBSSE, kcal/mol) of the Cl

π complexes of aromatic compounds 8
12, 1,3,5-trifluorobenzene and 1,4-difluorobenzene (red points), and [n]radialene compounds 14 and 15 (blue points).

Table 3. Interaction Energies at the RI-MP2/aug-cc-pVTZ Level of Theory with BSSE Corrections (EBSSE, kcal/mol), Equilibrium Distances from the Anion to the Mean Plane (Re, Å) for Complexes 38, 39, and 48
51, and Computed Merz
Kollman Charge of the Anion compound


Figure 6. Compounds and complexes 46
51.

tetrafluorocyclobutadiene is 12.2 ppm, which agrees with its strong antiaromatic character. When tetrafluorocyclobutadiene interacts with Cl
, the value of NICS is significantly reduced to 10.3 ppm. Therefore, the very favorable interaction energy computed for this complex is related to a reduction of its antiaromatic character. Previous studies have also demonstrated that hexafluorobenzene increases its aromaticity when it interacts with anions. At the level of theory used in this work, hexafluorobenzene has an NICS(1) value of
12.7 ppm, which increases to
13.6 ppm when it is interacting with Cl
. Therefore, both

nF

EBSSE

EBSSE/nF

Re

q (e)

38 (12 þ Cl )

6


14.83


2.47

3.074


0.84

39 (12 þ Br
) 48 (46 þ Cl
)

6 4


13.69
10.19


2.28
2.55

3.242 3.046


0.87
0.86

49 (46 þ Br
)

4


9.23


2.31

3.221


0.89

50 (47 þ Cl
)

6


12.12


2.02

3.092


0.85

51 (47 þ Br
)

6


11.22


1.87

3.250


0.88

aromatic and antiaromatic compounds are better anion
π acceptors than nonaromatic compounds because they either increase their aromatic character or reduce their antiaromatic character upon complexation. The computed value of NICS(1) 7855

dx.doi.org/10.1021/jp2038416 |J. Phys. Chem. A 2011, 115, 7849–7857

The Journal of Physical Chemistry A for hexafluorofulvene is only
6.9 ppm, one-half the value of hexafluorobenzene, indicating that it is not an aromatic molecule, in agreement with previous results.40 The value of NICS(1) increases slightly upon complexation of chloride (
7.3 ppm), indicating that aromatic effects are not important in the hexafluorofulvene complexes.

’ CONCLUSIONS In summary, we have studied nonadditivity effects of the anion
π interaction by analyzing the energy features of several anion
π complexes where the number of double bonds and electron-withdrawing substituents of the π system is progressively increased. The results are in reasonable agreement with the explanation offered by Wheeler and Houk regarding the nature of the anion
π interaction. However, some nonadditivity effects in the aromatic and nonaromatic compounds require a more profound interpretation of the data. We shed some light in this topic by partitioning the interaction energy and demonstrated that polarization effects are extremely important. We also analyzed the interaction using Bader’s theory of atoms in molecules and observed a different trend for the aromatic compounds when the interaction energy is correlated with the charge density at the cage critical point that emerges upon complexation. Finally, we studied the anion
π complexes of tetrafluorocyclobutadiene (an antiaromatic ring) and observed a significant enhancement of the anion
π interaction due to a reduction of the antiaromatic character of the ring. Therefore, a simple electrostatic model is not sufficient to provide an accurate description of the anion
π interaction. Rather, additional effects such as the aromaticity and polarizability of the ring are required. ’ ASSOCIATED CONTENT

bS

Supporting Information. Cartesian coordinates of RI-MP2/ aug-cc-pVTZ-optimized structures. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT We thank CONSOLIDER
Ingenio 2010 (CSD2010-0065) and the MICINN of Spain (Project CTQ2008-00841/BQU, FEDER funds) for financial support. We thank the CESCA for computational facilities. C.E. thanks the MEC of Spain for a predoctoral fellowship. D.Q. thanks the MICINN of Spain for a “Ramon y Cajal” contract. ’ REFERENCES (1) Schneider, H. J. Angew. Chem., Int. Ed. 2009, 48, 3924. (2) (a) Schneider, H. J.; Yatsimirski, A. In Principles and Methods in Supramolecular Chemistry; Wiley: Chichester, U.K., 2000. (b) Paulini, R.; M€uller, K.; Diederich, F. Angew. Chem., Int. Ed. 2005, 44, 1788. (c) Meyer, E. A.; Castellano, R. K.; Diederich, F. Angew. Chem., Int. Ed. 2003, 42, 1210. (3) (a) Hunter, C. A. Angew. Chem., Int. Ed. 2004, 43, 5310. (b) Schneider, H. J.; Yatsimirsky, A. Chem. Soc. Rev. 2008, 37, 263. (c) Gohlke, H.; Klebe, G. Angew. Chem., Int. Ed. 2002, 41, 2644. (4) Muller-Dethlefs, K.; Hobza, P. Chem. Rev. 2000, 100, 143.

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