Cation-π versus anion-π interactions: a comparative ab initio study based on energetic, electron charge density and aromatic features

Chemical Physics Letters 392 (2004) 85–89 www.elsevier.com/locate/cplett

Cation-p versus anion-p interactions: a comparative ab initio study based on energetic, electron charge density and aromatic features ~onero, Pau Ballester, Carolina Garau, Antonio Frontera *, David Quin Antonio Costa, Pere M. Dey
a* Departament de Quımica, Universitat de les Illes Balears, Crta. de Valldemossa km 7,5, 07122 Palma de Mallorca, Spain Received 28 March 2004 Available online 8 June 2004

Abstract Several complexes of benzene with cations and hexafluorobenzene with anions have been optimized at the MP2/6-31++G**, B3LYP/6-31++G** and HF/6-31++G** levels of theory. Different aspects of the cation-p interaction have been compared to those of anion-p, including changes in the aromaticity of the ring upon complexation, charge-transfer effects using the Merz–Kollman charges and the contribution of dispersion energies by comparing the complexation energies computed at the B3LYP and MP2 levels of theory. Ó 2004 Elsevier B.V. All rights reserved.

1. Introduction Interactions involving aromatic rings are important binding forces in both chemical and biological systems and they have been recently reviewed by Meyer et al. [1]. Many studies on energetic decomposition analysis of the cation-p interaction are present in the literature [2–6]. The cation-p interaction is, in general, dominated by electrostatic and cation-induced polarization [2]. The benzene-hexafluorobenzene face-to-face stacking favorable interaction has been studied [7] and a comprehensive analysis carried out by Williams [8] points out the important role of the large, permanent quadrupole moment (Qzz ) of the two molecules, which are similar in magnitude but of opposite sign. Recently, Mascal et al. [9], Alkorta et al. [10] and our group [11] have studied theoretically the favorable p-interaction of anions with electron deficient aromatic rings. Our group has used the term ‘anion-p interaction’ to describe the interactions between anions and hexafluorobenzene, where the anion is positioned over the *

Corresponding authors. Fax: +37-971-17-34-26. E-mail address: [email protected] (A. Frontera).

0009-2614/$ - see front matter Ó 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2004.05.049

ring along the C6 axis [11]. The anion-p interaction is dominated by electrostatic and anion-induced polarization [10,11]. Similarly to the cation-p, the nature of the electrostatic component is explained by means of the positive Qzz of hexafluorobenzene. Our group has reported several studies on other electron deficient aromatic rings with anions [12,13] and the simultaneous interaction of aromatic rings with both anions and cations [14]. More recently, we have reported a topological study of the anion-p interaction in several complexes of aromatic compounds with positive quadrupole moment and Cl
, where we have shown that the electrostatic component of the interaction correlates with the magnitude of the Qzz of the aromatic ring and the anion-induced polarization correlates with the molecular polarizability (ak ) of the aromatic compounds [15]. In this Letter, we report a comparative analysis of several features corresponding to cation-p and anion-p interactions for a series of p-complexes of benzene (BEN) and hexafluorobenzene (HFB), see Fig. 1. In particular, we study the change in aromaticity of the ring upon complexation in both interactions, charge-transfer effects and other contributions to the total interaction energy, apart from polarization and electrostatic terms,

86

C. Garau et al. / Chemical Physics Letters 392 (2004) 85–89 Y+

X-

F6

1, Y=H 2, Y=Li 3, Y=Na 4, Y=K

5, X=H 6, X=F 7, X=Cl 8, X=Br

Fig. 1. Cation-p (1–4) and anion-p (5–8) complexes.

that are expected to be less important, i.e., correlation and dispersion contributions. Finally, we examine the variation of the magnitude of the polarization term to the total binding energy depending on the interacting atom by means of the molecular interaction potential with polarization (MIPp) energetic partition scheme [16] for the two series of complexes. Kim et al. [17] have recently reported a theoretical study on anion-p interactions where they conclude that the largest contributions to the total interaction energy are the electrostatic and polarization terms, in agreement with our previous results. However, in their partition energy analysis using symmetry adapted perturbational theory (SAPT) calculations [17], they obtain a surprising result, the following trend is observed for the polarization term depending on the anion Br
> Cl
> F
. Polarization effects are expected to drastically diminish with the distance (approximately proportional to r
4 [18]). Here we show that the observed trend by Kim et al. [17] using SAPT calculations is not in agreement with MIPp calculations, which have been successfully used to study non-covalent interactions [19], including cation-p [2].

2. Theoretical methods The geometry of all the complexes included in this study was fully optimized at the MP2/6-31++G**, B3LYP/6-31++G** and HF/6-31++G** levels of theory using the GA U S S I A N -98 program [20]. The binding energy was calculated at the same level with and without correction for the basis set superposition error (BSSE) using the Boys–Bernardi counterpoise technique [21] and zero-point energy (ZPE) corrections. The minimum nature of all complexes has been confirmed by frequency calculations at the same level, except for the Hþ complex which presents two degenerate imaginary frequencies at the three levels of theory used in this study. Additionally, at the B3LYP and MP2 levels, the F
complex presents two and three imaginary frequencies, respectively. The corresponding minimum consists in a nucleophilic attack of the anion to the aromatic ring. In this complex (6), C6v symmetry has been imposed at the two levels. Finally, at the B3LYP level the Br
complex

presents three imaginary frequencies and at the MP2 the Kþ complex presents one imaginary frequency. However, because the aim of this work is to compare the anion/cation recognizing tendency of these p systems and to obtain a new insight into the nature of the interaction we present the energetic and geometrical features of all complexes at all levels of theory. The contributions to the total interaction energy have been computed using the MIPp [16], which is an improved generalization of the molecular electrostatic potential (MEP) where three terms contribute to the interaction energy: (i) an electrostatic term identical to the MEP [22], (ii) a classical dispersion–repulsion term, and (iii) a polarization term derived from perturbational theory [23]. Calculation of the MIPp of benzene interacting with Liþ , Naþ , and Kþ and hexafluorobenzene with F
, Cl
, and Br
was performed using the HF/ 6-311+G* wavefunction of the aromatic rings by means of the MO P E T E -98 program [24]. The ionic van de Waals parameters for F
and Liþ were taken from [25] and for Naþ , Kþ , Cl
and Br
from [26,27]. The HF method does not include electron correlation, therefore its contribution to the total interaction energy can be estimated as the difference between the binding energy of the complexes computed at the MP2(full)//MP2 and HF//MP2 levels of theory. Additionally, the dispersion interactions are not given by the DFT B3LYP level of theory but are given at MP2 level [28], thus the difference between MP2(full)//MP2 and B3LYP//MP2 binding energies can be considered as an approximate contribution of the dispersion term to the total binding energy. We have used the nucleus independent chemical shift (NICS) [29] criterion to evaluate the aromaticity of benzene and hexafluorobenzene 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  above the arising mainly from the r bonds. NICS(1) (1 A plane of the ring) essentially reflects p effects and it is a better indicator of the ring current than the value at the center. NICS were computed at GIAO-HF/6-31++G** [30] level of theory using the MP2 optimized structures. The topological analysis of the electron charge density performed for the complexes 1–8 was determined using Bader’s theory of AIM [31]. The electronic density analysis was performed using the AI M P A C program [32] at the HF/6-31++G** level of theory.

3. Results and discussion Table 1 reports the energies and equilibrium distances corresponding to the interaction of BEN with a series of

C. Garau et al. / Chemical Physics Letters 392 (2004) 85–89

87

Table 1 Interaction energies at several levels of theory (HF/6-31++G**, B3LYP/6-31++G** and MP2/6-31++G**) with the BSSE and ZPE corrections  and the contribution of correlation (EBSSE , kcal/mol), the number of imaginary frequencies (NImag) are in parenthesis, equilibrium distances (Re , A) (Ecorr , kcal/mol) and dispersion (Edis , kcal/mol) terms to the total interaction energy for complexes 1–8 Compound

BEN  Hþ (1) BEN  Liþ (2) BEN  Naþ (3) BEN  Kþ (4) HFB  H
(5) HFB  F
(6) HFB  Cl
(7) HFB  Br
(8)

EBSSEþZPE (NImag)

Re

HF

B3LYP

MP2

HF

B3LYP

MP2

)116.17(2) )34.68(0) )22.37(0) )14.44(0) )10.18(0) )17.81(0) )10.60(0) )10.07(0)

)128.23(2) )35.35(0) )23.16(0) )14.90(0) )14.84(0) )17.50(2) )10.91(0) )10.37(3)

)124.38(2) )31.66(0) )20.07(0) )16.17(1) )13.48(0) )19.60(3) )12.59(0) )11.60(0)

0.935 1.907 2.472 3.033 3.034 2.669 3.404 3.479

0.917 1.835 2.395 2.943 2.802 2.656 3.310 3.367

0.865 1.899 2.429 2.894 2.693 2.570 3.148 3.201

cations (complexes 1–4) and HFB with a series of anions (complexes 5–8) at three levels of theory. In all cases, the binding energy is large and negative indicating that the formation of the p-complexes is favorable. Some differences between anion and cation-p complexes can be extracted from Table 1. First, the formation of cation-p complexes is more favorable than the anion-p, probably because the equilibrium distances are shorter in cation-p complexes and consequently the electrostatic and polarization contributions are more important. A peculiar case is complex 1, due to the special nature of the proton a very short equilibrium distance (Re ) is found and the interaction of BEN with Hþ can not be defined simply in terms of non-covalent bonding [33]. Second, for cation-p complexes, the interaction energies are more favorable at the B3LYP than at the MP2 level of theory. This result is unexpected since dispersion interactions are not accounted at B3LYP, but are given at MP2 level, thus one should expect that the B3LYP binding energy should always be less than the MP2. In contrast to cation-p complexes, the binding energies computed for anion-p complexes 5–8 are more favorable at the MP2 than at the B3LYP level of theory. Third, the contribution of the dispersion energy in cation-p complexes is modest, in agreement with previous studies of Kim et al. [4] computed using the SAPT methodology. In contrast, the dispersion energy in anion-p complexes is important,

Ecorr

Edis

)12.31 )1.67 )2.45 )2.79 )7.30 )2.58 )8.15 )9.38

)0.37 )1.17 )1.86 )2.21 )2.27 )2.50 )7.45 )8.01

specially for Cl
and Br
complexes. The contribution of the correlation energy is also more important in anion-p than in cation-p complexes, apart from the special case of complex 1. In Table 2, we compare some interesting aspects of cation and anion-p complexes. For instance, we have measured the strength of the charge-transfer effect in these systems determining the atomic charges of the 1–8 complexes using the Merz–Kollman method [34], which it has been demonstrated that provides high quality charges [35]. We have also included the Mulliken charges in Table 2. In general the charge-transfer is more important in cation-p than in anion-p interactions. Another interesting feature that has been studied is the variation of the electron charge density in the six CAC bond critical points of the aromatic rings upon complexation of the ion. Because the electron density at the bond critical point provides a measure of the bond order, it can be reasonably assumed that the change in electron density at the bond critical point induced upon complexation gives a measure of the variation in the strength of the bond. The computed charge density values at the six bond critical points of the ring and its variation upon complexation are present in Table 2. Curiously, the Dq values are negative for cation-p complexes, indicating a reduction in the strength of the CAC bonds. On the contrary, the values are positive for

Table 2 Merz–Kollman (MK) and Mulliken (Mull) charges (q, e) of the ions (X/Y) in 1–8 complexes, topological properties of the electron density at the  below aromatic CAC bond critical point (q, a.u.) in 1–8 complexes and their change upon complexation (Dq, a.u.) and NICS values in ppm at 1.0 A the aromatic ring (opposite to the ion) and their change upon complexation Compound þ

BEN  H (1) BEN  Liþ (2) BEN  Naþ (3) BEN  Kþ (4) HFB  H
(5) HFB  F
(6) HFB  Cl
(7) HFB  Br
(8)

q (X/Y) (MK)

q (X/Y) (Mull)

10q (a.u.)

10Dq (a.u.)

NICS(1)

DNICS(1)

0.19 0.65 0.76 – )0.81 )0.80 )0.90 )0.90

0.28 0.39 0.73 0.97 )0.80 )0.93 )0.92 )0.87

3.21 3.23 3.23 3.25 3.44 3.45 3.43 3.43

)0.06 )0.04 )0.04 )0.02 0.03 0.04 0.02 0.02

)8.25 )11.34 )11.13 )11.43 )15.27 )14.19 )14.36 )14.43

3.25 0.16 0.37 0.07 )1.71 )0.63 )0.80 )0.87

88

C. Garau et al. / Chemical Physics Letters 392 (2004) 85–89

anion-p complexes indicating an increase in the strength of the CAC bonds. Finally, the variation of the aromaticity of the ring induced upon complexation is also present in Table 2. The cation-p complexes give a positive variation of the NICS indicating a diminution in the aromaticity of the BEN upon complexation of the cation. In contrast the variation in the aromaticity of HFB upon complexation of the anions is negative, indicating a gain in the aromaticity of the ring. Latter results are in agreement with the variation of the density at the six CAC bond critical points of the ring upon binding of the ion in 1–8 complexes. We have analyzed the physical nature of the anionp interaction in these systems, evaluating it using the energetic partition scheme of the MIPp. We have explored the electrostatic (Ee ), polarization (Ep ), van der Waals (Evw ) and total (Et ) interaction energies when Liþ , Naþ and Kþ approach a benzene molecule perpendicular to the center of the aromatic ring along the C6 symmetry axis and when F
, Cl
and Br
approach a HFB molecule in the same direction. In Table 3, we summarize the contribution of the three terms and the total energy at the point along the C6 axis where the MIPp is minimum and we also present the MP2 interacting energies and equilibrium distances (Re ) of the optimized complexes for comparison purposes. It is worth mentioning that the MIPp energies are computed from the wavefunction of BEN and HFB interacting with the corresponding ions considered as classical particles, therefore the changes in the geometry of the ring in the complex are not accounted in MIPp calculations. The results present in Table 3 point out that the performance of MIPp calculations is notable, giving results comparable to MP2 in both energies and equilibrium distances. For the interaction of lithium and sodium cations with BEN, the polarization term is greater than the electrostatic term. For potassium cation, the electrostatic term is about 2 kcal/mol more negative than the polarization. These results are in qualitative agreement with the work of Tsuzuki et al. [18] and Kim et al. [4]. In contrast to the interaction of cations with BEN, the interaction of anions with HFB is dominated by the electrostatic

term at the MIPp minimum. The polarization term is smaller in the interactions of HFB with anions than those of BEN with cations probably due to the difference in van der Waals radii of the ions, which are bigger in anions than in cations and consequently the distance to the center of the ring in anion complexes is greater. The large intermolecular distances of the Cl
and Br
complexes are the cause of their modest Ep values. These results are in disagreement with the recent work of Kim et al. [17] where they found that the induction (polarization) energy is greater for Br
than Cl
and the latter greater than F
. However, the results obtained using the MIPp partition scheme are in agreement with the fact that the polarization energy is very sensitive to the distance (proportional to r
4 ). To illustrate this, we represent in Fig. 2a, the variation of Ee and Ep in both series of anion-p (dashed lines) and cation-p (solid lines) complexes computed at the MIPp minima. At short equilibrium distances, i.e., complexes 2 and 3, the polarization term clearly dominates the interaction, however, when the equilibrium distance is larger (ions with bigger van der Waals radius) the electrostatic term becomes the most important. This behavior is also observed in the representation (Fig. 2b) of the energy profiles, Ee , Ep , Evw (sum of repulsion and dispersion energies) and Et for the approach of Naþ to the center of the benzene ring along the C6 axis. Ep is very significant at short distances, where the Evw term is very positive, preventing the binding. At the distance where Et is minimum, the Ee and Ep contributions are similar. Lastly, at dis the electrotances larger than approximately 2.7 A static term is slightly more negative than the polarization term. In summary, results derived from this study reveal several differences between cation and anion-p interactions. Since BEN and HFB have a very similar magnitude of permanent quadrupole moment but of opposite sign, a direct comparison between both series of complexes is possible. The energies of cation-p interactions are more negative than anion-p principally because cation complexes have shorter equilibrium distances that allow them to polarize the p-cloud of

Table 3 Contributions to the total interaction energy (kcal/mol) calculated using MIPp for the BEN and HFB compounds interacting with several cations  where the MIPp is minimum and anions at the distance (d, A) Compound þ

BEN  Li BEN  Naþ BEN  Kþ HFB  F
HFB  Cl
HFB  Br


Ee

Ep

Evw

Et

d

EBSSE (MP2)

Re (MP2)

)16.60 )14.55 )9.75 )14.00 )10.39 )9.90

)25.67 )16.35 )7.71 )9.92 )5.24 )4.74

2.59 4.70 2.43 2.86 )0.24 )0.20

)39.68 )26.20 )15.03 )21.06 )15.87 )14.84

2.0 2.4 3.1 2.8 3.4 3.5

)31.66 )20.07 )16.17 )19.60 )12.59 )11.60

1.899 2.429 2.894 2.570 3.148 3.201

 corresponding to MP2 optimized For comparison purposes the binding energies (EBSSEþZPE , kcal/mol) and equilibrium distances (Re , A) complexes are included.

C. Garau et al. / Chemical Physics Letters 392 (2004) 85–89

89

Acknowledgements

(a) 0.0 Cl Br -

-5.0

FE (kcal/mol)

-10.0

Na+

Li+

-15.0

We thank the DGICYT and Govern Balear of Spain (Projects BQU-2002-04651 and PRDIB-2002GC1-05, respectively) for financial support. We thank the CESCA for computational facilities. C.G. thanks the MECD for a pre-doctoral fellowship. A.F. thanks the MCyT for a ‘Ram on y Cajal’ contract.

K+

Ee cation series

-20.0

Ep cation series Ee anion series

-25.0

Ep anion series

References

-30.0 1.7

2.2

2.7

3.2

3.7

d (Å) Ee

40.0

Ep

30.0

Evw

20.0

Et

E (kcal/mol)

(b) 50.0

10.0 0.0 -10.0

Na+

-20.0

d

-30.0 -40.0 -50.0 1.0

2.0

3.0

4.0

5.0

d (Å)

Fig. 2. (a) Representation of the magnitude of the Ep and Ee components evaluated using MIPp at the minimum for cation and anion series. (b) Energy profiles computed using the MIPp partition scheme for the approach of Naþ to benzene along the C6 axis.

the aromatic ring in a more effective way. Correlation and dispersion energies are more important in anion-p than in cation-p complexes. In comparison with the MP2 level, the B3LYP binding energies overestimate the interaction in cation-p complexes and underestimate the interaction in anion-p complexes. A very interesting feature is that the formation of anion-p complexes implies an increase in the aromaticity of the ring, whereas the formation of cation-p complexes behaves the contrary. This fact is confirmed by the change in the value of the charge density at the bond critical points of the aromatic rings upon complexation (Dq) and by the variation in the NICS values upon binding (DNICS(1)). Finally, the partition energy scheme of MIPp allows us to analyze the variation of the different contributions to the total interaction energy in the series of anion and cation-p complexes. Due to the different van der Waals radii of anions and cations, the polarization contribution dominates the interaction in cation-p complexes whereas in anion-p complexes the more important contribution is the electrostatic term.

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