Cation – π complexes between alkaline cations and molecular bowls related with fullerene : a DFT study

The formation of complexes between alkaline cations and molecular bowls (MBs), curved conjugated systems related with fullerene (C60), is studied using DFT calculations. The series of MBs is constructed starting with benzene and additional hexagonal or pentagonal rings are added symmetrically to complete the C60 structure. All the MBs studied form stable cation–π complexes by both of its sides: concave and convex. In all cases complexes with the cation in the convex side are more stable than their corresponding partner inside the bowl. The stability of the complexes is determined by the polarizing power of the cation and by the molecular electrostatic potential and the polarizability of the bowl. Additionally, size effects are observed when bulky cations are placed in the concave side of the largest bowls.


Introduction.
Noncovalent interactions play a variety of roles in many areas of chemistry and biochemistry because it is believed that all take part in determining the structures and controlling the functions of biological macromolecules.Among the noncovalent binding forces are included salt bridges, hydrophobic interactions, hydrogen bonds, π-stacking interactions and ion-π interactions.In the case of cation-π interactions, many studies suggest its involvement in molecular recognition processes 1 and ion channels. 2For that reason, the interaction of Na + and K + with a variety of π systems have been widely studied because they are the most biologically important alkali metal cations. 3Cation-π interactions also influence the stability of proteins and protein-DNA complexes. 4  Finally, it is believed that through the appropriate addition of substituents to the aromatic ring, the strength of cation-π interactions between a metal cation and π-binding ligands can be tailored so as to devise new chemical separation strategies for the removal of unnecessary and toxic species from environmental sources such as water streams. 5 Studies of alkali metal cations binding to model aromatic systems and characterization of these metal-ligand interactions in the gas phase are an important part of the process for understanding the nature and strength of cation-π interactions.To obtain a complete picture of cation-π interactions, the contributions that the fundamental intermolecular forces make to these interactions need to be elucidated.The prevailing opinion is that electrostatic interactions play the main role in cation-π interactions. 6Other theoretical studies have shown that polarization is also an important factor in determining the strength of cation-π interactions because the cation produces a strong electric field. 7In systems with extended conjugation the inductive effect acquires more importance and its relative contribution to the total interaction can be bigger than the contribution made by the electrostatic interaction.Furthermore, the geometry of the π system is another variable to take in account.In the absence of desymmetrizing substituents, the two faces of planar π systems must have equivalent electrostatic potentials.However, in non-planar π systems that symmetry is broken, and the electrostatic potentials of the two faces no longer remain the same because one surface is more electron rich than the other.That is the situation in sumanene, semibuckminsterfullerene, circumtrindene and other curved conjugated systems related with buckminsterfullerene (see Fig. 1).The molecules that consist of fragments of C 60 are also known as buckybowls, open geodesic polyarenes, π bowls or simply as molecular bowls (MBs).From a coordination chemistry viewpoint, MBs are unique because they can provide not only convex surfaces but also open concave surfaces for metal binding.The preparation and characterization of MBs complexes of various metals that are in a variety of coordination modes, have been reported for over a decade. 8The face preference of the metal in the MBs/cation complexes and the nature of the contributions to their interaction are matter of theoretical study, sometimes with controversial results.
In this work the formation of complexes between alkaline cations and MBs is systematically studied using DFT calculations.All the MBs structures of the series considered here have a hexagonal ring in its center (bottom).Both extreme structures: benzene (a planar system) and C 60 (the complete, closed ball) are included in the study too (see Fig. 1) and binding of ions to both, concave and convex faces of the curved surfaces, are considered.

Computational Details.
All the calculations were carried out with Gaussian03 suite of programs, 9 with the B3LYP method. 10The 6-31+G* basis set was used for all MBs and for Li + , Na + and K + cations.
For Rb + and Cs + , the effective core potential basis set LANL2DZ (Los Alamos National Laboratory 2 double ζ) was employed. 11This combination of hybrid DFT method with a split valence plus polarization basis set quality has proven 12 to be a good choice for obtaining reliable results with low-to-moderate computational cost in similar systems.
The studied complexes were fully optimized without symmetry restrictions starting from structures with the cation originally located centered on the benzene ring, the bottom of the MBs and one hexagonal face of fullerene.The curved π systems (MBs and C 60 ) were explored by their both sides, concave (inner) and convex (outer).All the complexation energies were corrected for the basis set superposition error using the Boys and Bernardi method.Nevertheless, as we will see later, the total interaction energy reaches significant negative values in the inner complexes between these two MBs and the smallest alkaline cations, indicating that the electrostatic contribution is not always the more important one in these systems.In fact, the polarizabilities of this series increase significantly with the sizes until it stabilizes at values close to those of fullerene (9.8, 35.2, 55.2, 61.0, 62.2, 71.7, 79.4, 79.2, 78.6 and 81.0 in Å 3 , from H0 to C 60 , at the level of calculation used here) suggesting a major role of inductive effects as the MB grows.
Table 1.Distances (in Ångstrom) from the cations to the benzene plane, to the bottom plane of the MBs and to the plane of the nearest hexagonal face of fullerene.In the inner complexes of C 60 with K + , Rb + and Cs + the cation is placed in the center of the fullerene structure.The MBs with unsaturated carbon atoms are marked with an *.

Complexes (MB/cation).
At the level of calculation used in this work the alkaline cations form stable complexes with all the studied bowls on both sides, convex and concave.Table 1 shows the distances between the cation and the center of the bottom face for complexes with the ion inside and outside of the MBs.In complexes by the convex side of all bowls and C 60 the distances facecation are similar to the separation observed in other complexes between π systems (for example benzene) and the same alkaline cation.On the other hand, in the concave side only Li + , Na + and K + show a similar behavior and only in the first half of the series (from H0 to H23).Into the bigger MBs (from H3 to C 60 ), all the alkaline cations locate at different distances.For bigger cations (Rb + and Cs + ) inside the MBs a pulling out of the cation is observed after just the first bowl whereas for the smaller cations the furthering becomes later (Na + and K + in H3, and Li + in H33).In H34 the walls of the bowl start closing over the cations and repulsion forces move them to positions nearer the bottom.In the inner complexes of C 60 with K + , Rb + and Cs + the cations are placed in the center of the fullerene cage, its interaction energy is positive (see below) and increases with the cation size.Table 2. Counterpoise corrected complexation energies (in kcal/mol) for complex formation between alkaline cations and benzene, the bottom face of the molecular bowls and the hexagonal face of fullerene, calculated with the B3LYP method and 6-31+G* (for C, H, Li, Na and K) or LANL2DZ (for Rb and Cs) basis set.The structures with unsaturated carbon atoms are marked with *.  -40.47 -41.21 -28.03 -29.16 -19.90 -20.56 -15.77 -16.94 -12.85 -14.49H2 = C 30 H 12 -40.06 -42.68 -27.87 -30.64 -23.31 -21.74 -16.45 -18.15 -13.61 -15.60 H22 = C 36 H 12 -38.12 -42.37 -26.58 -30.64 -19.00 -21.74 -16.31 -18.25 -13.71 -15.68 *H23 = C 39 H 12 -37.01 -44.71 -25.05 -32.60 -16.61 -23.27 -12.48 -19.61 -7.24 -16.94 *H3 = C 45 H 12 -35.80 -43.56 -24.13 -31.74 -17.70 -22.48 -14.51 -18.83 -9.36 -16.16 H32 = C 48 H 12 -34.61 -42.20 -22.36 -30.21 -17.12 -21.24 -14.77 -17.68 -12.16 -15.14 *H33 = C 51 H 12 -34.43 -42.80 -20.57 -30.80 -13.81 -21.78 -11.59 -18.17 -4.72 -15.62 H34 = C 54 H 6 -25.92 -36.41 -12.77 -25.12 -6.71 -16.69 -0.20 -13.61 +12.38 -11.29 H face of C 60 -20.81 -32.95 -7.07 -21.90 +0.58 -13.86 +8.27 -10.71 +21.98 -8.65 Table 2 presents the complexation energies for the complexes between the alkaline cations and benzene, C 60 and the MBs studied.With all curved structures the outer complexes are always more stable than their inner partners.These results are in agreement with previous calculations of complexes between cations and curved π systems 14 as well as with some experimental results. 15  The reverse situation, i.e. the preferential binding of cations to the concave side of MBs or some of these kind of molecules with more negative MEP inside has been reported also, 16

Cs +
The complexation energies are represented in Fig. 3 that shows graphically the mentioned stability differences caused by the in/out asymmetry of the MBs as well as the influence of the MBs size.In comparison with benzene, all the alkaline cations form complexes more stable with the first members of the MBs series by both of their sides.This stabilization occurs despite of the augment of the MEP values on both sides of the bottom hexagone, which are less negative as the MBs grow, and must be caused by the conjugation enhancement.The general pattern exhibited by the interaction energies can be rationalized as the result of two main contributions: the electrostatic interaction, which reduces with the size of the MBs, and the inductive interaction, that increases with the extension of the conjugation.It is interesting to observe the different influence of the saturated carbon atoms in the stability of the complexes depending on the side where the cation is placed.The unique difference among the members of the couples H22 -H23 and H32 -H33 are three sp3 carbon atoms.In both cases, the complexes between the five alkaline cations with the bigger bowl (the one with the sp3 atoms) of each couple are more stable if the cation is outside but less stable if the cation is in the inner side.This last behavior can be the result of the cation repulsion by the hydrogen atoms bonded to the sp3 carbon atoms and directed into the bowl.The additional stabilization of the outer complexes of these MBs pairs need to be studied in more detail and could be produced by subtle effects in the electrostatic and/or the inductive contributions.

Conclusions.
In this work we have studied the interaction of alkaline cations and molecular bowls (MBs), curved π systems derived from C 60 , using B3LYP method with 6-31+G* (for C, H, Li, Na and K) and LANL2DZ (for Rb and Cs) basis sets.At this level of calculation, all the alkaline cations form stable complexes with the cation centered on the hexagonal ring at the bottom of the MBs by both of their sides: concave and convex.The curvature of these π systems generates an in/out asymmetry in the electrostatic potential of the bowls that shows more negative MEP always in its convex (outer) side.In consequence, for every MB/cation combination, the more stable complexes are always formed with the cation in the outer side.A combination of electrostatic and inductive forces governs the interaction energy.The MEP distributions obtained show that the first of these contributions reduces with the size of the MBs while the second increases, as indicated the calculated polarizabilities.The most favourable electrostatic + inductive combination determines which MB forms the most stable complex with each cation.Additionally, when the MB has a closed structure and the cation is in the concave (inner) side, the repulsive interactions play an important role in the complexation with larger cations (K + , Rb + and Cs + ).When is analyzed the influence of the MBs size on the stability of the complexes formed, the presence of unsaturated carbon atoms in some of the structures studied causes irregularities in the patterns followed.

Fig. 1 .
Fig. 1.Top and side views of benzene, fullerene and the Molecular Bowls studied.

Fig. 2 .
Fig. 2. Molecular electrostatic potential maps generated at B3LYP/6-31+G* level for benzene, the molecular bowl series and fullerene.Electrostatic potentials are mapped on the surface of the electron density of 0.0002 au.The red zones corresponds to a negative regions of the electrostatic potential (-0.023 au), whereas the blue color corresponds to regions where the potential is positive (+0.023 au).
So, there are two different behaviors: that of the closed structures of H34 and C 60 and that of the open structures of H1-to-H22 ; with H3-to-H33 with an almost tubular cavity showing an intermediate and more complicated behavior.
nevertheless, the level of calculation used in these works (AM1 in ref. 16 a, AM1; HF/6-31G* and pBP/DN** in ref. 16 b and B3LYP/3-21G in ref. 16 c) seems to be not enough for describing well the electronic properties of MBs and their interactions with cations.