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Endohedral metallo [80] fullerene interactions with small polar molecules
Computational Materials Science 44 (2009) 1065–1070
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Endohedral metallo [80] fullerene interactions with small polar molecules Abraham F. Jalbout * Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Mexico D.F., Mexico
a r t i c l e
i n f o
Article history: Received 13 December 2007 Received in revised form 17 July 2008 Accepted 21 July 2008 Available online 27 December 2008 Keywords: [80] Fullerene Polar species Alkali metals BLYP
a b s t r a c t The interaction of M@C80 (M = Li, K and Na) with small polar molecules (H2O, CH3OH, HF and NH3) is described by density functional theory (DFT) calculations. Our theoretical studies show that in several computed cases the binding energies of M@C80 complexes with small polar molecules increases upon encapsulation. The observed behavior can be accounted for by charge transfer effects between the encapsulated metal and the surface of the C80 cage. These assertions have been solidified by a corresponding analysis of the thermochemistry, vibrational frequencies and HOMO molecular orbital plots of the optimized species. Ó 2008 Published by Elsevier B.V.
1. Introduction There are a variety of investigations that appear to concentrate on the functionalization of fullerene structures which can be used to improve solubility properties. Fullerenes are unique since they are capable of conserving important charge transfer mechanisms between atoms located endohedrally and the external molecular surface [1–10]. This is important because it permits the establishment of assertions used to describe reactivity based on surface modifications [11]. Similar studies on the La@C80 system [12] reveal interesting metal-like conductive properties above 29 K (which is a property related to charge transfer effects). Traditional [60] fullerenes are used to propagate particular properties for use in materials science, but the alternate [80] fullerene can also be used [13]. The applicability of endohedral metallofullerenes is related to the fact that the corresponding metallic properties can be harnessed in the design of novel electronic devices. The larger fullerene structure possesses the inherent property that the larger size of the cavity can lead to stability upon metal encapsulation. This is important in situations where larger metals are used for surface property manipulations that arise from increased charge-radius ratios. Previous calculations [11–13] suggest that larger metals generally lead to improved charge transfer properties with the molecular surface. The fact that C60 has a smaller diameter prevents favorable interactions to occur due to steric hindrance. Because the C80 cage has an increased diameter the enclosed metals have a higher degree of freedom. This is important since * Tel.: +52 55 24 22 72; fax: +52 55 16 22 17. E-mail address: [email protected] 0927-0256/$ - see front matter Ó 2008 Published by Elsevier B.V. doi:10.1016/j.commatsci.2008.07.038
the metals can translate to specific regions in the cage to donate an excess electron to the surface of the system. The excess charge localizes along the benzene rings of the fullerene system causing the issue of increased degrees of freedom to be significant. Professor Csizmadia [14a,b] has truly demonstrated the efficacy of such approaches in the quantification of biological interactions at specific points. The usefulness of these approaches in biochemical applications has been explored by others [14c,d]. Our notion is that if we modify the interactive properties of fullerenes specific interactions (as in enzymes and peptides) can be controlled. Fullerenes have a geometrical arrangement composed of five and six membered rings that permits several competitive reactive channels. This manuscript is geared at obtaining methods of using metallic encapsulation in the C80 fullerene in order to promote charge transfer effects. The charge-transfer effects could cause increased interactions with small polar species as well as larger macromolecules. It is our understanding that the dispersion of the charge throughout the host material will cause the doped fullerenes to be insensitive to the applied electric field. Experimental [5] and theoretical [15] studies describe techniques by which electrons transfer correlates to superconductivity and solubility. Theoretical calculations [7,16–19] state that Li and Na alkali atoms are distorted from the center of the [C60] fullerene cage by approximately 1.2 and 0.6 Å, respectively. Alternatively, in the K@C60 molecule the potassium atom is located exactly at the center of the complex. Presently, there is lack of information on metallic endohedral complexes of alkali metals in C80. Based on our investigations we have observed that the metals prefer to localize at the center of the C80 cage. The objective of this work is to look into complexes formed by alkali metals encapsulation inside of the [C80] fullerene. Once such
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stable interactions are modified these molecules are formed. It can be noted that the increase in molecular interactions with small polar molecules has a direct effect on their structural properties and charge transfer mechanisms. The solubility of nanomaterials has been the focus of debates [17–23] but again scant investigations are available on the theoretical mechanism of the process. The ability of the fullerenes to delocalize excess electrons on their surfaces will be used to increase their solubility [24,25]. The importance of the calculations lies in the quantification of the interaction between local charge distributions and polar molecules. It is our belief that pockets of charge (as a result of the donated electron density to the surface of the molecules by the metals) can be linked to the interaction with the polar molecules on the exterior. Such interactions occur by formation of a temporary state which is created between the excess electronic density and the dipole of the resulting polar species. Calculations show [24] that electron–polar molecule coupling on molecular surfaces, permits solvation of the systems under consideration. We have demonstrated that H2O, CH3OH, NH3 and HF adequately adhere to molecular surfaces which possessed excess electrons on their exteriors. In light of these observations we report on the interaction of M@C80 (M = Li, Na and K) with small polar molecules to analyze the effects of charge transfer on corresponding molecule binding energies. 2. Computational methods The quantum chemical calculations performed herein were carried out with the DMol3 [26] numerical-based density-functional computer software as implemented in the Materials Studio Modeling 3.1 package from Accelrys Inc. Geometrical optimizations and frequency calculations were done with the BLYP general-gradient potential approximation in conjunction with the double-numerical plus diffusion basis set (denoted as DND). Fine convergence criteria and global orbital cutoffs were employed on basis set definitions which have been proven to useful in the study of weak van der Waals complexes [27–29]. Furthermore, the absorption energies (DEabs ) for the complexes have been defined as (where M = Li, Na and K):
DEabs ¼ EM@C80 Molecule ðEM@C80 þ EMolecule Þ: Vibrational analysis computations were calculated to verify if the structures were minima along the potential energy surface. The metals as well as polar molecules have been shifted to ensure that the lowest energy structures were also calculated. 3. Results and discussion The central objective in the present work is to encapsulate IA group alkali metals into the cavity of C80. These calculations were performed to evaluate tertiary small molecule interactions. To accomplish this we have incorporated the Li, Na and K metal atoms and the H2O, CH3OH, NH3 and HF small polar molecules (which are also common solvents). Several positions of the polar molecules and the metals were considered in order to ensure that the structures calculated were in fact minimum energy structures along a global potential energy curve. Firstly, we will begin by discussing the geometrical properties of M@C80-polar molecule (where M = Li, Na and K) interactions. Scheme 1 presents the general reactive sites on the fullerene surface, and in Table 1 we present various geometrical parameters. Our calculations on the isolated Li@C80, Na@C80 and K@C80 yielded atomic displacement of M by 0.11 Å (compared to 1.19 Å for Li@C60), 0.07 Å (compared to 0.00 Å for Na@C60) and 0.09 Å (compared to 0.59 Å for K@C60) Å from the center, respectively. The rea-
C1
C3 C2
C4
Scheme 1. Graphical representation for the description of the bond distance parameters discussed in Table 1.
Table 1 The shortest distances (in Å) between the small polar molecules and carbon atoms in the M@C80-small molecule systems (see Scheme 1) Polar molecule-fullerene intermolecular distances (in Å) Solvent a
H2O CH3OHb NH3c HFa
Non-metal
Lid
2.20–2.26 6.31–5.07 3.70–3.76 3.83–2.93
3.01–3.04 6.30–5.06 3.80–3.89 3.00–2.97
Nad [0.22] [0.06] [0.06] [0.15]
3.00–3.61 5.97–5.07 4.00–3.96 3.81–3.92
Kd [0.07] [0.05] [0.01] [0.14]
4.18–4.55 5.49–6.30 3.79–3.90 3.70–3.85
[0.05] [0.04] [0.02] [0.03]
a Coordination of the hydrogen atom with the C1/C2 atoms without the metals, and coordination between the oxygen atom (or fluorine) and C2/C3 atoms with the metals. b Two interactions that can be described as follows: (1) between the H atom and C4 atom, and (2) for the O distance with the C3/C4 atoms. c Coordination of a hydrogen atom with the C2/C3 atoms. d Relative distortions from the center of the [80] fullerene, whereby Li@C80 had a distortion of around 0.11 Å, Na was 0.07 Å and K had a distortion of around 0.09 Å from the center.
son as to why the distortions are smaller for Na and K is that the larger masses cause them to be focused at the center. Since they are large it is more difficult for them to move freely along the interior surface of the fullerene molecules as compared to Li. Table 1 shows the intermolecular distances of the interactions of the small polar molecules with regions of the fullerene molecular surface. In the H2O and HF cases we can see that the hydrogen atom coordinates with the C1/C2 atoms without the metals. Alternatively, the oxygen atom (or fluorine atom) interacts with the C2/ C3 atoms in the metal encapsulated complexes. In the CH3OH cases there are two primary interactions, one between the hydrogen atom and C4 and another interaction between the oxygen atom and C3/C4. Finally, for the NH3 complexes there is an interaction between the hydrogen atom and the C2/C3 atoms. For the H2O case, we can see that the non-metal case yields an interaction at 2.2 and 2.26 Å with the surface of the fullerene (which corresponds to the coordination distances of the hydrogen atom with the C1/C2 atoms shown in Scheme 1). These same parameters are increase when encapsulation by Li (values of 3.0 and 3.04 Å) and Na (values of 3.0 and 3.61 Å) are taken into account. On the contrary, the change in geometry for this case is most drastically observed in K (values of 4.18 and 4.55 Å). This can be attributed to the fact that in K there some repulsion due to the larger diameter of K coupled to its smaller off-center distortion of 0.05 Å (the values in brackets). This change is a result of interactions that can be accounted for by electrostatic contributions which are used to quantify the observed trends in the energies. The possible link between the interactions of K inside of the fullerene and the external polar molecular can be attributed to the three body interactions. These interactions are additive effects that arise from the interaction of the polar molecular with the electron donated by the endohedral metal atom. Such quantities are difficult to characterize but sufficient evidence to explain this effect has been given. The values observed in the Li and Na cases are quite similar while as for K the distances increase due to the overall ability of
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K to donate a larger extent of its valence electronic density to the surface of the C80 molecule. This can be attributed to by the lowered ionization potential of K as we go down the IA group when the metal ions have higher ionic charge-to-size ratio. Such a trend can lead to a decent description of why the K encapsulated system tends to interact with H2O leading to larger intermolecular distances. If we now consider the CH3OH case, we can see that without the metal the intermolecular separations are quite large, which are somewhat reduced in Li. For Li we can see that the off-center displacement in this example is 0.06 Å compared to 0.11 Å without the small polar molecule. Perhaps a coupling between the two species leads to larger intermolecular distances in order to minimize repulsions. For the Na and the K cases we observe decreasing intermolecular separations as well as lower off-center displacements. These decreases in the distances as well as off-center displacements are attributed to the coupling of the transferred electron density to the surface of the fullerene and the external polar molecule. Such interactions are strong attractive binding forces that arise from the charge potentials between the localized electronic density (donated by the metal atom) and the external partially polarized molecule. Next, we can consider the NH3 case which shows an interaction at 3.7 and 3.76 Å with the fullerene surface. In Li we can see that the distance slightly rises to 3.8 and 3.9 Å while in Na it is about 4 Å in both cases. For the K endohedral species the distances are similar to those in Li with minimal off-center displacements. This is due to the fact that this system has several hydrogen atoms that actively form non-covalent interactions with the fullerene surface. The intermolecular distances for this case tend to increase upon metal doping as we can see from the tabulated data. These effects are accounted for by the weaker coupling of NH3 with the excess electron donated to the surface of the fullerene cage [24c,32]. In our previous investigations we have shown that the electron coupling is stronger in oxygen containing species [24a,24b] which is related to the discrepancy observed in these examples [33]. In the HF case, the intermolecular separations without the metals are 3.83 and 2.93 Å, for the coordination distances of the hydrogen atom with the C1/C2 atoms, respectively. These values decrease in the Li case as a result of further interactions with the surface of the fullerene. When Li is inserted inside of the fullerene cage, the off-center displacement is slightly higher than the nonmetal case. For the Na and K species the intermolecular separation increases, with K having a marginal off-center displacement of 0.03 Å from the center of the fullerene cage. The smaller displacements observed for the K doped cases are related to the larger size of this metal causing it to prefer to be in the center of the cage. The distances between the Na and K metals are similar whereas that for Li insertion is smaller. This trend can be explained by the fact that in the latter cases the excess donated density to the surface causes a degree of steric crowding that when coupled to three body interactions causes the molecules to separate. Table 2 displays selected vibrational modes and frequencies computed at the BLYP/DND level of theory for the fullerene-molecule interactions. From the table we can observe that in the H2O case, there are slight differences between the vibrational frequencies for the various complexes calculated. The Li@C80 complex has the smallest stretching coupling mode with the fullerene species that is followed by Na and K. These variations can again be attributed to what we discussed on charge transfer properties and translation of the metals along the axis of the C80 molecule. For the water (H2O) case we can observe that the frequencies between the fullerene cage and the oxygen atom are similar for Li and K while Na has the smallest value. We obtain values of 205, 73.5 and 205.3 cm1 for the C80–O (H2O) stretching mode
Table 2 Normal modes and their vibrational frequencies (in cm-1) calculated at the BLYP/DND level of theory Vibrational mode analysis (cm-1) Solvent
Li
Na
K
Description
H2O
205.0 265.1 295.2 310.8 196.5 248.9 291.9 302.3 196.7 250.4 281.2 349.2 195.5 247.5 284.9 308.9
73.51 411.4 553.3 609.3 457.9 507.6 531.4 613.8 433.2 590.8 610.0 619.3 45.13 289.9 384.3 495.2
205.3 240.1 394.1 633.2 458.2 507.8 531.5 547.3 453.3 566.2 618.8 650.5 54.81 349.9 385.8 499.7
C80–O(H2O) stretching Rocking Rocking Breathing Ma,b–O(CH3OH) stretching Asymmetrical stretching Stretching Stretching C80–N(NH3) stretching Breathing Stretching Asymmetrical stretching C80–F(HF) stretching HF rocking Stretching Breathing
CH3OH
NH3
HF
a
M corresponds to Li, K or Na ions. This mode is a quantification device of the strength of the metal interaction with methanol. b
which is the most significant difference that describes the basic coupling of the small polar molecule to the fullerene surface. The rest of the modes for this species are consistent with Na having a higher rocking vibrational mode which suggests that such modes are dominant and should be experimentally observed. What is interesting to observe is the mode that corresponds to the oxygen stretching with the surface is strong. The improvement of the frequency coupling of the oxygen atom to the fullerene surface upon K doping is inherently related to the electron coupling capabilities of H2O [24a]. The very fact that K donates a more significant contribution of its electron density to the surface reinforces the interaction with water as we can see from the vibrational frequencies in Table 2. The largest differences observed in this category are for the breathing modes for which we obtain values of 310.8, 609.3 and 633.2 cm1 for the Li, Na and K cases, respectively. This value transmits to us the information that the coupling between H2O and the C80 cage causes structural changes in the fullerene cage directly correlated to the degree of charge transferred to the surface. For methanol (CH3OH) we can see that while Li exhibits a series of weak interactions with the molecule while the Na and K metal atoms have larger vibrational modes. The greatest difference is observed between the Li, Na and K values of 196.5, 457.9 and 458.2 cm1, respectively, for the interaction of the metal species with the oxygen atom of CH3OH. This is especially evident for the oxygen coupling mode that is almost two times higher than for H2O. The stretching modes are similar as can be seen from the data and as we will discuss the larger vibrational modes are associated to a stronger dissociation energy pattern for the latter metal atom species. The other frequencies are widely modified especially with the asymmetrical stretching modes of the fullerene for which we obtain values of 291.9, 531.4 and 531.5 cm1 for Li, Na and K, respectively. The values of Na and K are in agreement since in this case the degree of charge transferred to the surface is roughly the same. The stretching modes observed at 302.3, 613.8 and 547.3 cm1 for Li, Na and K, respectively, posses observable differences that should be experimentally quantifiable. This latter stretching mode is also caused as a result of the electron population transfer to the surface of the molecule and can be used to explain the affinity of the metallo-complexes with this polar molecule. The observations are consistently observed in the ammonia case (NH3), whereby the Na and K species show an increased affin-
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ity for the small polar molecule. Again we must emphasize that the low-range C80–N (NH3) coupling frequencies calculated at 196.7, 433.2 and 453.3 cm1 for Li, Na and K, respectively, can be used to segregate these compounds. It is important to note that the same principles described above are maintained in the current set of vibrational frequencies. The asymmetrical stretching modes are also worth noting since we observe values of 349.3, 619.3 and 650.5 cm1 for the Li, Na and K cases, respectively. These values are attributed to modifications in the surface properties of the fullerene upon excess electron mediation and are differ to such an extent that characterization based on these values can be performed adequately. Finally for hydrogen fluoride (HF) case we can see that in all cases the vibrational modes are generally weak, but for Li there is an increased coupling between the F of HF and the fullerene surface. The values of 195.5, 45.1 and 54.8 cm1 are calculated for the Li, Na and K cases, respectively. Interestingly, this coupling parameter is stronger for Li than for Na and K, signifying that the HF species has a weaker coupling to the excess electron as in the H2O and CH3OH cases. This value is overcome by larger stretching and breathing modes observed in the Na and K cases which cause the dissociation energies to vary markedly. Namely, the largest breathing modes are 308.9, 495.2 and 499.7 cm1 for the Li, Na and K cases, respectively. These differences in the higher end modes can be used to quantify the amount of interaction between the HF species and the electron density at the fullerene surface. While the lowest frequency dominates in the Li case the other vibrational modes compensate such a variation leading to stronger binding affinities. Table 3 shows the interaction energies as well as the HOMO/ LUMO gaps in kcal/mol (the latter value is displayed in parenthesis). For the non-metal case we can see that the dissociation energy of water is 1.98 kcal/mol compared to 11.09, 5.23 and 7.63 kcal/mol for the Li, Na and K cases, respectively. The positive adsorption energies observed for H2O and HF can be accounted to do by the failure of these species to adequately solvate fullerenes [34–36]. This value is properly described since it correlates well to experimental observations. Additionally, since the charge transfer properties of water tend to form repulsive interactions with the fullerene this can help to explain the observed behavior. The calculations on this parameter were attempted with several competing DFT and ab initio methods and in all cases similar results were obtained. The negative value obtained for CH3OH is quite small which in reality approaches zero and that of NH3 is larger as a result of the increased interaction of the three hydrogen atoms of this species with the fullerene face cap. Additionally, studies have shown that fullerene species prefer NH3 than the other species considered that can be accounted for by its smaller polarity as well as differences in the HOMO/LUMO gap separation. However, in the case of H2O and HF these are highly polar molecules that without the donated electron will interact weakly with the [80] fullerene [37]. This same effect has been observed with interactions of fullerenes with polar amino acids [38].
Table 3 Absorption energies (DEabs ) in kcal/mol computed using the BLYP/DND level method for M@C80–small molecule systems by which HOMO/LUMO gaps (in kcal/mol) are displayed in parenthesis Solvent
Non-metal
Li
Na
H2O CH3OH NH3 HF
1.98 0.17 1.51 1.16
11.09 (11.53) 8.56 (11.15) 7.02 (10.93) 1.38 (12.04)
5.23 9.03 9.55 4.37
(11.94) (11.83) (11.66) (12.00)
K (11.73) (11.17) (9.65) (11.37)
7.63 (11.64) 10.02 (11.16) 8.47 (10.68) 4.80 (11.35)
This observed trend is interesting since without the metal atoms the fullerene has an endothermic heat of formation which when metals are added is actually a favorable process. The HOMO/LUMO gaps also are lowered which is directly correlated to the metal atom. As suspected previously, the Li complex showed a higher vibrational coupling between the oxygen atom of water and the fullerene surface as is exemplified by its overall increased dissociation energy. For the next case (CH3OH) we observe that insertion of endohedral metal ions increases the binding affinity. This is observed by dissociation energies of 8.6, 9.0 and about 10.0 kcal/mol for the Li, Na and K cases, respectively. One can note from the previous table the vibrational mode strength can be correlated to the exothermicity of the small polar species-fullerene association. The HOMO/LUMO gaps are also much lower which corresponds to increased reactivity and stability of the complexes formed. From our experiences there exists [24] methanol–electron coupling effects that dominantly influence the strength of the interaction of two molecules. This is inherently the case here due to the fact that the metal atoms donate an excess electron to the fullerene surface which in turn forms a connection to the small polar species. From the table we observe that systems with lowered HOMO/ LUMO gaps tend to cause the polar molecules to donate a portion of its electron density to the conduction states of the fullerene species. Due to the fact that the molecules explored have significant HOMO-LUMO gaps there is minimal charge transfer from the molecules. While some weak hybridization is feasible it is a different type of interaction. Since the metals have essentially donated their excess density to the surface of the molecule, their unique electronic capabilities will allow them to mediate the interaction of the polar molecule to the localized electron density on the fullerene surface. This trend is in agreement with previous arguments observed in related systems in accordance to this study. For the NH3 case we can see that coupling process is also favorable but is improved when metals are inserted endohedrally inside the C80 molecule. From the data it is visible that Na shows the highest coupling to the molecule with the lowest HOMO/LUMO band gap indicative of stability in these species. What is very interesting is that in the Na case this binding to the fullerene cage is improved when compared to the other cases. This is related to the inherent reactivity of Na with NH3 [40] that have been previously alluded to in the literature. In reality the systems described have interactions that are dominated by three body interactions but due to the large intermolecular distances such forces are rather weak and the charge transfer aspect should be negligible. The contrast between Na (H2O) and Na (NH3) has been reported which can be attributed to by the much smaller relaxation energy for the latter structure [41]. Additionally, Na provides excellent stability for such a molecular species when compared to other alkali metals. Finally, in the HF case the non-metal case is an endothermic process with respect to complex formation, but is exothermic upon metal insertion in all cases observed. The HOMO/LUMO band gaps are the highest in these cases meaning that the reactivity should decrease as well. The trends observed are similar to previous observations by which the K atom donates a larger degree of its electron density to the surface leading to improved interaction energies with the polar molecule. This can be explained by the ability of K to form stable complexes with HF on the surface of metallic surfaces or other unusual binding sites [42]. The differences in complex stability can be discussed by observing the highest occupied molecular orbital (HOMO) electron density from Fig. 1. In the H2O case, the electron density is located on both the fullerene and the small molecule, while in CH3OH the electron density is localized on the fullerene cage. This effect seen in methanol can be explained by the formation of strong elec-
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Fig. 1. HOMO isosurfaces (at a 0.02 a.u. contour level) for the interactions of the metal atoms with the small polar molecules.
tron–CH3OH coupling forces that have been shown to be important in molecular surface chemistry [24,31]. Therefore, it appears that since methanol has the highest dissociation energy for the cases studied the localization of the electron on the fullerene cage is indeed stabilized. In this example, the charge is mediated by the surface as a result of this unique coupling. If we consider the NH3 and HF cases, it is observed that there is more distribution of the electron density on both systems to a larger degree than the oxygen containing systems. It is interesting that in the latter cases the polar molecules attempt to mediate a portion of the charge density. This can be related to the modifications of the induced charge potentials under the surface of the molecule which arises from the metal encapsulation. It appears that the instability and repulsion causes the electron density to maintain patterns as those seen in the figure. 4. Conclusions We have explored a series of M@C80–molecule (where M = Li, Na and K) complexes with small polar molecules. The computations show that metal encapsulation can have favorable effects on C80 solvation with polar molecules. A theoretical method is shown that can be used to solubilize fullerene systems. From the calculations reported it is adequately shown that metal encapsulation can effectively yield routes towards the enhancement of tertiary polar molecule interactions [30]. The advantage of using the C80 fullerene as discussed previously is due to the larger case size that permits increased electron transfer properties since it is capable of delocalizing a larger amount of its electronic charge. In addition, since it does have a larger diameter one can use this for the future encapsulation of larger metal
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atoms which due to steric effects will be favorably hosted by this class of fullerene species. We believe that such interactions can be viewed by the angle of charge transfer effects in the molecules being explored. Other studies reveal [13] that metals in C80 will freely rotate to site next to external metal contacts. Therefore, if multiple metal surfaces are used we can sandwich the endohedral metallofullerene with electrons by a series of unique charge transfer mechanisms. This in turn will lead to an electronic nano-device that will have transport properties which are influenced by the charges present. We have seen that when metals are inserted this will permit coupling to the external surfaces of polar molecules to a higher extent that can be used as a starting point for the construction of charge-transfer nano-bridges. The interactions of the small polar molecules with the fullerene systems can be discussed from the viewpoint of charge transfer potentials with the surface of the [80] fullerene. It is known that the interaction of ionized or partially charged species (as in polar molecules) causes the properties of the complexes to be modified. These variations include localized collective electronic oscillations that can be excited by radiation effects and adsorption of molecules [39a]. To properly account for the interactions and changes of the chemical reactivity we must propose a suitable physical description. The interaction of a charge with the surface of a curved molecule (i.e. fullerene) creates an image potential on the surface [39b,39c]. These potentials can form by spatially extended electronic states that form near the molecular surface and occur by external charge polarization below the surface of the molecule. It has been proposed that ‘‘tubular image states” form near the surface of nanostructures, and are directly related to the ability of these molecules in creating of van der Waals species. The formation of image potentials can also help to describe the increases in intermolecular separations observed in some of the examples as well as stronger vibrational modes. These image potentials (calculated by modified Bessel functions) cause the fullerene to exert an outward attraction which can interact with the external polar molecule. Essentially, what we observe is a coupling between this potential and the center of mass of the polarizable charge density localized on the interacting molecule. These interactions can occur between the p-electrons that provide a justification for the interaction potentials observed in the H2O and CH3OH cases. The presented method allows us to quantify the electron–solvent coupling forces on fullerene surfaces which are brought about via charge-transfer mechanisms with alkali metal atoms. Additionally, we have seen that larger metals will indeed cause a greater degree of electron density to be transferred to the surface of molecular surfaces. Generally, this yields stronger molecule interactions with the species under consideration. The methanol case has the highest dissociation energies which is due to the greater degree of electron coupling to the density donated to the fullerene surface by the metal atom. The calculated values were further studied on the bases of HOMO molecular orbital plots as well as analysis of the corresponding vibrational coupling modes. Therefore, this localization of excess charge (that arises from the internally placed metal atoms) can be linked to external solvent molecule leading to an improved affinity as a result of the formation of ‘‘image potentials”. This work is important since it provides a theoretical route for stronger molecule interactions in fullerene systems. The physical nature of the binding between the localized electronic density and the external polar molecule is of interest. This explanation attempts to explain the interaction between an induced ‘‘image potential” and external species which are connected by their mutual charge mediation capacities. The current results are important
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in the design of fullerenes which can be used in the design of novel electrical conduits. Acknowledgment The UNAM is kindly thanked for providing financial and computation resources used to perform the research herein. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
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Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Endohedral metallo [80] fullerene interactions with small polar molecules Abraham F. Jalbout * Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Mexico D.F., Mexico
a r t i c l e
i n f o
Article history: Received 13 December 2007 Received in revised form 17 July 2008 Accepted 21 July 2008 Available online 27 December 2008 Keywords: [80] Fullerene Polar species Alkali metals BLYP
a b s t r a c t The interaction of M@C80 (M = Li, K and Na) with small polar molecules (H2O, CH3OH, HF and NH3) is described by density functional theory (DFT) calculations. Our theoretical studies show that in several computed cases the binding energies of M@C80 complexes with small polar molecules increases upon encapsulation. The observed behavior can be accounted for by charge transfer effects between the encapsulated metal and the surface of the C80 cage. These assertions have been solidified by a corresponding analysis of the thermochemistry, vibrational frequencies and HOMO molecular orbital plots of the optimized species. Ó 2008 Published by Elsevier B.V.
1. Introduction There are a variety of investigations that appear to concentrate on the functionalization of fullerene structures which can be used to improve solubility properties. Fullerenes are unique since they are capable of conserving important charge transfer mechanisms between atoms located endohedrally and the external molecular surface [1–10]. This is important because it permits the establishment of assertions used to describe reactivity based on surface modifications [11]. Similar studies on the La@C80 system [12] reveal interesting metal-like conductive properties above 29 K (which is a property related to charge transfer effects). Traditional [60] fullerenes are used to propagate particular properties for use in materials science, but the alternate [80] fullerene can also be used [13]. The applicability of endohedral metallofullerenes is related to the fact that the corresponding metallic properties can be harnessed in the design of novel electronic devices. The larger fullerene structure possesses the inherent property that the larger size of the cavity can lead to stability upon metal encapsulation. This is important in situations where larger metals are used for surface property manipulations that arise from increased charge-radius ratios. Previous calculations [11–13] suggest that larger metals generally lead to improved charge transfer properties with the molecular surface. The fact that C60 has a smaller diameter prevents favorable interactions to occur due to steric hindrance. Because the C80 cage has an increased diameter the enclosed metals have a higher degree of freedom. This is important since * Tel.: +52 55 24 22 72; fax: +52 55 16 22 17. E-mail address: [email protected] 0927-0256/$ - see front matter Ó 2008 Published by Elsevier B.V. doi:10.1016/j.commatsci.2008.07.038
the metals can translate to specific regions in the cage to donate an excess electron to the surface of the system. The excess charge localizes along the benzene rings of the fullerene system causing the issue of increased degrees of freedom to be significant. Professor Csizmadia [14a,b] has truly demonstrated the efficacy of such approaches in the quantification of biological interactions at specific points. The usefulness of these approaches in biochemical applications has been explored by others [14c,d]. Our notion is that if we modify the interactive properties of fullerenes specific interactions (as in enzymes and peptides) can be controlled. Fullerenes have a geometrical arrangement composed of five and six membered rings that permits several competitive reactive channels. This manuscript is geared at obtaining methods of using metallic encapsulation in the C80 fullerene in order to promote charge transfer effects. The charge-transfer effects could cause increased interactions with small polar species as well as larger macromolecules. It is our understanding that the dispersion of the charge throughout the host material will cause the doped fullerenes to be insensitive to the applied electric field. Experimental [5] and theoretical [15] studies describe techniques by which electrons transfer correlates to superconductivity and solubility. Theoretical calculations [7,16–19] state that Li and Na alkali atoms are distorted from the center of the [C60] fullerene cage by approximately 1.2 and 0.6 Å, respectively. Alternatively, in the K@C60 molecule the potassium atom is located exactly at the center of the complex. Presently, there is lack of information on metallic endohedral complexes of alkali metals in C80. Based on our investigations we have observed that the metals prefer to localize at the center of the C80 cage. The objective of this work is to look into complexes formed by alkali metals encapsulation inside of the [C80] fullerene. Once such
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stable interactions are modified these molecules are formed. It can be noted that the increase in molecular interactions with small polar molecules has a direct effect on their structural properties and charge transfer mechanisms. The solubility of nanomaterials has been the focus of debates [17–23] but again scant investigations are available on the theoretical mechanism of the process. The ability of the fullerenes to delocalize excess electrons on their surfaces will be used to increase their solubility [24,25]. The importance of the calculations lies in the quantification of the interaction between local charge distributions and polar molecules. It is our belief that pockets of charge (as a result of the donated electron density to the surface of the molecules by the metals) can be linked to the interaction with the polar molecules on the exterior. Such interactions occur by formation of a temporary state which is created between the excess electronic density and the dipole of the resulting polar species. Calculations show [24] that electron–polar molecule coupling on molecular surfaces, permits solvation of the systems under consideration. We have demonstrated that H2O, CH3OH, NH3 and HF adequately adhere to molecular surfaces which possessed excess electrons on their exteriors. In light of these observations we report on the interaction of M@C80 (M = Li, Na and K) with small polar molecules to analyze the effects of charge transfer on corresponding molecule binding energies. 2. Computational methods The quantum chemical calculations performed herein were carried out with the DMol3 [26] numerical-based density-functional computer software as implemented in the Materials Studio Modeling 3.1 package from Accelrys Inc. Geometrical optimizations and frequency calculations were done with the BLYP general-gradient potential approximation in conjunction with the double-numerical plus diffusion basis set (denoted as DND). Fine convergence criteria and global orbital cutoffs were employed on basis set definitions which have been proven to useful in the study of weak van der Waals complexes [27–29]. Furthermore, the absorption energies (DEabs ) for the complexes have been defined as (where M = Li, Na and K):
DEabs ¼ EM@C80 Molecule ðEM@C80 þ EMolecule Þ: Vibrational analysis computations were calculated to verify if the structures were minima along the potential energy surface. The metals as well as polar molecules have been shifted to ensure that the lowest energy structures were also calculated. 3. Results and discussion The central objective in the present work is to encapsulate IA group alkali metals into the cavity of C80. These calculations were performed to evaluate tertiary small molecule interactions. To accomplish this we have incorporated the Li, Na and K metal atoms and the H2O, CH3OH, NH3 and HF small polar molecules (which are also common solvents). Several positions of the polar molecules and the metals were considered in order to ensure that the structures calculated were in fact minimum energy structures along a global potential energy curve. Firstly, we will begin by discussing the geometrical properties of M@C80-polar molecule (where M = Li, Na and K) interactions. Scheme 1 presents the general reactive sites on the fullerene surface, and in Table 1 we present various geometrical parameters. Our calculations on the isolated Li@C80, Na@C80 and K@C80 yielded atomic displacement of M by 0.11 Å (compared to 1.19 Å for Li@C60), 0.07 Å (compared to 0.00 Å for Na@C60) and 0.09 Å (compared to 0.59 Å for K@C60) Å from the center, respectively. The rea-
C1
C3 C2
C4
Scheme 1. Graphical representation for the description of the bond distance parameters discussed in Table 1.
Table 1 The shortest distances (in Å) between the small polar molecules and carbon atoms in the M@C80-small molecule systems (see Scheme 1) Polar molecule-fullerene intermolecular distances (in Å) Solvent a
H2O CH3OHb NH3c HFa
Non-metal
Lid
2.20–2.26 6.31–5.07 3.70–3.76 3.83–2.93
3.01–3.04 6.30–5.06 3.80–3.89 3.00–2.97
Nad [0.22] [0.06] [0.06] [0.15]
3.00–3.61 5.97–5.07 4.00–3.96 3.81–3.92
Kd [0.07] [0.05] [0.01] [0.14]
4.18–4.55 5.49–6.30 3.79–3.90 3.70–3.85
[0.05] [0.04] [0.02] [0.03]
a Coordination of the hydrogen atom with the C1/C2 atoms without the metals, and coordination between the oxygen atom (or fluorine) and C2/C3 atoms with the metals. b Two interactions that can be described as follows: (1) between the H atom and C4 atom, and (2) for the O distance with the C3/C4 atoms. c Coordination of a hydrogen atom with the C2/C3 atoms. d Relative distortions from the center of the [80] fullerene, whereby Li@C80 had a distortion of around 0.11 Å, Na was 0.07 Å and K had a distortion of around 0.09 Å from the center.
son as to why the distortions are smaller for Na and K is that the larger masses cause them to be focused at the center. Since they are large it is more difficult for them to move freely along the interior surface of the fullerene molecules as compared to Li. Table 1 shows the intermolecular distances of the interactions of the small polar molecules with regions of the fullerene molecular surface. In the H2O and HF cases we can see that the hydrogen atom coordinates with the C1/C2 atoms without the metals. Alternatively, the oxygen atom (or fluorine atom) interacts with the C2/ C3 atoms in the metal encapsulated complexes. In the CH3OH cases there are two primary interactions, one between the hydrogen atom and C4 and another interaction between the oxygen atom and C3/C4. Finally, for the NH3 complexes there is an interaction between the hydrogen atom and the C2/C3 atoms. For the H2O case, we can see that the non-metal case yields an interaction at 2.2 and 2.26 Å with the surface of the fullerene (which corresponds to the coordination distances of the hydrogen atom with the C1/C2 atoms shown in Scheme 1). These same parameters are increase when encapsulation by Li (values of 3.0 and 3.04 Å) and Na (values of 3.0 and 3.61 Å) are taken into account. On the contrary, the change in geometry for this case is most drastically observed in K (values of 4.18 and 4.55 Å). This can be attributed to the fact that in K there some repulsion due to the larger diameter of K coupled to its smaller off-center distortion of 0.05 Å (the values in brackets). This change is a result of interactions that can be accounted for by electrostatic contributions which are used to quantify the observed trends in the energies. The possible link between the interactions of K inside of the fullerene and the external polar molecular can be attributed to the three body interactions. These interactions are additive effects that arise from the interaction of the polar molecular with the electron donated by the endohedral metal atom. Such quantities are difficult to characterize but sufficient evidence to explain this effect has been given. The values observed in the Li and Na cases are quite similar while as for K the distances increase due to the overall ability of
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K to donate a larger extent of its valence electronic density to the surface of the C80 molecule. This can be attributed to by the lowered ionization potential of K as we go down the IA group when the metal ions have higher ionic charge-to-size ratio. Such a trend can lead to a decent description of why the K encapsulated system tends to interact with H2O leading to larger intermolecular distances. If we now consider the CH3OH case, we can see that without the metal the intermolecular separations are quite large, which are somewhat reduced in Li. For Li we can see that the off-center displacement in this example is 0.06 Å compared to 0.11 Å without the small polar molecule. Perhaps a coupling between the two species leads to larger intermolecular distances in order to minimize repulsions. For the Na and the K cases we observe decreasing intermolecular separations as well as lower off-center displacements. These decreases in the distances as well as off-center displacements are attributed to the coupling of the transferred electron density to the surface of the fullerene and the external polar molecule. Such interactions are strong attractive binding forces that arise from the charge potentials between the localized electronic density (donated by the metal atom) and the external partially polarized molecule. Next, we can consider the NH3 case which shows an interaction at 3.7 and 3.76 Å with the fullerene surface. In Li we can see that the distance slightly rises to 3.8 and 3.9 Å while in Na it is about 4 Å in both cases. For the K endohedral species the distances are similar to those in Li with minimal off-center displacements. This is due to the fact that this system has several hydrogen atoms that actively form non-covalent interactions with the fullerene surface. The intermolecular distances for this case tend to increase upon metal doping as we can see from the tabulated data. These effects are accounted for by the weaker coupling of NH3 with the excess electron donated to the surface of the fullerene cage [24c,32]. In our previous investigations we have shown that the electron coupling is stronger in oxygen containing species [24a,24b] which is related to the discrepancy observed in these examples [33]. In the HF case, the intermolecular separations without the metals are 3.83 and 2.93 Å, for the coordination distances of the hydrogen atom with the C1/C2 atoms, respectively. These values decrease in the Li case as a result of further interactions with the surface of the fullerene. When Li is inserted inside of the fullerene cage, the off-center displacement is slightly higher than the nonmetal case. For the Na and K species the intermolecular separation increases, with K having a marginal off-center displacement of 0.03 Å from the center of the fullerene cage. The smaller displacements observed for the K doped cases are related to the larger size of this metal causing it to prefer to be in the center of the cage. The distances between the Na and K metals are similar whereas that for Li insertion is smaller. This trend can be explained by the fact that in the latter cases the excess donated density to the surface causes a degree of steric crowding that when coupled to three body interactions causes the molecules to separate. Table 2 displays selected vibrational modes and frequencies computed at the BLYP/DND level of theory for the fullerene-molecule interactions. From the table we can observe that in the H2O case, there are slight differences between the vibrational frequencies for the various complexes calculated. The Li@C80 complex has the smallest stretching coupling mode with the fullerene species that is followed by Na and K. These variations can again be attributed to what we discussed on charge transfer properties and translation of the metals along the axis of the C80 molecule. For the water (H2O) case we can observe that the frequencies between the fullerene cage and the oxygen atom are similar for Li and K while Na has the smallest value. We obtain values of 205, 73.5 and 205.3 cm1 for the C80–O (H2O) stretching mode
Table 2 Normal modes and their vibrational frequencies (in cm-1) calculated at the BLYP/DND level of theory Vibrational mode analysis (cm-1) Solvent
Li
Na
K
Description
H2O
205.0 265.1 295.2 310.8 196.5 248.9 291.9 302.3 196.7 250.4 281.2 349.2 195.5 247.5 284.9 308.9
73.51 411.4 553.3 609.3 457.9 507.6 531.4 613.8 433.2 590.8 610.0 619.3 45.13 289.9 384.3 495.2
205.3 240.1 394.1 633.2 458.2 507.8 531.5 547.3 453.3 566.2 618.8 650.5 54.81 349.9 385.8 499.7
C80–O(H2O) stretching Rocking Rocking Breathing Ma,b–O(CH3OH) stretching Asymmetrical stretching Stretching Stretching C80–N(NH3) stretching Breathing Stretching Asymmetrical stretching C80–F(HF) stretching HF rocking Stretching Breathing
CH3OH
NH3
HF
a
M corresponds to Li, K or Na ions. This mode is a quantification device of the strength of the metal interaction with methanol. b
which is the most significant difference that describes the basic coupling of the small polar molecule to the fullerene surface. The rest of the modes for this species are consistent with Na having a higher rocking vibrational mode which suggests that such modes are dominant and should be experimentally observed. What is interesting to observe is the mode that corresponds to the oxygen stretching with the surface is strong. The improvement of the frequency coupling of the oxygen atom to the fullerene surface upon K doping is inherently related to the electron coupling capabilities of H2O [24a]. The very fact that K donates a more significant contribution of its electron density to the surface reinforces the interaction with water as we can see from the vibrational frequencies in Table 2. The largest differences observed in this category are for the breathing modes for which we obtain values of 310.8, 609.3 and 633.2 cm1 for the Li, Na and K cases, respectively. This value transmits to us the information that the coupling between H2O and the C80 cage causes structural changes in the fullerene cage directly correlated to the degree of charge transferred to the surface. For methanol (CH3OH) we can see that while Li exhibits a series of weak interactions with the molecule while the Na and K metal atoms have larger vibrational modes. The greatest difference is observed between the Li, Na and K values of 196.5, 457.9 and 458.2 cm1, respectively, for the interaction of the metal species with the oxygen atom of CH3OH. This is especially evident for the oxygen coupling mode that is almost two times higher than for H2O. The stretching modes are similar as can be seen from the data and as we will discuss the larger vibrational modes are associated to a stronger dissociation energy pattern for the latter metal atom species. The other frequencies are widely modified especially with the asymmetrical stretching modes of the fullerene for which we obtain values of 291.9, 531.4 and 531.5 cm1 for Li, Na and K, respectively. The values of Na and K are in agreement since in this case the degree of charge transferred to the surface is roughly the same. The stretching modes observed at 302.3, 613.8 and 547.3 cm1 for Li, Na and K, respectively, posses observable differences that should be experimentally quantifiable. This latter stretching mode is also caused as a result of the electron population transfer to the surface of the molecule and can be used to explain the affinity of the metallo-complexes with this polar molecule. The observations are consistently observed in the ammonia case (NH3), whereby the Na and K species show an increased affin-
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ity for the small polar molecule. Again we must emphasize that the low-range C80–N (NH3) coupling frequencies calculated at 196.7, 433.2 and 453.3 cm1 for Li, Na and K, respectively, can be used to segregate these compounds. It is important to note that the same principles described above are maintained in the current set of vibrational frequencies. The asymmetrical stretching modes are also worth noting since we observe values of 349.3, 619.3 and 650.5 cm1 for the Li, Na and K cases, respectively. These values are attributed to modifications in the surface properties of the fullerene upon excess electron mediation and are differ to such an extent that characterization based on these values can be performed adequately. Finally for hydrogen fluoride (HF) case we can see that in all cases the vibrational modes are generally weak, but for Li there is an increased coupling between the F of HF and the fullerene surface. The values of 195.5, 45.1 and 54.8 cm1 are calculated for the Li, Na and K cases, respectively. Interestingly, this coupling parameter is stronger for Li than for Na and K, signifying that the HF species has a weaker coupling to the excess electron as in the H2O and CH3OH cases. This value is overcome by larger stretching and breathing modes observed in the Na and K cases which cause the dissociation energies to vary markedly. Namely, the largest breathing modes are 308.9, 495.2 and 499.7 cm1 for the Li, Na and K cases, respectively. These differences in the higher end modes can be used to quantify the amount of interaction between the HF species and the electron density at the fullerene surface. While the lowest frequency dominates in the Li case the other vibrational modes compensate such a variation leading to stronger binding affinities. Table 3 shows the interaction energies as well as the HOMO/ LUMO gaps in kcal/mol (the latter value is displayed in parenthesis). For the non-metal case we can see that the dissociation energy of water is 1.98 kcal/mol compared to 11.09, 5.23 and 7.63 kcal/mol for the Li, Na and K cases, respectively. The positive adsorption energies observed for H2O and HF can be accounted to do by the failure of these species to adequately solvate fullerenes [34–36]. This value is properly described since it correlates well to experimental observations. Additionally, since the charge transfer properties of water tend to form repulsive interactions with the fullerene this can help to explain the observed behavior. The calculations on this parameter were attempted with several competing DFT and ab initio methods and in all cases similar results were obtained. The negative value obtained for CH3OH is quite small which in reality approaches zero and that of NH3 is larger as a result of the increased interaction of the three hydrogen atoms of this species with the fullerene face cap. Additionally, studies have shown that fullerene species prefer NH3 than the other species considered that can be accounted for by its smaller polarity as well as differences in the HOMO/LUMO gap separation. However, in the case of H2O and HF these are highly polar molecules that without the donated electron will interact weakly with the [80] fullerene [37]. This same effect has been observed with interactions of fullerenes with polar amino acids [38].
Table 3 Absorption energies (DEabs ) in kcal/mol computed using the BLYP/DND level method for M@C80–small molecule systems by which HOMO/LUMO gaps (in kcal/mol) are displayed in parenthesis Solvent
Non-metal
Li
Na
H2O CH3OH NH3 HF
1.98 0.17 1.51 1.16
11.09 (11.53) 8.56 (11.15) 7.02 (10.93) 1.38 (12.04)
5.23 9.03 9.55 4.37
(11.94) (11.83) (11.66) (12.00)
K (11.73) (11.17) (9.65) (11.37)
7.63 (11.64) 10.02 (11.16) 8.47 (10.68) 4.80 (11.35)
This observed trend is interesting since without the metal atoms the fullerene has an endothermic heat of formation which when metals are added is actually a favorable process. The HOMO/LUMO gaps also are lowered which is directly correlated to the metal atom. As suspected previously, the Li complex showed a higher vibrational coupling between the oxygen atom of water and the fullerene surface as is exemplified by its overall increased dissociation energy. For the next case (CH3OH) we observe that insertion of endohedral metal ions increases the binding affinity. This is observed by dissociation energies of 8.6, 9.0 and about 10.0 kcal/mol for the Li, Na and K cases, respectively. One can note from the previous table the vibrational mode strength can be correlated to the exothermicity of the small polar species-fullerene association. The HOMO/LUMO gaps are also much lower which corresponds to increased reactivity and stability of the complexes formed. From our experiences there exists [24] methanol–electron coupling effects that dominantly influence the strength of the interaction of two molecules. This is inherently the case here due to the fact that the metal atoms donate an excess electron to the fullerene surface which in turn forms a connection to the small polar species. From the table we observe that systems with lowered HOMO/ LUMO gaps tend to cause the polar molecules to donate a portion of its electron density to the conduction states of the fullerene species. Due to the fact that the molecules explored have significant HOMO-LUMO gaps there is minimal charge transfer from the molecules. While some weak hybridization is feasible it is a different type of interaction. Since the metals have essentially donated their excess density to the surface of the molecule, their unique electronic capabilities will allow them to mediate the interaction of the polar molecule to the localized electron density on the fullerene surface. This trend is in agreement with previous arguments observed in related systems in accordance to this study. For the NH3 case we can see that coupling process is also favorable but is improved when metals are inserted endohedrally inside the C80 molecule. From the data it is visible that Na shows the highest coupling to the molecule with the lowest HOMO/LUMO band gap indicative of stability in these species. What is very interesting is that in the Na case this binding to the fullerene cage is improved when compared to the other cases. This is related to the inherent reactivity of Na with NH3 [40] that have been previously alluded to in the literature. In reality the systems described have interactions that are dominated by three body interactions but due to the large intermolecular distances such forces are rather weak and the charge transfer aspect should be negligible. The contrast between Na (H2O) and Na (NH3) has been reported which can be attributed to by the much smaller relaxation energy for the latter structure [41]. Additionally, Na provides excellent stability for such a molecular species when compared to other alkali metals. Finally, in the HF case the non-metal case is an endothermic process with respect to complex formation, but is exothermic upon metal insertion in all cases observed. The HOMO/LUMO band gaps are the highest in these cases meaning that the reactivity should decrease as well. The trends observed are similar to previous observations by which the K atom donates a larger degree of its electron density to the surface leading to improved interaction energies with the polar molecule. This can be explained by the ability of K to form stable complexes with HF on the surface of metallic surfaces or other unusual binding sites [42]. The differences in complex stability can be discussed by observing the highest occupied molecular orbital (HOMO) electron density from Fig. 1. In the H2O case, the electron density is located on both the fullerene and the small molecule, while in CH3OH the electron density is localized on the fullerene cage. This effect seen in methanol can be explained by the formation of strong elec-
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Fig. 1. HOMO isosurfaces (at a 0.02 a.u. contour level) for the interactions of the metal atoms with the small polar molecules.
tron–CH3OH coupling forces that have been shown to be important in molecular surface chemistry [24,31]. Therefore, it appears that since methanol has the highest dissociation energy for the cases studied the localization of the electron on the fullerene cage is indeed stabilized. In this example, the charge is mediated by the surface as a result of this unique coupling. If we consider the NH3 and HF cases, it is observed that there is more distribution of the electron density on both systems to a larger degree than the oxygen containing systems. It is interesting that in the latter cases the polar molecules attempt to mediate a portion of the charge density. This can be related to the modifications of the induced charge potentials under the surface of the molecule which arises from the metal encapsulation. It appears that the instability and repulsion causes the electron density to maintain patterns as those seen in the figure. 4. Conclusions We have explored a series of M@C80–molecule (where M = Li, Na and K) complexes with small polar molecules. The computations show that metal encapsulation can have favorable effects on C80 solvation with polar molecules. A theoretical method is shown that can be used to solubilize fullerene systems. From the calculations reported it is adequately shown that metal encapsulation can effectively yield routes towards the enhancement of tertiary polar molecule interactions [30]. The advantage of using the C80 fullerene as discussed previously is due to the larger case size that permits increased electron transfer properties since it is capable of delocalizing a larger amount of its electronic charge. In addition, since it does have a larger diameter one can use this for the future encapsulation of larger metal
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atoms which due to steric effects will be favorably hosted by this class of fullerene species. We believe that such interactions can be viewed by the angle of charge transfer effects in the molecules being explored. Other studies reveal [13] that metals in C80 will freely rotate to site next to external metal contacts. Therefore, if multiple metal surfaces are used we can sandwich the endohedral metallofullerene with electrons by a series of unique charge transfer mechanisms. This in turn will lead to an electronic nano-device that will have transport properties which are influenced by the charges present. We have seen that when metals are inserted this will permit coupling to the external surfaces of polar molecules to a higher extent that can be used as a starting point for the construction of charge-transfer nano-bridges. The interactions of the small polar molecules with the fullerene systems can be discussed from the viewpoint of charge transfer potentials with the surface of the [80] fullerene. It is known that the interaction of ionized or partially charged species (as in polar molecules) causes the properties of the complexes to be modified. These variations include localized collective electronic oscillations that can be excited by radiation effects and adsorption of molecules [39a]. To properly account for the interactions and changes of the chemical reactivity we must propose a suitable physical description. The interaction of a charge with the surface of a curved molecule (i.e. fullerene) creates an image potential on the surface [39b,39c]. These potentials can form by spatially extended electronic states that form near the molecular surface and occur by external charge polarization below the surface of the molecule. It has been proposed that ‘‘tubular image states” form near the surface of nanostructures, and are directly related to the ability of these molecules in creating of van der Waals species. The formation of image potentials can also help to describe the increases in intermolecular separations observed in some of the examples as well as stronger vibrational modes. These image potentials (calculated by modified Bessel functions) cause the fullerene to exert an outward attraction which can interact with the external polar molecule. Essentially, what we observe is a coupling between this potential and the center of mass of the polarizable charge density localized on the interacting molecule. These interactions can occur between the p-electrons that provide a justification for the interaction potentials observed in the H2O and CH3OH cases. The presented method allows us to quantify the electron–solvent coupling forces on fullerene surfaces which are brought about via charge-transfer mechanisms with alkali metal atoms. Additionally, we have seen that larger metals will indeed cause a greater degree of electron density to be transferred to the surface of molecular surfaces. Generally, this yields stronger molecule interactions with the species under consideration. The methanol case has the highest dissociation energies which is due to the greater degree of electron coupling to the density donated to the fullerene surface by the metal atom. The calculated values were further studied on the bases of HOMO molecular orbital plots as well as analysis of the corresponding vibrational coupling modes. Therefore, this localization of excess charge (that arises from the internally placed metal atoms) can be linked to external solvent molecule leading to an improved affinity as a result of the formation of ‘‘image potentials”. This work is important since it provides a theoretical route for stronger molecule interactions in fullerene systems. The physical nature of the binding between the localized electronic density and the external polar molecule is of interest. This explanation attempts to explain the interaction between an induced ‘‘image potential” and external species which are connected by their mutual charge mediation capacities. The current results are important
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in the design of fullerenes which can be used in the design of novel electrical conduits. Acknowledgment The UNAM is kindly thanked for providing financial and computation resources used to perform the research herein. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
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