Feasibility of Single-Walled Carbon Nanotubes as ... - ACS Publications

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Feasibility of Single-Walled Carbon Nanotubes as Materials for CO2 Adsorption: A DFT Study David Quiñonero,* Antonio Frontera, and Pere M. Deyà Departament de Química, Universitat de les Illes Balears, Crta. de Valldemossa km 7.5, 07122 Palma de Mallorca, Spain S Supporting Information *

ABSTRACT: The adsorption of CO2 by zigzag and armchair singlewalled carbon nanotubes (SWNTs) of different diameters (4.70−10.85 Å) has been studied using DFT with empirical dispersion correction (B97-D/SVP). Different binding sites have been considered, namely, in the interior (side-on and end-on binding modes) and on the surface (parallel or perpendicular) of the nanotube. Our calculations predict larger interaction energies for interior than exterior adsorption, with the strongest interactions observed for the (9,0) and (5,5) SWNTs (−12.8 and −12.5 kcal·mol−1, respectively). Therefore, these SWNTs can be considered to be very good potential candidates for carbon capture and storage in reducing CO2 emissions, as corroborated by the computed ΔH and ΔG adsorption energies. Moreover, we predict that interior adsorption would be more favorable than interstitial adsorption in bundles for (9,0), (10,0), (11,0), and (5,5) nanotubes. Furthemore, the diffusion of CO2 from the outside to the interior of the (5,5) SWNT is an energetically barrierless and favorable process. We have also analyzed the interplay between CO2·SWNT and CO2·CO2 interactions when more than one CO2 molecule is inside the tube, showing interesting cooperativity effects for SWNTs with large diameters. Finally, the symmetryadapted perturbation theory partition scheme was used to investigate the physical nature of the interactions and to analyze the different energy contributions to the binding energy.

1. INTRODUCTION During the past few decades, a great deal of research has been conducted on the development of novel porous carbon materials because of their extensive applications in gas storage and separation, catalyst support, and battery electrodes.1 Among them, activated carbons are a typical representative of porous carbons widely used in these fields. The adsorption of CO2 on carbonaceous surfaces is a subject of great interest in the technological and atmospheric fields. From the atmospheric point of view, the reduction of the CO2 concentration on the atmosphere is an urgent requirement. Sequestration of the greenhouse gas CO2 is therefore one of the most pressing issues in environmental protection.2 Carbon capture and sequestration, or storage, is rapidly becoming a key element in our nascent efforts to minimize the emissions of CO2 generated during combustion and perhaps even to regulate the amount of CO2 in the atmosphere, storing it in a suitable place. Carbon nanotubes3 have been proven to possess good potential as adsorbents for removing many kinds of organic and inorganic pollutants,4,5 such as CO2, which is mainly attributable to their pore structure because they are hollow cylinders and can behave as efficient gas containers. Conceptually, a single-walled carbon nanotube (SWNT) is constructed by rolling up graphene along a certain direction to form a cylinder. The circumference of the SWNT is determined by its chiral vector Ch = na1 + ma2, where (n,m) are integers known as the chiral indices and a1 and a2 are the unit vectors of © 2012 American Chemical Society

the graphene lattice (Figure 1). Perpendicular to Ch, the vector T points to the long axis of the SWNT. Ch and T are referred to as chiral vector and translational vector (the tube axis), respectively. Together, they define the unit cell of a SWNT. The chiral indices (n,m) are commonly used to label SWNTs. If

Figure 1. Graphical representation of the various types of SWNTs that can be formed by rolling up a graphite sheet. Received: July 3, 2012 Revised: September 12, 2012 Published: September 13, 2012 21083

dx.doi.org/10.1021/jp306586f | J. Phys. Chem. C 2012, 116, 21083−21092

The Journal of Physical Chemistry C

Article

fail to describe adequately dispersive interactions.13 However, general empirical dispersion corrections have been proposed by Stefan Grimme to describe the interatomic dispersive interactions. In this article, we first report preliminary calculations on complexes of benzene, naphthalene, anthracene, coronene, (9,0), and (5,5) (as nanotube models) interacting with CO2 to validate the B97-D/SVP level of theory, a DFT with the inclusion of the correction for dispersion effects, as an excellent methodology to use for our SWNTs systems. Second, we use the B97-D/SVP method to study the interior (end-on and sideon binding modes) and exterior CO2 binding to SWNTs with different symmetries, for example, armchair and zigzag. Moreover, we explore different sizes of SWNT diameters, from 5 to 11 Å for the different symmetries, with tube lengths of ca. 20 Å and compare with interstitial binding in bundles. Because we are also interested in studying the adsorption of more than one CO2 molecule per nanotube fragment, we have performed DFT calculations in this regard to look into possible cooperativity effects. Finally, the symmetry-adapted perturbation theory (SAPT) partition scheme14 is utilized to analyze the different energy contributions to the binding energy.

m = 0, then the nanotubes are called zigzag. If n = m, then the nanotubes are called armchair. Otherwise, they are called chiral. The CO2 adsorption on SWNTs has been theoretically and experimentally studied. However, the available literature on quantum mechanics calculations of CO2·SWNT systems is scarce compared to other gases. For instance, Zhao et al. have carried out Local Density Approximation (LDA) DFT calculations on zigzag (10,0) and (17,0) and armchair (5,5) nanotubes as well as graphene interacting with CO2.6 They observed that CO2 is weakly adsorbed on the exterior of the nanotubes, with equilibrium distances between 3.2 and 3.5 Å and adsorption energies ca. 2 kcal·mol−1, leading to the conclusion that there is no clear dependence of adsorption on the tube size and chirality. In another article, Li and coworkers reported7 that SWNTs adsorb nearly twice the volume of CO2 compared to activated carbon with an experimental heat of adsorption of 2.3 kJ·mol−1, ca. 0.6 kcal·mol−1. Calculations at the MP2 and CCSD(T) levels of theory on models for graphene and a (9,0) nanotube yielded a similar binding energy of 0.8 kcal·mol−1 and they showed that the CO2 molecule is physisorbed side-on to the nanotube. Similarly to Zhao’s results,6 binding energies do not vary significantly with tube size. LDA-DFT calculations were also carried out to study the intra- and intermolecular interactions of a (10,10) nanotube with CO2.8 The authors observed that for different orientations of CO2 the adsorption energy is larger for interior adsorption than on the exterior, with the largest binding energy (−4.1 kcal·mol−1) for CO2 adsorbed parallel to the surface. Interaction energies in groove and interstitial sites of bundles were also reported, which are slightly more negative than in pore sites. Very recently, Tabtimsai et al. studied the adsorption of CO2 perpendicular to the exterior of the surface of an armchair (5,5) SWNT using the B3LYP/LanL2DZ method,9 yielding an equilibrium distance of 3.269 Å and a very small adsorption energy (−0.39 kcal·mol−1). One important drawback of the density functional theory (DFT) is that the dispersion forces are not well-described, forces that are supposed to play an important role in the CO2·SWNT interaction. It was not until recently that DFT calculations with correction for dispersive interactions were performed to study the adsorption of CO2 inside an (8,8) SWNT.10 According to the authors, when this correction was included, reasonable binding energies of −4.3 kcal·mol−1 were obtained, a value much like those previously reported by LDADFT studies.6,8 The idea of studying the interaction of large π-extended carbon nanotubes with neutral and apolar molecules such as CO2 is a challenge for a computational chemist, who has to think about the level of theory to use without compromising the accuracy of the results. In our case, electron correlation is critical; furthermore, dispersion forces are most likely going to be critical in the binding. A relatively accurate and simple way to account for electron correlation in ab initio calculations is Møller−Plesset second-order perturbation theory (MP2). However, the MP2 method usually overestimates intermolecular binding energies for systems dominated by dispersion interactions.11 The spin component scaled-MP2 (SCS-MP2) method removes the most serious problem of the MP2 method, namely, the strong overestimation of dispersion energies, yielding better geometries and binding energies for such systems.12 Nevertheless, the use of these post-HF methods is prohibitive due to the size of the systems in our study. DFT methods, although reducing the computational expense, often

2. COMPUTATIONAL METHODS We carried out geometry optimizations by means of DFT calculations at the B97-D15 level of theory. This approach is based on Becke’s GGA functional introduced in 199716 and is explicitly parametrized by including damped atom-pairwise dispersion corrections of the form C6·R−6. We optimized the geometry of all compounds using restricted Kohn−Sham DFT.17 In these calculations, the Ahlrichs double-ζ basis for all atoms (def-SVP basis set, SVP hereafter)18 was used, unless stated otherwise. Our DFT calculations were carried out using the resolution of the identity (RI) B97-D, which uses an auxiliary fitting basis set19 to avoid treating the complete set of two-electron repulsion integrals, thus speeding up calculations by a factor of 10. Because of the time-consuming nature of the calculations, we used the parallel RIDFT19,20 methodology. Fast evaluation of the Coulomb potential for electron densities by using a multipole-accelerated RI approximation linear scaling [O(N)] for large molecules was also used.21 For our preliminary calculations, we have used the spin-component scaled MP2 method (SCS-RI-MP2), which is based on the scaling of the standard MP2 amplitudes for parallel- and antiparallel-spin double excitations.22 The SCS-RI-MP2 correlation treatment yields structures that are superior to those from standard MP2, particularly in systems that are dominated by dispersive interactions.12 Geometries of all structures were optimized with the analytical gradient method without imposing any symmetry constraints, unless stated otherwise. The vibrational frequencies were calculated at the RI-BP86-D/ def-SVP level of theory. The default scaling factor (0.9914) was used for the ZPE and chemical potential correction values. All thermodynamic parameters were computed using f reeh routine for T = 250−350 K (ΔT = 2 K) and P = 0.1 MPa. All of the theoretical calculations described herein were carried out by using TURBOMOLE version 6.1.23,24 The partitioning of the interaction energies into the individual electrostatic, induction, dispersion, and exchangerepulsion components was carried out by performing DFT calculations combined with the symmetry-adapted perturbation theory (DFT-SAPT) approach14 with MOLPRO progam.25 The DFT-SAPT intermolecular interaction is given in terms of 21084



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the first-, second-, and higher-order correction interaction terms that are indicated by the superscripts in eq 1

RI-MP2/TZVP level of theory and computed its binding energy at the SCS-RI-MP2/AVTZ level of theory. The geometric and energetic results of these calculations are gathered in Table 1. From the energetic point of view, regardless of the computational method used, all interaction energies are negative, indicating that the formation of the complexes between the aromatic systems and CO2 is favorable. The largest binding energy corresponds to the nanotube complexes, which dramatically decreases for the next-in-size coronene complex and then monotonically decreases when the aromatic system gets smaller. Comparison of the DFT energy values yields larger uncorrected binding energies for the SVP basis set than for the TZVP results. Moreover, the DFT/SVP interaction energies, as opposed to the DFT/TZVP energies, are in very good agreement with the MP2 results, with energy differences as large as 0.3 kcal·mol−1 for BEN, NAP, ANT, COR, and (9,0) complexes. For instance, the uncorrected interaction energies for the BEN (COR) complex at the DFT/ SVP and MP2 levels are −2.9 (−4.5 kcal·mol−1) and −2.6 kcal·mol−1 (−4.7 kcal·mol−1), respectively. For the (5,5) complex, the binding energy difference between the DFT/ SVP and MP2 results is larger (ca. 3 kcal·mol−1) than that for the rest of the complexes because the binding energy for the nanotube is also large (−17.0 kcal·mol−1 at the DFT/SVP level). The same trend is also observed from the comparison of the BSSE corrected binding energies for all complexes computed at the DFT/SVP and MP2 levels of theory. Unlike the uncorrected values, the BSSE-corrected binding energies are similar for both basis sets, where the SVP results are slightly less negative than the TZVP results. From the geometrical point of view, a comparison has also been made among the different levels of theory, with two points worth being remarked. On one hand, the equilibrium distances obtained at the DFT/TZVP level are generally longer (≥0.10 Å) than the ones obtained at the DFT/SVP level. (See Table 1.) For instance, for the BEN·CO2 complex, a 0.15 Å difference in length is observed. The only exceptions are the nanotube complexes, yielding very similar equilibrium distances, although 0.02 Å shorter at the DFT/TZVP level. On the other hand, the DFT/SVP equilibrium distances are in good agreement with the MP2 ones, with differences in length as large as 0.06 Å. For instance, the equilibrium distances for the COR ((5,5)) complex at the DFT/SVP and MP2 levels are 3.24 (3.29 Å) and 3.20 Å (3.26 Å), respectively. From the results gathered in Table 1 it can be deduced that the DFT method with the SVP basis set nicely reproduces all of the interactions. TZVP results deviate a little bit, especially for equilibrium distances. Therefore, the comparison of DFT and MP2 results clearly validates the use of RI-B97-D/SVP level of theory to study the interaction of SWNTs with CO2. From now on, this is the computational methodology that will be used throughout the manuscript. We have also evaluated the effect that the elongation of the tube would have on the CO2 adsorption energies. In Table 2, we include the length of the tube together with the interaction energies for a series of (5,5) SWNTs. From the inspection of these data, reasonable results are obtained from lengths of 8.6 Å. In addition, we observe that saturation in the interaction energy is achieved for armchair SWNTs with T values greater than 7, that is, for tubes longer than 16.1 Å. 3.2. Binding Studies of SWNTs with a Single CO2 Molecule. 3.2.1. Complexes with Zigzag SWNTs. The zigzag SWNTs we used in our study have tube lengths of ca. 20 Å,

1 2 2 2 2 E int = Eel1 + Eexch + E ind + E ind − exch + Edisp + Edisp − exch

+ δ(HF)

E1el

(1)

E1exch

where and are the sum of the electrostatic interaction energy and the first-order exchange energy, respectively. E2ind, E2ind‑exch, E2disp, and E2disp‑exch denote the induction (with response) energy, the second-order induction-exchange (with response) energy, the dispersion energy, and the exchange-dispersion contribution, respectively. δ(HF) is the Hartree−Fock correction for higher-order contributions to the interaction energy and thus is not included in DFT-SAPT calculations. The cc-pVDZ, aug-cc-pVDZ, and aug-cc-pVTZ basis sets were used to compute this correction. For brevity, we will often refer to the cc-pVDZ, aug-cc-pVDZ, and aug-cc-pVTZ results by the shorthand notation VDZ, AVDZ, and AVTZ, respectively. Physically meaningful separation of the interaction energy may be obtained by classifying the cross terms induction-exchange E2ind‑exch and dispersion-exchange E2disp‑exch as a part of the induction and the dispersion, respectively.26 The VDZ, AVDZ and AVTZ basis sets were used for the DF-DFT-SAPT calculations. As auxiliary fitting basis set, the JK-fitting basis of Weigend27 was employed. The cc-pVTZ JK-fitting basis was used for all atoms. For the intermolecular correlation terms, that is, the dispersion and exchange-dispersion terms, the related MP2-fitting basis of Weigend, Köhn, and Hättig28 was employed, that is, the VDZ, AVDZ, and AVTZ MP2-fitting basis. In the DFT-SAPT calculations the BP86 functional (the B88 exchange functional29 in combination with P86 gradient correction)30 was employed using the B97-D/SVP optimized geometries.

3. RESULTS AND DISCUSSION 3.1. Preliminary Studies. We chose different aromatic systems to interact with CO2 as models for nanotubes, namely, benzene (BEN), naphthalene (NAP), anthracene (ANT), coronone (COR), and finally a (9,0) and (5,5), T = 4 (Figure 1) carbon nanotube model (Figure 2). We carried out B97-D/ SVP, B97-D/TZVP, and SCS-RI-MP2/aug-cc-pVTZ (AVTZ) geometry optimizations for all complexes, constraining the symmetry to the C2v group, except for the complex with the (5,5) nanotube. For this complex, we imposed the Cs symmetry and, particularly, for the MP2 optimization we used the SCS-

Figure 2. Complexes employed in our preliminary study. 21085



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Table 1. Interaction Energies without and with the BSSE Correction (E and EBSSE, in kcal·mol−1) and Equilibrium Distances (Re, in Å) of the Complexes of CO2 with Benzene (BEN), Naphthalene (NAP), Anthracene (ANT), Coronene (COR), (9,0), and (5,5) SWNT Models at the RI-B97-D and SCS-RI-MP2 Levels of Theory RI-B97-D E

SCS-RI-MP2

EBSSE

E

EBSSE

Re

complexes

SVP

TZVP

SVP

TZVP

SVP

TZVP

AVTZ

AVTZ

AVTZ

BEN·CO2 NAP·CO2 ANT·CO2 COR·CO2 (9,0)·CO2 (5,5)·CO2

−2.9 −3.5 −3.5 −4.5 −12.8 −17.0

−2.0 −2.4 −2.4 −3.3 −8.9 −13.3

−1.7 −1.9 −2.1 −2.9 −8.5 −11.6

−1.9 −2.2 −2.2 −3.1 −8.3 −11.6

3.36 3.22 3.30 3.24 3.43 3.29

3.51 3.36 3.40 3.36 3.41 3.27

−2.6 −3.6 −3.8 −4.7 −12.7 −20.5

−1.8 −2.3 −2.4 −2.5 −8.6 −13.7

3.39 3.22 3.24 3.20 3.40 3.26

Re

(9,0)·CO2) show that this binding mode exhibits much smaller adsorption energies compared with the CO2 interacting parallel to the surface. Therefore, hereafter, we will only discuss the out complexes with the CO2 molecule parallel to the surface. For the out interaction sites, we observe that the binding energies are more or less the same, around −3 kcal·mol−1, with a slight preference for the big nanotubes. In this regard, the interaction energies for the (6,0) and (12,0) SWNTs are −2.6 and −2.8 kcal·mol−1, respectively. However, the interaction energies for the in sites are quite different depending on the diameter of the tube. Thus, for (6,0) the interaction is repulsive because the CO2 molecule cannot fit inside a nanotube with such a small diameter (4.70 Å). A repulsive behavior is also observed for the (7,0), meaning that its diameter of 5.48 Å is still too small to place a CO2 molecule in its interior. For (8,0), the interaction energy becomes negative (E = −4.8 kcal·mol−1) and reaches a maximum (in absolute value) of −12.8 kcal·mol−1 for the (9,0) SWNT. The binding energies for (10,0), (11,0), and (12,0) progressively decay from −11.5 to −8.9 and finally to −6.8 kcal·mol−1, respectively. Therefore, the binding energies for the in complexes of (8,0), (9,0), (10,0), (11,0), and (12,0) are larger than those for the out complexes, as would be expected because due to the curvature of the nanotube, the interior sites present more nearest-neighbor carbon atoms at a reasonable equilibrium distance to an internally adsorbed CO2 molecule than the exterior sites. Moreover, from these results, it can be inferred that the CO2 molecule will be perfectly accommodated inside the (9,0) nanotube.

Table 2. Interaction Energies without and with the BSSE Correction (E and EBSSE, in kcal·mol−1) and Length of the Tube (L, in Å)a of the Complexes of CO2 with (5,5) Armchair SWNTs at the RI-B97-D/SVP Level of Theory

a

Ta

E

EBSSE

L

3 4 5 6 7 8 9

−15.5 −17.0 −17.5 −17.8 −17.6 −17.9 −17.9

−10.4 −11.6 −12.1 −12.4 −12.4 −12.5 −12.5

6.1 8.6 11.1 13.6 16.1 18.6 21.1

See Figure 1.

which correspond to a value of T = 5 (Figure 1). We did calculations starting from the (6,0), C120H12, to the (12,0), C240H24, nanotubes covering diameters from 4.70 to 9.39 Å. We also considered different (n,0)·CO2 complexes depending on the location of the CO2 molecule with respect to the nanotube, that is, in the interior (in configuration) or exterior (out configuration) of the nanotube. In Table 3, we include the interaction energies, the diameter of the nanotubes, and the CO2···SWNT equilibrium distances, measured as OCO···SWNT mean distance, for the two different interaction sites, inside and outside the tube. For the out complexes, we have not considered the CO2 molecule interacting with its axis perpendicular to the surface of the nanotube since because studies8 and this work (see Table 3,

Table 3. Interaction Energies without and with the BSSE Correction (E and EBSSE, in kcal·mol−1) and Equilibrium Distances (Re, in Å)a of the Complexes of CO2 with Graphene (GPH) and (n,0) Zigzag SWNTs (n = 6−12) at the RI-B97-D/SVP Level of Theory and Diameter of the Nanotubes (Ø, in Å) E

Re

Ø

complexes

in

out

in

out

in

out

(6,0)·CO2 (7,0)·CO2 (8,0)·CO2 (9,0)·CO2

91.1 2.0 −11.4 −17.1

103.0 11.3 −4.8 −12.8

3.23 3.23 3.22 3.21 3.08b 3.20 3.20

4.70 5.48 6.26 7.05

−14.8 −11.7 −10.8c −10.3 −9.5c −5.3

−2.6 −2.6 −2.6 −2.7 −1.3b −2.8 −2.7

2.29 2.65 3.04 3.44

(10,0)·CO2 (11,0)·CO2

−4.3 −4.3 −4.2 −4.3 −2.4b −4.5 −4.5

3.19

9.40

(12,0)·CO2 GPH·CO2 a

EBSSE

−4.5

−11.5 −8.9 −7.9c −7.6 −6.8c −3.5

−2.8

3.17 3.09 3.13c 3.07 3.05c 3.12

7.83 8.61

OCO···SWNT mean distance. bCO2 molecule interacting with its axis perpendicular to the surface of the nanotube. cEnd-on conformation. 21086



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From the comparison of the interaction energy for the in complexes versus the diameter of the nanotube, an interesting trend is observed; the energy profile is very similar to that of a binding curve. Thus, for the smallest nanotubes ((6,0) and (7,0)), the interaction is repulsive, decaying very rapidly as the diameter increases, reaching a minimum for (9,0). For larger diameters ((10,0), (11,0), and (12,0)) the interaction energy shows an asymptotic behavior. In fact, at the infinity, because the nanotube will become a graphene sheet, the interaction energy must be that of the graphene complex with CO2, which is −3.5 kcal·mol−1 at the B97-D/def-SVP level (Table 3). Therefore, for SWNTs larger than (12,0), the interaction energy for the in complexes is expected to be confined between −7.6 and −3.5 kcal·mol−1. Following the same reasoning, for the out complexes, as the diameter increases, the interaction energy becomes very slightly more negative tending, at the infinity, to the interaction energy of the graphene complex. Let us compare our SWNT·CO2 in binding results with those of a hypothetical homogeneous bundle of zigzag SWNTs interacting with CO2. First, we considered only the interstitial binding site because it is energetically the most favorable.31 Second, in the interstitial binding site of a SWNT bundle, only three nanotubes interact with the CO2 molecule through their convex surfaces. In the best case scenario, we could consider that CO2 is interacting with the out sites of three SWNTs with an extrapolated total binding energy three times that of one CO2 adsorbed at the out site of one SWNT, as described in Table 3. For instance, the interstitial interaction energy for the (9,0) SWNTs bundle would be three times the interaction energy of the (9,0) out complex (3 × −2.7 = −8.1 kcal·mol−1). Therefore, the in adsorption for the (9,0) SWNT (−12.8 kcal·mol−1, Table 3) would be very much preferred over the interstitial bundle adsorption (−8.1 kcal·mol−1). The same trend would be observed for the bigger nanotubes, although the energy difference between in and interstitial adsorption diminishes when the diameter of the tube increases (ΔE = −4.7, −3.1, and −0.8 kcal·mol−1 for (9,0), (10,0), and (11,0), respectively). Following the trend, for the next-in-size nanotube, (12,0), the energy difference would be reversed, and now the interstitial bundle adsorption (−8.4 kcal·mol−1) would be more favorable than the in adsorption (−7.6 kcal·mol−1). Thus, in or endohedral adsorption would be more favorable than interstitial adsorption for zigzag nanotubes smaller than (12,0) and larger than (8,0). Temperature effects have also been taken into account for the in (9,0) adsorption complex by computing ΔH and ΔG values between 250 and 350 K. From the inspection of the results in Table S1 of the Supporting Information, we observe that the ΔH values are more or less constant with the temperature; for example, at 250 and 350 K, the ΔH values are −13.6 and −13.7 kcal·mol−1, respectively. However, as expected, ΔG results vary from −6.5 kcal·mol−1 at 250 K to −3.3 kcal·mol−1 at 350 K with a room temperature ΔG value of −4.9 kcal·mol−1 (Table S1 of the Supporting Information). These thermal results indicate that the in adsorption of CO2 by the (9,0) SWNT is favored even at high temperatures. The equilibrium distances for the out complexes are very similar for all SWNTs (ca. 3.20 Å, Table 3). However, if we take a closer look, then we will notice that the equilibrium distances for the out complexes slightly decrease as the diameter of the SWNT increases, from 3.23 to 3.19 Å for (6,0) and (12,0), respectively, in agreement with the observed increase in the binding energies. The preferred location of the CO2

molecule in these complexes is along the a2 direction (Figure 1), placing its C atom right on the middle of the C−C common bond between two rings of an a2 1D array of hexagons (Figure 3). The arrangement of the CO2 molecule in the in complexes

Figure 3. Out (left) and in (side-on (center) and end-on (right)) interaction sites for zigzag nanotube complexes.

is not the same for all nanotubes. For instance, for the (6,0), (7,0), (8,0), and (9,0) nanotubes, the CO2 molecule is placed parallel to the tube along its axis (side-on conformation, there is no other choice, Figure 3). For the (10,0) and (11,0) SWNTs, the CO2 is also placed parallel to the tube but a little bit off the center of the nanotube. In particular, for the (11,0) complex, the CO2 molecule has enough room to adopt another conformation (transversal or end-on conformation, Figure 3), although the side-on binding is more favored (Table 3). The same behavior is observed for the (12,0) nanotube complex. This fact can be understood by looking at the geometry of the end-on and side-on conformations for both (11,0) and (12,0) complexes. The interaction of both O atoms of CO2 with the nanotube makes possible closer CO2·SWNT contacts with a greater number of carbon atoms of the nanotube in both sideon than in both end-on complexes (Table 3), thus favoring the former binding. In general, our computed binding energies are slightly larger than the values reported in the literature for the out complexes.6,7 For instance, Zhao and coworkers6 have reported a CO2 adsorption energy of −2.24 kcal·mol−1 for the (10,0) SWNT, as opposed to our results, −2.8 kcal·mol−1, although the equilibrium distances are the same (3.20 Å). In addition, Li and coworkers7 have reported a CO2 binding energy of −0.81 kcal·mol−1 for a model of a (9,0) nanotube, a very small value compared with our interaction energy of −2.7 kcal·mol−1. To our knowledge, interaction energies computed for the in complexes of zigzag nanotubes are absent in the literature. 3.2.2. Complexes with Armchair SWNTs. The armchair SWNTs we studied are ca. 21 Å long, corresponding to a value of T = 9 (Figure 1). We did calculations starting from the (4,4), C144H16, to the (8,8), C288H32, nanotubes covering diameters from 5.42 to 10.85 Å. Two different interaction sites for CO2 were considered, that is, inside and outside the tube, the latter parallel to the surface. The interaction energies, the diameter of the nanotubes, and the CO 2 ···SWNT equilibrium distances, measured as OCO···SWNT mean distance, for the in and out complexes are gathered in Table 4. As for the zigzag nanotubes, the interaction energies for the out complexes very slightly increase with the size of the SWNT. In this regard, the interaction energies for the (4,4) and (8,8) SWNTs are −2.6 and −2.9 kcal·mol−1, respectively, in agreement with the tendency to give the interaction energy of the graphene complex (−3.5 21087



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Table 4. Interaction energies without and with the BSSE Correction (E and EBSSE, in kcal·mol−1) and Equilibrium Distances (Re, in Å)a of the Complexes of CO2 with (n,n) Armchair SWNTs (n = 4−8) at the RI-B97-D/SVP Level of Theory and Diameter of the Nanotubes (Ø, in Å) E

Re

Ø

complexes

in

out

in

out

in

out

(4,4)·CO2 (5,5)·CO2 (6,6)·CO2 (7,7)·CO2

13.2 −17.9 −10.6 −9.7 −8.2b −8.6 −8.3b

−4.3 −4.4 −4.5 −4.6

22.4 −12.5 −7.8 −7.3 −6.8b −6.3 −5.8b

−2.6 −2.7 −2.7 −2.8

2.63 3.30 3.21 3.10 3.53b 3.08 3.09b

3.21 3.19 3.17 3.16

5.42 6.78 8.14 9.49

3.16

10.85

(8,8)·CO2 a

EBSSE

−4.6

−2.9

OCO···SWNT mean distance. bEnd-on conformation.

kcal·mol−1) at the infinity. The interaction energies for the in sites depend on the diameter of the tube. As can be extracted from Table 4, the interaction energies are negative for all armchair SWNTs in complexes with the exception of the (4,4) nanotube, which is too small to accommodate the CO2 molecule inside. In fact, the diameter of the armchair (4,4) nanotube (5.42 Å) is similar to the zigzag (7,0) SWNT (5.48 Å), for which we also observed a repulsive behavior. The largest binding energy is observed for the (5,5) SWNT, with a value of −12.5 kcal·mol−1. The interaction energies for the rest of the series, (6,6), (7,7), and (8,8), progressively decrease from −10.6 to −9.7 and finally to −8.6 kcal·mol−1, respectively. Therefore, from the inspection of the energy values, it can be deduced that the (5,5) nanotube is a perfect match to trap inside the CO2 molecule. In fact, the (5,5) SWNT shows a similar binding energy compared with that of the zigzag (9,0) SWNT. The comparison of the interaction energy for the in complexes versus the diameter of the nanotube yields more or less the same trend as that for zigzag SWNTs; for the smallest nanotube (4,4), the interaction is repulsive, decaying rapidly to a minimum for the (5,5); then, the interaction energy becomes less negative for the rest of the SWNTs, tending to the value of the graphene complex (−3.5 kcal·mol−1). Therefore, for nanotubes larger than (8,8), the interaction energy for the in complexes is expected to be confined between −6.3 and −3.5 kcal·mol−1. Let us compare our SWNT·CO2 in binding results with those of a hypothetical homogeneous bundle of armchair SWNTs interacting with CO2 at interstitial sites. Following the same reasoning as that described above for the zigzag nanotubes, the interstitial interaction energy for the (5,5) SWNTs bundle would be three times the interaction energy of the (5,5) out complex (3 × −2.8 = −8.4 kcal·mol−1). Therefore, the in adsorption (−12.5 kcal·mol−1, Table 4) would be more favorable than the interstitial bundle adsorption (−8.4 kcal·mol−1) for the (5,5) SWNT. However, for bigger nanotubes the interstitial binding adsorption would be preferred over the in adsorption, with interaction energy differences of ΔE = 0.3, 1.1, and 2.4 kcal·mol−1 for (6,6), (7,7) and (8,8), respectively. Therefore, in or endohedral adsorption would be more favorable than interstitial adsorption only for the (5,5) armchair nanotube. We have also considered temperature effects for the in (5,5) adsorption complex that are similar to those observed for the (9,0) complex. From these thermodynamic results (Table S1 of the Supporting Information), we notice that ΔH is constant with the temperature (ΔH = −12.7 kcal·mol−1 at 250 K and ΔH = −12.5 kcal·mol−1 at 350 K). In addition, ΔG values are

comprised between −4.3 kcal·mol−1 at 250 K and −1.0 kcal·mol−1 at 350 K with a room temperature ΔG = −2.7 kcal·mol−1 (Table S1 of the Supporting Information). These thermal results indicate that the in adsorption of CO2 by the (5,5) SWNT is favored even at high temperatures, although less favored than for the (9,0) case. The adsorption of the CO2 molecule at the interior of a nanotube is only possible if the CO2 molecule is capable of entering the SWNT from the exterior. For this purpose, we have computed the interaction energies of the (5,5) SWNT with a CO2 molecule at different distances along the tube axis. Initially we started at 16 Å away from the center of the tube, that is, at ca. 4.4 Å from the closest oxygen atom of CO2 to the plane defined by the hydrogen atoms. Then, we approached the CO2 in 0.4 Å intervals, computing the resulting interaction energy by performing a rigid scan. The results are represented in Figure 4. At first, we observe that the interaction energy is

Figure 4. Graphical representation of the interaction energy of (9,0)·CO2 in complex and the distance separation from the center of the tube to the CO2 molecule. The positions where the hydrogens and the first carbon atoms are located are represented by the green and red dots, respectively.

slightly negative and more or less constant until the CO2 reaches the hydrogen atoms of the nanotube, changing abruptly (going from −2.1 kcal·mol−1 for d = 11.6 Å to −10 kcal·mol−1 for d = 8.0 Å), indicating that the CO2 molecule is entering the SWNT. Once the CO2 is inside the tube, the interaction energy moderates its decay until a plateau is reached at d ≤ 2.8 Å. Therefore, the diffusion of CO2 from the outside to the interior of the (5,5) SWNT is an energetically barrierless and favorable process. 21088



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The equilibrium distances for the out complexes decrease as the diameter of the SWNT increases, from 3.21 to 3.16 Å for (4,4) and (8,8), respectively. In these complexes, the CO2 molecule is preferably placed along an array of fused hexagons (just like for the zigzag out complexes) parallel to the nanotube axis, locating its C atom on the middle of the C−C common bond between two hexagons (Figure 5). For the in complexes,

Table 5. Synergetic Energies with BSSE Correction and Interaction Energies without and with the BSSE Correction (ESYN, E, and EBSSE, respectively, in kcal·mol−1), Equilibrium and CO2···CO2 Distances (Re and D, respectively, in Å) of the in Complexes of One, Two, and Three CO2 Molecules with (9,0), (5,5), (12,0), and (8,8) SWNTs at the RI-B97-D/ SVP Level of Theory SWNT

#CO2

E

EBSSE

(9,0)

1 2 3 1 2 3 1 2 3 1 2 3

−16.3 −34.0 −49.8 −17.9 −35.7 −52.9 −9.5 −21.6 −33.2 −8.3 −18.7 −29.0

−12.0 −24.7 −35.8 −12.5 −24.9 −36.5 −6.8 −15.6 −23.3 −5.8 −13.0 −20.0

(5,5)

(12,0)

(8,8)

Figure 5. Out (left) and in (side-on (center) and end-on (right)) interaction sites for armchair nanotube complexes. a

we observe both side-on and end-on CO2 binding modes. The side-on interaction is found for all complexes, regardless the size of the nanotube. However, the end-on complexes are only observed for the biggest (7,7) and (8,8) SWNTs, due to the geometrical requirements for this binding to occur. For these two nanotubes, nonetheless, the lowest binding mode corresponds to the side-on arrangement, as also observed for the zigzag SWNTs. A likely explanation is that the interaction of both O atoms of CO2 with the nanotube makes possible closer and greater number of CO2···SWNT contacts for the side-on than for the end-on complexes, favoring the former conformation, a fact that can be related to the observed predilection of the CO2 molecule to be aligned with a 1Ds array of fused hexagons. As a general trend, the computed binding energies presented in this study are slightly larger than the values reported in the literature for the out complexes. For instance, Zhao and coworkers6 reported a CO2 adsorption energy of −2.5 kcal·mol−1 for the (5,5) SWNT, which compares reasonably well with our result of −2.7 kcal·mol−1. However, our reported equilibrium distance is much shorter (3.19 vs 3.54 Å). As for the in complexes, Du and coworkers10 have reported a side-on CO2 binding energy of −4.3 kcal·mol−1 for a model of an (8,8) nanotube, a small value compared with our interaction energy of −6.3 kcal·mol−1. Moreover, for this system, the reported equilibrium distance (ca. 3.2 Å) is longer than ours (3.08 Å). 3.3. Binding Studies of SWCNTs with Multiple CO2 Molecules. In the previous section, we have studied the adsorption of one single CO2 molecule by both zigzag and armchair SWNTs of different diameters. In this section, we have further investigated the CO2···SWNT interaction by adding a second and a third CO2 molecule to a selection of nanotubes to look into possible cooperativity effects. In this regard, we chose the zigzag (9,0) and armchair (5,5) nanotubes to study the side-on binding mode, and the zigzag (12,0) and armchair (8,8) to study the end-on binding mode. In Table 5, we have collected selected energetic and geometrical data of SWNT complexed to one (studied in previous section), two, or three CO2 molecules. From the geometrical point of view, we can differentiate between two kinds of complexes based on the relative position of the CO2

ESYN 0.8 2.4 0.0 0.8 −1.1 −1.0 −0.3 −0.5

Re 3.44 3.44 3.44 3.30 3.30 3.30 3.05 3.07 3.07 3.09 3.08 3.08

D 4.04a 3.20a 5.14a 3.66−3.73a 3.07b 3.11−3.15b 3.14b 3.20−3.21b

OCO···OCO distance. bOCO···CO2 distance.

molecules. The first group (side-on group) is formed by complexes of (9,0) and (5,5) SWNTs, where the CO2 molecules are forced to be bound side-on and, therefore, they are expected to be collinear and placed parallel to the nanotube axis. The second group (end-on group) is formed by complexes of (12,0) and (8,8) SWNTs, where the CO2 molecules may not necessarily be in a side-on conformation because they may also adopt an end-on binding mode. Let us first analyze the side-on group. As expected, in complexes with two and three CO2 molecules, these are found collinear, as can be seen in Figure 6. The separation between

Figure 6. Top: On-top (left) and side (right) views of (9,0) SWNT complexed to three CO2 molecules. Bottom: On-top (left) and side (right) views of (5,5) SWNT complexed to three CO2 molecules.

the CO2 molecules differs a little depending on the system (Table 5). For instance, for the (9,0)·2CO2 complex, the CO2 molecules are 4.04 Å away from each other. However, the separation distance is larger, 5.14 Å, for the (5,5)·2CO2 complex. Similar results are obtained for the SWNT·3CO2 complexes; that is, for the (9,0) complex, the CO2 molecules are separated by 3.20 Å, whereas for the (5,5) complex they are 3.66 and 3.73 Å away. These differences in the distances led us to analyze more carefully the binding, by the nanotube, of the CO2 molecules depending on their distance separation by investigating the effect of the (9,9) and (5,5) nanotubes on the 21089



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inferred that more CO2 molecules might form a concentric CO2 nanotube, as predicted by Koga et al.32 and later observed using X-ray diffraction by Maniwa et al.33 for the interaction between nanotubes and water where ordered concentric “ice nanotubes” form inside SWNTs. This conformation can be achieved because the CO2 molecules have spare room to reorient themselves, yielding pseudo parallel-displaced geometries, thus maximizing the quadrupole−quadrupole interactions among the CO 2 molecules, establishing two OCO···CO2 interactions per CO2 pair (Figure 7). In fact, the observed parallel-displaced geometries of the CO2 molecules inside the nanotube are found to be the absolute minima of the complexes exclusively formed by either two or three CO2 molecules, with BSSE-corrected interaction energies of −1.0 and −2.0 kcal·mol−1, respectively. This is in agreement with previous experimental34 and theoretical35 results where the gasphase CO2 dimer is known to form a slipped parallel configuration in the ground state that results from a competition between van der Waals and electrostatic interactions. The distance between the CO2 molecules was measured from the C atom of a molecule to the closest O atom of another molecule. These distances are shorter than those for the complexes of the side-on group (Table 5), due to the weaker binding character of the collinear CO2 dimer and trimer, which have BSSE-corrected interaction energies of 0.1 and 0.2 kcal·mol−1, respectively. To shed some light on the possibility of having cooperativity effects when more than one CO2 molecule is located inside a nanotube, we defined what we entitle synergetic energy (ESYN, Table 5). This energy is the result of subtracting from the total interaction energy of the complex, the interaction energies of all combinations of two molecules fully optimized. For instance, we computed the synergetic energy of (5,5)·3CO2 by subtracting three and two times the binding energies of (5,5)·CO2 and CO2···CO2 complexes, respectively, from the

proximity of two confined CO2 molecules (Table S2 of the Supporting Information). As it turns out, at 2.5 Å the two molecules are too close, and they repel each other, and starting from a 3.5 Å separation, the energy profile is quite shallow and close to the minimum energy value, which is located at a distance of 4.0 Å. The same reaction coordinate was carried out for two isolated CO2 molecules (Table S2 of the Supporting Information), and a very similar energy profile was obtained when compared with those of the nanotube complexes. Therefore, it seems that the SWNT does not have any meaningful effect on the energetics of the two CO2 molecules. Let us continue our analysis now with the end-on group. In these complexes, as opposed to the side-on group, the CO2 molecules are not found to be collinear. Instead, the CO2 molecules are placed in a helicoidal stairway-like conformation, giving rise to a hollow nanotube (Figure 7). Actually, it can be

Figure 7. Top: On-top (left) and side (right) views of (12,0) SWNT complexed to three CO2 molecules. Bottom: On-top (left) and side (right) views of (8,8) SWNT complexed to three CO2 molecules.

Table 6. SAPT Total Interaction Energies and Their Partitioning into the Electrostatic, Induction, Dispersion, and Exchange Contributions (in kcal·mol−1) and the Hartree−Fock Correction for Higher-Order Contributions δ(HF) (in kcal·mol−1) for the Complexes of CO2 with Benzene (BEN), Naphthalene (NAP), Anthracene (ANT), Coronene (COR), and (9,0), and (5,5) SWNTs at the BP86 Level of Theory Using the DF-DFT-SAPT Approach contributions

basisa

BEN

NAP

ANT

COR

(9,0)

(5,5)

electrostatic

VDZ AVDZ AVTZ VDZ AVDZ AVTZ VDZ AVDZ AVTZ VDZ AVDZ AVTZ VDZ AVDZ AVTZ VDZ AVDZ AVTZ

−1.78 −1.75 −1.71 −0.09 −0.13 −0.14 −1.92 −3.11(38%) −3.46(45%) 3.34 3.42 3.38 −0.09 −0.15 −0.16 −0.53 −1.72 −2.08

−1.63 −1.60 −1.57 −0.19 −0.25 −0.25 −2.89 −4.59(37%) −5.07(43%) 4.66 4.67 4.63 −0.20 −0.26 −0.27 −0.25 −2.03 −2.52

−1.29 −1.25 −1.23 −0.11 −0.17 −0.17 −2.68 −4.28(37%) −4.67(43%) 3.73 3.68 3.64 −0.10 −0.15 −0.16 −0.45 −2.16 −2.58

−1.52 −1.44 −1.40 −0.12 −0.18 −0.17 −3.27 −5.11(36%) −5.53(41%) 4.46 4.37 4.32 −0.14 −0.18 −0.15 −0.58 −2.54 −2.94

−4.05 −3.60 −3.43 −0.24 −0.34 −0.34 −8.46 −13.34(37%) −14.43(41%) 9.79 9.84 9.73 −0.18 −0.26 −0.29 −3.14 −7.70 −8.76

−4.61 −4.54 ≈ −0.45 −0.59 ≈ −11.75 −18.65c −19.92c 14.23 14.36 ≈ −0.46 −0.60 ≈ −3.04 −10.02 −11.29

induction

dispersionb

exchange

δHF

total

VDZ = cc-pVDZ, AVDZ = aug-cc-pVDZ, AVTZ = aug-cc-pVTZ basis sets. bValues in parentheses correspond to 100 × [E(AVXZ)disp − E(VXZ)disp]/E(AVXZ)disp for X = D,T. cExtrapolated values (see text). a

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SCS-RI-MP2/AVTZ//SCS-RI-MP2/TZVP reported value (Table 1).

interaction energy of the (5,5)·3CO2 complex. These synergetic energies give valuable information regarding the interplay between both noncovalent interactions present in the complexes. For the side-on group, these values are small and positive, suggesting that there is no cooperativity between the CO2···SWNT and the CO2···CO2 interactions. However, for the end-on group, the synergetic energies are small but negative, which is indicative of cooperativity effects, although minor, for both kinds of interactions. The latter results are relevant because the possibility that the entrance of the first CO2 molecule could facilitate the entrance of the second one and so on would have important consequences on the potential use of these materials as CO2 containers. 3.4. SAPT Energetic Partition Scheme. SAPT partition energy scheme has been used to analyze the physical nature of the forces involved in the CO2···SWNT interaction and to understand the bonding mechanism. SAPT rigorously decomposes the interaction energy into several contributions, which are electrostatic, induction, dispersion, and exchange. The ultimate goal is to compute SAPT on a SWNT complex. However, in computational terms this calculation is extremely expensive, specifically the dispersion term. Therefore, to circumvent this problem we considered other systems and three basis sets, that is, VDZ, AVDZ, and AVTZ. Therefore, the systems under study are those collected in Figure 2, that is, complexes where the CO2 molecule is interacting with benzene (BEN), naphthalene (NAP), anthracene (ANT), coronene (COR), (9,0), and even the big (5,5) SWNTs models. The SAPT results are summarized in Table 6. As expected, the main contribution to the total interaction energy comes from the dispersion term, regardless of the basis set used. The other common feature is that the induction term is always attractive but almost negligible, only accounting for ca. 3% of the attractive forces. Moreover, the electrostatic contribution is negative for all complexes. For our model systems, the addition of diffuse functions to the VDZ basis set does not significantly change the electrostatic, induction, and exchange contributions (Table 6). Therefore, for all complexes except the (9,0), the addition of diffuse functions lowers the electrostatic contribution by as much as −0.08 kcal·mol−1. For the (9,0), this variation is much larger (−0.45 kcal·mol−1) although small compared with the overall interaction energy of −7.70 kcal·mol−1. The same observation applies to the induction term where the change in the basis set lowers this contribution only by less than −0.10 kcal·mol−1. Furthermore, the AVTZ results do not alter the electrostatic, induction and exchange contributions obtained by means of the AVDZ basis set. However, the dispersion contribution is very much affected by the basis set in all cases (Table 6). In fact, if we pay a closer look, we will notice that the variation on going from the VDZ to the AVDZ basis sets corresponds to ca. 37% change. Moreover, this variation is increased to ca. 41% on going from the VDZ to the AVTZ basis sets. From these results, we are confident of extrapolating the dispersion contribution to the (5,5) nanotube (because a SAPT calculation with the augmented basis sets is prohibitive for that many atoms). So, if we apply the 41% increment in the dispersion term for the (5,5) complex, we obtain a large dispersion contribution of −19.92 kcal/mol for the AVTZ basis set (Table 6), which corresponds to 80% of all attractive forces. Therefore, considering the remaining contributions constant, we obtain an overall interaction energy of −11.29 kcal·mol−1 close to the

4. CONCLUSIONS In conclusion, we have studied the adsorption of CO2 by means of SWNTs of different symmetries (zigzag and armchair) and diameters (from 4.70 to 10.85 Å). Different binding sites have been considered, namely, in the interior of the nanotube (sideon and end-on binding modes) and on the surface (parallel or perpendicular) of the nanotube. Preliminary studies on model systems demonstrate that the B97-D/SVP method is an excellent level of theory to tackle this research. In general, the binding energies are larger than those found in the bibliography. In addition, the binding energies increase with tube size until a diameter of ca. 7.0 Å is reached, showing (9,0) and (5,5) SWNTs as the best CO2 adsorptions. Then, the binding energies decrease tending to the value of the interaction with graphene. In fact, the (9,0) and (5,5) SWNTs show favorable adsorption thermodynamics that facilitate CO2 capture and release. Therefore, both (9,0) and (5,5) SWNTs can be considered very good potential candidates for carbon capture and storage in reducing CO2 emissions. Moreover, we predict that interior adsorption would be more favorable than interstitial adsorption in bundles for (9,0), (10,0), (11,0), and (5,5) nanotubes. The diffusion of CO2 from the outside to the interior of the (5,5) SWNT has also been studied, leading to the conclusion that it is an energetically favorable and barrierless process. The binding of more than one CO2 molecule has also been considered. The reported results stress the importance of the mutual effects between noncovalent interactions involving more than one CO2 molecule and SWNTs, which very much depend on the diameter of the tube. Therefore, we have demonstrated that no cooperativity effects are observed when the CO2 molecules are only allowed to interact side-on with the nanotube. However, small synergetic energies are obtained when the end-on binding mode is established, a fact that could be very important when considering the entrance of a great number of CO2 molecules inside the tube. Moreover, for this binding mode, it can be inferred that more CO2 molecules might form a concentric CO2 nanotube, as experimentally observed for the interaction between nanotubes and water. In addition, by means of SAPT calculations, we have studied the physical nature of the binding forces. The main contribution to the total interaction energy comes from the dispersion forces, which are extremely important and very much basis-set-dependent, accounting for more than 80% of all attractive forces. The electrostatic term is relatively important, and the induction contribution is almost negligible.

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ASSOCIATED CONTENT

S Supporting Information *

ΔH and ΔG energies of CO2 adsorption for the (9,0) and (5,5) SWNTs at different temperatures and relative interaction energies with the BSSE correction, equilibrium OCO···OCO distance of the in complexes of two CO2 molecules with and without (9,0) and (5,5) SWNTs at the RI-B97-D/SVP level of theory. This material is available free of charge via the Internet at http://pubs.acs.org. 21091



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Mura, M. E.; Nicklass, A.; Palmieri, P.; Pflüger, K.; Pitzer, R.; Reiher, M.; Shiozaki, T.; Stoll, H.; Stone, A. J.; Tarroni, R.; Thorsteinsson, T.; Wang, M.; Wolf, A. MOLPRO, version 2010.1, a package of ab initio programs. http://www.molpro.net (accessed 1 July 2012). (26) (a) Sinnokrot, M. O.; Sherrill, C. D. J. Am. Chem. Soc. 2004, 126, 7690. (b) Arnstein, S. A.; Sherrill, C. D. Phys. Chem. Chem. Phys. 2008, 10, 2646. (27) Weigend, F. Phys. Chem. Chem. Phys. 2002, 4, 4285. (28) Weigend, F.; Köhn, A.; Hättig, C. J. Chem. Phys. 2002, 116, 3175. (29) Becke, A. D. Phys. Rev. A 1988, 38, 3098. (30) Perdew, J. P. Phys. Rev. B 1986, 33, 8822. (31) Matranga, C.; Chen, L.; Bockrath, B.; Johnson, J. K. Phys. Rev. B 2004, 70, 165416. (32) Koga, K.; Gao, G. T.; Tanaka, H.; Zeng, X. C. Nature 2001, 412, 802. (33) Maniwa, Y.; Kataura, H.; Abe, M.; Suzuki, S.; Achiba, Y.; Kira, H.; Matsuda, K. J. Phys. Soc. Jpn. 2002, 71, 2863. (34) Weida, M. J.; Sperhac, J. M.; Nesbitt, D. J. J. Chem. Phys. 1995, 103, 7685. (35) Welker, M.; Steinebrunner, G.; Solca, J.; Huber, H. Chem. Phys. 1996, 213, 253.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +34 971173498. Fax: +34 971173426. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank CONSOLIDER-Ingenio 2010 (CSD2010-0065) and the MICINN of Spain (project CTQ2011-27512/BQU, FEDER funds) for financial support. We thank the CESCA for computational facilities. D.Q. thanks the MICINN of Spain for a “Ramón y Cajal” contract.

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