Reducing properties of superalkalis on pyridinic graphene surfaces: a computational study

The hyperlithiated species Li k+1 F k (k=1, 2, 3, and 4) have been studied by quantum mechanical (QM) methods. Diﬀerent structures have been localized for each molecule by the CBS-QB3 composite method: all the isomers show superalkali properties and strong tendency to donate an electron to carbon dioxide forming stable Li k+1 F k • • • CO 2 complexes. With the aim to ﬁnd molecular systems able to stabilize superalkalis, geometries of complexes between superalkalis and pyridine and superalkalis and graphene surfaces doped with a pyridinic vacancy were calculated. The pyridinic graphene sheets were modeled with two ﬁnite molecular systems C 69 H 21 N 3 and C 117 H 27 N 3 . The interaction with one pyridine molecule is quite weak and the superalkali maintains its structure and electron properties. The aﬃnity for graphene sheets is instead stronger and the superalkalis tend to deform their geometry to better interact with the graphene surface. However, the superalkalis continue to show the tendency to transfer electrons to carbon dioxide reducing CO 2 , as found in graphene absence. graphene than Li 5 F 4 whereas, on the contrary, a smaller aﬃnity for CO 2 than Li 5 F 4 . Within the limits of our molecular models, our calculations indicates, therefore, that pyridinic sites on graphene surfaces can signiﬁcantly adsorb hyperlithiated species without changing their reducing ability towards carbon dioxide.

However, the superalkalis continue to show the tendency to transfer electrons to carbon dioxide reducing CO 2 , as found in graphene absence.

Introduction
The physical and chemical properties of cluster systems often differ from those of the bulk and can depend on the size, geometry, and composition of the cluster [1][2][3][4]. A special class of clusters are called "superatoms," which are molecular species that mimic atomic behavior [5][6][7]. Superatoms of special interest are superalkalis and hyperlithiated compounds that present ionization energies lower than alkalis. These compounds have attracted considerable attention both theoretically and experimentally. In 1978 Kudo et al. [8] and in 1979 Wu at al. [9] observed that gaseous Li 3 O shows an ionization energy (3.59 ± 0.2 eV) lower than that of solid lithium (5.36 ± 0.01 eV) [10]. Afterwards, also hyperlithiated fluorides produced by laser-ablation source showed superalkali properties [11]. Gutsev and Boldyrev [12,13] proposed the formula M k+1 L, where M is the alkali metal and L is the electronegative atom with valence k. Applications of superalkalis in many fields of material science have drawn much attention in the past decades. Tendency of hyperlithiated compounds to form clusters with non linear optical properties have been shown by various theoretical studies [14][15][16][17]. The electron transfer from superalkalis can be potentially utilized for the conversion of the greenhouse gas CO 2 into useful products, such as methanol fuel and carboxylic acid. For example, the superalkali Li 3 F 2 [18] can be employed to easily reduce carbon dioxide CO 2 [19] and nitrogen N 2 [20] with high stability and selectivity. Srivastava has shown that also the smaller Li 2 F is able to reduce carbon dioxide [21]. Reduction of CO 2 can occur also with superalkalis composed by transition metal complexes as well as organic molecules [22]. Srivastava [23] has found that superalkalis can reduce the major air pollutants NO x into NOx anions. More recently, Meloni et al. [24] showed as Li 3 F 2 can be employed to capture volatile organic compounds. Although hyperlithiated compounds are potentially a new class of catalysts for CO 2 activation, the quite extreme conditions necessary to produce them undoubtedly constitute a factor that limits their practical applications. An interesting aspect can be the search of molecular systems able to stabilize the superalkalis without changing their reducing properties. It is well known that the adsorption ability of graphene can be significantly strengthened by doping it with heteroatoms [25][26][27]. For example, the presence of nitrogen on graphene sheets (N-doped graphene) enhances their affinity towards lithium atoms and lithium compounds [28]. To address these issues, we have investigated the interaction between some hyperlithiated compounds and pyridinic nitrogen atoms on graphene sheets. By starting from some complexes between superalkali and pyridine, we studied their structure and stability and how the tendency to coordinate carbon dioxide is modulated by the presence of pyridine. The study was extended to the interaction between superalkalis and graphene sheets by employing two models of graphene with a vacancy consisting of three pyridinic nitrogen atoms. Very recently a theoretical investigation [29] has been carried out on the interactions between alkalis, superalkalis, and nitrogen doped graphene focusing attention on the non linear optical properties of such systems. The aim of the present study is to investigate the superalkalis ability of reducing carbon dioxide in presence and in absence of graphene by considering different structures between graphene, superalkalis, and carbon dioxide. Geometries, energies, and charge distribution were calculated using the CBS-QB3 [30] composite model for smaller systems and Density Functional Theory (DFT) for the systems with graphenic units.
Two polyaromatic hydrocarbons (PAH) were chosen as models to simulate the graphene surface. These highly symmetric (D 3h ) molecules are composed of 28 and 48 benzene rings, including 72 and 121 carbon atoms, respectively. For both PAH's, the pyridinic vacancy was created in the center of the molecule by replacing three carbon with nitrogen atoms and forming the C 69 H 21 N 3 and C 117 H 27 N 3 species. Both studied systems have been optimized removing the planarity constraint within D 3 symmetry. Subsequently, the interaction of the pyridinic vacancy surface with lithium was evaluated in different environments. Firstly, the lithium affinity was estimated by adding a single lithium atom along the C 3 symmetry axis and by studying the geometry and stability of the relative complexes. Secondly, two superalkalis were considered, Li 3 F 2 and Li 5 F 4 . Each molecule was approached to the pyridinic vacancy of the graphene models and stability and geometries of the relative complexes were evaluated. Lastly, the interaction of superalkali and graphene has been again evaluated in presence of CO 2 by considering the molecular complex between graphene, superalkali, and CO 2 units. The CBS-QB3 method employed to analyze smaller clusters is computationally too expensive to yield the energetics of graphene-containing systems. Geometry and energetics of these large models were, therefore, obtained at the B3LYP/6-31G(d) level. The B3LYP method is a reliable and high quality density functional method recently used in the study of graphene and adsorption phenomena [26,[36][37][38][39], also in conjuction with the 6-31G(d) basis set [40]. The interaction energies, binding energy (BE), of all the molecular complexes were calculated as difference between the energy of the interacting species and the energies of the separated molecules. According to this definition, negative or positive values of BEs correspond to exothermic or endothermic processes, respectively. The spin densities have been obtained on Mulliken population analysis [41], whereas the ESP method [42] has been utilized to find partial atomic charges. The charge transfer (∆q) between the molecular units forming the complex has been estimated using the calculated partial atomic charges.

Results and discussion
3.1 Li k+1 F k , CO 2 , and pyridine The main purpose of the present study is to show the reduction capability of Li k+1 F k towards CO 2 when the superalkali is bonded to pyridinic nitrogen atoms. In the first section we show the structures of complexes between pyridine and some hyperlithiated species, like Li 3 F 2 and Li 5 F 4 . As reference, we firstly present the optimized structures and relative highest singly occupied molecular orbital (SOMO) of some isolated superalkalis in Figure 1. The planar C 2v symmetry structures of Li 2 F and Li 3 F 2 , already determined in a previous computational study [18], are now compared with the larger Li 4 F 3 and Li 5 F 4 species with the aim to investigate if superalkali properties can be affected by the size of the molecular species. For an easy comparison, all the compounds were initially considered within the C 2v planar symmetry, although Li 3 F 2 , Li 4 F 3 , and Li 5 F 4 can be found also with alternative structures. For example, a C s planar structure has been found for Li 3 F 2 at only 3 kJ/mol above the C 2v isomer [18]. Li 4 F 3 has instead various isomers: a second planar isomer ( Figure 1) and different non planar structures. The global minimum has C 3v symmetry. The relative stabilities of the planar isomers are 14 kJ/mol (C s ) and 23 kJ/mol (C 2v ). Preference for a non planar geometry is also found for the larger Li 5 F 4 (C 3v ) that shows an isolated Li tail and a typical cyclic (LiF) n polymeric structure. An alternative non planar isomer and a C 2v symmetry isomer are 21 kJ/mol and 57 kJ/mol, respectively, higher in energy. All the structures are reproduced in Figure  1. The SOMO's of all the species reported in Figure 1 are very similar with the unpaired electron localized onto the terminal lithium atoms. The calculated AIE's of 3.86 eV for Li 4 F 3 and 3.91 eV for Li 5 F 4 are lower than the experimental ionization energy of lithium (5.39 eV) and very close to the AIE of Li 3 F 2 (3.80 eV) and Li 2 F (3.88 eV) proving that all these species are superalkalis.
Interaction of superalkalis and pyridine was investigated for two systems of the series, Li 3 F 2 and Li 5 F 4 . Since the equilibrium structure of Li 3 F 2 has C 2v symmetry, its interaction with pyridine was evaluated approaching the central Li atom to the nitrogen along the C 2 symmetry axis and calculating geometries and binding energies. Two structures of C 2v symmetry were proposed: a structure where pyridine and superalkali are coplanar, and a non planar geometry where pyridine is orthogonal to the planar superalkali. A Figure 1: Optimized geometries of Li 2 F(a), Li 3 F 2 (b), Li 4 F 3 (c) and Li 5 F 4 (d), and their visualized singly occupied molecular orbitals SOMO's third structure, again planar, describes the interaction between the C s isomer of Li 3 F 2 and pyridine. The binding energies of the three complexes are indeed very similar and the N...Li intermolecular distances are substantially independent from the structure and orientation of the superlkali. Therefore, Figure 2a shows only the geometry of the most stable planar C 2v structure. The salient result is that interaction with pyridine is quite weak (68 kJ/mol) with intermolecular N...Li distance of 2.037Å and a modest charge transfer. As a consequence, the molecular properties of each interacting molecule are not expected to drastically change upon complexation. For example, the internal LiF bonds undergo small lengthening, whereas the terminal LiF remains substantially unchanged; the only significant geometrical effect of pyridine interaction is the narrowing of the FLiF bond angle from 129 • to 121 • . In the case of the Li 5 F 4 -pyridine complex, all the three structures of Li 5 F 4 were considered and their geometries are reproduced in Figure 2b. The binding energies of the C 2v isomer is comparable with that of Li 3 F 2 , whereas the non planar structures show a higher affinity towards pyridine (83 k/mol for the C 3v isomer and 91 kJ/mol for the other non planar isomer). Another important result emerging from the SOMO's ( Figure 2) inspection of all the structures is that the unpaired electron continues to be localized on the hyperlithiated unit and, in particular, on the lithium terminal atoms, like for the isolated species. Before interacting with pyridine these Li atoms of Li 3 F 2 , for example, carry the extra electron with a spin density of 0.58 each; upon interaction they show a small increase of spin density (0.66 each) confirming the strong localization of the extra electron on the terminal Li atoms.
In addition, the removal of an electron from the Li 3 F 2 -pyridine and Li 5 F 4pyridine complexes of C 2v symmetry leaves the binding energy of the complexes nearly unchanged (71 kJ/mol). This value is calculated by taking the difference between the sum of the energy of the superalkali cation and pyridine and the energy of the complex cation. It is also worth observing that the AIE's of the Li 3 F 2 -pyridine (3.76 eV) and Li 5 F 4 -pyridine complexes (3.88 eV) are not far from 3.80 eV (Li 3 F 2 ) and 3.91 eV (Li 5 F 4 ) of the isolated species proving that the hyperlithiated compounds continues to have superalkali properties upon interaction with pyridine. Figure 3 shows the interaction structures of Li k+1 F k with CO 2 . The previous study [19] revealed that Li 3 F 2 has a strong tendency to donate an electron to CO 2 taking a bent structure and forming a stable Li 3 F 2 · · · CO 2 complex. Similar results are found for the other superalkalis here considered, Li 2 F, Li 4 F 3 , and Li 5 F 4 . Each superalkali isomer may interact with carbon dioxide and in all the cases the bent structure assumed by CO 2 upon interaction is close to that calculated for the CO 2 isolated anion (OCO bond angle = 134 • and CO bond distance = 1.244Å) at the B3LYP/CBSB3 level. As for Li 3 F 2 · · · CO 2 [19], two planar cyclic C 2v structures, labeled as (a) and (b) in Figure 3, can be formed with comparable stability. In both the structures each oxygen interacts with a single terminal Li, but the bent CO 2 is differently oriented with respect to the superalkali unit. The value of the OCO bond angle is almost constant (134 • ) in all the cyclic structures labeled as (b) in Figure 3. On the contrary, in the alternative cyclic structures of Figure  3 and labeled as (a), CO 2 increases progressively its bending from 142 • in Li 2 F · · · CO 2 to 134 • in Li 5 F 4 · · · CO 2 . As for the Li 4 F 3 and Li 5 F 4 isolated superalkalis, the non planar structures, labelled as (c) in Figure 3, have been found to be the preferred superalkali · · · CO 2 configuration. Once again the global minima are those where the superalkali takes the local C 3v symmetry (see Table 1). It is interesting to note that whereas the relative stabilities of different isomers of each complex seem to depend on the size and structure of the superalkali, the binding energy of the Li k+1 F k · · · CO 2 systems reveals that the interaction with carbon dioxide does not change drastically with the size of the superalkali (Table 1) with the exception for the C 3v isomer of Li 5 F 4 . This structure interacts more effectively with CO 2 since the excess electron of the superalkali is located on the "anionic cavity" formed by three lithium atoms that, therefore, may interact with carbon dioxide.
The charge transfer, ∆q, has been calculated using the ESP method for all the complexes and the values (Table 1) reveal the ionic character of the interaction with a charge flow from the superalkali to CO 2 . The amount of charge transfer depends on the size of the superalkali: it decreases from 0.83 (Li 2 F) to 0.62 (Li 3 F 2 ), whereas it remains almost unchanged for the symmetric structures of Li 4 F 3 (0.62) and Li 5 F 4 (0.63). The non planar complexes of Li 4 F 3 and Li 5 F 4 show a more effective charge transfer, close to that calculated for Li 2 F. Figure 4a shows the optimized structure where pyridine, Li 3 F 2 and CO 2 form a stable complex. By comparing the stabilities of Li 3 F 2 -CO 2 , Li 3 F 2 -pyridine and Li 3 F 2 -CO 2 -pyridine we can derive the interaction energy of superalkali with CO 2 in presence of pyridine. As reported in Table 1, Li 3 F 2 has an affinity towards CO 2 almost independent of its interaction with pyridine. This agrees with the results discussed above showing that pyridine does not substantially change the properties of the superalkali. Consistently, the intermolecular O...Li distances (1.822Å) are very close to 1.812Å found for the Figure 3: Optimized structures of (1) Li 2 F · · · CO 2 , (2) Li 3 F 2 · · · CO 2 , (3) Li 4 F 3 · · · CO 2 and (4) Li 5 F 4 · · · CO 2 complexes Figure 4: Optimized structures of Li 3 F 2 · · · CO 2 · · · pyridine (a) and Li 5 F 4 · · · CO 2 · · · pyridine (b) complexes and relative visualized SOMO's Li 3 F 2 -CO 2 complex. The bent geometry of carbon dioxide (O-C-O=135 • ), the CO bond distance (1.24Å), the features of the SOMO's, and its strong localization on the CO 2 portion of the complex, in particular on the carbon atom, indicate that the superalkali easily reduces CO 2 also when it interacts with pyridine ( Table 1). The charge is prevalently localized on CO 2 (-0.74) and the charge transfer occurs mainly from superalkali (0.52) and only marginally from pyridine (0.22). As for Li 3 F 2 , also Li 5 F 4 reduces CO 2 in presence of pyridine with a comparable charge transfer to CO 2 . In Figure  4b we show the complex between the Li 5 F 4 C 3v isomer , pyridine and CO 2 : in this case the superalkali and carbon dioxide are bonded by -158 kJ/mol, a value again very close to that calculated for the isolated Li 5 F 4 ...CO 2 complex (-174 kJ/mol). This suggests that the reducing properties of Li k+1 F k towards carbon dioxide are not significantly altered by the weak interaction with pyridine.

Li k+1 F k , CO 2 , and graphene
Structural features and electronic properties of the graphene-containing systems described in this section were obtained at the B3LYP/6-31G(d) level of theory. The choice of the B3LYP method for these large molecular systems has been driven by some considerations. Firstly, this DFT functional has already been successfully applied in the study of adsorption phenomena on graphene surfaces [26,[36][37][38][39]. Secondly, the CBS-QB3 results obtained for superalkalis and their complexes with CO 2 and pyridine are not drastically far from those obtained at the B3LYP/6-31G(d) level, (see Table 1) with differences in binding energies no higher than 30 kJ/mol. C 69 H 21 N 3 and C 117 H 27 N 3 composed by 28 and 48 aromatic rings ( Figure 5), respectively, are our models used as finite-size pyridinic graphene sheets. Both the systems show a pyridinic vacancy by three nitrogen atoms localized at the center. Their geometries were optimized within the D 3h symmetry.
Interaction between 3N-graphene and lithium has been investigated approaching a lithium atom along the C 3 axis and optimizing the geometry of the complex. The lithium atom is pulled above the graphene plane and, moreover, the graphene structure is slightly distorted from planarity in the region of the interaction. The strong affinity for lithium is well witnessed by the large binding energy (-400 kJ/mol) for both the molecular systems. It means that lithium is strictly connected to three pyridinic nitrogen through quite short Li...N bond distances (1.833Å). The structural distortions of  the graphene system are limited to the pyridinic rings: lithium coordination causes an increase of the CN bond distance, from 1.332Å to 1.349Å, and the CNC ring bond angles, from 122.3 • to 123.8 • . The ionic component of the lithium graphene interaction is clearly suggested by the significant charge transfer, ∆q, from lithium to graphene (0.54). Figure 6 shows the SOMO for the C 117 H 27 N 3 ...Li complex visualized at different distances between lithium and graphene plane. The unpaired electron is mainly localized on graphene when lithium is bonded to the surface (2Å), whereas the contribution on lithium arises when atom is progressively removed from the surface (from 3 A upwards).
The determination of graphene and superalkalis structures is certainly a complex problem since the number of local minima of the potential energy surface is quite large and a systematic search is outside our computational capabilities. Therefore, we considered this interaction through a limited number of models: Li 3 F 2 and Li 5 F 4 were positioned above the graphene plane with a local and initial C 2v symmetry structure and by orienting the superalkali perpendicularly to the graphene sheet with the central lithium atom approaching the center of the graphene surface, which is towards the pyridinic vacancy. Both the C 69 H 21 N 3 and C 117 H 27 N 3 systems were considered and the geometries of their complexes with superalkalis were fully optimized without any symmetry constraint. For some complexes different isomers were local- Figure 8: Some optimized structures of graphene · · · Li 3 F 2 · · · CO 2 (A, C) and graphene · · · Li 5 F 4 · · · CO 2 complexes (B,D).
ized and relative stabilities are reported in Table 2. In all the cases the central lithium tends to interact with three nitrogen atoms, as found in the case of Li-doped graphene previously discussed, although the Li...N distances are longer (ranging from 2.11Å to 2.35Å). In the case of Li 3 F 2 and C 69 H 21 N 3 , the marked affinity of graphene for lithium implies that the superalkali changes its structure by orienting the remaining lithium atoms towards the graphene plane to favour such interactions. Consequently, the initial C 2v symmetry structure of Li 3 F 2 is deformed to allow further lithium-graphene interactions involving the second ( Figure 7A) and the third lithium atom ( Figure 7B). It means that in presence of graphene some less stable isomers of Li 3 F 2 , as the C s symmetry one (Figure 1), are now preferred to the C 2v isomer. In particular, the bent W arrangement assumed by Li 3 F 2 on the graphene surface ( Figure 7B), found as the most favorable structure, can be thought as derived from an alternative isomer, having a quasi linear structure, that for the isolated Li 3 F 2 was found 71 kJ/mol higher in energy. Binding energies of such complexes, calculated as difference between the energy of the complex and those of graphene and Li 3 F 2 (C 2v ), indicate that the superalkali strongly adsorbs on graphene. Interaction is stronger for the W isomer (-311 kJ/mol) than for the A isomer (-276 kJ/mol) because the geometry of the W isomer allows the simultaneous interaction of three lithium atoms with graphene: the central lithium with three nitrogens and the terminal atoms with the graphene surface. For the larger graphene model, (C 117 H 27 N 3 ) we considered only the most favorable W structure of Li 3 F 2 : its binding energy (-266 kJ/mol) is slightly smaller than that of Li 3 F 2 ...C 69 H 21 N 3 . The situation changes for Li 5 F 4 . Herein the superalkali, after interaction with graphene, may preserve the orientation upward of the terminal lithium atoms ( Figure 7C), as found for the isolated molecule. This structural arrangement shows a smaller affinity towards graphene: binding energy is -97 kJ/mol when the surface is modeled by C 69 H 21 N 3 and -85 k/mol when the surface is described by C 117 H 27 N 3 . For the C 69 H 21 N 3 model system, additional structures were found where Li 5 F 4 assumes orientations able to improve the interactions with graphene surface as witnessed by the structure reproduced in Figure 7D. Also in this case, the interaction with graphene is weaker (-121 kJ/mol) than that found for Li 3 F 2 . The weaker affinity of Li 5 F 4 could depend on the structure of the superalkali that tends to take non planar geometries. However, we started optimizations from the planar structure of Li 5 F 4 to have a homogeneous comparison with the planar Li 3 F 2 .
The visualization of the SOMO's of the Li 5 F 4 -graphene structures (Figure 7) indicates that the unpaired electron continues to be localized on the terminal lithium atoms and only marginally on the graphene unit. This electronic distribution suggests that the electron properties of the hyperlithiated species seem to be not strongly altered by the graphene adsorption. From these results, it is worthwhile to notice that the binding energy of the superalkalis with pyridine is much weaker than that of the superalkalis with pyridinic graphene because in the larger systems more Li atoms can interacts with more N atoms, therefore, stabilizing the complex. Lastly, we considered the interaction of superalkalis with carbon dioxide in presence of pyridinic graphene by approaching CO 2 to Li 3 F 2 and Li 5 F 4 , initially oriented with the terminal lithium atoms upward in order to favor interaction with CO 2 . For such three-molecular systems we found a complex ( Figures 8A and 8B), where the superalkali and CO 2 form the same cyclic structure already observed in absence of graphene. This structure was localized on both the C 69 H 21 N 3 and C 117 H 27 N 3 surfaces. As for the pyridine case, we evaluated the interaction energy between superalkali and CO 2 on graphene by comparing stabilities of the superalkali-graphene-CO 2 and superalkaligraphene systems. Similarly, we can evaluate the binding energy of graphene and superalkali in presence of CO 2 as difference between the energy of the system CO 2 · · · superalkali · · · graphene and those of CO 2 · · · superalkali and graphene. The results reported in Table 2 indicate that graphene may affect the binding energy of the superalkali-CO 2 complex. In particular, the coordination with carbon dioxide is weakened when the superalkali species strongly interacts with graphene, as for Li 3 F 2 . The C 2v symmetry isomer of Li 3 F 2 is bonded to CO 2 by -118 kJ/mol on C 69 H 21 N 3 and by -147 kJ/mol on C 117 H 27 N 3 , whereas the binding energy of the Li 3 F 2 -CO 2 complex is -180 kJ/mol in absence of graphene at the same level of calculation, B3LYP/6-31G(d). In this case, charge transfer to CO 2 involve both the superalkali species (0.36) and graphene (0.21). Consistently, the binding energy between Li 3 F 2 and graphene weakens in presence of CO 2 (see Table 2). On the contrary, when the superalkali is not so strongly bonded to the graphene surface, as for Li 5 F 4 , its energy interaction with carbon dioxide is nearly unchanged (-169 kJ/mol on C 69 H 21 N 3 and -175 kJ/mol on C 117 H 27 N 3 ) with respect to the value calculated in graphene absence, -179 kJ/mol. Similarly, the presence of CO 2 does not significantly affect the binding energy between Li 5 F 4 and graphene. In this case, the charge analysis indicates that the charge flux towards CO 2 comes mainly from the superalkali (+0.7) and only marginally from graphene (+0.1). The SOMO's analysis of these complexes shows again a strong localization of the unpaired electron on the CO 2 unit along with a smaller contribution from graphene carbon atoms. The competition between graphene surface and carbon dioxide towards lithium atoms of the superalkali can lead to the formation of further structures reproduced in Figure 8. Li 3 F 2 and Li 5 F 4 may orient their LiF groups in order to simultaneously coordinate graphene and carbon dioxide, as occurs in Figures 8C and 8D. These structures are quite similar to those determined for the isolated superalkali...CO 2 complexes with Li...O distances not far from the values optimized for the complexes in graphene absence. As observed in graphene absence, again, the complexes containing asymmetric structures of Li 3 F 2 and Li 5 F 4 represent lower energy geometries. In addition, the geometry of the carbon dioxide as well as the charge flux towards CO 2 indicates that reduction of carbon dioxide occurs also in these alternative structures. However, the high number of geometrical degrees of freedom of these systems gives a high structural flexibility to the superlkalis · · · CO 2 complexes on pyridinic graphene and we cannot exclude that alternative non planar geometries can be formed on graphene substrates.

Conclusions
Reduction capability of the hyperlithiated species Li k+1 F k (k=1, 2, 3, and 4) towards carbon dioxide has been evaluated by quantum mechanical methods. The isolated hyperlithiated species are superalkali compounds with AIE lower than lithium. Except for Li 2 F, different structures have been localized: C 2v , C s , and non planar isomers. Preference for non planar geometries have been found for Li 4 F 3 and Li 5 F 4 with equilibrium structures of C 3v symmetry.
The SOMO of each structure shows that the unpaired electron is localized on the terminal lithium atoms and can be transferred to carbon dioxide to form stable Li k+1 F k ...CO 2 complexes. The bent geometry of CO 2 , the CO bond distances, and the SOMO's features of the complexes indicate that all the superalkalis of different sizes easily reduce carbon dioxide. Such reducing properties have been then evaluated proposing some molecular systems able to stabilize the superkalis. The affinity of lithium towards pyridinic nitrogen atoms has been considered by investigating firstly the interaction with pyridine. Li 3 F 2 and Li 5 F 4 can interact quite weakly with one molecule of pyridine forming a molecular complex with a modest charge transfer, maintaining their superalkali properties and continuing to reduce carbon dioxide as occurs in pyridine absence. Electron properties of Li 3 F 2 and Li 5 F 4 have been then considered in presence of graphene sheets doped with pyridinic vacancy by modeling the graphene surface with two molecular systems C 69 H 21 N 3 and C 117 H 27 N 3 . The presence of a pyridinic vacancy by three nitrogen atoms localized at the centre of the sheet allows strong interactions between lithium atoms of the superalkalis and graphene surface. The marked affinity of pyridinic graphene for lithium implies that the superlkali can change the initial C 2v structure by orienting the terminal lithium atoms towards the graphene surface. This tendency depends on the size of the superalkali: while Li 5 F 4 may preserve initial upward orientations of the LiF bonds, Li 3 F 2 deform quite easily its initial geometry. When the graphene surface and carbon dioxide are simultaneously considered, we found structures where the superalkali coordinates both the molecular units. Both Li 3 F 2 and Li 5 F 4 , upon interaction with graphene, can still reduce carbon dioxide forming cyclic structures as found for the isolated species. Reduction of carbon dioxide may occur for all the structures with lithium terminal atoms, both symmetric, as the initial C 2v isomer, and asymmetric. As a general trend we can conclude that there is a competition between graphene and CO 2 towards the superalkali. On the basis of our results, we observe that Li 3 F 2 shows a higher affinity for graphene than Li 5 F 4 whereas, on the contrary, a smaller affinity for CO 2 than Table 1: Relative stability, ∆E, between isomers and binding energy, BE, of superalkali...CO 2 complexes obtained from CBS-QB3 calculations; charge transfer, ∆q(a.u.), from the superalkali to CO 2 and electric charge q(a.u.) on each molecule calculated using the ESP method.