Ab Initio Study of Charge Transfer between Lithium and Aromatic

Article pubs.acs.org/JPCA

Ab Initio Study of Charge Transfer between Lithium and Aromatic Hydrocarbons. Can the Results Be Directly Transferred to the Lithium−Graphene Interaction? N. Sadlej-Sosnowska* National Medicines Institute, Chełmska 30/34, 00-725 Warsaw, Poland ABSTRACT: We have used electronic density calculations to study neutral complexes of Li with aromatic hydrocarbons. The charge transferred between a Li atom and benzene, coronene, circumcoronene, and circumcircumcoronene has been studied by ab initio methods (at the HF and MP2 level). Toward this aim, the method of integrating electron density in two cuboid fragments of space was applied. One of the fragments was constructed so that it enclosed the bulk of the electron density of lithium; the second, the bulk of the electron density of hydrocarbon. It was found that for each complex two conformations were identified: the most stable with a greater vertical Li−hydrocarbon distance, on the order of 2.5 Å, and another of higher energy with a corresponding distance less than 2 Å. In all cases the transfer of a fractional number, 0.1−0.3 electrons, between Li and hydrocarbon was found; however, the direction of the transfer was not the same in all complexes investigated. The structures of complexes of the first configuration could be represented as Liσ−···AHσ+, whereas the opposite direction of charge transfer was found for complexes of the second configuration, with higher energy. The directions of the dipole moments in the complexes supported these conclusions because they directly measure the redistribution of electron density in a complex with respect to substrates.

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the basis of the natural population analysis (NPA) charges8 and the profile of electron density in a plane perpendicular to graphene containing the lithium atom, he suggested that charge transfer from lithium to graphene would not take place. This work was criticized from the point of view that coronene is too small to properly account for the electronic structure of graphene9 and has an electron affinity lower (0.47 eV) than other PAHs of similar sizes and far lower than graphene’s electron affinity (4.5 eV).10 In another investigation at the MP2 level, the Li charges in a Li−C6H6 complex were checked: they were −0.215 (Mulliken) and −0.005 (NPA).11 These results were subsequently commented that the authors did not observe charge transfer between Li and benzene.10 Theoretical results using DFT have also been reported.5,9,10,12−15 The graphite layer was represented by PAHs of 7, 10, 12, and 14 conjugated rings13 or by pyrene, anthracene, and phenanthrene.12 In ref 13, transfer of about 0.4 e from Li to the investigated PAH was found, whereas 0.2 e was transferred according to ref 12. ́ Martinez et al. investigated the adsorption of lithium on coronene, but despite being of the opinion that the hydrocarbon was too small to simulate graphene, they shared the general consensus that the bonding of the Li atom to graphene is mainly ionic.9 This belief was supported by the investigation of Valencia at al.14 of the interaction of Li not with PAH but with a model of the graphene surface consisting of 16 graphitic

INTRODUCTION Graphene, a one-atom thick layer of graphite, is a material arousing much interest in recent years, due to its properties1 and due to the prospect of graphene applications.2,3 An example of the latter is hydrogen storage, under intensive investigation because hydrogen-based fuel cells are promising solutions for the efficient and clean delivery of electricity.4 Experimental results have suggested that the presence of alkali metals in carbonaceous adsorbents would intensify hydrogen adsorption. This sorption would even be 2 times larger than on pristine material.5 A significant charge transfer from alkali metal to substrate was postulated as a mechanism responsible for this intensification. Another anticipated application is rechargeable Li-ion batteries, achieved thanks to the replacement of lithium metal electrodes by lithium intercalated carbon hosts.6 In the emerging technological area the electrical properties of the carbonaceous materials such as graphite or graphene and their interactions with metals are an interesting subject. A number of theoretical investigations of interactions involving aromatic rings and alkali metals have been discussed in recent years. The generally accepted methodology for modeling metal complexes with graphene has been to substitute it with a polycyclic aromatic hydrocarbon (PAH). Planar PAH containing only six-membered rings, such as coronene, provide the most frequently accepted molecular models. The investigated structures are such that a Li atom is adsorbed on the “middle hollow site” above a hexagonal aromatic ring. One of the key issues is the charge transfer between the metal and the graphene/graphitic surface. For example, Ferre-Vilaplana in his study at the MP2 level used a coronene-like planar sheet as a model of graphene.7 On © 2014 American Chemical Society

Received: December 21, 2013 Revised: June 28, 2014 Published: July 28, 2014 7044

dx.doi.org/10.1021/jp4125292 | J. Phys. Chem. A 2014, 118, 7044−7051

The Journal of Physical Chemistry A

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compounds is shown in Figure 1. Our calculations are based on the ab initio methods: Hartree−Fock and second-order

surface cells, in a slab geometry. They found that one valence electron is entirely transferred from the atom to the surface, which gives rise to a strong interaction between the lithium ion and the cloud of π-electrons in the substrate. Another study of Li’s interaction with an explicit graphene sheet was carried out by means of periodic plane-wave DFT.15 It was concluded that there is a substantial charge transfer from both lithium and carbon atoms to a region between the Li and graphene at the minimum energy configuration. This redistribution of charge density leaves a positively charged cation at the original location of the Li atom. In spite of many results obtained by the DFT method with the help of various functionals, indicating that up to one valence electron is transferred from the Li atom to the graphene’s surface, in a study by Baker and Head-Gordon the results were not so unequivocal.10 The authors stated that all common density functionals suffer, to varying degrees, from the selfinteraction error16 and density functional theory will artificially delocalize an electron and favor charge transfer between Li and PAHs. For most of ten lithium−PAH complexes, two stable configurations were found at different Li−PAH distances: an ionic configuration, distorted due to the Jahn−Teller effect, and a nonionic Li−PAH planar structure. In this study, the spin density on lithium was used as a measure of charge transfer. It was found that in the ionic configuration Li+PAH− a spin density of ∼0 on lithium indicates that the unpaired 2s electron on lithium has been transferred to PAH. In the nonionic configuration, a spin density on Li of ∼1 was found, which was accepted as evidence that no charge transfer takes place in the complex. Ferre-Vilaplana investigating Li−coronene complexes also found two qualitatively different solutions with the Mulliken populations on the lithium atom: +0.59 and −0.21 electrons.7 ́ The results were criticized by Martinez who had not encountered the problem of dual solutions.9 Just as, in the first (unless we are mistaken) theoretical study on neutral Li− C6H6, only one (planar) conformation is mentioned with a vertical distance 2.600 Å (at the MP2/6-31G(d) level).17 This short introduction provides evidence that the problem of charge transfer from lithium to PAH, and eventually to larger carbonaceous structures, is not yet conclusively resolved. The conclusions quoted in references considering the interaction of lithium (and other alkali metals) with PAH roughly fall into two classes: there is either no charge (electron) transfer between them or there is an electron transfer of the valence electron from an alkali metal to a hydrocarbon. In addition, both effects could be found in two Li complexes with the same hydrocarbon, differing in their geometry. However, the existence of two types of complexes has also been questioned.9 Taking this into account, the paper aimed to determine whether one or two optimized structures of the investigated complexes exist. Our next aim was the application of another method for investigating electric density transfer, based on the calculation of electron density in the selected fragments of space: one enclosing the bulk of the electron density centered at Li, and the other in which electron density due to hydrocarbon is dominant. The direction of the charge transfer was also followed using the sense of the dipole moment of the complexes. In our calculations four highly symmetric planar aromatic hydrocarbons (AHs) were investigated: benzene, coronene, circumcoronene, and circumcircumcoronene, belonging to the C6n2H6n homologue series. Geometry of the last three

Figure 1. PAHs studied in this report: coronene (a); circumcoronene (b); circumcircumcoronene (c).

Møller−Plesset (MP2). For the smallest AHs, benzene and coronene, some results have also been obtained by the CCD method.

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METHODS All the quantum chemical calculations in this work were carried out with the Gaussian 0918 suite of programs. The complexes’ geometries were optimized at the HF and MP2 levels, with the 3-21G and 6-311++G** basis sets;19 the details are given in tables in the Results. Whenever possible, the geometries of complexes were optimized at the UMP2/6-311++G** level and the electron densities were calculated by that method. The HF calculations were done at the unrestricted HF level, except in those cases where such optimization could not be performed owing to the convergence failure and the restricted open-shell (ROHF) method was applied. The geometry of the “tight” complexes (see later) was frequently first optimized at the B3LYP20 level and then by HF or MP2, because application of the B3LYP functional facilitated optimization of complexes with a small distance between Li and hydrocarbon. The “tight” complexes could also be optimized following an instruction of ref 10, i.e., by solving as a first step the electronic structure for the core Hamiltonian. Determination of the Atomic Charges. For the Li− benzene complexes six different algorithms were used to partition the total electron density between Li and the atoms of benzene: Mulliken,21 NPA,8 Löwdin,22 AIM,23 and Hirshfeld,24 and that based on fitting charges to the electrostatic potential, CHelpG.25 The charges based on the atoms in molecules theory23 were calculated according to the AIM2000 program.26 Calculation of the Electron Redistribution as a Consequence of Complex Formation. For the key issue, namely, evaluating the electron transfer between Li and hydrocarbons, we decided to take into consideration the spatial distribution of the electron density instead of treating charge associated with electrons as a contribution to atomic point charges. To this aim we adopted a method of calculating electron density in a volume of space occupied by Li and in a volume occupied by AH. The first step was to determine a border plane between the two components of a Li−AH complex. For this purpose, we based our strategy on the paper of Politzer and Murray,27 who indicated that the electrostatic potential V(Rmin) along the internuclear axis at some point R = Rmin must reach a minimum. Evidence was presented that V(Rmin) represents a physically meaningful boundary point between two bonded atoms. It follows that an element of charge dq placed at the Rmin point feels zero electrostatic force from either direction along the axis. 7045



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number on the left side, which indicates that the electron density in a volume encompassing Li (volume 1) as a part of the complex is less than the sum of two individual electron densities in that volume: one, generated by Li alone, and the other one, generated by AH being present in volume 2. On the other hand, the result of summation on the right side of eq 2 should be less than the number on left side. Therefore, in such a case the following inequality should hold:

Due to the symmetry of the benzene−Li planar system, a plane passing through all six Rmin points (along the Li−C axes) was parallel to the benzene plane and perpendicular to the line connecting Li with the hydrocarbon center. For the “boat” configuration (see later) the plane was tracked parallel to the plane passing through four carbon atoms of the central benzene ring, which are situated in a common plane. For other complexes, in which the central ring was not perfectly planar, the border plane was averaged between the six Vmin points. First, the electron density was calculated28 within a cuboid comprising the complex inside, and its dimensions were so large as to ensure that less than 0.01 au of the electron density of the complex remained outside. Next, the cuboid was divided into two parts by the border plane traced as above and the electron densities were calculated separately for the two parts: dens1(Li+AH) and dens2(Li+AH). The caption “(Li+AH)” added to the two densities is to remember that in contrast to the atomic nuclei, which may definitely be found in volume 1 (Li) or volume 2 (AH), the electron density cannot be arbitrarily divided into a part originating from Li and a part originating from AH. Dens1 and dens2 were calculated for the whole Li + AH complex in the two regions. The two volumes of space inside which electron density was integrated for the planar Li−C6H6 complex can be seen in Figure 2.

dens1(Li+AH) < dens1(Li) + dens1(AH)

(3)

and consequently, dens2(Li + AH) > dens2(Li) + dens2(AH)

(4)

In the case of electron transfer from volume 2 to volume 1, the signs of inequalities 3 and 4 are changed to their opposites.

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RESULTS Li−Benzene Complex. The first step was, as usual, optimization of the complexes’ geometries, beginning from Li−benzene and keeping in mind that two different forms of the complex can exist. To find the two forms, we applied two different initial Li−AH distances and different initial guesses for the wave function: for a larger distance that of Harris (a default in G09) whereas for a smaller distance a core initial guess was applied, according to ref 10. We did obtain two structures: the first was planar, and the second resembled a boat. At the MP2/ 6-311++G** level, the first was of lower energy by 6.28 kcal/ mol. Side views of the two complexes of Li with benzene are shown in Figure 3.

Figure 2. Two volumes of space inside which electron density is integrated to determine the amount of electron density transferred between Li atom and a hydrocarbon (here benzene).

The number of points along the z-axis connecting the Li and the hydrocarbon was so fitted as to have the step size in this direction be 0.02 Å. The step size along the two perpendicular axes was adjusted to 0.04 Å. The first step size was lower to better scan the electron density in the region where the electron densities of both components of the complex overlap. The integration of electron densities was carried out with the core electrons included. Next, we calculated the electron densities in the same two volumes, in the case where only one component of the complex was left, the second being removed; thus we obtained dens1(Li), dens2(Li), dens1(AH), and dens2 (AH). The index “1” denotes the volume on the side of Li, whereas index “2” denotes the volume on the side of hydrocarbon. For example, dens1(AH) is the integrated electron density in volume 1 originating from the hydrocarbon left alone in volume 2. Similarly, dens2(AH) is the integrated electron density originating from hydrocarbon alone in volume 2 surrounding the hydrocarbon. In the case where no density transfer took place, the following equalities would hold: dens1(Li+AH) = dens1(Li) + dens1(AH)

(1)

dens2(Li+AH) = dens2(Li) + dens2(AH)

(2)

Figure 3. Two configurations of the Li−benzene system, with planar (a) and nonplanar (b) benzene molecule.

With regard to the divergence in the results concerning the electron transfer between an alkali metal and an AH, we decided to look first at the charges ascribed to Li atom complexed with the simplest AH, benzene, according to several algorithms of calculating atomic charges. The procedure consists in partitioning the total electron density of a system among particular atoms carrying a positive or negative charge and allows one to ignore the wave character of the electrons. Many methodologies have been devised to compute partial charges. They can generate very different results29 and, what is more, there is no universally agreed upon “best” procedure for computing partial atomic charges.16 In references concerning Li−PAH we have noticed the partial charges of Li (or other metals) calculated only according to the Mulliken scheme7,11−13 or according to natural population analysis (NPA).7,11 Here, the six following algorithms were applied: the two of Milliken and NPA, those proposed by Löwdin and Hirshfeld, AIM charges calculated according to the atoms in molecules method,23 and CHelpG charges reproducing molecular electrostatic potential. The

In the case of electron density transfer resulting from complex formation, e.g., from Li to AH, the result of the summation on right side of eq 1 should be higher than the 7046



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Table 1. Charge on the Li Atom in a Planar Complex with Benzene, Calculated at Different Levels Using Six Algorithms for Partition of the Total Electron Density among Individual Atoms method of calculation of atomic charge level of calculation of charge//level of geometry optimization

Mulliken

NPA

Löwdin

Hirshfeld

AIM

CHelpG

UHF/3-21G//UHF/6-311++G** UHF/6-311++G**//UHF/6-311++G** UMP2/3-21G//UMP2/3-21G CCD-3-21G//UMP2−3-21G UMP2/6311++G**//UMP2/6311++G**

−0.11 −0.12 −0.13 −0.13 −0.17

−0.04 −0.05 −0.06 −0.06 −0.07

−0.36 −0.36 −0.45 −0.45 −0.13

−0.20 −0.19 −0.25 −0.25 −0.24

0.10 0.10 0.10 0.10 0.10

−0.15 −0.15 −0.21 −0.21 −0.20

Table 2. Charge on the Li Atom in a Boat Complex of Li with Benzene, Calculated at the MP2-6-311++G** Level Using Six Different Algorithms for Partition of the Total Electron Density among Individual Atoms method of calculation of atomic charge level of calculation of charge//level of geometry optimization

Mulliken

NPA

Löwdin

Hirshfeld

AIM

CHelpG

UMP2/6-311++G**//UMP2/6-311++G**

0.51

0.79

0.08

0.36

0.90

0.48

Table 3. Dipole Moment of the Planar Li−C6H6 Complex and the Electron Density Transferred between the Two Volumes (Figure 2): One Encompassing Li, the Second Containing Benzene geometry optimization distance Li−HA (Å) level of calculation of electron density electron density transfer dipole moment (debye) dipole moment (e Å)

UHF/6-311++G** 2.311 UHF/3-21G UHF/6-311++G** 0.23 −6.59 −1.37

UMP2/3-21G

0.20 −5.85 −1.22

0.28 −6.43 −1.34

UMP2/6-311++G** 2.241 UMP2/6-311++G** CCD/3-21G 0.25 −5.78 −1.20

0.28 −6.72 −1.40

CCD/6-311++G** 0.25 −6.57 −1.37

Table 4. Dipole Moment of the Boat Li−C6H6 Complex and the Electron Density Transferred between the Two Volumes (Figure 2): One Encompassing Li, the Second Containing Benzene geometry optimization distance Li−HA (Å) level of calculation of electron density electron density transfer dipole moment (debye) dipole moment (e Å)

UMP2/3-21G 1.776 UMP2/3-21G −0.10 2.33 0.49

UMP2/6-311++G** 1.801 UHF/6-311++G** UMP2/6-311++G** −0.21 −0.15 3.44 2.67 0.72 0.56

occupied by the complex into two parts; one surrounding the Li atom, and the second, the hydrocarbon. This step was common to all the investigated complexes for which transfer of electron density was evaluated. Figure 2 shows the intersection of the cuboid volume encompassing planar Li−C6H6 complex to the two volumes: one containing Li, and the second, enclosing benzene. Tables 3 and 4 display the results of transferring the electron density for the two Li−benzene complexes. In Tables 3−8 the entries headed “electron density transfer” are equal to dens1(Li−AH)−dens1(Li)−dens1(AH). The values of the electron density transfer indicate that about 0.25e of the electron density is transferred from the volume containing benzene to the volume containing Li, because the positive sign of the expression dens1(Li−AH)−dens1(Li)− dens1(AH) means that direction of the electron transfer is from volume 2 to volume 1. Table 4 presents similar entries for the second, boat conformer of the Li−benzene complex. It can be seen that in this case the direction of the charge transfer is the reverse of that in Table 3, indicating a transfer of electron density from volume 1 (Li) to volume 2 (benzene). The value of the transferred charge is somewhat smaller than for the planar complex with a greater distance from Li to hydrocarbon. Therefore, we may conclude that the direction of

results for the two Li−benzene complexes obtained by the six methods are presented in Tables 1 and 2. All frequencies of the two Li−benzene structures optimized at the HF/6-311++G**, MP2/3-21G, and MP2/6-311++G** levels were positive. As can be seen, according to five out of the six methods, the charge on Li appeared to be negative for different levels of geometry optimization as well as at different levels of calculation of the charges. One can notice that the negative charges on Li generated by the five methods differ between each other, as can be expected, but each of them indicate that the Li atom in the complex is loaded with a modest negative charge. This would suggest the direction of electron transfer is from hydrocarbon to Li, in contrast to the intuitive course from the Li to the hydrocarbon. Only the results obtained by the AIM method allow for a small electron transfer (0.1 e) from Li to benzene. However, different results could be seen for the second, nonplanar structure of higher energy. They are displayed in Table 2. In this case one would rather expect an electron transfer from lithium to benzene. As a next step in evaluating the electron transfer between Li and benzene we took into consideration the spatial distribution of the electron densities instead of treating the charge of electrons as a contribution to atomic point charges. As a starting point, we traced out a plane dividing the space 7047



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Table 5. Dipole Moment of the “Loose” Li−Coronene Complex and Electron Density Transferred between Two Volumes (Figure 1): One Encompassing the Li Atom, the Second Containing the Coronene Li above central coronene ring geometry optimization distance Li−HA (Å) level of calculation of electron density electron density transfer dipole moment (debye) dipole moment (e Å)

UHF/3-21G 2.597 UHF/3-21G

UMP2/3-21G

UMP2/3-21G

2.283 MP2/6-311++G**

CCD/3-21G

Li above peripheral coronene ring UMP2/6-311++G**

ROHF/3-21G

UMP2/3-21G

2.843 UMP2/6-311++G**

2.441 ROHF/3-21G

2.236 UMP2/3-21G

0.18

0.25

0.20

0.23

0.12

0.22

0.27

−5.55

−6.04

−4.95

−6.07

−3.18

−6.02

−6.26

−1.16

−1.26

−1.03

−1.33

−0.66

−1.25

−1.30

also slightly distorted from planarity. Instead, the terms “tight” and “loose” will be used. The results in Tables 5 and 6 are qualitatively analogous to those in Tables 3 and 4.

charge transfer depends on the distance of the Li atom from the hydrocarbon center, despite the distances in Table 4 not being very different from those in Table 3 (for the structures optimized at the MP2/6-311++G** level the difference was 20%). One can say that the old saying “the devil is in the details” applies. Then, let us consider the charge transfer predicted by the dipole moments of the Li complexes. The orientation of the complexes in Tables 3 and 4 was such that the center of the hydrocarbon and the Li were positioned on the z-axis of the Cartesian coordinates, the z-coordinate of the latter being more positive. Neither an isolated Li atom nor an isolated hydrocarbon molecule has a dipole moment. So the dipole moment of the complex is equal to its difference due to the charge transfer between Li and AH. For example, the dipole moment of the planar Li−benzene complex is −5.78 D at the MP2/6-311++G** level; that is, −1.2 e Å, going from the Li atom to benzene, as the vector representing dipole moment is directed along the dipole axis from the negative charge to the positive one. It corresponds formally to polarity of the Li−··· benzene+. Were the negative charge concentrated on the Li and the positive charge on a dummy atom in the center of the benzene ring, the dipole moment (−1.2 e Å) would indicate a transfer of charge of about 0.5 e, taking into consideration the distance between the Li and the benzene center is 2.241 Å for the planar complex (at the MP2/6-311++G** level). In reality, the charges are not concentrated at these two points, but the charge transfer is equivalent to a shift in a diffused electron density along the positive sense of the z-axis. Taking into consideration the rough estimate of the charge transfer (0.5 e) with the help of point charges, the agreement of this value with that calculated by integrating the electron density (0.25e) is quite good (Table 3). In our opinion, however, the most persuasive conclusion based on the change of dipole moment is the same direction of the electron transfer as predicted by the electron density integration. Li−Coronene Complexes (Li−C24H12). For the Li− coronene complex, two geometries were considered because coronene is composed of six-membered rings of clearly different types. In the first geometry the Li was in the central position, whereas in the second, the Li atom was positioned above a peripheral six-membered ring. For the central geometry only one structure with a larger Li−hydrocarbon distance was found, whereas for Li above a peripheral ring two structures, with larger and smaller Li−coronene distance, were optimized. Regarding the complexes with coronene and circumcoronene, the terms “planar” and “boat”, describing the geometries of the benezene−Li complexes, no longer apply because the complexes with a longer distance from Li to hydrocarbon, are

Table 6. Dipole Moment of the “Tight” Li−Coronene Complex and the Electron Density Transferred between Two Volumes (Figure 1): One Encompassing the Li Atom, the Second Containing the Coronene geometry optimization distance Li−HA (Å) level of calculation of electron density electron density transfer dipole momenta (debye) dipole momenta (e Å)

UMP2/6-311++G** 1.804 UMP2/6-311++G** ROHF/6-311++G** −0.12

−0.16

3.36

2.68

0.70

0.56

In the “tight” conformer, due to its geometry, the dipole moment vector had two significant components along two perpendicular axes. In the table the component along the z-axis, perpendicular to the hydrocarbon plane, is shown. a

Optimization at the HF/3-21G, MP2/3-21G, and MP2/6311++G** levels led to complexes in which the Li−AH distance was in the range 2.2−2.8 Å. However, at the HF/6311++G** level, this distance was larger, 5.4 Å. The amount of electron transfer was strongly correlated with distance; when it exceeded 5 Å, almost no electron transfer was observed. The sign of the electron density transfer and that of the dipole moment in Table 5 show that the electron density was shifted from the coronene region to the region occupied by Li. It can also be seen that for a given distance (2.283 Å at the MP2/321G level) the amount of transferred charge is nearly independent of the level at which the electron density was integrated in space. A “tight” structure in which the Li− coronene distance was significantly diminished was also found (Table 6). For that conformation the sense of the electron transfer from Li to hydrocarbon was the reverse of that in Table 5. Complexes of Li with Circumcoronene (Li−C54H18). Similar to the complexes of Li with benzene and coronene, two conformations, “loose” and “tight”, were found for the circumcoronene complex, differing in the distance between the Li and the hydrocarbon and in energy. The dipole moments and the transferred electron densities are shown in Tables 7 and 8. Complexes of Li with Circumcircumcoronene (Li− C96H24). For these complexes the results are scant because the system is prohibitively large to be optimized at the MP2 level. 7048



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Table 7. Dipole Moment of the “Loose” Li−Circumcoronene Complex and the Electron Density Transferred between Two Volumes (Figure 1): One Encompassing the Li Atom, the Second Containing the Circumcoronene geometry optimization distance Li−HA (Å) level of calculation of electron density electron density transfer dipole moment (debye) dipole moment (e Å) a

UMP2/3-21G 2.271 UMP2/6-311++G** 0.18 −4.40 −0.92

UMP2/3-21G 0.22 −5.58 −1.16

ROHFa/3-21G 2.547 ROHF/3-21G 0.18 −5.45 −1.13

The calculations were made at the ROHF level, because at the UHF level HF convergence was not met.

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Table 8. Dipole Moment of the “Tight” Li−Circumcoronene Complex and Electron Density Transferred between Two Volumes (Figure 1): One Encompassing Li, the Second Containing Circumcoronene geometry optimization distance Li−HA (Å) level of calculation of electron density electron density transfer dipole moment (debye) dipole moment (e Å)

ROHFa/3-21G 1.818 ROHF/3-21G

ROHFa/6-311++G** 1.784 ROHF/6-311++G**

−0.33 5.39 1.12

−0.22 4.18 0.87

DISCUSSION Previous results of the investigations of the lithium and AHs complexes differ for the conclusions concerning charge transfer between the two substrates: from no charge transfer (nonionic complexes of ref 10), through partial electron transfer from Li to AH12,13 to the transfer of one electron from Li to AH9,10,14 (ionic complexes in ref 10). Sometimes the conclusions were extrapolated to the interaction of Li with graphene or graphite substrates.7,9,13 The conclusions of the studies where more realistic graphite14 or graphene15 substrates were examined were also different. All the mentioned results were obtained by DFT methods. Baker and Head-Gordon10 who found two solutions (“ionic” and “nonionic” ones) remarked that in much of the previous work only an ionic solution was discussed and stated that there is a need to revaluate the previous conclusions. In our study two configurations were also found, named “loose” and “tight”. They corresponded to those named “nonionic and “ionic”.10 In the “loose” configuration the Li−PAH distance was larger than in that named “tight”. Our results concerning the key issue, e.g., the amount of electron transfer, were made by the ab initio (HF, MP2, CCD) methods, and confirmed by the direction and, to some extent, by the value of the complexes’ dipole moments. We also performed the electron-density integration by using the DFT method, but the results obtained for different functionals were conflicting with one another. For instance, direction of the electron density transfer obtained with B3LYP and with the dispersion-corrected functionals (wB97XD and B97D) for the “loose” complexes was opposite to that calculated with ab initio methods. Yet, the latter results were congruous with those produced by using M05-2X, a strongly parametrized functional. It appears that an effective and trustworthy functional for calculating densities of delocalized electrons remains to be found. The problem whether DFT can accurately predict spin densities has also been negotiated with regard to iron-nitrosyl complexes,30 for which different exchange-correlation functionals yielded very different spin densities.31

a

The calculations were made at the ROHF level, because at the UHF level HF convergence was not met.

Therefore, we calculated the amount and direction of the density transferred at that level after optimizing the geometry at the semiempirical AM1 level. The vertical distance Li−AH was 2.164 Å, and dipole moment was −7.61 D. The electron transfer (0.2 e) was found to take place from the hydrocarbon to Li. For another conformation with an Li−AH distance of 1.782 Å the dipole moment was 4.91 D, and the charge (0.28 e) was transferred in the opposite direction, from Li to hydrocarbon. Therefore, we may say that the same behavior as for the preceding hydrocarbons was also found in this case. Comparison of Binding Energies of the Li Complexes. Binding energies, defined as the difference in energy between the total system (Li−AH) and the isolated fragments (Li and AH) are tabulated in Table 9. It can be seen that the energies of the “loose” complexes point to attractive interactions whereas opposite is true for the “tight” complexes. The data for all “loose” complexes are of similar value. Table 9. Interaction Energies of Two Conformations: “Loose” and “Tight” of the Li−Hydrocarbon Complexes, Calculated at the UMP2/3-21G Levela

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CONCLUSIONS In this study, calculation of the charge transferred in Li− aromatic hydrocarbon complexes by means of integrating the electron density was proposed. The results were dependent on the initial guess made during geometry optimization and on the level applied. It was found that for benzene one of the conformations was planar, whereas the structure of the second could be termed a “boat” on the basis of its resemblance to the structure of the glucose ring. In the planar Li−benzene complex the dihedral angles in the ring differed from zero by not more than 0.04°, and the Li···C distance was 2.643 Å (calculated at the MP2/6311++G** level). In the boat configuration the largest dihedral

interaction energies (eV) hydrocarbon benzene, C6H6 coronene, C24H12 circumcoronene, C54H18 circumcircum−coronene, C96H24

“loose”

“tight”

−0.42 −0.40 −0.33b −0.39 −0.45

0.33 1.28b 1.1 0.54

a

The energies are not corrected for the basis set superposition error. The two values were calculated for the complex in which binding site of the Li atom was in the vicinity of a peripheral six-membered ring. All other data concern complexes with Li adsorbed above a central hexagonal ring.

b

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that purpose elaboration of an effective functional, yielding the reliable spin densities, is needed.

angle between adjacent carbon atoms was 18°, and two C···Li distances were found due to the nonplanarity of the ring, namely 2.148 and 2.285 Å (at the same level). These findings are in agreement with the results quoted in ref 10 where two possible forms of Li−PAH complexes were reported. For complexes of higher HAs with Li, the structures of the two conformations differed less in terms of planarity. The conformers with the smaller Li−C distance were called “tight”, whereas the others were called “loose”. In all cases the “loose” conformers were of lower energy than the corresponding “tight” ones. It was found that in the loose complexes the direction of transfer of electron density was from the region occupied by the hydrocarbon to the region occupied by Li. In the tight complexes, in contrast, the direction was reversed. Geometry optimization at the UHF level sometimes led to structures with very long Li··· distances, and consequently very low transferred charge. However, no calculation method in any complex anticipated the transfer of a full electron between the two regions: the transferred electron density amounted to 0.1−0.3 electrons. Therefore, our results indicate transfer of a fractional number of electrons; that is, the electron is delocalized over spatially separated fragments Liσ+···AHσ− or Liσ−···AHσ+. This conclusion is in agreement with the values of atomic charges calculated by six algorithms. What is more, in five cases the sign of the Li atomic charge coincided with the direction of electron transfer indicated by integration of electron densities. However, for the planar complex of benzene, the AIM charge (0.1) was in disagreement with the direction of electron transfer shown by other methods. The cause of this discrepancy as yet remains obscure. It should be added that the conformations in which some electron density is transferred from Li to AH (Liσ+···AHσ−) are of higher energy such that the conformation for which the electron density transfer has the opposite direction, (Liσ−··· AHσ+), as can be seen in Table 9. In the most stable configuration of the complexes, a fragmental electron density from the hydrocarbon to Li takes place; this result is incompatible with some results based on the application of the Mulliken population.10,12,13 However, Ferre-Vilaplana, who investigated the Li−coronene complex, found +0.59 and −0.21 electrons as Mulliken population for the lithium atom in two configurations obtained using two different initial guesses.7 The latter, negative value characterized the solution of lower energy. Our values of the electron density transfer in complexes of Li with four hydrocarbons correspond with this result. As far as the graphene itself is concerned, it is generally presumed that Li and other alkali metals finding themselves in the vicinity of graphene surface will donate their s electron to it.5,10,14 Our results, based on the homologue series C6n2H6n up to n = 4, show the opposite direction of the fractional electron transfer. Although our results are of necessity limited to making use of the models of finite dimensions, data in Tables 3−8 show that amounts of the transferred charge are similar in the four investigated Li−HA complexes in their lowest energy states. The same can be said of the binding energies of the complexes (Table 9). This fact allows us to expect that the results can be extrapolated to larger carbonaceous systems, despite the possible differences as, e.g., lower electron affinity of PAHs compared with that of graphene. However, the convergence behavior with respect to the size of the substrate yet remains to be verified, preferably by DFT calculations. For

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AUTHOR INFORMATION

Corresponding Author

*Tel: +(48-22) 8419435 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The computing grant G44-18 from the Interdisciplinary Center for Mathematical and Computer Modeling (ICM) of Warsaw University and the financial support from the Polish Ministry of Science and Higher Education are gratefully acknowledged. We also think Dr. Douglas J. Fox from Gaussian Inc. for his helpful assistance.

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REFERENCES

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Ab Initio Study of Charge Transfer between Lithium and Aromatic

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