First-Principles Study of the Lithium Interaction with Polycyclic

Ab Initio Study of Charge Transfer between Lithium and Aromatic Hydrocarbons. Can the Results Be Directly Transferred to the Lithium–Graphene Intera...
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11986

J. Phys. Chem. B 2001, 105, 11986-11993

First-Principles Study of the Lithium Interaction with Polycyclic Aromatic Hydrocarbons Shigeru Ishikawa,*,† Galia Madjarova,‡,§ and Tokio Yamabe‡,| Department of Chemistry, Faculty of Science, Tokai UniVersity, 1117 Kitakaname, Hiratsuka 259-1292, Japan, and Institute for Fundamental Chemistry, 34-4 Takano-Nishihiraki-cho, Sakyo-ku, Kyoto 606-8103, Japan ReceiVed: April 26, 2001; In Final Form: September 20, 2001

We have performed first-principles calculations in order to understand the binding mechanism of Li atoms in disordered carbon materials that are used for negative electrodes of rechargeable lithium batteries. We used pyrene, anthracene, and phenanthrene molecules as parts of disordered carbon. We examined several binding sites for two Li atoms in these aromatics and found that they are bound with substantial negative binding energies. The most negative one was -142.8 kJ/mol for Li-containing pyrenes, -211.0 kJ/mol for anthracenes, and -146.2 kJ/mol for phenanthrenes at the B3LYP/6-31G*//HF/6-31G* level of calculation. Li atoms are bound to interstitial (ring-over) and edge sites. In addition to these binding mechanisms, we found that Li atoms could be bound, forming a Li dimer in anthracene and phenanthrene. Their binding energies are -200.5 and -146.2 kJ/mol, respectively, being larger in magnitude than Li2 dissociation energy. These aromatics lose their planarity when they accommodate Li atoms. We found that larger distortion brings more strong interaction between the aromatics and Li atoms. The amount of energy required for the distortion increases in the order the interstitial, edge, and Li-dimerized sites. The highest occupied molecular orbital energy, which is closely related to the electrode potential during discharge process, decreases in that order. This energy lowering may be related to the origin of the hysteresis observed during the charge/discharge cycles.

Introduction Carbonaceous materials have been used for negative electrodes of rechargeable lithium batteries because they usually have higher specific charges and more negative redox potentials than other electrode materials, such as metal oxides, chalcogenides, and polymers, and they also show better charge/ discharge cycling performance than lithium alloys.1 Carbonaceous materials are classified into graphitic and nongraphitic carbons. Graphitic carbons have layered structure consisting of graphene sheets. Upon intercalation with Li, they can accommodate one Li atom per six C atoms (372 mAh/g as the specific charge). They show small hysteresis during charge/ discharge cycles. These anodes operate near the reduction potential for elemental lithium, which can deposit in a highly reactive form during cell cycling.2,3 Nongraphitic carbons are prepared by pyrolysis of organic polymers or hydrocarbon precursors at different temperatures. They consist of a hexagonal carbon network arranged disorderly. They are further classified as “soft” and “hard” carbons depending on whether they graphitize or not upon heat treatment from ∼1500 to ∼3000 °C. Nongraphitic carbons prepared at temperatures from ∼500 to ∼1000 °C show higher specific charges than graphitic ones. For example, the “soft” carbon prepared from petroleum pitch heated to 550 °C yields a reversible capacity of ∼900 mAh/g and the “hard” carbon from resole resin heated to 1000 °C gives * To whom correspondence should be addressed. Fax: +81-463-502094. E-mail: [email protected]. † Tokai University. ‡ Institute for Fundamental Chemistry. § Permanent address: Faculty of Chemistry, University of Sofia, Sofia1126, Bulgaria. | Present address: Nagasaki Institute of Applied Science, 536 Aba-machi, Nagasaki 851-0193, Japan.

∼560 mAh/g.4a The voltage profiles of the “soft” and “hard” carbons differ qualitatively in the high specific charge region. The “soft” carbons show appreciable hysteresis (∼1V) during charge/discharge cycles, while the “hard” ones do not. This means that different Li insertion mechanisms are operative in the cases of “soft” and “hard” carbons. Several insertion mechanisms have been proposed for the high specific charge carbons.4-7 The “soft” carbons in the high specific charge region contain a substantial number of hydrogen atoms that terminate their edges. Dahn et al. showed the correlation between the amount of specific charges and H/C atomic ratio by preparing a series of “soft” carbon materials at different temperatures, and they concluded that Li atoms are bound near hydrogens.4a The extent of the hysteresis is proportional to the hydrogen content in the carbon materials. They suggested that Li atom insertion would change the C-H bonding and thus cause the hysteresis. Yata et al. also found that the specific charge increases with the increase of H/C atomic ratio in their polyacenic semiconductor (PAS) material, prepared from phenol resin at temperatures from 600 to 700 °C.7 They reported that a PAS material with appropriate H/C ratio could store Li atoms up to LiC2 composition. The ESR measurements showed that this was achieved without formation of Li clusters.8 The 7Li NMR measurement showed that the Li nucleus is more loosely bound than in the LiC6 stage of graphite and the 1H decoupling measurement showed no specific interaction between Li and H nuclei.9 On the other hand, Sato et al.6 proposed the formation of Li2 molecule in a disordered carbon material based on a 7Li NMR experiment. However, its existence has been suspected due to the strong repulsion between Li cations. To resolve the binding mechanism of “soft” carbons in the high specific charge region, several molecular orbital calculations have been done using small aromatic hydrocarbons.10-12

10.1021/jp011597n CCC: $20.00 © 2001 American Chemical Society Published on Web 11/08/2001

Li Interaction with Polycyclic Aromatic Hydrocarbons AM1 calculations by Papanek et al. evidenced that Li atoms are bound to the carbon atoms at the edge of aromatic hydrocarbon molecules,10 with local geometry resembling the organolithium molecule C2H2Li2.13 They showed that Li atoms occupy both edge and interstitial sites up to LiC3 composition. The authors found that the difference in total energies of edge and interstitial sites is very small and concluded that both insertion mechanisms occur at nearly the same potential. Ago et al., using the ab initio HF/3-21G method, examined both the acene-edge and phenanthrene-edge for Li binding sites, as well as ring-over sites.12b They estimated the energy barrier to be small enough to allow Li atoms to migrate at room temperature. These calculations showed that both hydrocarbon edges and interstitial (ring-over) sites could bind Li atoms. In this paper, we have studied further Li binding sites using first-principles calculations. We employed density functional theory to include correlation energy because Hartree-Fock theory gave poor results for Li binding energy. We examined anthracene and phenanthrene molecules and compared the results with those for pyrene, which has been studied by Papanek and Ago. Two Li atoms were added to each hydrocarbon. In addition to the edges and ring-over sites, we found that anthracene and phenanthrene have other binding sites where Li atoms are dimerized with large binding energies. The hydrocarbons lose their planarity when they accommodate Li atoms. This distortion could be an activated process that causes the hysteresis. We have calculated the energy required for this distortion and the stabilization energy when they accommodate Li atoms. The highest occupied molecular orbital (HOMO) energy of Li-containing hydrocarbons, which is closely related to the electrode potential during discharge process, is compared with the stabilization energy.

J. Phys. Chem. B, Vol. 105, No. 48, 2001 11987

Figure 1. Optimized geometries of 2Li-doped pyrene systems. The Li atoms are located over (Py1) the center of benzene rings (ring-over site), (Py2) the same side of the next nearest-neighbor ring-over position, (Py3) the peripheral C atoms (phenanthrene-edge site), and (Py4) the opposite side of ring-over position. Li-Li and Li-C distances are indicated by broken lines and the Li charges are shown.

Method of Calculation Ab initio molecular orbital calculations were performed using Gaussian9414a and Gaussian 98W14b programs. Molecular structures were optimized at the restricted Hartree-Fock (HF) level with the 6-31G* basis set (HF/6-31G*). The atomic calculation was done by the unrestricted HF level. Vibrational frequency calculation was performed for each optimized structure to confirm that it was located at the minimum of the potential energy surface. Density functional theory (DFT) was employed to calculate electron correlation energy. Kohn-Sham (KS) molecular orbital calculation was performed for the geometry obtained at the HF/6-31G* level using Becke’s 3-parameters hybrid exchange and Lee-Yang-Parr correlation functional with 6-31G* basis set (B3LYP/6-31G*//HF/6-31G*). This method yields 84.3 kJ/mol for the dissociation energy of Li2 (without zero-point correction), which is 80% of the experimental value (106 kJ/mol), and gives a better result than the MP2(FULL)/6-31+G*//MP2(FULL)/6-31+G* calculation (61.0 kJ/mol). The atomic charges were calculated at the B3LYP/6-31G*//HF/6-31G* level using Mulliken population analysis. Results and Discussion 1. Li-Doped Pyrene. We examined several types of 2Licontaining pyrenes in order to discuss the site-stability dependence and to compare our results with previous studies10,12b at different levels of theory. The optimized structures of four energetically favorable configurations with data for Li-Li and Li-C distances and Li charges are shown in Figure 1. The

binding energies were calculated as the total energy difference between the reactants and products:

binding energy ) (total energy of 2-Li-carbon) (total energies of carbon + 2Li atoms) In structure Py1, Li atoms occupy opposite sides of the nonneighboring hexagonal rings. Among all geometries the ringover site configuration of Py1 was found to be the most stable. This result is in good agreement with previous theoretical studies.10,12b The binding and relative energies of 2Li-doped pyrene structures are shown in Table 1. The AM1 method described the Li-insertion processes as endothermic (by 390420 kJ/mol).10 The HF/3-21G method gave a slightly negative binding energy (-18.4 kJ/mol) only for the two Li atoms in Py1.12b In contrast to these results, the B3LYP/6-31G*//HF/631G* method used here gave a reasonable negative binding energy for each structure. The magnitude of binding energy per one Li atom for Py1 (71.4 kJ/mol) is larger than the H3C-Li dissociation energy (46.4 kJ/mol). The structure Py2 has Li atoms on the same side of the molecular plane. This is less stable than Py1 by 8.2 kJ/mol. Structures Py3 and Py4 are less stable than Py1 by 31.0 and 40.3 kJ/mol, respectively. In structure Py3 two Li atoms are bound on the peripheral carbon atoms of the central fragment (phenanthrene-edge site). The positions of the peripheral carbon atoms largely deviate from their original planarity. In structure Py4 two Li atoms occupy the opposite sides of the ring-over position at one of the nonneighboring hexagons.

11988 J. Phys. Chem. B, Vol. 105, No. 48, 2001

Ishikawa et al.

TABLE 1: Binding and Relative Energies (kJ mol-1) of Two Li Atoms in Pyrene, Anthracene, and Phenanthrenea structures

binding energy

relative energy

Py1 Py2 Py3 Py4 An1 An2 An3 An4 An5 An6 Ph1 Ph2 Ph3 Ph4 Ph5

-142.8 -134.6 -111.8 -102.5 -211.0 -200.5 -193.2 -189.8 -188.1 -108.4 -146.2 -128.0 -116.1 -84.1 -82.4

0.0 (0.0) 8.2 31.0 (28.5) 40.3 (26.8) 0.0 10.5 17.8 21.2 22.9 102.6 0.0 18.2 30.1 62.1 63.8

a Relative energies are shown with respect to the minimum energy structure. The AM1 results of Papanek et al.10 are shown in parentheses.

We also optimized 2Li-doped pyrenes using the MP2(FC)/ 6-31G* method. The MP2 binding energies for Py1, Py2, and Py3 are -133.3, -129.8, and -117.2 kJ/mol, and the energy differences between MP2 and B3LYP/6-31G*//HF/6-31G* are +9.5, +4.8, and -5.4 kJ/mol, respectively. The Li-C (Li-Li) distances for Py1, Py2, and Py3 obtained by MP2 are 2.141 (5.960), 2.290 (4.190), and 2.160 (3.840) Å, while those by HF are 2.128 (6.167), 2.123 (5.234), and 2.041 (3.831) Å, respectively. MP2 gives longer Li-C distances than HF, especially for Py2 and Py3 by more than 0.1 Å. It gives the relative Li-C distances as Py1 < Py3 < Py2, while HF shows Py3 < Py2 < Py1. Moreover the Li-Li distance for Py2 is very different between the two methods. Then we further optimized 2Li-doped pyrenes using the B3LYP/6-31G* method. It has been recognized that the DFT calculation with the B3LYP hybrid functional reproduces molecular geometries quite well. The DFT binding energies for Py1, Py2, and Py3 are -145.0, -136.7, and -117.1 kJ/mol, and the energy differences from the B3LYP/6-31G*// HF/6-31G* methods are -2.2, -2.1, and -5.3 kJ/mol, respectively. The DFT binding energies are closer to those of B3LYP/ 6-31G*//HF/6-31G* than those of MP2. The Li-C (Li-Li) distances for Py1, Py2, and Py3 by DFT are 2.107 (5.930), 2.100 (5.000), and 2.080 (3.740) Å, respectively. DFT calculates Li-C distances shorter than HF by 0.02-0.04 Å, and it gives the same relative Li-C distances (Py3 < Py2 < Py1) as HF. The Li-Li distance for Py2 obtained by DFT is closer to the HF result than the MP2 result. We think that the molecular geometries obtained by HF are good substitutes for those by DFT. Although MP2 usually yields better results than HF for many molecules, it seems that the second-order calculation is not sufficient for these Li-containing aromatics and the higherorder levels should be needed for accuracy. Recently, models such as structure Py3 attract attention because it is thought to be a possible model of Li insertion in disordered carbon materials. Previous theoretical research10,12 suggests covalent bond interaction between Li and C atoms for the phenanthrene-edge site in Py3. The nature of the Li-C bond has been extensively studied for the case of methyllithium.15-17 The latter has a large dipole moment, which indicates its ionic character. Natural population analysis at the HF/6-31G* level gave +0.822 for the charge of Li, while Mulliken population analysis at the B3LYP/6-31G*//HF/6-31G* level gave +0.346. Mulliken population analysis shows a strong basis set dependence and fails to give appropriate charges for the compounds having significant ionic character.17,18 However, comparing the

Figure 2. Orbital patterns of HOMO and LUMO of pyrene. Frontier orbitals are asymmetric with respect to rotation at symmetry axis C2.

values, we may conclude that the ionic character of Li in pyrene is weaker than in methyllithium. The covalent nature of the bond interaction between Li and C atoms can be recognized from the shorter Li-C interatomic distances and smaller Li charges. The Li-C distance and Li charge in Py1, respectively, are 2.128 Å (2.107 Å) and +0.298 (+0.265), where DFT results are shown in parentheses. The Li-C distance of 2.041 Å (2.080 Å) in Py3 is shorter, and the Li charge of +0.251 (+0.245) is less positive than those in Py1. Li atoms in Py3 are bonded to the peripheral carbon atoms of pyrene. This requires changes in the electronic state of these carbon atoms, and deviation from planarity is an evidence for the possible change of hybridization from sp2 to sp3.10 Py2 has a shorter Li-C distance of 2.123 Å (2.100 Å) than Py1 and has the smallest Li charge of +0.248 (+0.218) among them. The peripheral carbon atoms where Li atoms are bonded in Py2 lose planarity and the change of the hybridization is expected as in Py3. A detailed look at the frontier molecular orbital pattern shows that the HOMO and LUMO of pyrene are asymmetric with respect to rotation about the symmetry axis C2 (or to reflection in the mirror symmetry plane σ) containing more than two π-centers. The coefficients of the atoms lying on the symmetry axis are zero and the electronic density of the HOMO and LUMO is localized within the fragment shown in Figure 2. It follows from the LUMO symmetry of pyrene that the phenanthrene-edge C atoms are expected to carry the largest charge and it is at this point that the largest deviation from planarity takes place. It was shown12b,17 that the low-energy lithium 2p orbitals play an active role in the bonding of carbon-Li containing compounds and can be regarded as valence orbitals. Thus, orbital overlap between 2p orbitals of Li and LUMO of pyrene would stabilize the HOMO of the Li-carbon complex. In the case of 2Li-doped pyrene, Py3 has the lowest HOMO among all the obtained geometries. Above the calculated molecular geometry where Li atoms occupied ring-over and edge sites are in a good agreement with

Li Interaction with Polycyclic Aromatic Hydrocarbons

J. Phys. Chem. B, Vol. 105, No. 48, 2001 11989

Figure 3. Optimized geometries of 2Li-doped anthracene systems. The Li atoms are located over (An1) the opposite side of the nearest-neighbor ring-over site, (An2) the C-C bond (bond-over site), (An3) the same side of the nearest-neighbor ring-over site, (An4) the opposite side of the next nearest-neighbor ring-over site, (An5) the same side of the next nearest-neighbor ring-over position, and (An6) the C atoms (atom-over site). The Li-Li and Li-C distances are indicated by broken lines and the Li charges are shown.

present published data. In addition, taking into account the high accuracy of the Becke three-parameter hybrid exchange and Lee-Yang-Parr correlation functional with the 6-31G* basis set (B3LYP/6-31G*//HF/6-31G*), we obtained reliable negative binding energies and can conclude that the used method is quite reliable for describing organolithium systems. 2. Li-Doped Anthracene and Phenanthrene. The next Lidoped aromatic hydrocarbons, anthracene and phenanthrene, are isoelectronic systems with different topologies. These aromatic molecules involve two distinct edge structures “acene-edge type” (or zigzag-edge type) and “phenanthrene-edge type” (or armchair-edge type). The characterization of the electronic structures of these molecules is a classical problem in quantum chemistry19,20 It is interesting to analyze changes of the molecules upon doping and preferable positions for Li dopants. 2.1. Li-Doped Anthracene. Optimized molecular structures of 2Li-containing anthracene are shown in Figure 3. Two types of Li-dimerized structures (An2 and An6), two types of ringover site structures where Li atoms occupy the opposite sides of molecular plane (An1 and An4) and two types of ring-over site structures where Li atoms occupy the same side of molecular plane (An3 and An5) were obtained. The binding energies of the two Li atoms and the relative energies with respect to the structure An1 are shown in Table 1. The most stable among them was found to be An1, where the Li atoms are bound on neighboring rings oppositely. The binding energy is lower than that of Py1 by 65 kJ/mol. The geometry of An1 is very similar to that of bis[(tetramethylethylenediamine)lithium(I)] anthracenide ([LiTMED]2C14H10), whose geometry was determined by single-crystal X-ray analysis.21 The carbon skeleton shows a significant nonplanarity. The other interstitial configuration An4 is less stable than An1 by 21.2 kJ/mol. An4 is similar to Py1 as two Li atoms occupy opposite sides of the next-nearest-neighbor site. The hydrocarbon parts of both structures remain planar. Li-dimerized structures An2 and An6, where Li atoms respectively occupy a bond-over and an atom-over site, are very

interesting form the theoretical point of view. The formation of the Li2 molecule in a disordered carbon material has been suggested by Sato et al.6 based on a 7Li NMR experiment. The high-density lithium intercalated graphite22 and carbon nanotube23 have been synthesized up to LiC2 composition under highpressure conditions by Nalimova et al. However, it has been thought that this composition could not be achieved under ambient conditions bearing in mind the strong repulsion between Li cations.4a On the other hand, Sakurai et al. reported the structure of bis[(tetrahydrofuran)lithium(I)] hexakis(trimethylsilyl)benzenide,24 in which the both Li atoms are located on the same side of the benezene ring with the Li-Li distance 2.722 Å. Ab initio calculations have been done for dilithiobenzenide.25 Furthermore, the infrared absorptions attributed to the Li2C6H6 stoichiometry have been observed for the lithiumbenzene complex in solid argon.26 Then we make a detailed analysis of the Li-dimerized structures An2 and An6. An2 is less stable than An1 by only 10.5 kJ/mol, but it shows a larger nonplanarity than An1. The Li-Li distance of 2.460 Å is much shorter than that of the Li2 molecule (2.807 Å at HF/6-31G* level). The Li atomic charge (+0.200) is less positive than that of An1 (+0.232 and +0.265) from whence comes the following important conclusion: the ionic character of Li atoms in Li-dimerized structure An2 is weaker than in the ring-over site position. The magnitude of the binding energy is much larger than the calculated dissociation energy of the Li2 molecule by 116 kJ/mol, so that a strong interaction between the Li atoms and anthracene is expected. To account for the Li-dimer formation in An2, the orbital interaction between frontier orbitals of anthracene and the bonding orbitals of the Li2 molecule is considered. In Figure 4 are shown the HOMO and LUMO of anthracene and the HOMO-1 and HOMO of An2. The frontier orbitals of anthracene central ring show benzene-like pattern. The orbital interaction diagram is shown in Figure 5. It is seen that the HOMO and LUMO of anthracene can overlap with the π-orbital and σ-orbital of Li2 molecule by an in-phase manner, respec-

11990 J. Phys. Chem. B, Vol. 105, No. 48, 2001

Ishikawa et al. TABLE 3: HOMO (eV), Distortion (kJ mol-1), and Stabilization Energies (kJ mol-1) at the B3LYP/6-31G*//HF/ 6-31G* Levela

Figure 4. Orbital patterns of HOMO and LUMO of anthracene and HOMO-1 and HOMO of An2.

Figure 5. Orbital interaction between An2 and Li2 together with the orbital energies calculated at the B3LYP/6-31G*//HF/6-31G* level. The unit is au.

TABLE 2: Orbital Populations of Li Atoms in An2 of 2Li-Doped Anthracene and Li2 Moleculea atomic orbital

An2

Li2

1s 2s 2px 2py 2pz d total

2.001 0.268 0.199 0.156 0.128 0.048 2.800

2.002 0.930 0.046 0 0 0.022 3.000

a The z- and x-axes are set to the C axis of anthracene, which stands 2 perpendicular to the molecular plane and the molecular axis of Li2, respectively.

tively. The HOMO of anthracene and the π-orbital of Li2 molecule (the latter being parallel to the molecular plane of the anthracene) form the HOMO-1 of An2. The LUMO of anthracene and the σ-orbital of the Li2 molecule form the HOMO of An2. The LUMO of anthracene overlaps mainly with the 2p atomic orbitals in the σ-bonding molecular orbital of the Li2 molecule. The 2p orbitals in the Li2 molecule standing perpendicularly to the molecular plane of anthracene also occurs in this overlap. This overlap enhances the electron population in these 2p orbitals and brings about the increase of the electron density between Li nucleus, which leads to a smaller Li-Li distance than in the Li2 molecule. In Table 2 are presented the orbital populations of the Li atom in An2 and those in the Li2 molecule. As the Li atom in An2 has a positive charge of 0.200, the total orbital population is 2.800. The z-axis is set to the C2 axis of anthracene perpendicular to the molecular plane. The x-axis runs parallel

Py1 Py2 Py3 Py4 An1 An2 An3 An4 An5 An6 Ph1 Ph2 Ph3 Ph4 Ph5 a

HOMO energy

distortion energy

stabilization energy

-2.48 (-3.64) -2.67 (-3.76) -3.03 (-4.41) -2.93 (-4.02) -3.18 (-4.57) -4.21 (-5.91) -3.39 (-4.75) -2.48 (-3.63) -2.61 (-3.71) -2.98 (-3.71) -3.95 (-5.59) -2.75 (-3.95) -3.03 (-4.45) -2.32 (-3.56) -2.71 (-3.71)

69.5 83.7 148.1 129.6 121.6 238.2 147.9 37.5 43.8 16.4 253.9 111.7 159.6 111.4 60.9

212.3 218.2 259.9 232.1 332.6 438.7 341.1 227.3 231.8 124.8 400.1 239.7 275.7 195.5 143.3

The HF/6-31G* results are shown in parentheses.

to the molecular axis of Li2. The σ-bonding orbital in Li2 is constructed from 2s and 2px atomic orbitals. The 2s population decreases from 0.930 to 0.268 as Li2 is inserted in An2, while the 2px population increases from 0.046 to 0.199. The 2pz orbitals are mixed with the σ-bonding orbital when Li2 is attached to anthracene. The 2pz population increases from 0 to 0.128. The 2py orbitals also contribute to the Li-Li bonding by interacting with the HOMO of anthracene. The 2py population in An2 is 0.156. The contribution of d-type polarization functions is small. Li dimer is also formed in An6, with an Li-Li distance of 2.800 Å. The Li charges are less positive than in An2. The magnitude of the binding energy for the two Li atoms is lower than the Li2 dissociation energy by only 24.1 kJ/mol, and the carbon skeleton is relatively flat. Therefore, it can be regarded as that the Li2 molecule is adsorbed due to intermolecular forces between Li2 and anthracene. This conclusion is also supported by the comparison of HOMO energies of Li-dimerized structures An2 and An6 (see Table 3). The HOMO of An2 shows a larger stabilization than An6 by 1.23 eV. Nalimova et al. measured the IR spectra of the high-density lithium intercalated graphite, and they carried out the normal coordinate analysis using the force field method.22 They attributed the bands at 880 cm-1 to the Li-Li bond vibrations in the equilateral triangles of the Li atoms and the bands at 650 and 450 cm-1 to the Li-C bonds. The Li-Li bond vibrations were also found in the lithiated carbon nanotubes.23 In this connection, we compared the vibrational frequencies of An2 with anthracene and An1. In general, the HF method overestimates vibrational frequencies due to the lack of the correlation effect. In addition, the HF method fails to predict the binding energies of the Li atoms to the hydrocarbons so that the curvature of the HF potential surface is not reliable. Then we adopted a higher level of calculation in evaluating the vibrational frequencies. We optimized these molecules at the B3LYP/631G* level and obtained the vibrational frequencies. The Li binding energies for An1 and An2 at this level are -211.7 and -200.2 kJ/mol, respectively. These energies are close to those obtained at the B3LYP/6-31G*//HF/6-31G*. For An1, the distance from the edge carbon to the Li is 2.110 Å and the central carbon to the Li is 2.170 Å. The Li-Li and the Li-C distances in An2 are 2.480 and 2.060 Å, respectively. Vibrational frequencies and their relative intensities for anthracene, An1, and An2 are shown in Figure 6. For anthracene, IR peaks appearing at 486, 745, and 892 cm-1 are

Li Interaction with Polycyclic Aromatic Hydrocarbons

Figure 6. Vibrational frequencies and their relative intensities for anthracene, An1, and An2 obtained at the B3LYP/6-31G*//B3LYP/ 6-31G* level. The circle and cross designate the IR and Raman active modes, respectively.

attributed to the C-H out-of-plane bending modes, which are not observed in graphite. A weak IR peak at 618 cm-1 and an intense Raman peak at 1445 cm-1 are the ring stretching modes. For An1, IR peaks at 759, 801, and 834 cm-1 are the C-H out-of-plane bending modes. The IR peaks at 1328 and 1444 cm-1, and the Raman peak at 1362 cm-1 are the ring stretching modes. The IR or Raman peaks at 457-517 cm-1 are the Li-C stretching modes, which correspond to the 450 cm-1 band of the high-density lithium intercalated graphite. For An2, the C-H out-of-plane bending and the ring-stretching mode are observed at 861 (Raman active) and 1281 cm-1 (IR and Raman active), respectively. The latter frequency is lower than those for An1. The Li-C stretching mode appears at 605 cm-1 (IR active), which is higher than An1. The intense Raman peaks appearing at 394 and 445 cm-1 are the Li-Li stretching modes. The B3LYP/6-31G*//B3LYP/6-31G* calculation shows that the stretching vibrational frequency of the Li2 molecule is 342 cm-1 (experimental value 351 cm-1). This blue shift occurring in the Li-Li stretching indicates that the Li-Li bond is strengthened when Li2 is inserted in An2. The Li-Li stretching in An2 exhibits lower frequency than the lithium intercalated graphite. This discrepancy is due to the arrangement of Li atoms in the graphite. The Li-Li stretching at 880 cm-1 appears only when Li atoms form an equilateral triangle network. The Li-Li stretching is also observed at 450 cm-1 with mixing the Li-C vibrations for this arrangement. An3 and An5 have Li atoms at the same side of molecular plane. They are less stable than An2 by 7.3 and 12.4 kJ/mol, respectively. Li atoms in An3 occupy the nearest neighbor rings.

J. Phys. Chem. B, Vol. 105, No. 48, 2001 11991 The distance between them is 3.510 Å. Li atoms in An5, being separated by 5.836 Å, occupy the next nearest neighbor rings. The Li charge in An5 is more positive than in An2, but smaller than in the structure that has Li atoms on the opposite sides of the molecular plane. From the relative energies and geometrical characteristics of the obtained structures we propose the following dynamics in 2-Li doped anthracene molecules: the carbon skeleton restores its planarity as the structure changes from Li-dimerized structure An2 to next neighbor ring-over site An5 via An3. 2.2. Li-Doped Phenanthrene. The optimized molecular structures of 2Li-containing phenanthrene are shown in Figure 7. Li-dimerized structure (Ph1), phenanthrene-edge structure (Ph3 and Ph5), and two types of ring-over structures (Ph2 and Ph4) were obtained. As shown in Table 1, the Li-dimerized Ph1 is the most stable among them. It has a short Li-Li distance (2.446 Å) and a large negative binding energy. Two Li atoms are located on the same side of phenanthrene at the bond-over site positions. This configuration is similar to An2 but here one of the Li atoms on the over peripheral C-C bond has an extremely low (+0.069) charge, as in the case of An3. The Mulliken method often yields rather unphysical atomic charges. Distortion of phenanthrene planarity takes place only in the part where the two Li atoms are located. In Ph3 Li atoms are bound to peripheral C atoms at the phenanthrene edge, which is similar to Py3 of pyrene. Therefore, there is considerable contribution of covalent interaction between Li and C atoms. In fact, our results emphasize the dual character of C-Li bond. Ph5 is another phenanthrene-edge bonded structure that is less stable than others. For Ph2 and Ph4 one can expect the same tendency as in the respective Li-doped anthracenes. The electronic properties of PAHs strongly depend on their size and especially on their edge structure. Recently, using the extended Hu¨ckel level of theory, we analyzed the band electronic structure of polyphenanthrene (PPh) and polyacene (PA) doped with lithium.27 It was shown that PPh should possess greater doping capability than PA, especially in heavy doping stages. Comparison of the site dependence of the stability in 2Lidoped anthracene and phenanthrene shows that in both molecules interstitial (ring-over) sites for Li atoms are possible. In phenanthrene Li atoms can occupy edge sites (model Ph3) where interaction between Li and C atoms has large covalent nature. Stable structure where Li atoms occupy phenanthreneedge structure was discussed also in Li-doped pyrene (Py3 model), which leads us to confirm that the phenanthrene edge structure in disordered hydrocarbons plays a very important role for the high capacity observed in this material. This conclusion is in very good agreement with recently published5b data of structural analysis of new carbonaceous material with very large capacity and high efficiency. In addition to these sites, the newly discussed Li-dimerized structure here could be one of the possible explanations for large capacity observed in this material. 3. Distortion Energy and the HOMO Level of 2Li-Doped Hydrocarbon. As we have seen, the aromatic hydrocarbons lose their planarity to some extent when they accommodate Li atoms. It has been pointed out that a bonding change in the host causes hysteresis of the electrochemical process.4a In Table 3, the energy required for the distortion of the hydrocarbon skeleton is shown. The phenanthrene-edge-bonded structure (Py3 or Ph3) shows a larger distortion energy than the ringover structures. The Li-dimerized structure (An2 or Ph1) shows a larger distortion energy than the other structures. Despite these large distortion energies, they exhibit substantial Li-binding

11992 J. Phys. Chem. B, Vol. 105, No. 48, 2001

Ishikawa et al.

Figure 7. Optimized geometries of 2Li-doped phenanthrene systems. The Li atoms are located over (Ph1) the C-C bond, (Ph2) the opposite side of the nearest-neighbor ring-over site, (Ph3) the peripheral C atoms (the phenanthrene-edge site), (Ph4) the opposite side of the next nearestneighbor ring-over site, and (Ph5) the phenanthrene-edge site. The Li-Li and Li-C distances are indicated by broken lines and the Li charges are shown.

Figure 8. Relation between the stabilization energy and distortion energy.

energies because the change of hybridization in C atoms brings a large stabilization when they interact with Li atoms. Actually, the phenanthrene-edge-bonded structure and Li-dimerized structure have significant covalent character in their Li-C bond. In Table 3, we show the stabilization energy, which is the energy difference between the distorted hydrocarbon and two Li atoms calculated as

stabilization energy ) (total energies of distorted hydrocarbon + 2Li atoms) (total energy of 2Li containing hydrocarbon) In Figure 8, the stabilization energy is plotted against the distortion energy. It is found that the stabilization energy

increases almost linearly as the distortion energy increases and a larger distortion gives a more favorable interaction between distorted hydrocarbons and Li atoms. The highest occupied KS orbital energy of Li-containing hydrocarbons is closely related to the electrode potential during the discharge process. It is well-known that this orbital energy is equal to the chemical potential of an electron if we use the exact exchange-correlation functional; however, adopting the approximate functional leads to a significant error. For comparison, we also show the Hartree-Fock orbital energies in Table 3. The HF theory gave more negative orbital energy than the KS theory; however, these theories gave almost the same trend in relative orbital energies. The linear dependence between KS and HF orbital energies has been reported.28 In Figure 9, we plotted the stabilization energy against the HOMO level. It is found that the larger stabilization energy results in a lower HOMO level. Comparison of Figures 8 and 9 also shows that the larger distortion brings a lower HOMO level. The stabilization energy decreases almost linearly as the HOMO energy increases except for An6 and Ph5, in which Li atoms are loosely bound. The HOMO level ranges from -4.2 to -2.3 eV (-5.9 to -3.6 eV at the HF/6-31G* level). In each hydrocarbon, the HOMO level becomes lower in this order: the ring-over, the edge-bonded, and the Li-dimerized structures. The HOMO of Li-dimerized structures were stabilized by ∼1 eV lower than HOMOs of the remaining structures. In the discharging process, electrons leave the anode and at the same time lithium ions diffuse spontaneously into the electrolyte. We think that electrons occupying the very lowlying HOMO levels cannot spontaneously leave with lithium ions, and these require some activation energy for the discharging process. In Figure 10, we show the electron flow in the discharging process. The electron begins to flow from anode to cathode since the electron prefers lower chemical potential. The existence of the edge and Li-dimerized structures may

Li Interaction with Polycyclic Aromatic Hydrocarbons

J. Phys. Chem. B, Vol. 105, No. 48, 2001 11993 References and Notes

Figure 9. Relation between the stabilization energy and HOMO energy.

Figure 10. Electron from anode to cathode.

reduce the cell voltage since they have a lower chemical potential than the ring-over structure. The activated process in the discharge would be like one such as An2 to An5 via An3. Conclusions Based on above discussion, the following can be concluded: 1. In addition to interstitial (ring-over) sites, Li atoms can occupy edge sites. The difference in total energies of obtained edge and interstitial sites is very small. Bond interaction between Li and carbon atoms from phenanthrene edge sites has dual character with a significant role of covalent contribution. 2. We found that anthracene and phenanthrene have other binding sites where Li atoms are dimerized with larger negative binding energies than the other sites. 3. The hydrocarbons lose their planarity when they accommodate Li atoms. The amount of energy required for the distortion increases in the order the interstitial, edge, and Lidimerized sites. Large distortion energy brings strong interaction between the aromatics and Li atoms and lowers the HOMO level. This energy lowering may be related to the origin of the hysteresis observed during the charge/discharge cycles. Acknowledgment. This work was supported by the “Research for the Future” program of the Japan Society for Promotion of Science (JSPS-RFTF96P00206).

(1) Winter, M.; Besenhard, J. O.; Spahr, M. E.; Novak, P. AdV. Mater. 1998, 10, 725. References for lithium insertion electrode materials are therein. (2) Tarascon, J.; Guyomard, D. Electrochim. Acta 1993, 38, 1221. (3) Shu, Z. X.; McMillan, R.; Murray, J. J. Electrochem. Soc. 1993, 140, 922. (4) (a) Dahn, J. R.; Zheng, T.; Xue, J. S. Science 1995, 270, 590. (b) Lui, Y.; Xue, J. S.; Zheng, T.; Dahn, J. R. Carbon 1996, 34, 193. (c) Dahn, J. R. Phys. ReV. B 1991, 44, 9170. (5) (a) Wang, S.; Matsui, H.; Tamamura, H.; Matsumura, Y.; Yamabe, T. Phys. ReV. B 1998, 58, 8163. (b) Wang, S.; Yata, S.; Nagano, J.; Okano, Y.; Kinoshita, H.; Kikuta, H.; Yamabe, T. J. Electrochem. Soc. 2000, 147, 2498. (6) Sato, K.; Noguchi, M.; Demachi, A.; Oki, N.; Endo, M. Science 1994, 264, 556. (7) (a) Yata, S.; Kinoshita, H.; Komori, M.; Ando, N.; Kashiwamura, T.; Harada, T.; Tanaka, K.; Yamabe, T. Synth. Met. 1994, 62, 153. (b) Yata, S.; Hato, Y.; Kinoshita, H.; Ando, N.; Anekawa, A.; Hashimoto, T.; Yamaguchi, M.; Tanaka, K.; Yamabe, T. Synth. Met. 1995, 73, 273. (8) Tanaka, K.; Ago, H.; Matsuura, Y.; Kuga, T.; Yamabe, T.; Yata, S.; Hato, Y.; Ando, N. Synth. Met. 1997, 89, 133. (9) Ago, H.; Tanaka, K.; Yamabe, T.; Takegoshi, K.; Terao, T.; Yata, S.; Hato, Y.; Ando, N. Synth. Met. 1997, 89, 141. (10) Papanak, P.; Radosavljevic, M.; Fischer, J. E. Chem. Mater. 1996, 8, 1519. (11) Bahn, C.; Lauderdale, W.; Carlin, R. Int. J. Quantum Chem., Qantum Chem Symp. 1995, 29, 533. (12) (a) Ago, H.; Nagata, K.; Yoshizawa, K.; Tanaka, K.; Yamabe, T. Bull. Chem. Soc. Jpn. 1997, 70, 1717. (b) Ago, H.; Kato, M.; Yahara, K.; Yoshizawa, K.; Tanaka, K.; Yamabe, T. J. Electrochem. Soc. 1999, 146, 1262. (13) Ro¨thlisberger, U.; Klein, M. L. J. Am. Chem. Soc. 1995, 117, 42. (14) (a) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Cioslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez C.; Pople, J. A. Gaussian 94, revision E.2; Gaussian Inc.: Pittsburgh, PA, 1995. (b) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (15) Reed, A.; Weinstock, R.; Weinhold, F. J. Chem. Phys. 1985, 83, 735. (16) Schiffer, H.; Ahlrichs, R. Chem. Phys. Lett. 1986, 124, 172. (17) Bickelhaupt, F.; Hommes, N.; Guerra, C.; Baerends, E. Organometallics 1996, 15, 2923. (18) Baerends, E.; Gritsenko, O. J. Phys. Chem. A 1997, 101, 5383. (19) Hosoya, H.; Yamaguchi, T. Tetrahedron Lett. 1975, 52, 4659. (20) Fukui, K. Science 1982, 218, 747. (21) Rhine, W.; Davis, J.; Stucky, G. J. Am. Chem. Soc. 1975, 97, 2079. (22) Bondarenko, G. N.; Nalimova, V. A.; Fateev, O. V.; D.Guerard, D.; Semenenko, K. N. Carbon 1998, 36, 1107. (23) Nalimova, V. A.; Sklovsky, D. E.; Bondarenko, G. N.; AlvergnatGaucher, H.; Bonnamy, S.; Be´guin, F. Synth. Met. 1997, 88, 89. (24) Sekiguchi, A.; Ebata, K.; Kabuto, C.; Sakurai, H., J. Am. Chem. Soc. 1991, 113, 1464. (25) Sygula, A.; Rabideau, P. W. J. Am. Chem. Soc. 1991, 113, 7797. (26) Manceron, L.; Andrews, L. J. Am. Chem. Soc. 1988, 110, 3840. (27) Madjarova, G.; Yamabe, T. J. Pys. Chem. B 2001 105, 2534. (28) Stowasser, R.; Hoffmann, R. J. Am. Chem. Soc. 1999, 121, 3414.