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Journal of the Chilean Chemical Society

versão On-line ISSN 0717-9707

J. Chil. Chem. Soc. v.48 n.4 Concepción dez. 2003

http://dx.doi.org/10.4067/S0717-97072003000400011 

J. Chil. Chem. Soc., 48, N 4 (2003) ISSN 0717-9324

QUANTUM CHEMICAL MODEL FOR LITHIUM ELECTROCHEMICAL INTERCALATION INTO MOLYBDENUM DISULFIDE*

Fernando Mendizábal1, María Angélica Santa Ana1, Eglantina Benavente2, and Guillermo González1.

1Department of Chemistry, Faculty of Sciences, Universidad de Chile. Casilla 653, Santiago de Chile.
2Department of Chemistry, Universidad Tecnológica Metropolitana, Avenida José Pedro Alessandri 1242, Santiago de Chile
(Received : July, 31, 2003-Accepted : August 18, 2003)

ABSTRACT

Voltage- and incremental charge capacity-composition curves for the electrochemical formation of intercalates LixMoS2 were analyzed at the molecular level by developing a quantum chemical model focused on the variation of the electron chemical potential. Experimentally observed trends of the charge capacity in the range 0<x<0.6 are successfully described by the global hardness index as defined within the density functional theory. Contrasting with classical descriptions like the gas lattice model assuming complete lithium-MoS2 one electron transfer, proposed model leads, agreeing with previous experimental evidence, to a system in which electron density is partially retained in the lithium atom. The model permits moreover to identify a sequence of octahedral and tetrahedral sites as the more favorable migration pathway for the diffusion of lithium through the interlaminar space.

Key Words: Electron chemical potential, quantum chemical model, molydenum disulfide, electrochemical charge capacity, lithium intercalation.

INTRODUCTION

The interest on the intercalation chemistry of molybdenum disulfide has been growing notoriously during the last years (1-5). Contrasting with other transition metal dichalcogenides as those of Ti, Ta or Zr, whose ability for intercalating a variety of chemical species was rather well known still in the 70’s (6-8), most molybdenum intercalation compounds have been described during the last decade. Such a late development certainly deserves some attention.

There are indeed features in both the thermodynamics and kinetics of the intercalation process in MoS2 which have retarded the progress of its chemistry. Normally the intercalation in transition metal dichalcogenides is associated to a redox process in which charge is transferred to the matrix (9,10). In systems with the Fermi level in the conduction band such a charge transfer is certainly thermodynamically easier than in a semiconductor like the MoS2 with a band gap of about 1.2 eV (11). In the latter, the charge transfer implies to occupy levels of relatively high energy in an originally empty conduction band. Such a hindrance should be apparently removed by a relatively drastic phase change. Thus, the pristine semiconducting 2Hb-MoS2 modification, exhibiting MoS6 units with a trigonal prismatic arrangement of sulfur atoms around the molybdenum, changes upon intercalation to a distorted 1T-MoS2 modification with the molybdenum coordinated octahedrically (12,13) which, as recently stablished by electron crystallographic studies, corresponds more properly to a WTe2 type structure (14). According to a qualitative description based on the comparison with the electronic band structure determined for TaS2, 1T-MoS2 should exhibit metal-like behavior because of a broad, partially occupied conduction band (15,16). Chemical lithium intercalation into MoS2 is widely known (17,18). The intercalation process is however relatively slow, so drastic reaction conditions or special procedures are necessary (19). Although the direct intercalation of amines or similar electron donors into MoS2 is not possible, a renaissance of the MoS2 intercalation chemistry has been observed. The key for such a development is an experimental method based on the exfoliation of the pristine matrix by a rapid hydrolysis of the lithiated product (5). The colloidal suspension of MoS2 molecular layers is then flocculated in the presence of the donor. The success of this procedure arises from the activation of the matrix by three ways: the reduction of the matrix by lithium intercalation, the stabilization of the octahedral modification, and the physical separation of the molecular layers. Intercalation dynamics is certainly also favoured by the activation process by lowering the energy barriers for lithium migration.

In spite of the singularities of the intercalation chemistry of MoS2 compared with those of other transition metal dichalcogenides, quantitative theoretical descriptions permitting to understand the peculiarities of its chemistry are still lacking.

Intercalation of lithium into layered transition metal dichalcogenides has been described frequently using models based on band theory calculations within the Rigid Band (RB) approach (20). There, a complete electron transfer leading to Li+ ions inserted in an anionic layered matrix (MS2)n is assumed (21, 9). However, there are experimental as well as theoretical evidences indicating that at least in certain cases only partial charge transfer occurs. Indeed, both 7Li NMR chemical shifts in LiTiS2 (22) and a theoretical model describing the same compound (23, 24) agree in considering that the transfer actually reaches only about 80 %. Moreover, for the case of the MoS2, we have also detected that charge transfer appears to be only partial (25) (vide infra). For dealing with these features it is necessary to go beyond the view offered by the RB approach. Main properties of the lattice electronic structure appear to be determined by lithium local environment, so application of the methods from the quantum chemistry, Molecular Orbital (MO) and Density Functional (DF) theories, should be a relevant approach for describing host-guest interactions in these systems (26-28).

Although some calculations of the 2Hb-MoS2 directed to interpret scanning tunneling microscopy patterns have been reported (29,30), most theoretical analyses of this molybdenum chemistry have been done essentially considering data calculated for other systems as TaS2 (20) or ReS2 (31). Calculations related with the dynamics of the intercalation into MoS2 are to our knowledge not reported until now.

In this work we discuss the charge capacity of MoS2 comparing features obtained from the electrochemical intercalation of lithium into MoS2 with those predicted by a new theoretical model based on quantum mechanical calculations of (MoS2)n clusters. The same model is applied moreover to investigate the reaction coordinates for the insertion of lithium into MoS2 by different reaction pathways.

THEORETICAL METHODS AND CALCULATIONS

The MoS2 basic unit constituted by the two hexagonal unit cells shown in Fig.1a was considered as a minimal model. Essential features of the 2Hb-MoS2 modification, as the van der Waals gap and the trigonal prismatic symmetry around the Mo atom, can be there observed. Bigger clusters are built up by adding successive units (s. Fig.1b).


Fig. 1. Cluster Model for 2Hb-MoS2. (a) Basic unit considering two hexagonal unit cells. (b) Cluster of three basic units, [Mo6S26H22]4-

With the purpose of both, reducing the high global charge of the model system and, specially, saturating the dangling orbitals on the sulfur atoms at the model boundary, the corresponding amount of hydrogen atoms was added.

For the calculations of the intercalated state


Figure 2. Cluster Model for LiMoS2 considering octahedral modification of MoS2 (1T-MoS2). Clusters of (a) three, [Mo6S26H22]4- and (b) seven basic Units, [Mo14S48H36]4-.

MoS6 units with octahedral symmetry (Fig. 2) were considered (1T-MoS2). The lithium atoms were located in octahedral sites on the van der Waals sulfur bilayer space, in line with the Mo atoms. Furthermore, a van der Waals gap expansion of 0.25 Å for the intercalated species was considered (32). Calculations of the different clusters were performed using the extended Hückel MO Code (CACAO version) (33).

Moreover, calculations of the Density of States (DOS) were made from the electronic structure of the clusters with and without intercalated lithium. The DOS was approached with a Gaussian distribution of the one-electron eigenstate, considering a bandwidth of 0.5 eV (34).

EXPERIMENTAL

The coulommetric titration for intercalation of lithium into MoS2 was carried out in the cell Li/0.5 M LiClO4 in EC/PC 1:1/MoS2 at a constant current density of 150 m A cm-2. The MoS2 cathode (Aldrich, 99%, size <2mwas prepared by pressing a powder mixture of MoS2-graphite (15%) into a steel gauze under 2 metric tons. Electrodes were separated by glass fiber paper soaked in a 0.5 M LiClO4 (Frederick Smith Chemical Co.) solution in dry propylene carbonate (PC)-ethylene carbonate (EC) (1:1) mixture. The cell, built up in a dry argon filled globe box, was kept hermetically sealed during the experiment. Pseudo-equilibrium potential values in the range 0<x<0.6 shown in Fig. 3 were obtained by stepwise intercalation as described in the insert in the same figure.


Fig. 3. Quasi-equilibrium Voltage-composition curve for the intercalation of lithium into LixMoS2. In the insert, voltage-time curve for the stepwise lithium intercalation in the range 0<x<0.6.

RESULTS AND DISCUSSION

In order to test the applicability of the theoretical model described in this work (vide infra), electrochemical experiments reproducing both, the discharge and the incremental charge capacity curves for the intercalation of lithium into 2Hb-MoS2 at room temperature illustrated in Figs. 3 and 4 respectively, were performed.

The most characteristic feature in the voltage-composition curve in Fig. 3 is the relatively steady voltage observed in the range x=0.2-0.4. The same feature can be more clearly detected as a maximum at x=0.3 in the incremental charge capacity-composition curve (Fig. 4).


Fig. 4. Relative incremental capacity as function of lithium concentration for the intercalation of lithium into LixMoS2 in the range x=0 - 0.6.

Results agree with those found in the literature (35). Although voltage-composition curves for the LixMoS2 system are in general hard to reproduce, reports on the first part of the curve 0<x<0.6 are in general rather coincident, so data in this range appears to be confident. At higher lithium content many hardly reproducible, abrupt changes of the incremental charge were observed.

The change of the voltage in Fig. 3 has been the subject of different interpretations including the decomposition of the compound at x>0.2 (9, 36, 37). However, now the dominant view is that the products of the Li insertion into 2Hb-MoS2 actually correspond to the intercalation compounds LixMoS2 (16, 35, 38-41) with x in the range 0>x>1. Superstructures arising from the lithium staging in the van der Waals gap has been also considered as a cause for the voltage change observed around x=0.25 (35-39). A phase change of the MoS2 from a 2H to a distorted 1T modification has been well established (16,42). As observed in the insert in Fig. 3, while current is flowing the potential drops to about 1V, which is the voltage where the conversion 2H to 1T, occurs 816). Moreover, considering that the lithium capacity of the 1T modification is much higher than that of the 2Hb-phase, thus the potential changes observed under quasi-equilibrium conditions are really reflecting only the intercalation of lithium into the octahedral modification. So the features in Fig. 3 should correspond to phase equilibriums of octahedral species. Any theoretical approach to the intercalation of lithium into MoS2 should explain, at least in part, the tendency observed in these experiments.

The behavior of the voltage as a function of x in intercalation systems is often explained by using a gas lattice model (43, 44). This model essentially considers the change in free energy associated to the formation of lithium ions in an interlaminar lattice of sites. Within this model -- considering the energy associated to the filling of an isolated lattice site, Eo; the ionic interaction energy between intercalated atoms, U; the number of sites coupled to a given site, g; and a term considering the configurational entropy, with k and T as the Boltzman constant and the absolute temperature respectively -- the chemical potential, m=e V, and the inverse derivative voltage, known as the relative incremental capacity, -dx/dV, can be described by


From Fig. 3 and 4 is possible to detect the occupation degree of available intercalation sites and the nature of the sites being occupied. However, questions as why this phase results to be saturated at a relative low value of x or how these features are related with experiments indicating the partial host-guest charge transfer (25) are not answered directly by such an approach which is intrinsically based on the total lithium-MoS2 electron transfer.

A more comprehensive view of the properties of the product as well as on the processes associated to the migration of lithium into MoS2 may be obtained by the quantum chemical approach described in this work which considers explicitly the local host-guest interactions.

The application of quantum chemistry methods implies to define a system with a discrete number of atoms. Therefore the first and very important problem is to select the minimal molecular structure or cluster of atoms able to describe correctly the local interactions to reproduce the electronic structure of the solid (45).

In a microscopic model, the Fermi level, defined as the reference state separating the occupied and unoccupied electronic levels, may be represented by the electron chemical potential mel. In the context of the DFT, this basic quantity may be defined as (46)


being E the electronic energy; N the number of electrons; V the external potential; I de ionization potential; and A the electron affinity. The quantities I and A may be defined within the MO theory (47,48) by using, for instance, the Koopman theorem (49), according to which they correspond approximately to the energy of the high occupied HOMO and low unoccupied LUMO molecular orbitals respectively. Within this approach the electron chemical potential may be therefore expressed by


Considering the intercalation process as an electron transfer reaction, the electron chemical potential, mel can be seen as a natural property of the system and used accordingly for both, describing the process and as a criterion for finding the minimal size of the cluster able to model the system (23). The electron chemical potential should remain approximately unchanged upon increasing the cluster size. Moreover, mel should correspond reasonably well to the electrochemical potential of the solid (26).


Fig. 5. Variation of the electron chemical potential with the cluster size.

Fig. 5 illustrates the variation of the electron chemical potential with increasing cluster size for lattices constituted by 1 to 8 units. For a three-unit structure a critical value of mel is reached, so the cluster [Mo6S26H22]4- (Fig. 1b) would represent, within the validity of the model, the solid 2Hb-MoS2.


Fig. 6. Variation of the electron chemical potential of the cluster [Mo6S26H22]4- with progressive lithium ntercalation.

Results of the stepwise intercalation of lithium into the clusters [Mo6S26H22]4- and [Mo14S48H36]4- calculated under such border conditions are reproduced in Fig. 6. As observed, after the intercalation of one lithium per molybdenum atom, the electron chemical potential remains approximately constant.

The change of mel with lithium content in the species LixMoS2 may be interpreted in terms of the absolute electronegativity (m) changes of the lattice (50). Indeed, within the scheme of the DFT, mcorresponds to the negative value of mel (46). According to the model proposed by Polytzer (51), the electronegativity change of any charged system, relative to the neutral state, may be expressed as a function of the charge Q acquired by the system. Within a first order approach m(Q) is then given by


The first term represents in our case the electronegativity of the MoS2 trigonal prismatic lattice in absence of lithium i.e. the host intrinsic electronegativity. The addition of lithium induces a progressive diminution of the electronegativity reaching a constant value. In other words, the trend to acquiring charge goes down with increasing lithium intercalation.

According to our model, during the intercalation of lithium in the cluster [Mo6S26H22]4- the average charge transfer to the matrix (average lithium ionicity) is about 52% (s. Table 1).


Table 1. Average Net Charge distribution in the cluster [Mo6S26H22]4- before and after lithium intercalation.


Atoms

Average Net Charge


[Mo6S26H22]4-

[Mo6S26H22]4--Li3

(a) [Mo6S26H22]7-

Mo

+1.895

+1.580

+1.636

S(vdW)

-1.535

-1.459

-1.584

Li

-

+0.524

-


(a)Simulation of the Rigid Band Approach through a three-electron transfer to the cluster.

Inserted lithium maintains therefore a relatively high metallic character. That agrees with some XPS experiments carried out for the compound Li0.8MoS2 [25]. Indeed in this compound the Li(1s) electron has a binding energy of 55.6 eV near to that of the metallic lithium (55.5 eV) and much lower than, for instance, in the lithium halides which, depending of the ionic bond character, are in the range 56.8-59.8 eV.

Calculations also indicate a change in the atomic charge distribution in the matrix upon intercalation. Calculated charge distributions before and after lithium intercalation are shown in Table 1. Lithium insertion appears to induce electronic density shifts in both molybdenum and sulfur atoms respect to the pristine compound, namely a slight charge increment and deficit in the Mo and S atoms respectively. Such an effect, which increases with increasing lithium content, may be rationalized by the mechanism in which, the initial Li-Mo charge transfer is followed by a sort of retro donation produced by the polarization of the sulfur orbitals, which is caused in turn by the presence of ionized lithium. Thus, a classical "push-pull" mechanism could answer to both, the relative high negative charge on lithium species and the simultaneous diminution of the electron density on the MoS2 sulfur atoms. Such an effect may be also visualized in Table 1, where the charge distribution calculated after the insertion of three electrons but in absence of the lithium atoms is reported.


Fig. 7. The Density of State (DOS) for the cluster [Mo6S26H22]4- with (bold line) and without (solid line) lithium.

The densities of states (DOS) corresponding to the electron densities calculated for the cluster [Mo6S26H22]4- illustrated in Fig. 7 show that the valence band (VB) presents a dominant sulfur 3p character while the conduction band is mostly composed by metallic T2g atomic orbitals. The mmel shift induced by lithium intercalation agrees with the guest-host charge transfer and the electron back-donation flow towards lithium through the sulfur atoms described above. Comparison of the DOS in the presence and absence of lithium shows indeed the shifting of the energy bands towards lower energies, specially, of the 3p sulfur VB.

Electronegativity changes as those discussed above are directly related to the ability of an atom or group of atoms to absorb additional electronic charge, i.e. with the Charge Capacity concept introduced by Huheey (k= 1/I-A) (52,53).

Considering the equation (3) above and the relationship between m(Q) and mel established by the DFT, it is possible to rewrite the Politzer expression in terms of the charge capacity (k) considering, furthermore, the relationship for the global hardness (m) proposed by Parr and Pearson (54).

where the finite variation expression for the global hardness is m=0.5(I-A).

From equations (6) and (7), the following expression for the charge capacity in terms of the electron chemical potential may be derived

The variation of k with lithium content may be observed in Fig. 8. After the intercalation of about 30% of the total amount of octahedral sites in the van der Waals gap, the capacity reaches a maximum, decreasing thereafter to a constant value.


Fig. 8. Relative charge capacity for the cluster [Mo6S26H22]4- (solid line) and [Mo14S48H36]4- (dashed line) as a function of lithium concentration.

These features totally agree with the electrochemical experiments displayed in Fig. 4 which show that the incremental charge capacity goes down at approximately x=0.30-0.40.

According to this model, the increase in the region 0<x<0.30 appears to be accounted mainly by the intrinsic electronegativity of the undoped lattice, i.e. for the first term of equation (5) . After addition of the first or second lithium into the [Mo6S26H22]4- or [Mo14S48H36]4- clusters respectively, the variation of m(Q) given by the second term of equation (5) causes the electronegativity of the doped system to decay dramatically respect to the undoped lattice until reaching a constant value, thus generating a decrease of the charge capacity. The successive additional lithium intercalation is thereafter governed exclusively by the second term of equation (5), the allowed charge being then probably determined by the equalization of the electronegativity in the system.

It is interesting to remark that although the model proposed here leads to a description of the incremental charge capacity similar to that of conventional models (44), both approaches are essentially different. Conventional treatments as the gas lattice model described by equations (1) and (2) are mainly focused on lithium ion activity, specially, on the force field at which this species is subjected by the presence of neighboring charged particles in the interlaminar spaces. Furthermore, total host-guest one-electron transfer is there always assumed. Thus in such cases, agreement between theoretical predictions and experimental evidences is often afforded by adjusting the geometry -- arrangements and distances among ions -- in the gas lattice. In the model described here, however, attention is focused on the electron activity, i.e. in the changes of the electronic structure of the host arising from the host-guest charge transfer. Flexibility of this model specially lies in the redistribution of the charge excess between both the host and the guest.

Finally, the model described above has been also applied to investigate the lithium intercalation dynamics studying the coordinates of the migration reaction by distinct diffusion pathways. The four pathways selected are indicated in the Scheme 1. Pathways 1 to 3 correspond to the migration in different directions through the interlaminar spaces in a 1T-MoS2 lattice. The fourth is analogous to pathway 1 but in a 2Hb-MoS2 lattice. Fig. 9 reproduces the reaction coordinates for these four pathways indicating the energy for each lithium location normalized respect to each particular energy minimum. The shapes of the curves are strongly affected by the size of the cluster whose borders are flanked by hydrogen atoms. In the solid, a regular shape similar to that arising from the center of the cluster should be found. The minimized total energy for these four pathways is reported in Table 2.


Table 2. Minimized total energy for the four iffusion pathways selected.


Pathway

Total Energy

(eV)

Relative Energy (eV)


1

- 6179.13123

0

2

- 6179.13123

0

3

- 6178.15008

+ 0.98115

4(2 Hb-MoS2)

- 6150.01304

+29.118


Clearly lower relative energies are found for the pathways 1 and 2. Route 1 which corresponds to the lithium moving along a sequence of tetrahedral (LiS4) and octahedral (LiS6) sites appears to be the more favorable one, since the barriers to migration (about 0.15 eV) is lower than for route 2 which corresponds to a series of tedrahedral sites. For the later, moreover, rather poor resolved minima were found.

In Fig 9 is also included the variation of the positive charge on lithium atom along lithium migration in the first pathway. According to this data guest-host charge transfer oscillates with lithium movement. Charge-transfer parallels the stability of the system.


Figure 9. Potential profile for the migration of one lithium atom in the extended structure along the four different pathways.

CONCLUSIONS

The formulation of a quantum mechanical model considering local effects arising from host-guest interactions has shown to be appropriate for explaining main observed features. Indeed the change of the incremental charge capacity in the range 0<x<0.6 is successfully explained by the variation of the intrinsic host electronegativity associated to the electron chemical potential changes during the intercalation. Contrasting with conventional descriptions assuming a complete guest-host one electron transfer, our results indicate that lithium retains a relatively high electronic charge in the intercalated state, which fully agrees with experimental XPS evidences. Moreover, the relative energies of intercalated phases with lithium in different environments (Table 2) clearly explain the phase change 2Hb->1T associated to the intercalation of lithium into MoS2. Proposed model also allows the description of the intercalation dynamic indicating that there is one mechanism, which is rather more convenient than others for the migration of lithium in the interlaminar spaces. An interesting result in such a description is that the electromotive force for the diffusion appears to be a dynamic in the guest-host charge transfer.

The novelty of proposed approach for describing the lithium intercalation into molybdenum disulfide consists in applying quantum chemical methods considering local host-guest interactions as well as in focusing the intercalation problem in the change of the electron chemical potential. Such a point of view is essentially different from current approaches as the gas lattice model, which is focused on the activity of lithium ion in the interlaminar spaces. The fact that both approaches permit to simulate in some extent electrochemical features is probably due to the symmetry or complementary character of both electron and lithium ion treatments. Correction of the calculations considering more realistic symmetry for the intercalated product (14) as well as the assumptions of preferential arrangements for the lithium ion lattices in the interlaminar spaces could probably improve the proposed cluster approach, specially, for explaining anomalies observed at high lithium content. Attempts in these directions as well as in studying the processes by 7Li-NMR methods are in progress.

ACKNOWLEDGMENTS

Reaseach partially founded by FONDECYT (Grants 198-1082, and 1010924), Fundación Andes (Grant C 12510) and DID Universidad de Chile.

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