J. Phys. Chem. C 2007, 111, 17795-17803
17795
Electric Dipoles and Susceptibilities of Alkali Clusters/Fullerene Complexes: Experiments and Simulations† F. Rabilloud, R. Antoine, M. Broyer, I. Compagnon, P. Dugourd,* D. Rayane, and F. Calvo UniVersite´ Lyon 1, CNRS, LASIM UMR 5579, baˆ t. A. Kastler, 43 Bd du 11 NoVembre 1918, F69622 Villeurbanne Cedex, France
F. Spiegelman Laboratoire de Chimie et Physique Quantiques, IRSAMC, UniVersite´ Paul Sabatier Toulouse 3, 118 Route de Narbonne, F31062 Toulouse, France ReceiVed: February 9, 2007; In Final Form: May 28, 2007
Using a combination of deflection experiments and atomistic modeling, we investigate the structural and electrostatic properties of lithium and sodium clusters on a C60 molecule. The electric susceptibilities χ are measured for LinC60 and NanC60 clusters containing up to n ) 20 alkali atoms. The electric dipole moments µ are inferred from these data through the use of the Langevin formula. We also parametrize a many-body force field for this problem, extending a previous work by Roques and co-workers (Phys. ReV. B 2003, 68, 205412) and investigate the most stable structures and finite temperature effects on the experimental observables. The two alkalis show similar behavior and coat the fullerene at low coverage, then form a clear segregated droplet above eight atoms. However, while the sodium droplet grows monotonically above this cross-over size, we find evidence that a second structural transition takes place in lithium-coated C60, possibly indicating a momentary resurgence of homogeneous coating.
1. Introduction The advent of fullerene chemistry, soon following the discovery of C60 by Smalley and co-workers,1 has opened new fields of research ranging from molecular chemistry to materials and condensed matter physics. In this respect, the metal-C60 interaction is of interest both from a fundamental point of view and for the applications of C60 fullerenes as bulk intercalation compounds with unique properties, including superconductivity in the case of alkali or alkaline earth elements.2 More recently, the coating of fullerenes and nanotubes by scandium, titanium, nickel, and lithium has been suggested as a possible route toward hydrogen storage materials.3-6 In the gas phase, such complexes can be conveniently investigated using electric dipole measurements, which probe the geometric structure of clusters and molecules.7,8 In particular, the wetting or nonwetting of a fullerene surface with metals can be seen as prototypical of nanoscience problems,9 in that it highlights the role of size on molecular properties. The exohedral MC60 system, with a single alkali atom M on a C60 molecule, has a large electric dipole due to charge transfer between the metal atom and the fullerene. It has been widely investigated both theoretically and experimentally.10,11 The first experiments on metal coated fullerenes were performed by recording mass spectra,12,13 and the proposed geometric arrangements were deduced from the sequences of magic numbers. From their results, these authors suggested a possible homogeneous coating of C60 by all alkali metals. However, on the basis of photoelectron spectroscopy measurements, Palpant et al.14 found evidence for a special stability of alkali trimers on C60 with a †
Part of the special issue “Richard E. Smalley Memorial Issue”. * Corresponding author.
more regular coating of trimers for increasing sizes. The most debated system has been NanC60, for which Dugourd et al.15 measured strong electric susceptibilities in molecular beam deflection experiments. The results were interpreted in terms of a high electric dipole induced by a complete segregation between Nan and C60 and a charge transfer between the two moieties, in clear contradiction with the previous interpretations.13 More recently, Pellarin et al.16 carried out photodissociation and photoionization experiments, whose results were interpreted in favor of a situation intermediate between complete segregation and homogeneous coating, depending on the number of sodium atoms. Concerning other alkali metal-C60 complexes, those were mainly studied by mass spectrometry with no definitive conclusion being reached regarding the geometric structure. Regarding theory, and even for such light elements as sodium, lithium, and carbon, the prediction of the most stable structures of MnC60 molecules is a hard task, especially for approaches based on first principles where the geometries are generally constructed by hand following chemical intuition. Hamamoto et al.11 performed density functional theory (DFT) calculations using the local density approximation (LDA) for MnC60 with n ) 2, 6, and 12 and M ) Li, Na, and K. The geometries were optimized assuming the C60 cage to be rigid, and the initial locations of the alkali atoms were restricted along the axes of the hexagonal and pentagonal rings. These authors found quite a regular coating of C60 by alkali atoms, with practically no static electric dipole. For Li12C60, the regular icosahedral coating over pentagons was found to be particularly stable, in agreement with the pioneering work by Kohanoff et al.17 This result is in apparent contradiction with the strong electric susceptibilities measured in NanC60 by Dugourd et al.,15 in particular for
10.1021/jp071126m CCC: $37.00 © 2007 American Chemical Society Published on Web 07/11/2007
17796 J. Phys. Chem. C, Vol. 111, No. 48, 2007 Na12C60. Roques and co-workers9,18 developed an empirical atomistic model trained to reproduce DFT calculations at the B3LYP level, as well as experimental properties such as the C60 polarizability. This model was used in a Monte Carlo frame to allow a significant statistical sampling of configuration space. The main predictions of this model for NanC60 were the initial coating of the fullerene at low sizes and a transition toward segregation with the formation of a metal droplet above n g 8. The model was mainly used for static calculations, but some dynamical and thermodynamical properties were also calculated at finite temperature.18 These theoretical results reproduce general trends for the experimentally measured susceptibilities, even if the calculated values computed for the sodium clusters/ fullerene complexes turn out to be significantly smaller than those measured in the experiment. Finally, Sun and co-workers6 recently performed DFT calculations of hydrogen adsorption on Li12C60. The results obtained by these authors indicate that 12 atoms should homogeneously coat the fullerene on the surface, preferentially to a full segregation. However, a full global optimization study is still beyond reach at the level of theory employed by Sun et al.6 Because all aforementioned experiments were performed at finite temperature, it seems unlikely that a complete interpretation could be reached on the basis of standard, static geometry calculations. Temperature effects are particularly important for susceptibility measurements, because of the possible dynamical electric dipole arising from the molecular vibrations, which contributes to the susceptibility in addition to the static polarizability. For example, the zero-temperature most stable structure of Na2C60 has a vanishing electric dipole because of the two sodium atoms being located over opposite hexagonal sites. Thermally induced symmetry breaking will cause the complex to acquire a finite dipole, hence a strong susceptibility. Therefore, a definitive conclusion cannot be made until a proper comparison is performed with theoretical calculations at finite temperature. In this paper, we present measurements of the electric susceptibilities of LinC60 clusters. The results are compared with NanC60 and with theoretical calculations based on a newly parametrized empirical atomistic model similar to the one of Roques et al.9,18 As will be seen below, using lithium as the coating element makes important differences with respect to sodium, especially at small sizes. The possible influence of the finite temperature is also taken into account, and the importance of the dynamical contribution of the electric dipole associated with molecular vibrations is clearly demonstrated for NanC60. The segregation between the metal part and C60, while being found in both systems for a sufficiently large number of metal atoms, evolves in a distinct nonmonotonic pattern in the case of lithium. While the theoretical model does not fully account for this observed behavior, it sheds light on possible structures that may be responsible for these unexpected features. The paper is organized as follows. The details and results of the experimental setup are given in the next section. The theoretical modeling, including the parametrization procedure and the theoretical results, are given in section 3. The two approaches are then compared and discussed in section 4. Some concluding remarks close the paper in section 5. 2. Experimental Techniques Electric dipole and susceptibility measurements have been performed by deflecting a well-collimated beam through a static inhomogeneous transverse electric field.15 The experiment is conducted in a laser vaporization source coupled to an electric
Rabilloud et al.
Figure 1. Experimental setup.
deflector and a mass spectrometer (Figure 1). LinC60 clusters are produced in a double rod laser vaporization source. The fourth harmonic of a Nd3+:YAG laser desorbs C60 molecules from a pure C60 rod (99.9%). C60 molecules are dragged along by an helium gas pulse. At a distance of 1 cm after the first rod, C60 molecules travel through a lithium vapor produced by laser ablation of an isotopically purified 7Li rod. The third harmonic of a second Nd3+:YAG laser is used. Clusters are then thermalized in a 5 cm long nozzle. After a skimmer, the beam is collimated by two 0.5 mm slits and goes through the electric deviator. The deflector produces a “two-wire” electric field. The electric field and its gradient in the deflector are F ) 1.63 × 107 Vm-1 and ∇F ) 2.82 × 109 Vm-2 for a voltage of 27 kV across the two poles. The molecules are ionized 1 m after the deflector in the extraction region of a position sensitive timeof-flight mass spectrometer. A low fluence ArF laser is used for the ionization (λ ) 193 nm and a fluence of 1 mJ/cm2). A mechanical chopper located in front of the first slit allows for selecting and measuring the velocity V of the beam. The deflection d of a cluster is related to the electric susceptibility χ by:
d ) Kχ
Fz ∂Fz mV2 ∂z
(1)
Here, z is the axis of the electric field Fz, ∂Fz/∂z its gradient, m the mass of the cluster, V its velocity, and K is a geometrical factor. The arrival time at the detector is a function of the mass of the particle and of the deflection d of the beam. In a first approximation, the difference in times of arrival between a deflected and a nondeviated molecule is proportional to the deflection d. Cluster velocities range from 1150 m/s around the size n ) 6 to 1100 m/s for n ) 20. The average deflection d as a function of the electric field in the deflector is determined by fitting the experimental profile with a Gaussian shape. The geometrical factor K was fixed by calibrating the setup with a supersonic beam of lithium atoms, whose polarizability is known with a good accuracy (24.3 ( 0.5 Å3).19 The overall accuracy depends on the calibration and the accuracy of the velocity and deflection measurements. Depending on cluster size, this leads to a precision of 10-15% on the absolute value. Experimental susceptibilities obtained at room temperature from eq 1 are reported in Figure 2 and Table 1 for n ) 1-22. They range from ∼700 Å3 to 4000 Å3 with a strong size dependence.
Alkali Clusters/Fullerene Complexes
J. Phys. Chem. C, Vol. 111, No. 48, 2007 17797 and lithium atoms do not regularly coat the fullerene surface but instead tend to form a metal droplet. 3. Theoretical Approach
Figure 2. Comparison between electric susceptibilities measured for LinC60 and NanC60.
TABLE 1: Measured Susceptibilities for LinC60 and NanC60 n
χLi (Å3)
χNa (Å3)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
1100 ( 132 937 ( 112 918 ( 110 1430 ( 151 1861 ( 200 2773 ( 332 1231 ( 147 957 ( 124 990 ( 138 933 ( 135 825 ( 112 696 ( 98 844 ( 115 2531 ( 303 2429 ( 291 2470 ( 296 2803 ( 336 2308 ( 277 2533 ( 304 3567 ( 428 3960 ( 475
1810 ( 180 988 ( 99 848 ( 85 982 ( 98 958 ( 96 1100 ( 110 930 ( 93 1129 ( 113 1030 ( 103
V(R) ) VM({ri}) + VC({r′j}) + Vinter(R) + VCoul(R) (3) where VM, VC, Vinter, and VCoul are the energies of the alkali and C60 parts, the covalent interaction between M and C60, and the Coulomb interactions, respectively. The last term accounts for the significant charge transfer between the metal and the fullerene. An empirical many-body potential in the second moment approximation (SMA) to the electronic density of states in the tight-binding theory21 was chosen for VM. This potential involves five parameters ξ0, 0, p, q, and r0 and reads
1296 ( 130 1537 ( 153 1603 ( 160 1572 ( 157
VM({ri}) ) 0
1686 ( 169 1733 ( 173 1599 ( 160
They are also compared with results obtained previously for NanC60 in the same experimental conditions.15 The electric susceptibilities of LinC60 are also large, but behave differently with n as compared with those of NanC60. For sodium, these susceptibilities vary quite regularly with a strong decrease from NaC60 to Na2C60 and then a slow increase for larger sizes. For lithium, there is no decrease from LiC60 to Li2C60 and then a more irregular behavior occurs: a local maximum in the susceptibility is found around n ) 6, then a strong increase for n ) 14, followed by a small plateau until n ) 19, then another increase at n ) 20. The susceptibilities χ are related to the electric polarizability R and to the thermal average 〈µ〉 of the electric dipole µ through the following relation
χ ) R + 〈µ 〉T/3kBT 2
We extend here the empirical atomistic model of Roques et al.9,18 used for NanC60 to LinC60, taking dynamical effects into account in the determination of the electric susceptibility at room temperature. 3.1. Empirical Modeling. We have constructed an empirical atomistic model based on previous experimental data and ab initio results. Details on this model have already been presented in ref 18. Briefly, the geometry of the MnC60 system is denoted as R ) {ri, rj′} with ri representing the three-dimensional positions of the n alkali atoms M ) Li or Na, and with rj′ representing those of the 60 carbon atoms. We assume that the whole cluster generally carries a total charge Q (which in the present case will be 0). The total potential energy V of the system is written as the sum of several contributions:
e-p(r /r -1) - ∑ [ξ20 ∑e-2q(r /r -1)]1/2 ∑ i
