Computer Simulations of Fulleride Anions in Metal-Ammonia Solutions

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J. Phys. Chem. B 2009, 113, 3324–3332

Computer Simulations of Fulleride Anions in Metal-Ammonia Solutions Christopher A. Howard* and Neal T. Skipper London Centre for Nanotechnology, Department of Physics and Astronomy, UniVersity College London, Gower Street, London, WC1E 6BT, United Kingdom ReceiVed: September 19, 2008; ReVised Manuscript ReceiVed: December 12, 2008

Monte Carlo computer simulation has been used to study the energetics and local structure of fulleride anions C60n- (n ) 0, 2, 4, 6) in metal-ammonia solutions. We find that the enthalpy of dissolution is markedly favorable only for n ) 2 and 4, which is in line with experimental observations. Analysis of the structure developed around the fulleride anions shows two strong solvation shells of ammonia at distances of around 6.75 and 9.5 Å from the fulleride center of mass. This is in excellent agreement with high-resolution neutron diffraction studies of K5C60 in ammonia. The uncharged fullerene (n ) 0) induces no discernible orientational order in the neighboring solvent. In contrast to this, there is progressively stronger hydrogen-bonding of the first-shell solvent to the anions (n ) 2, 4, 6), approaching one hydrogen-bond per molecule for n ) 6. This maximum of one hydrogen bond per ammonia to the fulleride anion is found to permit intersolvent hydrogen bonding within and across the solvation shells similar to that found in bulk liquid ammonia. Comparison of the cations Li+, Na+, K+, and Ca2+ shows that only the potassium has a tendency to form direct ion-pair complexes with the fulleride anion. This work therefore highlights the mechanisms by which metal-ammonia solutions are able to dissolve high concentrations of fullerene salts. Introduction 1

Since its discovery in 1985, Buckminsterfullerene (C60) and its derivatives have been the subject of intensive scientific and technological activity.2,3 However, our ability to manipulate fullerenes is limited by the low solubility of these molecules in most common solvents.4 This insolubility, together with the lack of molecular-level understanding of fullerene dissolution mechanisms, limits our ability to manipulate and characterize these molecules by solution techniques such as NMR.3,5 Indeed, a major breakthrough of experimental fullerene science was the discovery by Kra¨tschmer et al.6 that C60 is soluble in benzene to about 1.5 mg/ml.4 This allowed workable quantities of C60 (fullerite) crystal to be precipitated from solution. However, in aromatic liquids such as benzene the interaction energy of the fullerene with the solvent is of the same order as the interaction energy between fullerene molecules in the crystal solid.4 As a result, the C60 molecules tend to form fractal aggregates in such solutions. An important alternative route to fulleride dissolution involves metal-ammonia solutions.7-11 A wide variety of metals dissolve in liquid ammonia, including the alkali and alkali earth metals, and some lanthanides.12 These liquids contain solvated electrons, which allow us to exploit the redox chemistry of fullerene in solution via sequential reduction of C60 fullerite crystals to soluble C60n- anions (n ) 1 to 5). In addition to providing a unique arena in which to study fullerides and the underlying physical chemistry of nanoparticle solvation, fulleride-metalammonia solutions are showing great promise for purification, charge storage, and thin film deposition. Further interest stems from the fact that (reversible) removal of the ammonia produces fulleride salts, including the A3C60 superconductors.7 Recent high-resolution neutron diffraction studies of K5C60 in ammonia have revealed that metal-ammonia-fulleride solutions are highly ordered.9,10 They contain monodispersed ful* To whom correspondence should be addressed. E-mail: c.howard@ ucl.ac.uk.

leride anions, which are accommodated in solution by a reorganization of the ammonia solvent molecules to form two well-defined solvation shells. The first coordination shell forms hydrogen bonds to the fulleride anion with up to one hydrogen atom per molecule being directed toward the fulleride centerof-mass. However, the average solvent-solvent structure was found to be relatively unperturbed. Key questions now concern the effect of the fulleride anion charge, and the valence and radius of the metal counter-ions. It is particularly important for us to establish the location of the counter-ions with respect to the fulleride surfaces, for example, whether they form direct ion pairs, that is, in contact with the C60 or whether the ions are solvent-separated. Because of the low scattering weight of the counter-ions, this information is not well resolved by the neutron diffraction data. In this paper, we address the above issues by performing classical Monte Carlo computer simulations on metal-ammoniafulleride. First, we vary the anion charge on the C60n-, from n ) 0 to 6. We find that for uncharged fullerene (n ) 0) the interaction with the solvent is relatively weak with unfavorable enthalpy of dissolution and no preferential orientation of solvent in the neighborhood of the anion. In contrast to this, increasingly strong hydrogen bonding is found for n ) 2 to 6. Comparison of the cations Li+, Na+, K+, and Ca2+ shows that only potassium has a tendency to form direct ion pairs13 with the cation in contact with the fulleride anion. Our simulations therefore provide valuable molecular-level insight into the mechanisms of fulleride dissolution, and as such will help to guide and motivate experimental studies of these important species. Interaction Potentials and Simulation Method Classical Monte Carlo computer simulation has been conducted on fulleride C60n- (n ) 0, 2, 4, 6) in metal-ammonia solutions of lithium, sodium, potassium, and calcium. Interatomic interactions were represented by effective pair potentials of the form

10.1021/jp8083502 CCC: $40.75  2009 American Chemical Society Published on Web 02/24/2009

Fulleride Anions in Metal-Ammonia Solutions

Vij(rij) )

J. Phys. Chem. B, Vol. 113, No. 11, 2009 3325

[( ) ( ) ]

qiqj σRβ + 4εRβ rij rij

12

-

σRβ rij

6

(1)

where rij is the separation between particles i (of type R and charge qi) and j (of type β and charge qj). σRβ and εRβ are the Lennard-Jones parameters for the different atomic species and are given in Table 1. Where species differ, the Optimized Potentials for Liquid Simulations (OPLS) mixing rules are used: εRβ ) (εRRεββ)1/2 and σRβ ) (σRRσββ)1/2. The ammonia molecule used was the 4-site OPLS model.14 This has rigid bond lengths and angles and Coulomb partial charges placed on the hydrogen and nitrogen atoms and has been successfully employed in recent studies of bulk ammonia and metal-ammonia solutions.15,16 Counterion parameters were taken from the work of Chandrasekhar et al.17 (Li+ and Na+) and Aquist18 (K+ and Ca2+). TABLE 1: Lennard-Jones Pair Potential and Site Charge Parameters (Equation 1) Atom type, R

σRR (Å)

RR (kcal mol-1)

qR (e)

18

2.58 3.42 0.0 3.80 1.25 1.89 2.41

1.89 0.17 0.0 0.0659 6.25 1.60 0.46

1.00 -1.02 0.34 -n/60 1.00 1.00 2.00

K N14 H14 C19 Li17 Na17 Ca18

The carbon-C60 Lennard-Jones potentials were taken from the literature for one of the first simulation publications on C60, which correctly predicts the face-centered cubic (fcc) crystal structure that is adopted in the solid state.19 The charge on the fulleride C60n- was placed fractionally on each carbon atoms, that is, -n/60 on each carbon. The fulleride center-of-mass was treated explicitly as a noninteracting site, to permit us to calculate radial distribution functions. Each simulation box consists of one fulleride, 400 NH3 molecules, and the relevant number of cations; for example, see Figure 1. The simulation box sizes were all approximately 25 × 25 × 25 Å3, thereby ensuring that periodic images of the fulleride were sufficiently distant to allow the formation of at least two full solvation shells. The simulations were all performed at a temperature of 220 K and pressure of 1.01 × 105 Pa. Three-dimensional periodic boundary conditions were implemented, and long-range Coulombic interactions were calculated using an Ewald sum. Short-range interactions were cutoff at a value of 10 Å. Outside this sphere, a uniform particle density was assumed. Equilibration was conducted from a disordered starting point with cations placed at random at least 7 Å from the fulleride center of mass, via an isothermal-isobaric ensemble (constants N, p, and T). Equilibrium was conceded when the volume and energy fluctuated about their means. Once the average equilibrium density was established, it was then used for a production

Figure 1. Molecular graphics snapshot of the equilibrated Monte Carlo simulated solution of composition K6C60(NH3)400. Color key: carbon atoms, black; potassium cations, blue; hydrogen atoms, white; and nitrogen atoms, green.

TABLE 2: Computed Enthalpy of Dissolution, ∆HS, and Internal Energy Components, U, for Potassium-Fullerides (Equation 2) Energy/kcal mol-1

Structural Unit

K6 C606-

K4 C604-

K2 C602-

C60

Usolution Ucrystal Uammonia ∆HS

KxC60(NH3)400 KxC60 400 NH3 KxC60

-3776 ( 21 -1750 ( 4 -2021 ( 20 -3 ( 29

-3006 ( 19 -923 ( 3 -2021 ( 20 -56 ( 28

-2400 ( 20 -320 ( 8 -2021 ( 20 -59 ( 29

-2002 ( 19 -50 ( 4 -2021 ( 20 +70 ( 28

3326 J. Phys. Chem. B, Vol. 113, No. 11, 2009

Howard and Skipper

Figure 2. The solvation of C60n- (n ) 0, 2, 4, and 6) by ammonia in nKC60(NH3)400. (a) Partial distribution functions gC60-N(r) and (b) partial distribution functions gC60-H(r). Key: black, C606-; green, C604-; blue, C602-; red, C60. Please see Table 3 for numerical summary.

TABLE 3: The Solvation of C60n- (n ) 0, 2, 4, and 6) by Ammonia Nitrogen Atoms in nKC60(NH3)400, As Determined from Figure 3a n (e)

rN1 (Å) ( 0.02

rN2 (Å) ( 0.02

nN1 ( 2

nN1 ( 2

0 -2 -4 -6

7.02 6.90 6.83 6.76

11.63 11.46 11.34 10.97

47 45 47 48

145 144 145 137

a The peak positions of the first and second solvation shells are given in rN1 and rN2, and the coordination numbers nN1 and nN2, respectively.

isovolumetric (N, V, T) simulation. A typical number of iterations required to establish equilibrium was ∼12-15 M per system for the two successive ensembles. Production runs were then sampled over ∼20 M iterations. In terms of sampling, the most problematic issue is the small number of cations in our system and the concomitant difficulty of obtaining a meaningful measure of the fulleride-cation distribution. However, in this system there are no strong local

minima for the cations to become stuck in, as the negative charge is evenly distributed over the anion surface. We therefore judge that our simulations are sufficient to obtain statistically significant data. For calculation of the enthalpy of dissolution (eq 2), two reference systems were simulated for each solution: pure ammonia and fulleride-salt crystal. The AnC60 salts were simulated using a box containing at least 16 C60 anions. The ions were placed in the simulation in positions derived from an approximate bcc representation of the C60 salts or the fcc positions in the case of the pure fullerite crystal itself.2 The crystals were initially set up in slightly increased volumes from those found in the literature and then allowed to come to equilibrium under the isothermal-isobaric ensemble. Comparison of the total internal energies, U, of these systems provides the enthalpy of dissolution ∆HS. Here we define directions such that negative enthalpy of dissolution corresponds to an enthalpically favorable solution

∆HS ) Usolution - (Uammonia + Ucrystal) + p∆VS

(2)



TABLE 4: The Solvation of C60n- (n ) 0, 2, 4, and 6) by Ammonia Hydrogen Atoms in nKC60(NH3)400, as Determined from Figure 4a charge on the fulleride, n (e)

rH1 (Å) ( 0.02

nH1 ( 2

rH2 (Å) ( 0.02

nH2 ( 3

nH1+H2 ( 3

njH-B ( 0.05

0 -2 -4 -6

6.04 5.92 5.83

30 38 42

7.12 7.04 6.96

152 112 109 107

152 142 147 149

0 0.63 0.78 0.84

a

The peak positions of the first solvation shell are given in rH1 and rH2 and the coordination numbers nH1 and nH2, respectively. The total number of hydrogen atoms in the first solvation shell is given by nH1+H2, and the average number of hydrogen-bonds per ammonia in the first solvation shell to the C60n- is given by njH-B.

TABLE 5: Computed Enthalpy of Dissolution, ∆HS, and Internal Energy Components, U, for Metal-Fullerides MxC60 (Equation 2 and Figure 2) energy/k cal mol-1

structural unit

Li4 C604-

Na4 C604-

K4 C604-

Ca2 C604-

Usolution Ucrystal Uammonia ∆HS

MxC60(NH3)400 MxC60 400 NH3 MxC60

-3183 ( 20 -1031 ( 2 -2021 ( 20 -131 ( 28

-3113 ( 17 -927 ( 5 -2021 ( 20 -155 ( 27

-3006 ( 19 -923 ( 3 -2021 ( 20 -61 ( 28

-3236 ( 19 -1120 ( 4 -2021 ( 20 -95 ( 28

Throughout this work, the Ucrystal resulting from the simulation of the salt is referred to as the “lattice energy”, Uammonia from the ammonia solution is referred to as the “solvent energy”, Usolution from the solution is referred to as the “solution energy”, and ∆HS is referred to as “the enthalpy of dissolution”. Our simulation of the ammonia reference state produced the expected value for the internal energy Uammonia ) 21.1 kJ mol-1. The internal energies of our fulleride structures are given in Table 2. The simulation of pure fullerite reproduced the expected fcc structure,20 and our equilibrium lattice enthalpy was ∼50 ( 4 kcal/mol per C60. This value compares with the sublimation enthalpy of 41 ( 6 kcal/mol at 298 K, which is an average of several experimental measurements.3 K4C60 was set up using the standard cubic representation of the fulleride crystal with the potassium atoms placed in the approximate positions. Equilibration in our isothermal-isobaric ensemble results in a reduction in the c-direction, similar to the body-centered tetragonal distortion seen in the experimentally measured structure of this crystal. The unit cell measured by synchrotron diffraction and Reitveld refinement has dimensions a ) b ) 11.87Å, c ) 10.79Å.21,22 This compares with our simulation

results of a ) b ) 12.0 ( 0.1, c ) 10.5 ( 0.1. The average fulleride separation in the simulations is found to be ∼9.95 Å and is consistent with the experimentally measured value of 9.98 Å.21 The K6C60 simulation reproduces the body-centered cubic (bcc) structure that is observed experimentally with the nearest center C60-C60 distances of 10.0 Å. Homogenous crystals of K2C60, Li4C60, Na4C60, and Ca2C60 have not been reported in the literature,23 and indeed uniform crystals did not emerge from our simulations. The structure of our solutions is represented graphically via the one-dimensionally averaged radial pair distribution functions, gRβ(r)

gRβ(r) )

1 dnRβ(r) 4πFβr2 dr

(3)

where dnRβ(r) is the number of particles of species β at a distance between r and r + dr of a fixed particle of species R, and nRβ(r) is the running coordination number. The coordination number

Figure 3. The interaction of C60n- (n ) 0, 2, 4, and 6) with potassium cations in nKC60(NH3)400, as evidenced by the partial distribution functions gC60-K(r). Key: black, C606-; green, C604-; blue, C602-.


Howard and Skipper

Figure 4. Solvent-solvent structure in nKC60(NH3)400 solutions. The left-hand-side panels (a,c,e) are for C606- (n ) 6), and the right-hand-side panels (b,d,f) are for C602- (n ) 2). The figure plots gNN(r) (top), gNH(r) (middle), and gHH(r) (bottom) for the first (green) and second (blue) solvation shells and the bulk volume beyond these shells (black). Note that the second shell and bulk are almost indistinguishable.

nRβ(r1 f r2) of particles of type β at distances between r1 and r2 from a particle of type R is then given by

nRβ(r1 f r2) )

∫rr 4πFβgRβ(r)r2dr 2

1

(4)

In our work, as is common practice, the values of r1 and r2 are chosen to lie at the minima of gRβ(r).

Results and Discussion We have simulated the following species in liquid ammonia solution: C60, K2C60, K4C60, K6C60, Li4C60, Na4C60, and Ca2C60. Our studies of these systems have enabled us to investigate the effects on fulleride dissolution, solvation, and solution structure of (1) fulleride charge and (2) counterion. First, we have calculated the energetics of fulleride-salt dissolution, enabling us to comment on whether the process is enthalpically favorable.



TABLE 6: The Solvation of Counterions by Ammonia Nitrogen Atoms in MxC60(NH3)400 As Determined from Figure 6 and Compared with Experimental Neutron Scattering Data for Pure Metal-Ammonia Solutionsa simulation Cation +

K Na+ Li+ Ca2+

rN1 (Å) ( 0.02 2.90 2.42 2.00 2.51

experiment

nN1 ( 0.2 7.0 4.6 3.5 6.7

rN1 (Å) ( 0.02 24

2.87 2.4526 2.0615 2.4516

nN1 ( 0.2 6 5.5 3.8 7.1

a The peak positions and coordination numbers of the first solvation shells are given by rN1 and nN1, respectively.

We have then used the partial radial distribution functions and associated coordination numbers to provide a detailed picture of the fulleride solvation and solvent structure. The Effects of Fulleride Charge (C60, K2C60, K4C60, and K6C60 in Ammonia). The enthalpies of dissolution and their components, as defined in eq 2, are presented in Table 2. We note first that dissolution of uncharged C60 is energetically

unfavorable, at +70 ( 28 kcal mol-1. This is consistent with the observation that fullerene forms only fractal aggregates in solution. If we now turn to the potassium-fulleride salts, we see that the lattice internal energy, Ucrystal, becomes more negative as we simultaneously increase the number of counterions and fulleride charge. This effect is only partially compensated by the more favorable solution internal energy, Usolution. As a result, ∆HS is only significantly negative for K2C60 and K4C60. The enthalpy of dissolution of K6C60, on the other hand, is marginal at -3 ( 29 k cal mol-1. For this reason, it is debatable whether the anion C606- will form spontaneously in potassium-ammonia-fulleride solutions at this concentration. Indeed, experiments on rubidium-ammonia-fulleride solutions, which proved the sequential and reversible reduction of the C60 anion, showed that upon addition of more metal to C60-5 ammonia solution, the spectrum of the solvated electrons returned rather than a new C60-6 spectrum.7 The detailed structure of our solutions is presented via the radial pair distribution functions, gRβ(r), and the coordination numbers, nRβ(r1 f r2). First, we focus on the distribution of ammonia molecules around the fulleride center of mass, which

Figure 5. The solvation of C60n- (n ) 4) by ammonia in MxC60(NH3)400. (a) Partial distribution functions gC60-N(r), and (b) partial distribution functions gC60-H(r). Key: black, K4C60; green, Li4C60; blue, Ca2C60; red, Na4C60. Please see Table 3 for numerical summary.


Figure 6. The solvation of cations by ammonia nitrogen atoms in MxC60(NH3)400, as evidenced by the partial distribution functions gM-N(r). Key: black, potassium; green, lithium; blue, calcium; red, sodium.

is derived from the functions gC60-N(r) and gC60-H(r) plotted in Figure 2a,b and summarized in Tables 3 and 4. We see immediately from Figure 2a that two distinct solvation shells of ammonia molecules are formed around the fullerides with radial density peaks at around 7 and 10 Å. The first solvation shell contains approximately 45 ammonia molecules in each case with an indication that this number increases by around 3 molecules on going from C602- to C606-. This is consistent with recent neutron diffraction data for C605-.9 In addition, we are now able to quantify the first solvation shell constriction of 0.75 Å, as fulleride charging increased from 0 to -6e and the concomitant peak narrowing (Figure 2a). When allied to the aforementioned changes in coordination numbers, this constriction implies a significant increase in solvent density as the fulleride charge is increased. The orientational organization of the ammonia molecules in the fulleride solvations shell can be extracted from gC60-H(r), Figure 2b and Table 4. In this case, we will start by noting that there is no preferential alignment of solvent around C60, because only single, unsplit, peaks are seen at 7 and 10 Å (i.e., in the same positions as the peaks in gC60-N(r)). In contrast to this, the charged fulleride ions induce increasing strong ammonia orientation in the first solvation shell: the first peak in gC60-N(r) leads to a doublet of peaks at around 6 and 7 Å in gC60-H(r). The first of these can be assigned to the formation of a hydrogen bonds to the fulleride surface with integration of this peak giving 30 bonds per fulleride around C602- up to 42 bonds around C606(nH1 in Table 4). This last value equates to almost one hydrogen bond per ammonia molecule (njH-B in Table 4). In the case of C604- and C606-, longer-range solvent organization is also manifest in the second solvation shell with a distinctly asymmetric peak between 9 and 10 Å. If we cast our minds back to the enthalpy of dissolution (Table 2), we are able to interpret Usolution in terms of the increased solvent order as a function of fulleride charge. The solvent-mediated interaction of fulleride with potassium cations is represented via the partial distribution functions gC60-K(r) shown in Figure 3. The key question here is whether the potassium remains in contact with the C60n- to form direct ion pair complexes,13 or whether it is fully solvated to form

Howard and Skipper either solvent separated ion pairs or “diffuse” species. We see that direct ion pairs are formed in each case, as indicated by the sharp peaks at around 6 Å. Integration of gC60-K(r) up to a limit of 10 Å yields the relevant coordination numbers (eq 4). We find that these species account for around half of the cations in all the systems considered here. In other words, approximately 1, 2, and 3 potassium ions per fulleride are in contact with the anion for n ) 2, 4, and 6, respectively. The remaining potassiums are fully solvated by ammonia as they would be in bulk solution and are located more than 10 Å from the C60ncenter-of-mass. The K · · · N distance obtained from our simulations is 2.90 Å, which is consistent with the value of 2.87 Å measured experimentally by neutron diffraction.24 The fulleride anion charges will not be fully screened from each other by the cations, as is consistent with the observed stability of monodispersed charged fullerides in ammonia solutions. Finally, we investigate the structure of the ammonia itself, via the solvent-solvent distribution functions shown in Figure 4. In view of the fact that we observed two distinct solvation shells around each fulleride ion, we have calculated separate distributions for three solvent populations, based on their distance from the fulleride center-of-mass: first shell (0 < r < 8 Å), second shell (8 Å e r < 12 Å), and bulk (8 Å e r). This analysis was performed for the solutions containing C606- and C602- anions. We note first that there are only quite subtle differences between the first and second shells and the bulk and that the reduced levels of the former beyond about 5 Å can simply be attributed to the volume occupied by the neighboring fulleride. This observation is consistent with experimental neutron diffraction studies of potassium-ammonia-fulleride, which showed that the average solvent structure was only weakly perturbed by the introduction of the fulleride.9 In more detail, the small shoulder at around 2.4 Å in gNH(r) can be assigned to hydrogen bonded N · · · H correlations. For reference, in the pure liquid each ammonia molecule forms ∼2.0 hydrogen bonds per nitrogen atom (approximately one as donor and one as acceptor).25 We have already seen that in the cases of C606- and C602- the solvent molecules donate ∼0.84 and 0.62 hydrogen bonds per molecule respectively to the fulleride. We might therefore expect to see a concomitant reduction in gNH(r). This is indeed the case for C602-, though the reduction is quite marginal, but for C606- we find an increase in the size of the shoulder at about 2.4 Å in gNH(r), which is indicative of a slight increase in the number of hydrogen bonds between solvent molecules. This is followed in the same function by a decrease in the size of the feature at found ∼3.5 Å, which can be attributed to a decrease in non-hydrogen-bonded adjacent ammonia molecules. The gHH(r) functions reveal more about the extent of hydrogen bonding. The feature at ∼2.9 Å, which arises from correlations between adjacent hydrogen bonds, is the same for the first shell of C606- as for the bulk solvent. However, the height of the peak at 3.9 Å is significantly smaller; this peak is attributed to the presence of non-hydrogen-bonded, adjacent ammonia, H · · · H correlations. The reduction of this peak is because nearly all of the hydrogen atoms of the ammonia molecules are incorporated into hydrogen-bonds: ∼0.84 to the fulleride and ∼2.0 to ammonia molecules. In the first shell of the C602- solution, the equivalent values are ∼0.62 and ∼2.0. We therefore conclude that the C60n- anions increase the propensity of the first shell solvent to form hydrogen bonds. We already know from Figure 2b that two of the three N-H bonds in each ammonia molecule lie close to radial around the fulleride, so we conclude that the solvation of C60n- anions results in a clathrate-like solvent structure.



Figure 7. The interaction of C60n- (n ) 4) with the cations lithium sodium, potassium, and calcium in MxC60(NH3)400, as evidenced by the partial distribution functions gC60-M(r). Key: black, K4C60; green, Li4C60; blue, Ca2C60; red, Na4C60.

The Effects of Counterion Species (Li4C60, Na4C60, K4C60 and Ca2C60 in Ammonia). The enthalpies of dissolution and their components, as defined in Equation 2, are presented for the C604- anion as a function of cation species in Table 5. We see immediately that the formation of salt solutions is favorable in each case, in the order Na4C60 > Li4C60 > Ca2C60 > K4C60. The reader will note that the internal energy of the crystal phase, Ucrystal, is a key factor in determining this sequence. For example, if we examine the internal energy of the solutions themselves, Usolution, we see that their energetic stability now follows the order Ca2+ > Li+ > Na+ > K+. This follows a trend with charge density of the cation: the larger the charge density the larger the Usolution. We do not envisage an equivalent to the hydrophobic effect for our unfunctionalised fulleride solute molecules. Therefore we can seek an explanation directly in terms of the solution structure, and in particular the solvation and location of the cations. The solvation of C604- is shown in Figure 5a,b, where we present the fulleride-ammonia radial distribution functions gC60-N(r) and gC60-H(r), respectively. In fact, these functions are remarkably insensitive to the nature of the cations, and we can therefore simply invoke the model proposed in Section 3.1. In brief, we find two well-distinguished solvation shells around the fulleride, giving rise to ammonia nitrogen atom density peaks at around 7 and 10 Å from the C604- center of mass. There is strong orientation of the ammonia molecules in the first solvation shell with a peak in the gC60-H(r) at 5.92 Å indicative of hydrogen bonding to the negatively charged fulleride surface (Tables 3 and 4). Cation solvation is likewise represented by the functions gMN(r) and gM-H(r) which are displayed in Figure 6 and summarized in Table 6. In the latter, we compare with recent experimental data from neutron scattering. This serves to confirm that our potential functions provide a faithful representation of the real systems, but also that the cation solvation in MxC60(NH3)400 is remarkably similar to that in the bulk metal-ammonia solutions. In each case, the ion is surrounded by a well-defined first coordination shell with strong orientation of the ammonia dipole moment toward the cation. We have already noted that the C604solvation is independent of the cation. The relative strengths of the cation-ammonia interactions must therefore mirror the

energetic stability Usolution (Table 5). If we revisit Figure 6, we see that this is indeed the case. It only then remains for us to report on the fulleride-cation interactions. The interaction of fulleride with the various cations is visualized via the radial density function gC60-M(r) shown in Figure 7. We preface our discussion by reiterating that by necessity our simulation box contains only a very small number of cations, and so the statistical significance of the fulleridecation distribution is rather low. Nonetheless, we can draw quite strong conclusions from our data. We observe that the only cation that forms direct ion pair complexes, that is, in contact with the C604- at a distance of about 6 Å, is potassium. In all other cases, the cations are fully solvated and are able to leave the charged anion surface. Once again, therefore, the screening of the fulleride by the cations is incomplete, and this accounts for the observed solubility of our MxC60 salts. On the basis of our simulations, we predict that Na4C60 will have the highest saturation solubility in ammonia (Table 5). Conclusions Monte Carlo computer simulation has been used to study the energetics and local structure of fulleride anions C60n- (n ) 0, 2, 4, 6) in metal-ammonia solutions of potassium, lithium, sodium and calcium. We find that the enthalpy of dissolution is markedly favorable only for n ) 2 and 4, in line with experimental observations. Purely on the basis of energetic considerations, we also predict that Na4C60 will have the highest saturation solubility. We find that uncharged fullerene, C60, is very feebly solvated by ammonia. This accounts for the observation of only fractal aggregates, rather than properly dissolved molecules. In contrast to this, the charged fulleride anions show two strong solvation shells of ammonia at distances of around 6.75 and 9.5 Å from the fulleride center of mass. This is in excellent agreement with high-resolution neutron diffraction studies of K5C60 in ammonia. There is progressively stronger hydrogen bonding of the firstshell solvent to the anions (n ) 2, 4, 6), approaching one hydrogen bond per molecule for n ) 6. We also find evidence for intra- and intersolvation shell hydrogen bonding of ammonia in a clathrate-like structure and weak orientation of ammonia as far out as the second solvation shell.

3332 J. Phys. Chem. B, Vol. 113, No. 11, 2009 Comparison of the cations Li+, Na+, K+, and Ca2+ shows that the fulleride solvation is insensitive to cation-type. The cations themselves are solvated as they would be in the bulk metal-ammonia solution. Only the potassium cation has a tendency to form direct ion pairs with the fulleride anion. Other more strongly solvated species are located at least 8 Å from the fulleride center of mass. This work therefore highlights the mechanisms by which metal-ammonia solutions are able to dissolve high concentrations of fullerene salts. We conclude that the controllability of charge on the fulleride anion and the potential for high concentrations of single C60n- species make these solutions an ideal arena for the manipulation and investigation of fulleride anions via solution based techniques such as NMR or film deposition. Acknowledgment. We would like to thank Helen Thompson, Jonathan Wasse, and Peter Edwards for many useful discussions and EPSRC for financial support. References and Notes (1) Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Smalley, R. E. Nature 1985, 318, 162. (2) Andreoni, W. The physics of Fullerene-based and fullerene related materials; Kluwer Academic Publishers: Dordrecht, 2000. (3) Kadish, K. M.; Ruoff, R. S. Fullerenes Chemistry Physics and Technology; Wiley-Interscience: New York, 2000. (4) Bezmel’nitsyn, V. N.; Eletskiıˆ, A. V.; Okun’, M. V. Phys.-Usp. 1998, 14 (11), 1091. (5) Reed, C. A.; Bolskar, R. D. Chem. ReV. 2000, 100, 1075.

Howard and Skipper (6) Kra¨tschmer, W.; Lowell, D. L.; Fostiropoulos, K.; Huffman, D. R. Nature 1990, 347, 354. (7) Fullagar, W. K.; Gentle, I. R.; Heath, G. A.; White, J. W. J. Chem. Soc., Chem. Comm. 1993, 6, 525. (8) Buffinger, D. R.; Ziebarth, R. P.; Stenger, V. A.; Recchia, C.; Pennington, C. H. J. Am. Chem. Soc. 1993, 115, 9267. (9) Howard, C. A.; Thompson, H.; Wasse, J. C.; Skipper, N. T. J. Am. Chem. Soc. 2004, 126, 13229. (10) Howard, C. A.; Wasse, J. C.; Skipper, N. T.; Thompson, H.; Soper, A. K. J. Phys. Chem. C 2007, 111, 5640. (11) Buffinger, D. R.; Ziebarth, R. P.; Stenger, V. A.; Recchia, C.; Pennington, C. H. J. Am. Chem. Soc. 1993, 115, 9267. (12) Thompson, J. C. Electrons in Liquid Ammonia; Clarendon: Oxford, 1976. (13) Sposito, G.; Prost, R. Chem. ReV. 1982, 82, 553. (14) Rizzo, R. C.; Jorgensen, W. L. J. Am. Chem. Soc. 1999, 121, 4827. (15) Thompson, H.; Wasse, J. C.; Skipper, N. T.; Howard, C. A.; Bowron, D. T.; Soper, A. K. J. Phys.: Condens. Matter 2004, 16, 5639. (16) Wasse, J. C.; Howard, C. A.; Thompson, H.; Skipper, N. T.; Delaplane, R. G.; Wannberg, A. J. Phys. Chem. 2004, 121 (2), 996. (17) Chandrasekhar, J.; Spellmeyer, D. C.; Jorgensen, W. L. J. Am. Chem. Soc. 1984, 106, 903. (18) Åqvist, J. J. Phys. Chem. 1990, 94, 8021. (19) Guo, Y. J.; Karasawa, N.; Goddard, W. A. Nature 1991, 351, 464. (20) Rosseinsky, M. J. J. Mater. Chem. 1995, 5, 1497. (21) Murphy, D. W. J. Phys. Chem. Solids. 1992, 53, 1321. (22) Kuntscher, C. A.; Bendele, G. M.; Stephens, P. W. Phys. ReV. B 1997, 55 (6), 3366. (23) Touzik, A.; Hermann, H.; Wetzig, K. Phys. ReV. B. 2002, 66, 75403. (24) Wasse, J. C.; Hayama, S.; Skipper, N. T.; Benmore, C. J.; Soper, A. K. J. Chem. Phys. 2000, 112, 7147. (25) Thompson, H. J. Am. Chem. Soc. 2003, 125, 2572. (26) Wasse, J. C.; Stebbings, S. L.; Masmanidis, S.; Hayama, S.; Skipper, N. T. J. Mol. Liq. 2002, 96, 341.

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Computer Simulations of Fulleride Anions in Metal-Ammonia Solutions

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