Electronic Shell and Dynamical Coexistence Effects in the Melting of

Letter pubs.acs.org/JPCL

Electronic Shell and Dynamical Coexistence Effects in the Melting of Aluminum Clusters: An Interpretation of the Calorimetric Experiments Through Computer Simulation Andrés Aguado* and José M. López Departamento de Física Teórica, Atómica y Ó ptica, Universidad de Valladolid, Valladolid 47011, Spain S Supporting Information *

ABSTRACT: We report first-principles computer simulations of the melting-like transition in AlQn (n = 35−37, Q = +1,0, −1) clusters. Melting induces an abrupt modification of the electronic shell structure, whereby the HOMO−LUMO gap and chemical hardness sharply decrease, and the size dependence of electronic properties becomes smoother. This intimate coupling between electronic and thermodynamic properties unveils an explicit electronic contribution to the latent heat and other melting properties. Dynamical coexistence involves the participation of a “hot solid” plastic phase, characterized by cooperative atomic rearrangements that do not destroy the structural order. The hot solid acts as a buffer thermodynamic phase connecting the solid and liquid states, and may lead to a double peak structure in the microcanonical heat capacities. A negative microcanonical heat capacity is predicted for neutral Al36. Finally, the average radial atomic densities of liquid clusters show layered profiles that lie on a universal curve if appropriately scaled variables are defined. The layering is interpreted as a premonitory freezing effect, which may have practical implications concerning the prediction of freezing points based purely on properties of the liquid phase. SECTION: Physical Processes in Nanomaterials and Nanostructures

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may induce postmelting features in the heat capacity; (f) both geometric and electronic shell structures may influence the melting properties. In particular, a marked dependence of the melting points of aluminum clusters on the number of electrons has been reported.11 Changing a single electron may also shift the melting point by more than 100 K. Although much progress has already been made in interpreting some of these problems by theoretical means, one of them in particular remains poorly understood, namely, the influence of the number of electrons on the melting properties. Initial work on relatively large Na+n clusters (n ≥ 55)1 revealed that local maxima in the q(n) curve correlate only with geometric shell closings. A tentative interpretation was advanced: as the number of electrons does not change across the phase transition, electronic shell closings might persist in the liquid phase and thus remain undetected in the latent heats. However, the more recent studies on Al+n and Al−n clusters10,11 have challenged such a simple interpretation. In this case, clusters differing only in the number of electrons but otherwise sharing the same number of atoms and identical geometrical structure, can show a substantially different melting behavior. A more general correlation that encompasses both sodium and aluminum cases was suggested: if the size dependence of the liquid cluster stabilities is sufficiently smooth, local maxima in

he melting-like transition of nanoscale particles has been attracting much attention recently due to both fundamental and technological reasons. An analysis of the size dependence of cluster properties can provide essential clues as to how condensed matter properties evolve from those of isolated atoms and molecules. The statistical complexity necessary for the establishment of the liquid phase and the concomitant solid−liquid phase transition, for example, will only emerge above some critical size, because small molecules do not melt. This fundamental physical problem has motivated many experimental1−13 and theoretical9−27 studies of the melting of small clusters, which have already revealed a fascinating set of emergent properties that are specific to the nanoscale. Some examples of these distinguishing properties are: (a) the melting transition is smoothed out or broadened due to finite size effects;13 (b) typical melting properties, such as the melting temperature Tm and the latent heat q, show sizable oscillations as a function of cluster size.1,5 Addition or removal of a single atom, for example, may shift the melting point by more than 100 K; (c) coexistence conditions in small isolated clusters are dynamical in nature: the whole cluster fluctuates between solid and liquid phases as a function of time;13 (d) the large fluctuations associated with a finite size break down the equivalence of the different statistical ensembles, and the microcanonical heat capacity may become negative at coexistence conditions;13 (e) liquid-like clusters may show some vestiges of an atomic shell structure when they approach the freezing point. These are identified as a pronounced layering in the atomic density profile,2,21,28 which © 2013 American Chemical Society

Received: June 12, 2013 Accepted: July 8, 2013 Published: July 8, 2013 2397

dx.doi.org/10.1021/jz401218u | J. Phys. Chem. Lett. 2013, 4, 2397−2403

The Journal of Physical Chemistry Letters

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q(n) will correlate with the enhanced cohesive energies of solid clusters.11 Whether the enhanced cohesive energies have an electronic or structural origin is a different problem, and it will depend on the material and size range considered. However, no theoretical study has explicitly addressed the interplay between electronic and thermal properties of aluminum clusters yet, and a full interpretation of calorimetry experiments is therefore lacking. In order to get a sound physical understanding of this problem, we report first-principles simulations of the melting process in nine aluminum clusters, AlQ35−37 with Q = +1,0,−1. The chosen size and charge intervals are particularly convenient as they cover a region with both electronic and geometric shell closings, displaying strong fluctuations in the electronic properties and relative stabilities of solid clusters.10,11 We will show that the electronic properties of aluminum clusters undergo a dramatic change upon melting, implying a strong coupling between electronic and thermodynamic magnitudes that ultimately explains the experimental results. Additionally, we will provide novel results about the detailed mechanisms of dynamic coexistence in Aln clusters, the sizable atomic layering in the liquid phase and its utility as a premonitory freezing effect, and a prediction of a negative microcanonical heat capacity in neutral Al36. The melting process was simulated by standard constantenergy Born−Oppenheimer molecular dynamics (MD), performed with the SIESTA code.29 Energies and forces were calculated within pseudopotential density functional theory (DFT) under the spin-polarized generalized gradient approximation of Perdew, Burke, and Ernzerhof.30 The basis set of localized atomic orbitals is the same as in our previous works.10−12 MD runs were performed at 30 different energy values for each cluster. Each run was 200 ps long, adding up to a total simulation time of 6 ns for each cluster. The multiplehistogram method31 was employed to extract the heat capacities in different statistical ensembles. The accuracy of the DFT approach chosen has been assessed in previous works.12,17,32,33 The global minimum (GM) structures, needed as an input for the heating runs and shown in Figure 1, were located in our previous works10,11 with the only exception of Al−37, which is reported here for the first time. From the electronic point of view, all clusters with an even number of electrons are spin singlets, while the remaining clusters are spin doublets, i.e., clusters always adopt the minimum spin multiplicity that is compatible with the total number of electrons. Al−35, Al36, and Al+37 have large highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO−LUMO) gaps as compared to neighboring sizes, and the size dependence of the ionization potential shows sharp drops precisely after those sizes, which can then be considered electronic shell closings.10,11 Al36 is a doubly magic cluster, as it displays closed electronic and geometric shells. Its GM structure contains a four-atom tetrahedral core. Each face of the tetrahedron is covered with a six-atom overlayer in face-centered cubic (fcc) epitaxy, which lowers the symmetry to D2d. The remaining eight atoms form two four-atom rows bridging the spatial gap in between the fcc overlayers. Those two atomic rows can be considered as dislocations as they are “misplaced” with respect to a perfect fcc structure, and they contain four low-coordinated atoms located at the corner sites. This structure is the same for all the AlQ36 clusters. AlQ35 is obtained by just removing one of the corner atoms from the Al36 reference structure. Similarly, Al+37 and Al37 are obtained by placing one adatom on top of the geometric shell closing. These clusters are thus interesting also

Figure 1. Putative GM structures and point group symmetries of AlQN clusters (n = 35 − 37, Q = +1,0,−1). For each size, the structure is the same for the three values of Q, with the only exception of Al−37. The four internal atoms are yellow, the atoms forming the fcc or hcp overlayers are in blue, while the atoms in the dislocation rows are either pink or orange, with orange reserved for those atoms with coordination number CN = 4 (either atoms at corner sites or adatoms).

from the point of view of analyzing the thermal disorder induced by a vacancy or an adatom. In the GM structure of Al−37, one of the faces of the tetrahedral core is covered with a seven-atom hexagonal close-packed (hcp) overlayer, which results in some nontrivial rearrangements of the atomic layers. This structure contains six low-coordinated atoms instead of four, and coincides with the recently reported GM structure of Ga37.25 Figure S1 of the Supporting Information (SI) − demonstrates that the electronic density of states of Al37 matches the measured photoemission spectrum much better than in our previous works,33 suggesting that it is the true GM. We want to emphasize that the structures of AlQ36 (or AlQ35) are really identical for the three different charge states: differences in bond lengths are smaller than 0.1%, and the vibrational frequencies differ by less than 1%. All the differences observed in the properties of Al+36, Al36, and Al−36, for example, have to be ascribed to electronic shell effects. Figure 2 shows the canonical specific heats, and compares them to the experimental results,10,11 available only for charged clusters. We can hardly overemphasize the excellent level of agreement between experiment and theory. All the trends regarding the size and charge dependence of the melting points, latent heats, and even the shapes of the heat capacity peaks, are well reproduced by the simulations. Therefore, we believe it is sensible to assume that our predictions are equally accurate for neutrals. The results of Figure 2 demonstrate that just adding or removing a single electron may shift the melting point of aluminum clusters by more than 100 K, even if they have the same geometrical structure. Clusters with higher electronic stability (Al−35, Al36 and Al+37) melt at a higher temperature and show well-defined, narrow heat capacity peaks, so they can be classified as “magic melters”. The maximum values of Tm and q are obtained for the doubly magic cluster Al36, showing the additional contribution of the geometric shell closing. Al+35, Al35, and Al37 have much broader transitions, while the remaining three clusters show an intermediate behavior. 2398



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Figure 2. The theoretical canonical specific heat (continuous red lines) is compared to experimental measurements (black lines and open symbols). Specific heats are given in units of the Boltzmann constant kB. The vertical dashed lines highlight the highest melting point found for each cluster size. Melting points Tm and latent heats per atom q are explicitly annotated.

Figure 3. The microcanonical specific heat of aluminum clusters, as obtained from the multiple histogram analysis, is plotted as a function of the internal energy per atom. Notice the different vertical scales in some graphs.

hiding two separate transitions, which can only be distinguished in the microcanonical results. What is the origin of the two transitions? In the following, we try to provide an interpretation of these results. An analysis of the MD trajectories reveals a noteworthy result: the detailed melting mechanism is the same for all clusters sharing the same structure (for example, for Al+36, Al36, and Al−36). The large differences observed in the corresponding heat capacities result only from the different temperatures (or internal cluster energies, if considering microcanonical results) at which those mechanisms are activated. The mechanism of melting involves, for all clusters, two different dynamical coexistence or “slush”14,19 regimes. For some clusters, such as Al35 and Al+36, the activation energies of the two regimes are sufficiently different as to produce a double peak structure in

Figure 3 shows the microcanonical heat capacities per atom, which provide a more sensitive indicator of phase transitions in finite systems.24 This is because canonical results involve an additional average over several microcanonical systems.34 The melting peaks of clusters with high electronic stability are considerably sharper than in the canonical ensemble. For example, the heat capacity per atom reaches 50 kB units for Al+37. For the doubly magic cluster Al36, the latent heat is sufficiently large35 for developing a negative microcanonical heat capacity at melting conditions and a backbending in the caloric curve (not shown explicitly). To the best of our knowledge, this is the smallest cluster size where a negative heat capacity has been predicted. The microcanonical analysis is equally rewarding for those clusters showing broad canonical heat capacity peaks. For some clusters (Al35, Al+36), the broad canonical peak is in fact 2399



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diffusion from one facet to another, a process in which the adatom should slide upon an edge and so temporarily acquire a very low coordination. The cooperative mechanisms characteristic of the hot solid phase have much lower barriers as they are observed many times along the MD runs. The separation of the dynamical coexistence regime into two different stages (see Figures S5−S8), with the hot solid acting as a buffer thermodynamic phase, is a fundamentally interesting issue as it might be characteristic of other metal clusters beyond aluminum. The curious point remains that, although the melting mechanisms are the same for clusters with the same geometric structure, they become activated at very different energy values. This implies that there must exist some intimate connection between melting properties and the electronic shell structure. Figure 4 shows the dissociation energies Ediss(n,T) = E(1) +

the microcanonical heat capacities; for the other clusters, we emphasize that the two different processes can still be distinguished in the atomic trajectories, but they become activated at similar energies so the two transitions merge into a single heat capacity peak. Melting is thus a two-stage process for all the clusters considered in this paper. The first stage of melting involves a dynamical coexistence between a completely solid phase (essentially the vibrationally excited GM structure) and what we call a hot solid phase, characterized by cooperative structural rearrangements involving only the shell atoms (i.e., the four-atom core remains completely solid). We remind the reader that in a dynamical coexistence regime, each of the two phases persists for a sufficiently long time during the MD trajectory as to develop converged values of thermodynamic averages. The second stage involves dynamical coexistence of hot solid and liquid phases. As usual, the liquid phase is characterized by the equivalence in the diffusive behavior of all atoms, and so implies the melting of the four-atom core. During the second melting stage, the GM structure can of course be revisited but only for very short times, so that the solid phase is clearly unstable from the thermodynamic point of view. In other words, fully liquid and fully solid phases do not directly coexist with each other, and the intermediate hot solid phase thus acquires a real physical significance. The hot solid phase has recently been described employing the term “half-solidity”,22,23 although the same effect had been observed before in the melting of some small sodium clusters16 and in the seminal works on Lennard-Jones clusters.14 It should not be confused with surface melting, as that implies the formation of a thin liquid layer, with full atomic disorder, on the cluster surface. In the hot solid phase, the cluster surface preserves a high degree of structural order. The atomic motion of the shell atoms is of a highly concerted type, and reminiscent of the soft vibrational modes of the cluster. As a matter of fact, the low-frequency vibrational modes of clusters typically involve concerted displacements of the low-coordinated surface atoms, in which close approaches between pairs of atoms are avoided (we provide in the SI animation files of the vibrational normal modes of Al+36). As typical examples of concerted atomic motions in the hot solid phase, we mention here the coherent motion of a whole ridge of atoms or the sliding of a whole facet over the cluster core (the interested reader may find a detailed description of isomerization mechanisms in Figures S2−S4). Some of these concerted motions have been previously identified in metal clusters, and their influence on the kinetics of cluster growth has been discussed.36,37 The most interesting aspect of these cooperative motions is that they can alter the spatial arrangement of structural defects (such as the dislocation rows, vacancies or adatoms). For example, after a typical sequence of such cooperative rearrangements, the original adatom of Al+37 is absorbed by the cluster shell, while another distant surface atom is expelled from the shell and promoted to the adatom layer. The thermal disorder induced by the structural defects is therefore subtle in nature: the different sites available for the adatom are sampled without involving the real diffusion of the adatom on the surface, and the same is true of the other two types of defects. Direct diffusion of adatoms has also been observed in the simulations, but it is a much less frequent process, which is moreover always restricted to a single facet. Although a calculation of activation barriers against diffusion is outside the scope of this paper, our simulations suggest that large barriers exist opposing the

Figure 4. The left panels show several electronic properties of the indicated aluminum clusters as a function of temperature. From top to bottom, these are the ionization potential (IP), the electronic affinity (EA) and the HOMO−LUMO gap. The right panels show the temperature dependence of some stability measures: the dissociation or evaporation energies for n = 36 and 37, and the second energy differences for n = 36.

E(n − 1,T) − E(n,T) for n = 36,37 and the second energy difference Δ2(n,T) = E(n − 1,T) + E(n + 1,T) − 2E(n,T) for n = 36, as a function of temperature. In these equations, E(1) is the energy of an isolated aluminum atom, while E(n,T) is the canonically averaged internal energy of the cluster (containing both potential and kinetic energy contributions) at temperature T, which is available from the multiple histogram analysis. Neutral Al36 is clearly much more stable than either Al+36 or Al−36 in the solid phase, and the only reason is the electronic shell closing. For n = 37, it is the cation that is most stable in the solid phase. However, the most remarkable result is that the stabilities of the different charge states become nearly equal in the liquid phase, implying that the size dependence of electronic properties is much smoother than in the solid phase. It is somehow ironic that the electronic shell closings are so marked in the solid phase and nearly absent in the liquid phase, because they have been traditionally explained by 2400



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resorting to liquid drop or similar structureless models. In any case, the theoretical liquid dissociation energies are in very good agreement with the experimental values, of about 2.9 eV in this size range,10 and the experimental liquid cohesive energies do indeed show a smooth size dependence,13 supporting the accuracy of our results. If the liquid stabilities have a smooth size dependence, the relative stabilities of the solid clusters will be reflected in the latent heats. Therefore, our results demonstrate that there is an intrinsically electronic contribution to the latent heat of aluminum clusters. In order to substantiate our claims, we also show in Figure 4 electronic properties such as the adiabatic ionization potentials and electron affinities, or the average HOMO−LUMO gap, as a function of temperature. For neutral clusters, the high stability of solid Al36 is reflected by a local maximum in the size dependence of the ionization potential (IP) and a corresponding local minimum in the electronic affinity (EA). Similarly, the maximum of the EA at n = 35 and the minimum of the IP at n = 37 are due to the closed electronic shells of solid Al−35 and Al+37, respectively. The liquid-like clusters, on the contrary, have much more similar IP and EA values, demonstrating that electronic properties in the liquid phase are not so sensitive to a change in the number of atoms. The melting transition also induces a substantial closure of the HOMO−LUMO gap, making clear that the electronic shell closings do not persist in the liquid phase. This is an important finding for catalysis, as it contributes to the higher reactivity of liquid-like clusters recently observed in beam collision experiments.12 In fact, the chemical hardness (not shown) is proportional to the band gap and it will be much lower in the liquid phase. The large variations induced by the melting transition on the IP and EA values highlight the origin of the electronic contribution to the latent heat. This is best understood by considering the melting transition as a kind of “chemical reaction” and building up a closed Born−Haber-like cycle with, for example, the caloric curves of Al36 and Al+36.11 Such simplified diagrams predict that the latent heat differences induced by electron charging should satisfy q(Aln) − q(Al+n ) = IP(solid) − IP(liquid) and q(Al−n ) − q(Aln) = EA(solid) − EA(liquid). These predictions are indeed quite well followed by the ab initio latent heats given in Figure 2, demonstrating the suitability and predictive power of this simple model. We complete our work with a discussion of the radial atomic density profiles, which are shown in Figure 5. At T = 0 (upper plot), the clusters contain three atomic layers about the empty center of mass (CM): the innermost one corresponds to the tetrahedral core, the outermost one contains the four outermost atoms located at corner sites, while the remaining surface atoms belong to the intermediate layer. Although we confirm the expected trend of the radial density profile gradually flattening with increasing temperature, a pronounced atomic layering persists well within the stability range of the liquid phase. Interestingly, the geometric radial shell structure is not the same in solid and liquid phases. Melting thus modifies both the electronic and the geometric shells of the solid clusters. On one hand, the four outermost atoms are closer on average to the CM than in the solid phase, so the liquid profile shows a lower density tail at long distances than the solid profile; on the other hand, an atom installs close to the CM position of the liquid cluster, and the number of core atoms increases from four in the solid phase to five in the liquid phase. In fact, Figure S9 shows that the root-mean-squared cluster radius decreases upon melting due to these structural

Figure 5. The temperature evolution of the radial atomic density profile of Al36 is shown in the upper panel. The other two graphs compare the layered atomic density profiles of the AlQ36 clusters in the liquid phase. In the middle plot, the comparison is done at the same absolute temperature. In the lower graph, the comparison is done at the same “reduced” temperature.

rearrangements, so the phase transition region is at the same time a region of “anomalous” negative thermal expansion. These findings are relevant as they can rationalize the experimental observation that some liquid aluminum clusters freeze into high energy metastable structures7,10,11 upon cooling. The disparity between the radial structures of liquid and solid can cause the innermost liquid atom to be kinetically arrested at the CM position upon cooling, promoting the freezing into an atom-centered solid structure. A comparison of the liquid density profiles of different clusters at the same temperature (middle plot) reveals small but measurable differences. However, if the profiles are compared at the same “reduced temperature” (T = Tm + 223 or T = Tm × 1.26; the accuracy of our results does not allow one to discriminate between these two scaling options), a sort of universal behavior emerges (see lower plot), in which the density profiles of Al−36, Al36, and Al+36 (not explicitly shown for better visualization) nicely coincide with each other. By additionally scaling the distance to the CM with the rootmean-squared cluster radius, we have checked that a universal density profile exists for the nine clusters studied in this work, if plotted at the same reduced temperature. Of course, the number of atomic layers in the liquid clusters will gradually increase with size, but if the size evolution is smooth, universal behavior is expected to prevail over restricted size intervals. This finding is important enough as to call for a more general study that encompasses a broader size range. If confirmed, it would provide support for the physical interpretation of the liquid atomic layering as a premonitory signal of the freezing transition. Moreover, it would allow to make useful inferences about the size and charge dependence of melting temperatures 2401



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based only on 1-phase simulations of the liquid phase, which are obviously much less time-consuming than complete simulations of the melting process. To conclude, we summarize and discuss the most relevant conclusions that emerge from our simulations: (1) the traditional picture of dynamical coexistence of solid and liquid phases does not hold for aluminum clusters. Instead, an intermediate thermodynamic phase (called “hot solid”) is needed as a buffer that connects the solid and liquid phases. The hot solid phase is characterized by cooperative motions of surface atoms that preserve a high degree of structural order, and so is distinctly different from solid, liquid, or surface melted phases. We expect that the more detailed picture of dynamical coexistence that emerges from this article also applies to many other metal clusters. In particular, gallium clusters with N = 35−37 have the same structures and properties as the corresponding aluminum clusters,25 and so we expect that the melting process in gallium clusters shares many similarities with the results of this work. (2) Our simulations reproduce and interpret for the first time the experimental results concerning the dependence of the melting properties on the number of electrons. Clusters with the same size and structure, differing only in the number of electrons, melt at substantially different temperatures and with different latent heats, even if the detailed dynamical mechanism of melting is the same. Electron shell closings do not persist in the liquid phase, and so the size dependence of the stabilities and the electronic properties becomes much smoother than in the solid phase. Therefore, the additional contribution of electron shell closings to the stability of solid clusters will be reflected in the latent heats. The closure of the gap implies that aluminum clusters are more “metallic” and more reactive in the liquid phase, a finding with potential applications in catalysis.12 (3) Neutral Al36 has a negative microcanonical heat capacity at melting conditions. To the best of our knowledge, this is the smallest cluster size for which this effect has been predicted. The probability of observing a negative Cv increases as the latent heat q increases,35 and for neutral Al36, q is very large due to the simultaneous occurrence of electronic and geometric shell closings. Therefore, purely electronic shell effects are also a potential source of S-loops in microcanonical caloric curves. (4) The radial atomic density profile of liquid aluminum clusters shows a pronounced layering, whose amplitude increases as the freezing point is approached upon cooling. The density profiles of the nine clusters studied in this paper converge to the same “universal” curve if appropriately scaled temperature and radius variables are defined. The radial geometric structure is very different in solid and liquid phases, with the liquid phase being more dense than the solid at coexistence conditions. While the solid clusters have a hollow core, in the liquid phase there is one atom at the CM position, which rationalizes the tendency of aluminum clusters to freeze into metastable geometries.7 All these conclusions deepen our present understanding of the complex physical processes occurring at phase transitions in finite systems.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Spanish “Ministerio de Ciencia e Innovación”, the European Regional Development Fund, and “Junta de Castilla y León” (Project Nos. FIS2008-02490/FIS and VA104A11-2).

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REFERENCES

(1) Haberland, H.; Hippler, T.; Donges, J.; Kostko, O.; Schmidt, M.; von Issendorff, B. Melting of Sodium Clusters: Where Do the Magic Numbers Come From? Phys. Rev. Lett. 2005, 94, 035701. (2) Hock, C.; Bartels, C.; Strassburg, S.; Schmidt, M.; Haberland, H.; von Issendorff, B.; Aguado, A. Premelting and Postmelting in Clusters. Phys. Rev. Lett. 2009, 102, 043401. (3) Shvartsburg, A. A.; Jarrold, M. F. Solid Clusters above the Bulk Melting Point. Phys. Rev. Lett. 2000, 85, 2530−2532. (4) Breaux, G. A.; Benirschke, R. C.; Sugai, T.; Kinnear, B. S.; Jarrold, M. F. Hot and Solid Gallium Clusters: Too Small to Melt. Phys. Rev. Lett. 2003, 91, 215508. (5) Breaux, G. A.; Neal, C. M.; Cao, B.; Jarrold, M. F. Melting, Premelting, and Structural Transitions in Size-Selected Aluminum Clusters with around 55 Atoms. Phys. Rev. Lett. 2005, 94, 173401. (6) Cao, B.; Starace, A. K.; Judd, O. H.; Jarrold, M. F. Phase Coexistence in Melting Aluminum Clusters. J. Chem. Phys. 2008, 130, 204303. (7) Cao, B.; Starace, A. K.; Judd, O. H.; Bhattacharyya, I.; Jarrold, M. F. Metal Clusters with Hidden Ground States: Melting and Structural Transitions in Al+115, Al+116, and Al+117. J. Chem. Phys. 2009, 131, 124305. (8) Zamith, S.; Labastie, P.; Chirot, F.; L’Hermite, J.-M. Two-Step Melting of Na+41 . J. Chem. Phys. 2010, 133, 154501. (9) Cao, B.; Starace, A. K.; Neal, C. M.; Jarrold, M. F.; Núñez, S.; López, J. M.; Aguado, A. Substituting a Copper Atom Modifies the Melting of Aluminum Clusters. J. Chem. Phys. 2008, 129, 124709. (10) Starace, A. K.; Neal, C. M.; Cao, B.; Jarrold, M. F.; Aguado, A.; López, J. M. Correlation between the Latent Heats and Cohesive Energies of Metal Clusters. J. Chem. Phys. 2008, 129, 144702. (11) Starace, A. K.; Neal, C. M.; Cao, B.; Jarrold, M. F.; Aguado, A.; López, J. M. Electronic Effects on Melting: Comparison of Aluminum Cluster Anions and Cations. J. Chem. Phys. 2009, 131, 044307. (12) Cao, B.; Starace, A. K.; Judd, O. H.; Bhattacharyya, I.; Jarrold, M. F.; López, J. M.; Aguado, A. Activation of Dinitrogen by Solid and Liquid Aluminum Nanoclusters: A Combined Experimental and Theoretical Study. J. Am. Chem. Soc. 2010, 132, 12906−12918. (13) Aguado, A.; Jarrold, M. F. Melting and Freezing of Metal Clusters. Annu. Rev. Phys. Chem. 2011, 62, 151−172. (14) Beck, T. L.; Jellinek, J.; Berry, R. S. Rare Gas Clusters: Solids, Liquids, Slush, and Magic Numbers. J. Chem. Phys. 1987, 87, 545−554. (15) Aguado, A. Competing Thermal Activation Mechanisms in the Meltinglike Transition of NaN (N = 135−147) Clusters. J. Phys. Chem. B 2005, 109, 13043−13048. (16) Aguado, A.; López, J. M. Small Sodium Clusters that Melt Gradually: Melting Mechanisms in Na30. Phys. Rev. B 2006, 74, 115403. (17) Aguado, A.; López, J. M. First-Principles Structures and Stabilities of Al+N (N = 46−62) Clusters. J. Phys. Chem. B 2006, 110, 14020−14023. (18) Joshi, K.; Krishnamurty, S.; Kanhere, D. G. “Magic Melters” Have Geometrical Origin. Phys. Rev. Lett. 2006, 96, 135703.

ASSOCIATED CONTENT

S Supporting Information *

Comparison to photoelectron spectrum for Al−37, animation files for visualization of the vibrational modes, temperature dependence of the cluster radius, and a detailed visualization of premelting mechanisms and phase coexistence. This 2402



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(19) Li, Z. H.; Truhlar, D. G. Nanosolids, Slushes, and Nanoliquids: Characterization of Nanophases in Metal Clusters and Nanoparticles. J. Am. Chem. Soc. 2008, 130, 12698−12711. (20) Pahl, E.; Calvo, F.; Koci, L.; Schwerdtfeger, P. Accurate Melting Temperatures for Neon and Argon from Ab Initio Monte Carlo Simulations. Angew. Chem., Int. Ed. 2008, 47, 8207−8210. (21) Núñez, S.; López, J. M.; Aguado, A. Atomic Layering and Related Postmelting Effects in Small Liquid Metal Clusters. Phys. Rev. B 2009, 79, 165429. (22) Kang, J.; Wei, S.; Kim, Y. Origin of the Diverse Melting Behaviors of Intermediate-Size Nanoclusters: Theoretical Study of AlN (N = 51−58,64). J. Am. Chem. Soc. 2010, 132, 18287−18291. (23) Kang, J.; Kim, Y. Half-Solidity of Tetrahedral-like Al55 Clusters. ACS Nano 2010, 4, 1092−1098. (24) Aguado, A. Stepwise Melting in Na41+: A First-Principles Critical Analysis of Available Experimental Results. J. Phys. Chem. C 2011, 115, 13180−13186. (25) Núñez, S.; López, J. M.; Aguado, A. Neutral and Charged Gallium Clusters: Structures, Physical Properties and Implications for the Melting Features. Nanoscale 2012, 4, 6481−6492. (26) Steenbergen, K. G.; Schebarchov, D.; Gaston, N. Electronic Effects on the Melting of Small Gallium Clusters. J. Chem. Phys. 2012, 137, 144307. (27) Susan, A.; Kibey, A.; Kaware, V.; Joshi, K. Correlation between the Variation in Observed Melting Temperatures and Structural Motifs of the Global Minima of Gallium Cluster: An Ab Initio Study. J. Chem. Phys. 2013, 138, 014303. (28) Polak, W. Global and Local Structure of Liquid Lennard-Jones Clusters near Freezing. Eur. Phys. J. D 2013, 67, 74. (29) Soler, J. M.; Artacho, E.; Gale, J. D.; Garc a, A.; Junquera, J.; Ordejón, P.; Sánchez-Portal, D. The SIESTA Method for Ab Initio Order−N Materials Simulation. J. Phys.: Condens. Matter 2002, 14, 2745−2779. (30) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (31) Calvo, F.; Labastie, P. Configurational Density of States from Molecular Dynamics Simulations. Chem. Phys. Lett. 1995, 247, 395− 400. (32) Henry, D. J.; Varano, A.; Yarovsky, I. Performance of Numerical Basis Set DFT for Aluminum Clusters. J. Phys. Chem. A 2008, 112, 9835−9844. (33) Ma, L.; von Issendorff, B.; Aguado, A. Photoelectron Spectroscopy of Cold Aluminum Cluster Anions: Comparison with Density Functional Theory Results. J. Chem. Phys. 2010, 132, 104303. (34) Touchette, H. Ensemble Equivalence for General Many-Body Systems. Europhys. Lett. 2011, 96, 50010. (35) Wales, D. J. Energy Landscapes; Cambridge University Press: Cambridge, U.K.; 2003. (36) Baletto, F.; Mottet, C.; Ferrando, R. Molecular Dynamics Simulations of Surface Diffusion and Growth on Silver and Gold Clusters. Surf. Sci. 2000, 446, 31−45. (37) Baletto, F.; Mottet, C.; Ferrando, R. Growth Simulations of Silver Shells on Copper and Palladium Nanoclusters. Phys. Rev. B 2002, 66, 155420.

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Electronic Shell and Dynamical Coexistence Effects in the Melting of

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