Accurate Melting Temperatures for Neon and Argon from Ab Initio Monte Carlo Simulations

Abstract

Although studied experimentally for centuries, the melting of solids is still a fascinating phenomenon whose underlying mechanisms are not yet well understood.[1] Predicting melting points is a nontrivial task: The standard computational method relies on analyzing the free energies of the solid and liquid phases obtained independently by thermodynamic [2] or Gibbs-Duhem [3] integration; this approach suffers from the difficulty of calibration. Alternatively, in coexistence methods the interface between the two phases must be described explicitly; [4] this interface is often hard to stabilize.[5]An alternative idea, which we pursue herein, is to obtain information about the melting transition by studying finite clusters and extrapolating the results to infinitely large systems. Here we present for the first time calculated melting temperatures reaching experimental accuracy obtained from Monte Carlo simulations of Ne N and Ar N clusters consisting of a "magic number" N of atoms (N = 13, 55, 147, 309, 561, 923) and of bulk samples. This was achieved by the use of accurate interaction potentials obtained from precise ab initio data having the same computational efficiency as the widely used empirical Lennard-Jones (LJ) potential, and without any experimental input whatsoever. Argon and neon adopt the face-centered cubic (fcc) periodic packing in the solid state, but their clusters with N < 1000 are most stable as complete Mackay icosahedra. The number of atoms in the first six shells of the cluster corresponds to the "magic numbers": N = 1 + 2 P n k¼1 (5k 2 +1) = 13, 55, 147, 309, 561, and 923.[6] These "magic numbers" have been provided by mass spectra in free-jet expansions of rare-gas clusters. [7,8] The unusual stability of these clusters is explained by the structure in which one to six completed shells of atoms surround a central atom (see the inset of Figure 1). [6] Previous work on determining melting curves for rare-gas clusters include Monte Carlo (MC) simulations by Labastie and Whetten [9] (N = 13, 55, 147). They found a well-defined single peak in the heat capacity, which becomes higher more intense and narrower as the cluster size increases. The apparent convergence towards the bulk limit was, however, questioned by Noya and Doye, [10] who found an additional premelting peak for the 309-atom cluster. As we show below, even though complicated premelting phenomena remain for all clusters with more than 309 atoms, the melting peak itself always turns out to be well defined. Furthermore, and to our knowledge, the 309-atom system is the largest rare-gas cluster studied so far for melting. To determine the bulk melting point T m by extrapolation to the macroscopic limit, inclusion of two more shells is required, as we demonstrate in this work.

Finite-temperature quantum simulations of mixed rare gas clusters

“…4,5,18 Although their presence has been known for a long time ͓e.g., the Axilrod-Teller term has been discussed in 1943 ͑Ref. 19͔͒, explicitly calculating them is computationally very demanding and has only become possible in the past few years.…”

“…3 The necessary corrections appeared larger for Kr-and Xe-containing systems but relatively small for Ar-containing clusters. More recently, melting temperatures for neon and argon clusters containing up to N = 923 atoms have been determined 4,5 using a range of potential energy functions, including conventional and extended Lennard-Jones potentials, interaction potentials including three-body terms, and potentials derived from experimental data. 6,7 The latter have been determined from fits to a range of experimental and theoretical data, including measured second virial coefficients, transport properties, spectroscopic data, and calculated C 6 , C 8 , and C 10 coefficients.…”

“…The Monte Carlo ͑MC͒ simulations with different potentials showed that using accurate representations of the intermolecular interactions provides melting temperatures T m for N → ϱ in close agreement with bulk measurements, whereas T m from simulations with conventional Lennard-Jones potentials were too low compared to experiment. 4,5 Also accurate interaction potentials and Lennard-Jones potentials have been used to investigate and compare the minimum energy structures of argon clusters up to Ar 55 . 8 Here, the only difference found was for the structure of Ar 21 .…”

Cluster melting: new, limiting, and liminal phenomena

“…In studying the melting temperatures of noble gas clusters, Pahl et al, have been able to demonstrate that only the very smallest clusters (ca. 13 atoms) have melting temperatures that diverge significantly from those of both larger clusters and the bulk, when mapped relative to the surface area to volume ratio (in proportion to N −1/3 ) [36]. This is significant as an extreme and limiting case, of the behaviour to be expected when the electronic structure -or nature of chemical bonding -remains the same in both small clusters and in the bulk.…”

“…These kinds of simulations can also be conducted using DFT or other ab initio electronic structure methods [33] although the use of effective potentials (which can also be based on ab intitio calculations) is more common, and straightforwardly extended to larger sizes [34][35][36].…”