The effects of quantum delocalization on the structure of Lennard-Jones clusters.

摘要

The global minimum configurations for LJ clusters belong predominately to two structural types, the Mackay and the anti-Mackay icosahedron, where the latter possesses a more disordered, liquid-like over-layer. At finite temperature a given cluster may undergo a structural transition, typically from the Mackay (M) to the anti-Mackay (aM), where the aM is favored at higher temperature in accord with its greater entropy. Additionally, different size ranges adopt certain ground state structural motifs. It has also been shown that the global minimum configuration (T → 0) depends on the quantum nature of the cluster. In the present study, how the ground state structure is affected by the quantum behavior of the constituent atoms is investigated, thereby introducing a third factor affecting structural transitions, to accompany those induced by size and temperature. The quantum nature of a cluster can be conveniently represented de Boer quantum delocalization parameter (Λ), where Λ = h/(sigma em ). To calculate the quantum energies and obtain the corresponding ground state configurations we use the Variational Gaussian Wavepacket (VGW) approximation, in which the atomic constituents are represented by Gaussian wavepackets and comprise solutions to the Bloch equation. In the two resulting papers, here referred to as paper I (J. Deckman, P. Frantsuzov, V. Mandelshtam, Phys. Rev. E, 77, 52102 (2008)) and paper II (J. Deckman, V. Mandelshtam, J. Phys. Chem. A, 113, 7394 (2009)), for different cluster sizes configurations are generated using Replica Exchange Monte-Carlo methods. After several thousand MC steps, the replicas are "quenched" at specific Λ and around the classical melting transition, to very low temperature to determine the quantum GS energy. After long Monte-Carlo runs, a number of the lowest energy configurations are saved and each is then propagated along a fine grid of Λ to obtain the quantum energy at each point, and from this the relative energies of the configurations are determined for different Λ. From these data structural changes are interpreted, indicated when a new motif becomes lowest in energy at certain Λ (Λ T). For a range of clusters, ΛT is plotted as a function of cluster size (n), which yields a size-dependent phase diagram. Paper I depicts this figure for sizes 31--45, and paper II continues for sizes up to and including n=147 (skipping every 5 for n > 55). The entire figure bears strong resemblance to the size-temperature dependent phase diagram found in Mandelshtam et al., J. Chem. Phys, 124, (2006) and it is concluded that quantum induced transitions are analogous to those induced by temperature.