Thermodynamics and equilibrium structure of Ne38 cluster: Quantum mechanics versus classical

Abstract

The equilibrium properties of classical LJ38 versus quantum Ne38 Lennard-Jones clusters are investigated. The quantum simulations use both the Path-Integral Monte-Carlo (PIMC) and the recently developed Variational-Gaussian-Wavepacket Monte-Carlo (VGW-MC) methods. The PIMC and the classical MC simulations are implemented in the parallel tempering framework. The classical heat capacity Cv(T ) curve agrees well with that of Neirotti et al [J. Chem. Phys. 112, 10340 (2000)], although a much larger confining sphere is used in the present work. The classical Cv(T ) shows a peak at about 6 K, interpreted as a solid-liquid transition, and a shoulder at ∼4 K, attributed to a solid-solid transition involving structures from the global octahedral (O h ) minimum and the main icosahedral (C5v) minimum. The VGW method is used to locate and characterize the low energy states of Ne38, which are then further refined by PIMC calculations. Unlike the classical case, the ground state of Ne38 is a liquid-like structure. Among the several liquid-like states with energies below the two symmetric states (O h and C5v), the lowest two exhibit strong delocalization over basins associated with at least two classical local minima. Because the symmetric structures do not play an essential role in the thermodynamics of Ne38, the quantum heat capacity is a featureless curve indicative of the absence of any structural transformations. Good agreement between the two methods, VGW and PIMC, is obtained. The present results are also consistent with the predictions by Calvo et al [J. Chem. Phys. 114, 7312 (2001)] based on the Quantum Superposition Method within the harmonic approximation. However, because of its approximate nature, the latter method leads to an incorrect assignment of the Ne38 ground state as well as to a significant underestimation of the heat capacity.

Structural Transitions and Melting in LJ74-78 Lennard-Jones Clusters from Adaptive Exchange Monte Carlo Simulations

“…10,11,[17][18][19] Depending on the structure of the global minimum, a LJ cluster may undergo one or more structural transformations according to the following general rules. Below size 31, the ground-state geometry is based on the polyicosahedral or antiMackay motif.…”

The thermodynamic and ground state properties of the TIP4P water octamer

“…In a series of works [63][64][65][66][67][68][69][70] we have extended the reweighted random series approach [104][105][106][107][108][109][110] to the imaginary time path integral in manifolds that are mappable by stereographic projections. The random series expansion of the path consists of k m core terms and an additional 3k m tail terms,…”

“…͑1͒ is identical to the partial averaging method derived from the original random series representation of the Brownian bridge. [104][105][106][107][108][109][110] The centerpiece of the imaginary time path integral approach is the density matrix ͑q , qЈ , ␤͒. In manifolds the following equation is convenient for developing the proper importance sampling algorithms, [113][114][115] and to derive the expressions for the finite difference estimators of the energy and heat capacity,…”

“…Our methods based on stereographic projection coordinates have been tested on a number of simple systems solvable by basis set methods, and several molecular clusters. 64,67,69 We extend the reweighted random series method [104][105][106][107][108][109][110] and the finite difference estimators 108 for cubically convergent path integral simulations to manifolds. 68 DMC simulations are nearly as straightforward to implement in curved spaces mapped with stereographic projection coordinates as they are with Cartesian coordinates.…”

Quantal Cumulant Mechanics as Extended Ehrenfest Theorem

“…Melting behavior of the finite quantum clusters were extensively investigated by many researchers using different kind of methodologies [34][35][36][37][38][39]. We here investigate the melting behavior of n particle Morse clusters (abbreviated as M n ) by means of the QCD2 method.…”