Orbital-free molecular dynamics simulations of melting in Na8 and Na20: Melting in steps

Abstract

The melting-like transitions of Na 8 and Na 20 are investigated by ab initio constant energy molecular dynamics simulations using a variant of the Car-Parrinello method which employs an explicit electronic kinetic energy functional of the density, thus avoiding the use of one-particle orbitals. Several melting indicators are evaluated in order to determine the nature of the various transitions, and are compared with other simulations. Both Na 8 and Na 20 melt over a wide temperature range. For Na 8 , a transition is observed to begin at ϳ110 K, between a rigid phase and a phase involving isomerizations among the different permutational isomers of the ground state structure. The ''liquid'' phase is completely established at ϳ220 K. For Na 20 , two transitions are observed: the first, at ϳ110 K, is associated with isomerization transitions among those permutational isomers of the ground state structure which are obtained by interchanging the positions of the surface-like atoms; the second, at ϳ160 K, involves a structural transition from the ground state isomer to a new set of isomers with the surface molten. The cluster is completely liquid at ϳ220 K.

Orbital-free molecular dynamics study of melting inK20,K55Aguado1 2001Phys. Rev. BSelf Cite18151View full textAdd to dashboardCite

“…The cut-offs used give a convergence of bond lengths and binding energies as good as that obtained for sodium clusters. 7 The fictitious mass associated with the electron density coefficients ranged between 6.3×10 8 and 4.0×10 9 a.u., depending on the material and on the temperature of the simulations. The equations of motion of K clusters were integrated using the Verlet algorithm 28 for both electrons and ions with a time step ranging from ∆t = 0.83 × 10 −15 sec.…”

“…The main features of the energy functional and the calculation scheme have been described at length in previous work, 3,7,13,17,19 and details of our method are as described by Aguado et al 7 In brief, the electronic kinetic energy functional of the electron density, n( r), cor-responds to the gradient expansion around the homogeneous limit through second order 15,[21][22][23] …”

“…Following Car and Parrinello, 14 the coefficients of that expansion are regarded as generalized coordinates of a set of fictitious classical particles, and the corresponding Lagrange equations of motion for the ions and the electron density distribution are solved as described in Ref. 7. The calculations used a supercell of edge 71 a.u.…”

“…7,8 The OFMD technique 13 is completely analogous to the method devised by Car and Parrinello (CP) to perform dynamic simulations at an ab initio level, 14 but the electron density is taken as the dynamic variable, 15 as opposed to the Kohn-Sham (KS) orbitals 16 in the original CP method. This technique, whose main advantage over KS-based methods is that the computational effort to update the electronic system scales linearly with cluster size, has been already used both in solid state 17,18 and cluster 3,7,8,19,20 physics.…”

“…The melting-like transition in small clusters composed of a finite number of atoms spreads instead over a temperature interval that widens as the cluster size decreases. A number of thermal properties sensitive to the cluster size and essentially different from those found in bulk materials emerge in the transition region defined by that temperature interval, which has motivated a lot of theoretical [1][2][3][4][5][6][7][8] and experimental [9][10][11][12] investigations. The experiments of Schmidt et al 10 have shown strong nonmonotonic variations of the melting temperature of free sodium clusters with size, which can not be completely explained either by electronic or geometric shell closing arguments.…”