Effects of geometric and electronic structure on the finite temperature behavior of Na₅₈, Na₅₇, and Na₅₅ cluster

Abstract

We report the equilibrium geometries and the electronic structures of Na_n clusters in the size range of n=55-62 using density-functional method. An analysis of the evolutionary trends in their ground state geometries reveals that Na₅₈ has a spherical shape which is driven by the closed-shell nature of the electronic structure. This structure shows a significant large network connected by short bonds among the surface atoms as well as between core and surface atoms, which affects its finite-temperature behavior. By employing ab initio density-functional molecular dynamics, we calculate the specific heat of Na₅₈ and Na₅₇. We observe two distinct features in their specific-heat curves as compared to that of Na₅₅: (1) Both clusters show very broad melting transition. (2) The calculated melting temperature of Na₅₈ is ~375 K, the highest one studied so far, and that of Na₅₇ is also relatively high (~350 K). Thus, when a cluster has a (nearly) geometric closed-shell structure as well as a (nearly) electronic closed-shell one, it shows a high melting temperature. Our calculations clearly bring out the size-sensitive nature of the specific-heat curve in sodium clusters.