Effect of geometric and electronic structures on the finite temperature behavior of Na$_{58}$, Na$_{57}$, and Na$_{55}$ clusters

TL;DR

This study investigates how geometric and electronic structures influence the finite-temperature behavior of sodium clusters Na$_{55}$, Na$_{57}$, and Na$_{58}$, revealing size-sensitive melting characteristics and the impact of electronic shell closure.

Contribution

It provides new insights into the relationship between electronic shell closure, structural connectivity, and melting behavior in sodium clusters using ab initio molecular dynamics.

Findings

Na$_{58}$ exhibits a higher melting temperature of 375 K.

Na$_{57}$ has a melting temperature of 350 K, higher than Na$_{55}$.

Electronic shell closure correlates with increased melting temperature.

Abstract

An analysis of the evolutionary trends in the ground state geometries of Na$_{55}$ to Na$_{62}$ reveals Na$_{58}$, an electronic closed--shell system, shows namely an electronically driven spherical shape leading to a disordered but compact structure. This structural change induces a strong {\it connectivity} of short bonds among the surface atoms as well as between core and surface atoms with inhomogeneous strength in the ground state geometry, which affects its finite--temperature behavior. By employing {\it ab initio} density--functional molecular dynamics, we show that this leads to two distinct features in specific heat curve compared to that of Na$_{55}$: (1) The peak is shifted by about 100 K higher in temperature. (2) The transition region becomes much broader than Na$_{55}$. The inhomogeneous distribution of bond strengths results in a broad melting transition and the strongly connected network of short bonds leads to the highest melting temperature of 375 K reported among the sodium clusters. Na$_{57}$, which has one electron less than Na$_{58}$, also possesses stronger short--bond network compared with Na$_{55}$, resulting in higher melting temperature (350 K) than observed in Na$_{55}$. Thus, we conclude that when a cluster has nearly closed shell structure not only geometrically but also electronically, it show a high melting temperature. Our calculations clearly bring out the size--sensitive nature of the specific heat curve in sodium clusters.