Binding between endohedral Na atoms in Si clathrate I; a first principles study

TL;DR

This study uses first-principles calculations to analyze the bonding nature of sodium atoms inside Si clathrate I, revealing ionic and covalent interactions that influence stability and occupancy.

Contribution

It provides a detailed first-principles analysis of the ionic and covalent bonding mechanisms of endohedral Na atoms in Si clathrate I, highlighting their stability preferences.

Findings

Na atoms lose 30% of their charge to the cage

Na atoms in Si$_{24}$ cages form more stable configurations

Covalent bonds explain occupancy preferences and displacement parameters

Abstract

We investigate the binding nature of the endohedral sodium atoms with the ensity functional theory methods, presuming that the clathrate I consists of a sheaf of one-dimensional connections of Na@Si$_{24}$ cages interleaved in three perpendicular directions. Each sodium atom loses 30% of the 3s$^1$ charge to the frame, forming an ionic bond with the cage atoms; the rest of the electron contributes to the covalent bond between the nearest Na atoms. The presumption is proved to be valid; the configuration of the two Na atoms in the nearest Si$_{24}$ cages is more stable by 0.189 eV than that in the Si$_{20}$ and Si$_{24}$ cages. The energy of the beads of the two distorted Na atoms is more stable by 0.104 eV than that of the two infinitely separated Na atoms. The covalent bond explains both the preferential occupancies in the Si$_{24}$ cages and the low anisotropic displacement parameters of the endohedral atoms in the Si$_{24}$ cages in the [100] directions of the clathrate I.