Stable Structures and NMR Analysis of (Na)<i>_n </i>with pore size in hard carbon by DFT calculations

The lithium ion batteries (LIB) which are a typical secondary batteries, is widely used as an energy storage system by having high voltage, good charge and discharge cycles. However, due to problems with the resources and costs of lithium in LIB, there is a growing interest in resource-rich sodium-ion batteries (NIB) with equivalent electrode potential. In recent years, a NIB using a Na metal oxide as the positive electrode and hard carbon (HC) as the negative electrode has attracted attention in particular. To develop a NIB with high capacity, high efficiency, long life, and acceptable safety, it is essential to elucidate the state of the sodium ion and the mechanism of charge and discharge on the electrode. The states of sodium electrochemically inserted in HC samples have been experimentally reported using solid 23Na NMR. In this study, in order to study the correlation of NMR shift of Na clusters (n = 1-8) with pore size in HC and structure, DFT calculations are performed at B3LYP/6-31G(d) level using the Gaussian 16. From NMR analysis it can be seen that the value of chemical shielding shifts significantly depending on the strength of bonding between Na atoms and the size of clusters.