The Ratio Law of the Structure Evolution and Stability for Ti${}_n$O${}_m$ ($n=3$-$18$, $m=1$-$2n$) Clusters

Abstract

Most theoretical investigations about titanium oxide clusters focus on (TiO${}_2$)${}_n$. However, many Ti${}_n$O${}_m$ clusters with $m\ne 2n$ are produced experimentally. In this work, first-principles calculations are performed to probe the evolution of Ti${}_n$O${}_m$ clusters. Our investigations show that for $n=3$-$11$, there exist one relatively stable specie; while for $n=12$-$18$, there are two relatively stable species: Ti-rich and O-rich species. HOMO-LOMO calculations show that the gap can be tuned by changing the size and configurations of Ti${}_n$O${}_m$ clusters. Our investigation provides insights into the evolution of cluster-to-bulk process in titanium oxide.