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

## TL;DR

This study uses first-principles calculations to explore the stability, electronic properties, and evolution of various Ti$_n$O$_m$ clusters, revealing stable species and tunable energy gaps relevant to cluster-to-bulk transition.

## Contribution

It introduces a comprehensive analysis of Ti$_n$O$_m$ clusters with varying compositions, extending beyond the commonly studied TiO$_2$ clusters, and identifies stable species and electronic properties.

## Key findings

- Identification of stable Ti$_n$O$_m$ species for different n ranges
- Demonstration of tunable HOMO-LUMO gaps based on size and configuration
- Insights into cluster evolution towards bulk titanium oxide

## Abstract

Most theoretical investigations about titanium oxide clusters focus on (TiO$_2$)$_n$. However, many Ti$_n$O$_m$ clusters with $m\neq 2n$ 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.

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Source: https://tomesphere.com/paper/1906.05354