Evolution of atomic and electronic structure of Pt clusters: Planar, layered, pyramidal, cage, cubic, and octahedral growth

Abstract

Ab initio calculations on Pt clusters having diameters of up to about 3 nm show planar, layered, pyramidal, cage, simple cubic, and octahedral growth. Planar structures are preferred up to ${\text{Pt}}_{9}$, while layered and pyramidal structures are favored in the range of ${\text{Pt}}_{n}$, where $n=10--20$. In some cases, simple cubic and octahedral isomers become competitive with layered growth, or they have the lowest energy. Between $n=21$ and 24, decahedral isomers are most favorable with a decahedral (empty center) cage for ${\text{Pt}}_{22}$. Around $n=24$, there is again a transition and simple cubic structures become most favorable up to around $n=38$. Beyond this size, our results suggest octahedral isomers to be most favorable among the different growth modes explored by us, such as simple cubic, cuboctahedral, decahedral, and icosahedral. To our knowledge, platinum clusters are the first example of transition metal clusters that grow in bulk structure from a relatively small size range of $n\ensuremath{\sim}40$ and for which a transition to commonly found closed packed icosahedral growth is unlikely. We find that a triangular isomer of ${\text{Pt}}_{6}$ and a square planar isomer of ${\text{Pt}}_{9}$ play the key role in the growth behavior and the formation of magic clusters of Pt that are rich in such triangular and/or square faces. Our results show that clusters with $n=6$, 9, 10, 14, 18, 22, 27, and 36 with complete atomic shells are magic and are relatively more stable. In most cases, the clusters are weakly ferromagnetic. However, in some cases, a mixed ferromagnetic-antiferromagnetic coupling is obtained, such as that for ${\text{Pt}}_{6}$. The magnetic moments decrease with an oscillatory behavior as the size increases. The electronic structure of large octahedral clusters with $n\ensuremath{\sim}200$ having (111) type faces develops similarity to bulk Pt (111) surface, but significant deviations exist that could lead to their different and size dependent behavior for reactions.