  We predict the structures of neutral gas-phase gold clusters ($Au_n$, $n$ =
5$-$13) at finite temperatures based on free-energy calculations obtained by
replica-exchange ab initio molecular dynamics. The structures of neutral
$Au_5$$-$$Au_{13}$ clusters are assigned at 100 K based on a comparison of
experimental far-infrared multiple photon dissociation spectra performed on
Kr-tagged gold clusters with theoretical anharmonic IR spectra and free-energy
calculations. The critical gold cluster size where the most stable isomer
changes from planar to nonplanar is $Au_{11}$ (capped-trigonal prism, $D_{3h}$)
at 100 K. However, at 300 K (i.e., room temperature), planar and nonplanar
isomers may coexist even for $Au_8$, $Au_9$, and $Au_{10}$ clusters.
Density-functional theory exchange-correlation functionals within the
generalized gradient or hybrid approximation must be corrected for long-range
van der Waals interactions to accurately predict relative gold cluster isomer
stabilities. Our work gives insight into the stable structures of gas-phase
gold clusters by highlighting the impact of temperature, and therefore the
importance of free-energy over total energy studies, and long-range van der
Waals interactions on gold cluster stability.
