Relative abundances and enantiomerization energy of the chiral Cu$_{13}$ cluster at finite temperature

This study reports the lowest energy structure of bare Cu$_{13}$ nanoclusters as a pair of enantiomers for temperatures ranging from 20 to 1200 K. Moreover, we compute the enantiomerization energy for the interconversion from $mathcal{M}$ to $mathcal{P}$ structures in the chiral putative global minimum for temperatures ranging from 20 to 1300 K. Additionally, employing statistical thermodynamics and nanothermodynamics, we compute the Boltzmann Probability for each particular isomer as a function of temperature. To achieve that, we explore the free energy surface of the Cu$_{13}$ cluster, employing a genetic algorithm coupled with density functional theory and statistical thermodynamics. Moreover, we discuss the energetic ordering of structures computed at the DFT level and compared to high level DLPNO-CCSD(T1) reference energies, and we present chemical bonding analysis using the AdNDP method in the chiral putative global minimum. Based on the computed relative abundances, our results show that the chiral putative global minimum strongly dominates for temperatures ranging from 20 to 1100 K.