**3.4 Boltzmann population of Be4B8 clusters**

As we mentioned earlier, the determination of the structure is the first step to study any property of a material. Moreover, we have to consider that an observed molecular property in a Boltzmann ensemble is a weighted sum of all individual contributions of each isomer that form the ensemble. At temperature 0 K, the electronic energy plus zero-point energy determine the putative global minimum and all nearby low-energy structures, whereas, at temperatures larger than 0 K, the Gibbs free energy defines the putative global minimum. **Figure 4a** shows the probability of occurrence computed at PBE0-D3/def2-TZVP level of theory for each particular chiral and achiral Be4B8 isomers for temperatures ranging from 20 to 1900 K. **Figure 4b** shows the probability of occurrence computed at CCSD(T) level of theory. Notice, there is not a significant difference in the probabilities of occurrence between the two panels, thus the computation of probabilities at DFT level of theory is very similar to those computed at CCSDT level of theory. A closer examination of the panel (b) shown that in the temperature ranging from 20 to 300 K, all molecular properties are dominated by the chiral structure depicted in **Figure 3a** because its probability of occurrence is almost constant. We point out that in this range of temperature, the C1, C2, and D2 symmetries strongly dominate with different probabilities of occurrence of 28, 14 y 7% respectively. At this point, there is

#### **Figure 4.**

*Panel (a) shows the probability of occurrence for temperatures ranging from 20 to 1900 K at the PBE0-D3/ def2-TZVP level of theory. Panel (b) shows the probability of occurrence for temperatures ranging from 20 to 1900 K at the CCSDT/def2-TZVP level of theory. In panel (a), the transition solid–solid point (Tss1-g) is located at 739 K with 16.6% of probability, while in panel (b) the Tss1-g is located at 780 K with 15% probability.*

a co-existence of chiral structures and achiral structures, shown in **Figure 3**, above this point the achiral structure (**Figure 3g**) becomes dominant. The second transformation solid–solid point located at 1017 K and 10% of probability also coexist the chiral putative global minimum with symmetry C1 and achiral structure (**Figure 3h**) located at 2.51 kcal/mol CCSDT energy at above the putative global minimum. The Boltzmann population computed at PBE0-D3/def2-TZVP level of theory follows the trend of the Boltzamnn population computed at CCSD(T) level of theory.
