**4. Conclusions**

We computed the Boltzmann population of anionic Be6B11 and neutral Be4B8 cluster at the SP CCSDT and DFT levels of theory. If one increases the system's temperature, entropic effects start to play an important role, and Gibbs free energy is minimized, and entropy is maximized. The fluxionality of the Be6B11 cluster is strongly dependent on temperature that is shown by its Boltzmann population. At the CCSDT level of theory, the Boltzmann population of the Be6B11 cluster indicate there are four competing structures, so a mixture of isomers co-exist at a specific temperature, so we expect that around a temperature of 350 K, four structures could be observed. The observed properties in a molecule are statistical averages over the ensemble of isomers. The molecular properties at cold temperatures are due to the lowest energy structure Be6B11 at CCSD(T) level of theory and zero temperature whereas at hot temperatures, the molecular properties are due to the coaxial Triple-Layered structure with C1 symmetry. At room temperature the molecular properties are due to a mixture of spectra of the three systems that coexist at 350 K. Regarding Be4B8 cluster, all molecular properties at cold and room temperatures are dominated by pair of enantiomers putative global minima. The computed Boltzmann populations at PBE0-D3/def2-TZVP level of theory is similar at the computed Boltzmann populations at CCSDT/def2-TZVP level of theory, so at the DFT level, the Boltzmann populations, hence the molecular properties are well calculated. As future work, the inclusion of anharmonic effects should be taken into account.

## **Acknowledgements**

C.E.B.-G. thanks Conacyt for a scholarship (860052). E.P.-S. thanks Conacyt for a scholarship (1008864). We are grateful to Dr. Carmen Heras, and L.C.C. Daniel Mendoza for granting us access to their clusters and computational support. Computational resources for this work were provided through the High-Performance Computing Area of the University of Sonora. We are also grateful to the computational chemistry laboratory for providing computational resources, ELBAKYAN, and PAKAL supercomputers.

### **Conflict of interest**

The authors declare no conflict of interest.

*Boltzmann Populations of the Fluxional Be6B11 and Chiral Be4B8 Clusters at Finite… DOI: http://dx.doi.org/10.5772/intechopen.100771*
