Nanoclusters and Nanoalloys of Group 13 elements B, Al, and Ga: Benchmark, structure, and property analysis

We present a benchmark study considering AEPA16 dataset comprising atomization energy for boron group clusters. This dataset covers 46 different methods from the different range of density functionals and post HF, where MRACPF is considered as the reference. The performance of basis set is analyzed by comparing the atomization energy with the CCSD(T)\CBS results. None of the GGA and meta-GGA are accurate and the popular PBE shows maximum error among the all methods, whereas B3LYP has moderate performance. M06 and RSHX DFAs have good performance among all the DFAs. NEVPT2 is the most accurate among all the methods considered followed by coupled cluster methods, i.e., CCSD(T) and DLPNO-CCSD(T), indicating the importance of perturbative correction. All the basis with M06 show promising results (absolute error \textless 1 \kmol) with respect to the CCSD(T)\CBS. From the cost -- accuracy investigation, def2-SVP is recommended in our study as it is the fastest. Hence, we have recommended M06/def2-SVP for boron group clusters. Furthermore, we have explored the structural progress of global and local minima of pure, binary, and ternary of boron group clusters up to size 12. One characteristic feature is that Ga clusters have more rectangular faces, whereas B and Al clusters have mostly trigonal units in pure cluster's form. We have got core-shell like structures, where, B makes core structure with both the Al and Ga atoms; however, Ga favors the outer position in the binary clusters. This behavior confirms the higher cohesive nature of B as compared to the Al and Ga atoms. The most favorable cluster is obtained with the maximum cluster size (12) with the equal composition of Al and Ga atoms for binary clusters. From the BE and ME of ternary clusters, we have obtained 16.67-40% B, 16.67-60% Al, and 20-50% Ga composition are favorable for the relatively stable ternary clusters as it shows negative ME.