Structure and properties of (AlB2)n and (MgB2)n (n = 1, …, 10) clusters

Toward size-dependent thermodynamics of nanoparticles from quantum chemical calculations of small atomic clusters: a case study of (B2O3)n

“…14,92 Therefore, as the size of the structures under analysis grows, the use of multistage hierarchical approaches comprising sequential optimization steps both at low and at high levels of treatment seems increasingly reasonable. 14,32,43,61,91…”

“…In the present study, as one such approach for the systematic search of global minima on the PESs related to (B 2 O 3 ) n clusters, the special heuristic algorithm, 61 which involves semiempirical methods, local spin-density and hybrid DFT functionals, was applied. For the finishing optimization of the lowest energy structures, we employed the B97-3 DFT functional 93 – a 2005 reparametrized version of Becke's B97 hybrid exchange–correlation functional.…”

“…For the finishing optimization of the lowest energy structures, we employed the B97-3 DFT functional 93 – a 2005 reparametrized version of Becke's B97 hybrid exchange–correlation functional. 94 In doing so, the global minima candidate structures resulting from the multistep hierarchical GO procedure 61 were optimized followed by vibrational frequency calculations at the spin unrestricted UB97-3/aug-cc-pVDZ level of theory. At the terminal stage, the lowest-lying energy forms of (B 2 O 3 ) n clusters selected allowing for the zero-point energy (ZPE) correction E ZP obtained using the UB97-3/aug-cc-pVDZ DFT model as well were assigned for final reoptimization at the higher UB97-3/aug-cc-pVTZ computational level.…”

“…Note that the choice of the B97-3 functional 93 for the finishing optimization of a structure is motivated by the fact that the B97- n family of DFT functionals, even when employing a moderate basis set (such as the correlation consistent double-zeta basis set with diffuse functions aug-cc-pVDZ 97 ), proved to be exceptionally successful (at least, as compared with other widespread DFT implementations) in describing the energetics of atomic clusters containing boron atoms. 14,58,60,61,98,99 Meanwhile, this DFT functional proved to be particularly accurate for the B–O atomic system as well. This is clearly seen from Table 1, which depicts the atomization energies E at for BO and B 2 O 3 species (ground electronic states are doublet and singlet, respectively 100 ) calculated using the B97-3 functional with the Dunning's correlation consistent basis sets of different size together with these obtained employing composite CBS-Q, 101 CBS-QB3, 102 G3MP2, 103 G4MP2 104 techniques and high-level CCSD(T) and MRCI ab initio approaches.…”

“…With the improvements of the computational methods of quantum chemistry and the power of the hardware, it has become straightforward to accurately determine the gas-phase thermochemistry (the canonical partition function, enthalpy of formation, Gibbs free energy, specific heat capacity) for relatively small atomic clusters from routine electronic structure calculations (see, for example, ref. 14, 30, 34, 43, 54 and 57–61). However, it has remained challenging to theoretically describe clusters and nanoparticles of larger size, mainly due to the nonlinear growth in computational cost required to precisely determine electronic energy and the set of vibrational frequencies (even within the HO framework) with the number of atoms in the system.…”