LAUSR

The valence electron binding energies of the atomic clusters $$\hbox {XAl}_3^-$$ XAl 3 - (X = Si, Ge, and Sn) and $$\hbox {YAl}_4^-$$ YAl 4 - (Y = Li, Na, and Cu) are investigated using a combination of the fixed-node diffusion quantum Monte Carlo method (FN-DMC), the density functional theory, and the Hartree–Fock approximation. A brief review of the used theoretical approaches is presented with emphasis on the variational and diffusion Monte Carlo techniques and their applications to study the electronic structures of atomic clusters. The obtained results for the vertical detachment energies (VDE) from the FN-DMC are in excellent agreement with available experimental photoelectron spectroscopy data. A comparison between the FN-DMC results and HF ones allows to quantify the electron correlation effects and their impact on the stability of the clusters. The analysis reveals that the electron correlation enhances the VDE of the atomic clusters significantly and plays an essential role in their stability.