The valence electron binding energies of the atomic clusters \(\hbox {XAl}_3^-\) (X = Si, Ge, and Sn) and \(\hbox {YAl}_4^-\) (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.

原子团簇\（\ hbox {XAl} _3 ^-\）（X = Si，Ge和Sn）和\（\ hbox {YAl} _4 ^-\）的价电子结合能（Y = Li，Na和Cu）是使用固定节点扩散量子蒙特卡罗方法（FN-DMC），密度泛函理论和Hartree-Fock近似方法进行研究的。简要回顾了使用的理论方法，重点介绍了变分和扩散蒙特卡罗技术及其在研究原子团簇电子结构中的应用。从FN-DMC获得的垂直分离能（VDE）的结果与现有的实验电子光谱数据非常吻合。FN-DMC结果和HF-DMC结果之间的比较可以量化电子相关效应及其对簇稳定性的影响。