Quantum Monte Carlo simulation for the many-body decomposition of the interaction energy and electron correlation of small superalkali lithium clusters

Using the fixed-node diffusion Monte Carlo (FN-DMC) method, we calculate the total energy of small lithium clusters Li-n (n = 2-6) to obtain the many-body decomposition of the interaction energy of 2- up to 6-body interactions. The obtained many-body decomposition of the interaction energy shows an alternating series with even and odd terms of attractive and repulsive contributions, respectively. The two-body attractive interactions guarantee the stability of the Li-2, Li-3, and Li-4 clusters. For larger clusters Li-5 and Li-6, the 4-body attractive interactions are required for their stabilization once the strength of the 3-body repulsive interactions overwhelms that of the 2-body attractive ones. With increasing the cluster size, the additive and nonadditive contributions to the interaction energy increase linearly in magnitude but with different slopes for the two-dimensional (2D) planar and three-dimensional (3D) cagelike clusters. The significant increment in nonadditive effects from the 4-atom to the 5-atom cluster has driven the structural transition from 2D to 3D. Combining the FN-DMC calculations with the Hartree-Fock many-body decomposition of the interaction energy, we extract the correlation effects, showing that an odd-even competition pattern in the many-body repulsive and attractive interactions is crucial for the stabilization of the clusters.