Creating Benchmarks for Lithium Clusters and Using Them for Testing and Validation

Metal clusters often have a variety of possible structures, and they are calculated by a wide range of methods; however, fully converged benchmarks on the energy differences of structures and spin states that could be used to test or validate these methods are rare or nonexistent. Small lithium clusters are good candidates for such benchmarks to test different methods against well-converged relative energetics for qualitatively different structures because they have a small number of electrons. The present study provides fully converged benchmarks for Li₄ and Li₅ clusters and uses them to test a diverse group of approximation methods. To create a dataset of well-converged single-point energies for Li₄ and Li₅, stationary structures were optimized by Kohn-Sham density functional theory (KS-DFT) and then single-point energy calculations at these structures were carried out by two quite different beyond-CCSD(T) methods. To test other methods single-point energy calculations at these structures were carried out by KS-DFT, Mo̷ller-Plesset (MP) theory, coupled cluster (CC) theory, five composite methods (Gaussian-4, the Wuhan-Minnesota (WM) composite method, and the W2X, W3X, and W3X-L composite methods of Radom and co-workers), multiconfiguration pair-density functional theory (MC-PDFT), complete active space second-order perturbation theory (CASPT2), and n-electron valence state second-order perturbation theory (NEVPT2). Our results show that rhomboid and trigonal bipyramid (TBP) geometries are the most stable structures for Li₄ and Li₅, respectively. Using the W3X-L method to obtain our best estimates, the mean unsigned deviations were calculated for other methods for several structures and spin states of both Li₄ and Li₅. Binding energies and M diagnostics were calculated for all structures. The data in this paper are valuable for assessing the reliability of current electronic structure theories and also developing new density functionals and machine learned models.