Creating Benchmarks\nfor Lithium Clusters and Using\nThem for Testing and Validation

Metal clusters often have a variety of possible structures,\nand\nthey are calculated by a wide range of methods; however, fully converged\nbenchmarks on the energy differences of structures and spin states\nthat could be used to test or validate these methods are rare or nonexistent.\nSmall lithium clusters are good candidates for such benchmarks to\ntest different methods against well-converged relative energetics\nfor qualitatively different structures because they have a small number\nof electrons. The present study provides fully converged benchmarks\nfor Li<sub>4</sub> and Li<sub>5</sub> clusters and uses them to test\na diverse group of approximation methods. To create a dataset of well-converged\nsingle-point energies for Li<sub>4</sub> and Li<sub>5</sub>, stationary\nstructures were optimized by Kohn–Sham density functional theory\n(KS-DFT) and then single-point energy calculations at these structures\nwere carried out by two quite different beyond-CCSD(T) methods. To\ntest other methods single-point energy calculations at these structures\nwere carried out by KS-DFT, Mo̷ller–Plesset (MP) theory,\ncoupled cluster (CC) theory, five composite methods (Gaussian-4, the\nWuhan–Minnesota (WM) composite method, and the W2X, W3X, and\nW3X-L composite methods of Radom and co-workers), multiconfiguration\npair-density functional theory (MC-PDFT), complete active space second-order\nperturbation theory (CASPT2), and <i>n</i>-electron valence\nstate second-order perturbation theory (NEVPT2). Our results show\nthat rhomboid and trigonal bipyramid (TBP) geometries are the most\nstable structures for Li<sub>4</sub> and Li<sub>5</sub>, respectively.\nUsing the W3X-L method to obtain our best estimates, the mean unsigned\ndeviations were calculated for other methods for several structures\nand spin states of both Li<sub>4</sub> and Li<sub>5</sub>. Binding\nenergies and <i>M</i> diagnostics were calculated for all\nstructures. The data in this paper are valuable for assessing the\nreliability of current electronic structure theories and also developing\nnew density functionals and machine learned models.