Generalized valence bond studies of metallic bonding: Naked clusters and applications to bulk metals

Using the generalized valence bond (GVB) method, we have examined the bonding in numerous small clusters of Li atoms (Li_n and Li_n⁺, n ≤ 13). Our conclusion is that the optimum bonding involves interstitially localized singly occupied orbitals, e.g., (1) bond-centered orbitals for one-dimensional clusters (e.g., rings such as Li₄, Li₆, Li₈, and Li₁₀ and linear chains such as Li₃⁺, Cu₃⁺, Li₈⁺, Li₈, Li₈^-, and Li₁₃⁺), (2) equilateral-triangle-centered orbitals for planar close-packed clusters (e.g., Li₁₀, Li₁₂⁴⁺, and Li₁₃⁺), and (3) tetrahedron-centered orbitals for three-dimensional clusters (examples here include three high-symmetry [icosahedral (I_h), face-centered cubic (fcc), and hexagonal close-packed (hcp)] Li₁₃⁺ structures and three low symmetry [γ-brass-like] Li₁₃⁺ structures. Of the three high symmetry Li₁₃⁺ clusters, I_h has the lowest energy while total energies for fcc and hcp are 0.26 and 0.56 eV higher, respectively. GVB wave functions for these three clusters suggest a set of rules predicting structures even more stable than the icosahedron. These lower energy structures [denoted as OPTET (optimum tetrahedral)] maximize the number of tetrahedra under the restrictions of the rules (e.g. minimizing the number of occupied tetrahedra sharing corners) and lead to relatively low symmetry, e.g. C_2v, C_s. These OPTET clusters coincide with truncations of the γ-brass structure. The lowest energy Li₁₃⁺ OPTET cluster [γ-(4,4,5), C_2v] has a total energy 0.58 eV lower than that of the icosahedron. Suggestions are given on the relevance of these results for stability and reactivity of small clusters and on the extension of these ideas to infinite systems.