Density-functional calculation for K lattices in condensed phase and quantum-chemical model for the cohesive energy of heavy alkali metals

Following a summary of deductions from experiment on the bonding of Rb and Cs in very different liquid and solid environments, energy calculations based on density-functional theory (DFT) are presented on ordered chains of K as a function of nearest-neighbor distances. At a given bond length, and sufficiently low density, a regime occurs in which modest zig-zag behavior is found to stabilize the original linear chains. As for Rb and Cs, we conclude that K may exhibit low coordination in highly expanded forms. The previous ab initio results on lattices of K atoms for coordination numbers $z=$ 8, 4, and 2 are analyzed by means of a quantum-chemical model in which a nearest-neighbor Heisenberg Hamiltonian is characterized by free-space ${\mathrm{K}}_2$ dimer potential energy curves. The satisfactory accord between the two different treatments has prompted us to present results also for Rb and Cs lattices for five different coordination numbers for which DFT calculations are not currently available. The relevance to experiments on expanded fluid Cs and to zig-zag chains of Cs on semiconductor substrates is briefly referred to.