Hamiltonian of theV15Spin System from First-Principles Density-Functional Calculations

We report first-principles all-electron density-functional-based studies of the electronic structure, magnetic ordering, and anisotropy for the ${\mathrm{V}}_{15}$ molecular magnet. From these calculations, we determine a Heisenberg Hamiltonian with five antiferromagnetic and one ferromagnetic exchange couplings. We perform direct diagonalization to determine the temperature dependence of the susceptibility. This Hamiltonian reproduces the experimentally observed spin $S=1/2\mathrm{}$ ground state and low-lying $S=3/2\mathrm{}$ excited state. A small anisotropy term is necessary to account for the temperature independent part of the magnetization curve.