Molecular oxygen tetramer: multiplet structure and global minima

In this study we apply a general treatment for calculating the interaction potential of all possible multiplet states in a given molecular oxygen cluster based on the uncoupled spin representation and a pairwise additive approximation to analyze the case of the tetramer. For the pair potentials we use accurate analytic potentials based on high quality ab initio calculations of the dimer. We concentrate on the global minima of the lowest state for a given spin: S = 0, 1, 2, 3, 4. For S = 0, 1 the structure resembles the unit cell found in the epsilon phase of the solid at high pressures (with longer distances) whereas for most of the higher spins it contains a structure similar to the most stable for a trimer and the fourth molecule adjusts around it. The septet presents a unique configuration in which the trimer configuration is strongly perturbed. The multiplet states are very close in energy and their stability decreases with increasing spin whereas the zero-point energies increase with decreasing spin state, bringing the states closer together. We predict a singlet ground state with quasi-degenerate triplet and quintet states.