Abstract The vertical spectrum for the low-lying excited states of the Li 4 cluster in its optimal rhombic geometry has been determined by a large-scale direct CI procedure. The energy of the lowest triplet state has also been computed by allowing for full nuclear relaxation. The optimum geometry is found to be a distorted tetrahedron. The atomization potential curves for the ground and several excited states have been determined. The nature of the wavefunctions for the excited states is discussed as well as the general role of p functions for bonding in alkali-metal clusters.