Low-lying electronic states of Rh 4 with different geometries are considered using the complete active space multiconfiguration self consistent field method (CASSCF) followed by large scale multi-reference singles + doubles configuration interaction (MRSDCI) computations that included up to 2.1 million configurations. Two nearly degenerate electronic states, namely, 1 A 1 (T d ) with a tetrahedron, 1 A 1 g (D 4 h ) with a rhombus geometries were found as candidates for the ground state of Rh 4 , although the tetrahedral geometry is favored. The ionization potential and dissociation energies are computed.