CASSCF, RASSCF, CASPT2, RASPT2 and MC-PDFT calculations were used to compute spin-state energies. The MC-PDFT calculations used the translated PBE (tPBE) functionals and an ultrafine quadrature grid; these calculations are referred to as CAS-tPBE or RAS-tPBE, depending on the reference wave function (and functional) used. For the CASPT2 and RASPT2 calculations, a default IPEA shift of 0.25 a.u. and an imaginary shift of 0.3 a.u. were used. The resolution-ofthe-identity/Cholesky decomposition (RICD) approximation was used to reduce the cost of two-electron integral calculations. For the multireference calculations, the basis set was def2-TZVP, except for H atoms, for which def2-SVP was used. The RASSCF, RAS-tPBE, and RASPT2 calculations used a (16e,16o) active space consisting of the two Cr(II) 3d shells, two occupied orbitals from each of the C5Me5 ligands, and two unoccupied orbitals from the bridging P5 ligand. The latter were found to mix strongly with two Cr 3d orbitals indicative of covalent bonding between the Cr atoms and the P5 ring (cf. Figure ). The RAS2 subspace was therefore taken as these two pairs of Cr-P5-Cr bonding/antibonding orbitals along with four singly occupied Cr 3d orbitals, for an overall subspace of (8e,8o). The RAS1 and RAS3 subspaces consisted respectively of the bonding and antibonding xz and yz orbitals from the C5Me5 ligands and the remaining Cr 3d orbitals, with up to two holes in RAS1 and up to two electrons occupying RAS3 (See Section 3 and Figure below). We also performed CASSCF(8e,8o) and corresponding CAS-tPBE and CASPT2 calculations in which the RAS1 and RAS3 subspaces from the above-described (16e,16o) active space were omitted.