Supporting Material MRCI investigation of Ni2O2 and Ni2O2

Figure S1 shows the energetic order of the different terms of Ni2O2 according to the MRCI calculations (without Davidson correction) that use the orbitals from the CASSCF calculations with the smaller active space (8 or 10 orbitals) at the Davidson corrected MRCI minimum structure of the Ag ground term. The other two terms that form the lowest-lying spin ladder together with the ground term are B1u and Ag at relative energies of 0.10 and 0.26 eV. With respect to the results that include the Davidson correction, there are only small differences. The relative energies (of the singlet terms) of the different spin ladders change by at most 0.07 eV, the inclusion of the Davidson correction increases the singlet quintet splitting by at most 0.05 eV. The occupation of the natural orbitals for selected terms by the CASSCF calculations is given in Tables S1 and S2. Taking as an example the terms of the lowest-lying spin ladder, it can be seen that the terms of different multiplicity of a given ladder have similar occupation patterns. The results with the larger active space that includes a part of the 2p orbitals of O indicate that the open shell domain in principle contains only the 3d orbitals. The occupation numbers of those active orbitals that are essentially oxygen 2p orbitals with minor contributions from the nickel 3d orbitals amount to values close to 2, between 1.97 and 1.99. Concerning the B1u term it is noticeabel that there are larger differences between the results with both active spaces. In this case, indeed the inclusion of the 2p orbitals has a larger effect. Table S3 contains the term energies, equilibrium distances and harmonic vibrational frequencies (of both totally symmetric modes) of the optimised structures of selected terms, using the CASSCF orbitals of the calculations with the smaller active space. The structure optimisations yield values for the term energies of the excited states that are lower by up to 0.06 eV than at the structure of the ground state. For the higher-lying terms of the lowest-energy spin ladder, B1u and Ag, the term energies amount to 0.11 and 0.28 eV including the Davidson correction. The structure determination yield values for Ni−Ni distances of the Ag ground term of 231.1 and 229.3 pm (without and with Davidson correction) and corresponding values for the O−O distance of 275.5 and 275.8 pm. Therefore, the values for the Ni−O distance amount to 178.8 and 179.3 pm (without and with Davidson correction). For all considered excited states the optimised structures are similar to that of the ground term. The Ni−Ni distances are elongated by at maximum 7 pm with respect to the ground state, the O−O distances by at maximum 3 pm. In case of the B3u term the O−O distance is shortened, namely by less than 1 pm. For the low-lying excited states B1u and Ag, the Ni−Ni distances amount to 231.0 and 233.3 pm with Davidson correction, and the O−O distances amount to 277.0 and 278.4 pm with Davidson correction. Hence, the step to a state of higher spin multiplicity comes along with a slight expansion of the structure. In general,