Multistate Transition Metal Carbonyl Bonding Beyond Minimum Energy Pathway: Nonlocality of Spin-Orbit Interaction

Transition metal carbonyl and transition metal dinitrogen are fundamental chemical complexes in many important biological and catalytic processes. Interestingly, binding between a transition metal (TM) atom and carbonyl or dinitrogen results in spin state change. However, no study has evaluated the spin-orbit (SO) effect along the association pathway of any TM-CO or TM-N₂ bond. Using multireference calculations with SO interaction, we calculated the association potential energy curve for 11 electronic states for the spin crossover reactions: Ni + CO → NiCO and Ni + N₂ → NiN₂. Through this multistate calculation, we found that the commonly used minimum energy pathway (MEP) gives reasonable energies for the asymptotes but has an incorrect physical picture in the intermediate bond length. MEP assumes strong SO at the energy crossing point that allows for direct spin crossover from the triplet to singlet state, but multireference calculations showed that SO interactions strengthen at bond length regions, 2.3-2.5 Å before the crossing point. Furthermore, this results in a spin barrier of 0.15 eV along the Ni adsorbate association pathway. These calculations provide a new understanding of the overlooked yet important effect of the spin barrier on the association process, which can change the association rate by several orders of magnitude.