The mechanisms including spin‐inversion have been systematically studied for the M+ + OCS → MS+ + CO/MO+ + CS (M denotes a transition metal from Sc to Cu) ion‐molecule reactions using the automated reaction path search method. We used the lowest mixed‐spin potential energy surface obtained from the diagonalization of the spin‐coupled Hamiltonian matrix, whose diagonal elements are taken to be the lowest two spin states. This scheme can effectively locate approximate minimum energy crossing points between the two potential energy surfaces with different spin multiplicities. The spin‐orbit couplings at spin‐inversion points have been calculated to understand the efficiencies of nonadiabatic transitions. The obtained reaction pathways and the calculated spin‐orbit couplings are employed to interpret previous experimental studies.

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Spin‐inversion mechanisms in O2 binding to a model heme complex, consisting of Fe(II)‐porphyrin and imidazole, were investigated using density‐functional theory calculations. First, we applied the recently proposed mixed‐spin Hamiltonian method to locate spin‐inversion structures between different total spin multiplicities. Nine spin‐inversion structures were successfully optimized for the singlet–triplet, singlet–quintet, triplet–quintet, and quintet–septet spin‐inversion processes. We found that the singlet–triplet spin‐inversion points are located around the potential energy surface region at short Fe–O distances, whereas the singlet–quintet and quintet–septet spin‐inversion points are located at longer Fe–O distances. This suggests that both narrow and broad crossing models play roles in O2 binding to the Fe‐porphyrin complex. To further understand spin‐inversion mechanisms, we performed on‐the‐fly Born‐Oppenheimer molecular dynamics calculations. The reaction coordinates, which are correlated to the spin‐inversion dynamics between different spin multiplicities, are also discussed.

β-Hydride elimination in Fe­(II)– and Co­(II)–alkyl complexes is known to occur through two different spin multiplicity states and is thus a good example of two-state reactivity. In this study, the automated reaction path search method combined with the mixed-spin effective Hamiltonian approach has been applied to understand the detailed reaction mechanisms including the characterization of the spin-inversion points between the high-spin and low-spin potential energy surfaces for the Fe­(II)–C2H5 and Co­(II)–C2H5 complexes supported by a β-diketiminate ligand. Density functional theory (DFT) with different exchange-correlation functionals has been used in the reaction path search calculations. We found that the β-hydride elimination process for these complexes consists of multiple steps including two spin-inversion points. We have also investigated the substituent effect in the β-diketiminate ligand to understand the steric and electronic effects on the spin-inversion process. The efficiency of the spin-inversion process has been discussed in terms of the calculated spin–orbit couplings between the high- and low-spin states.

Many chemical reactions of transition metal compounds involve a change in spin state via spin inversion, which is induced by relativistic spin-orbit coupling. In this work, we theoretically study the efficiency of a typical spin-inversion reaction, 3Fe(CO)4 + H2 → 1FeH2(CO)4. Structural and vibrational information on the spin-inversion point, obtained through the spin-coupled Hamiltonian approach, is used to construct three degree-of-freedom potential energy surfaces and to obtain singlet-triplet spin-orbit couplings. Using the developed spin-diabatic potential energy surfaces in reduced dimensions, we perform quantum nonadiabatic transition state wave packet calculations to obtain the cumulative reaction probability. The calculated cumulative reaction probability is found to be significantly larger than that estimated from the one-dimensional surface-hopping probability. This indicates the importance of both multidimensional and nuclear quantum effects in spin inversion for polyatomic chemical reaction systems.