| Summary: | 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, <sup>3</sup>Fe(CO)<sub>4</sub> + H<sub>2</sub> → <sup>1</sup>FeH<sub>2</sub>(CO)<sub>4</sub>. 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.
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