Spin-Forbidden Transitions between Electronic States in the Active Site of Rubredoxin

Rubredoxin is a small iron-sulfur protein involved in biological electron transfer, which is accomplished by changing the oxidation state of the iron atom in the active site. We investigate the possibility of spin-forbidden transitions between the lowest energy electronic states with different spin multiplicities in the rubredoxin active site models [Fe(SCH₃)₄]ⁿ (n = 2-, 1-, 0) using nonadiabatic transition state theory (NA-TST). The equilibrium structures, minimum energy crossing point structures and Hessians were obtained with density functional theory. The spin-orbit coupling (SOC) was calculated with the complete active space configuration interaction method using the two-electron spin-orbit Breit-Pauli Hamiltonian. We found several crossings between the lowest energy spin states associated with the changes in Fe coordination. However, only triplet/quintet crossings in [Fe(SCH₃)₄]^2- and [Fe(SCH₃)₄]⁰, as well as a quartet/sextet crossing in [Fe(SCH₃)₄]^- are characterized by nonzero first-order SOC responsible for transitions between these spin states. The rates of spin-forbidden transitions in the [Fe(SCH₃)₄]^2- complex are 1 and 2 orders of magnitude higher than the rates in the [Fe(SCH₃)₄]^- and [Fe(SCH₃)₄]⁰ complexes, respectively. These rate differences are related to a large variation of the SOC between the complexes with different charges, which in turn comes from different molecular orbitals involved in the spin-flip transitions. Finally, we demonstrate that the differences between the NA-TST rates and the rates calculated under the assumption of completely spin-allowed transitions could be as large as 4 orders of magnitude. This means that even in qualitative discussions of the reaction mechanisms involving changes in spin states the partially spin-forbidden nature of the transitions between these states must be taken into account.