Hybrid quantum and classical simulations of the formate dehydrogenase catalyzed hydride transfer reaction on an accurate semiempirical potential energy surface

Formate dehydrogenase (FDH) catalyzes the oxidation of formic acid to carbon dioxide using nicotinamide adenine dinucleotide (NAD ⁺) as a cofactor. In the current work we present extensive benchmark calculations for several model reactions in the gas phase that are relevant to the FDH catalyzed hydride transfer. To this end we employ G4MP2 and CBS-QB3 ab initio calculations as well as density functional theory methods. Using these results we develop a specific reaction parameter (SRP) Hamiltonian based on the semiempirical AM1 method. The SRP semiempirical Hamiltonian is subsequently used in hybrid quantum mechanics/molecular mechanics simulations of the FDH catalyzed reaction in Pseudomonas sp. 101 (PseFDH). The classical potential of mean force (PMF) is computed as a function of structural progress coordinates during the course of the hydride transfer reaction: The antisymmetric reactive stretch, the donor-acceptor distance, and an orbital rehybridization coordinate. The quantum PMF is computed using a centroid Feynman path-integral (PI) approach. Subsequently, kinetic isotope effects are computed using a mass-perturbation based PI method. Finally, the antisymmetric stretch vibrational frequency is computed for an azide ion in FDH and in aqueous solution.