Review of multicomponent molecular orbital method for direct treatment of nuclear quantum effect

We present the methodology and applications of multicomponent molecular orbital (MC_MO) method, which can take into account of the quantum effect of light particles, such as proton and deuteron, directly. We summarize the equations of the MC_MO method at the Hartree–Fock (HF) level and beyond the HF. The methodology of the MC_MO with fragment molecular orbital (FMO) method for large molecular systems is also described. We discuss the development of nuclear basis function based on the GTF, which is used in MC_MO and FMO‐MC_MO calculations. We present the applications of MC_MO and FMO‐MC_MO method for the analysis of geometrical isotope effect and kinetic isotope effect induced by H/D isotope effect.