Quantum tunneling is an important phenomenon concerned by many researchers, especially in the double-hydrogen transfer system. Experimentally, tunneling splittings are important observables, which can provide hydrogen transfer dynamics information. Theoretically, many approximate methods have been developed for the classical tunneling process with a single barrier; however, quantum mechanical methods have to be adopted for the sequential double-hydrogen transfer process with two barriers. Recently, we develop a kind of quantum dynamical PBFC-PIST method, and write the parallel program suite applicable for any tetra-atom system. PBFC-PIST not only has high computational efficiency, but also bears excellent parallel efficiency, which has been successfully applied to the exact quantum mechanical calculations of mode-specific tunneling splittings in the vinylidene-acetylene isomerization system.