The procedure of the quantum/classical mixed approach to the computation of vibrational spectra of complex molecular systems can be divided into two parts. This chapter describes the first part, construction of vibrational Hamiltonian. In the quantum/classical mixed approach, the translation and rotation of molecules are treated by classical mechanics through classical molecular dynamics (MD) simulations. The vibration of molecules is treated quantum-mechanically with vibrational Hamiltonian constructed at each time step along MD trajectories according to vibrational spectroscopic maps that are a set of parameters and expressions. In this chapter, we will learn what the vibrational spectroscopic maps are and how to construct the vibrational Hamiltonian by using them.