Quantum mechanical effects on nuclear motion play an important role in characterizing structure, dynamic and vibrational properties in condensed phase and molecular systems. Exact quantum treatments of these effects can be applied to systems having only a few degrees of freedom. Nonetheless, some advances have taken place in incorporating quantum nuclear effects, in an approximate way, into standard molecular dynamics simulations over the past decade. In this talk, I will give an overall description of these methods starting from semi-classical approach, passing through Langevin thermostats with colored noise technique and ending up with path- integral molecular dynamics. All of these methods will be examined in detail by simulating IR spectra of various isolated molecules (i.e. trans HONO isomer, phenol, some polycyclic hydrocarbons). Theses results will be compared with second-order perturbation method and with exact quantum calculations when available. The combination of semi-classical approach with quantum electronic Density Functional Theory is also investigated. The application of these methods in condensed phase such as water liquid and ionic liquids will be also discussed.

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