We report first principles investigation of time-dependent current of molecular devices under a step-like pulse. Our results show that although the switch-on time of the molecular device is comparable to the transit time, much longer time is needed to reach the steady state. In reaching the steady state the current is dominated by resonant states below Fermi level. The contribution of each resonant state to the current shows the damped oscillatory behavior with frequency equal to the bias of the step-like pulse and decay rate determined by the life time of the corresponding resonant state. We found that all the resonant states below Fermi level have to be included for accurate results. This indicates that going beyond wideband limit is essential for a quantitative analysis of transient dynamics of molecular devices. PACS numbers: 71.15.Mb, 72.30.+q, Anticipating a variety of technological applications, molecular scale conductors and devices are the subject of increasingly more research in recently years. One of the most important issues of molecular electronics concerns the dynamic response of molecular devices to external parameters 1,2,3,4,5,6,7 . For ac quantum transport in such small devices, atomic details and non-equilibrium physics must be taken into account. So, in principle, one should use the theory of non-equilibrium Green's function (NEGF) 8 coupled with the time-dependent density functional theory (TDDFT) 9 to study the time-dependent transport of molecular devices. Practically, it is very difficult to implement it at present stage due to the huge computational cost. One possible way to overcome this problem is to use the adiabatic approximation, an approach widely used in mesoscopic physics. In this approach, one starts from a steady-state Hamiltonian and adds the time dependent electric field adiabatically. This is a reasonable approximation since most of the time the applied electric field is much smaller than the electrostatic field inside the scattering region. In addition, it has been shown numerically 6 that dc transport properties such as I-V curve obtained from the equation of motion method coupled with TDDFT agrees with that obtained by the method of NEGF coupled with the density functional theory (DFT) 10,11 . Hence, under the adiabatic approximation, one could replace TDDFT by DFT and use the NEGF+DFT scheme to calculate ac transport properties of molecular devices. We consider a system that consists of a scattering region coupled to two leads with the external time dependent pulse bias potential v α (t). The time-dependent current for a step-like pulse has been derived exactly going beyond the wide-band limit by Maciejko et al 4 . Since the general expression for the current involves triple integrations, it is extremely difficult if not impossible to calculate the time-dependent current for real systems like molecular devices. In this regard, approximation has to be made in order to carry out time-dependent simulations of molecular devices. We note that the simplest approximation is the ...