We present a three-dimensional, fully parallelized, efficient implementation of ionizing ultraviolet (UV) radiation for smoothed particle hydrodynamics (sph) including self-gravity. Our method is based on the sph/tree code vine. We therefore call it iVINE (for Ionization + VINE). This approach allows detailed high-resolution studies of the effects of ionizing radiation from, for example, young massive stars on their turbulent parental molecular clouds. In this paper, we describe the concept and the numerical implementation of the radiative transfer for a plane-parallel geometry and we discuss several test cases demonstrating the efficiency and accuracy of the new method. As a first application, we study the radiatively driven implosion of marginally stable molecular clouds at various distances of a strong UV source and show that they are driven into gravitational collapse. The resulting cores are very compact and dense exactly as it is observed in clustered environments. Our simulations indicate that the time of triggered collapse depends on the distance of the core from the UV source. Clouds closer to the source collapse several 105 yr earlier than more distant clouds. This effect can explain the observed age spread in OB associations where stars closer to the source are found to be younger. We discuss possible uncertainties in the observational derivation of shock front velocities due to early stripping of protostellar envelopes by ionizing radiation.