In this paper we study the first application of adiabatic passage by light-induced potentials in polyatomic molecules. We analyze the effects of increasing the dimensionality of the system on the adiabatic requirements of the method and the role of intramolecular coupling among the vibrational modes. By using a model of two-dimensional displaced harmonic oscillators with or without rotation of the normal mode axis of the excited states (Duschinsky effect) we find that (1) it is possible to selectively transfer the vibrational population by adiabatic elongation of the bonds, (2) the adiabatic demands depend mainly on the energy barrier between the ground and excited electronic configurations, and not on the dimension of the system, (3) in the presence of intramolecular couplings the selective transfer can be achieved but at the cost of increasing the duration and/or the intensity of the pulses, which are needed to overcome small avoided crossings, and (4) the problem of selectivity becomes more important as the vibrational energy of the initial wave function increases.