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The vibrational excitation of N2 molecules adsorbed on a silver surface by low energy electron impact is studied within the newly developed coupled angular mode method. The process involves the formation of a transient negative molecular ion. The results account well for the observations of Demuth and coworkers. They also reveal that most of the vibrational excitation corresponds to electrons scattered into the metal and thus unobservable in a scattering experiment. PACS numbers: 34.80.Gs, The energy transfer between the electronic and nuclear motions in the course of an electron molecule is rather difficult due to the large mass ratio between electrons and nuclei. The situation is completely different if the incident electron can be captured by the target molecule to form a transient negative molecular ion. In gas-phase collisions, vibrational excitation at low energy is very often dominated by resonant processes [1]:The same kind of arguments hold for molecules adsorbed on a metal surface and indeed, resonant scattering is an important source of vibrational excitation. It was first observed in 1981 by Demuth and co-workers [2] and Sanche and Michaud [3]. In fact, the formation of transient negative ions enables an efficient energy transfer between electrons and nuclei and it has been invoked as an intermediate step in a variety of processes involving metal surfaces and molecules: desorption by electron impact [4], photodesorption [5], reactivity [6], and electronic deexcitation [7,8]. Studies of resonant scattering have also revealed that transient negative ions could be used as a probe of the molecule environment [9]. The possibility for a quantitative discussion of all the above processes depends on the availability of an accurate treatment of the resonant energy transfer. In the present paper, we report on the first study of the dynamics of vibrational excitation in electron collisions with adsorbed molecules that quantitatively takes into account the presence of the metal surface. It is applied to N2 molecules physisorbed on silver and it reveals some unexpected features on the importance of the vibrational excitation process. The N2 molecule and its N2~( 2 rig) resonance have been studied extensively in the gas phase: The resonance is located around 2.3 eV and is associated with an 1=2 wave. For adsorbed molecules, Demuth and co-workers [2] observed the same resonance, however, modified by the metal environment: The resonance energy is lowered, the oscillating structure of the cross section as a function of the energy has disappeared, and the overtone excitation is decreased. Similar results were observed for thick layers of N2 molecules condensed on other metals [10,11]. Since these pioneering works, resonant vibrational excitation has been observed in quite a few systems; they have been recently reviewed in [11,12]. Theoretical studies on this problem are more scarce. The first ones [13,14] studied vibrational excitation using simplified models with adjusted parameters: constant adjusted resonance lifeti...

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