In performance-based seismic design procedures Peak Ground Acceleration (PGA) and pseudo-Spectral acceleration ($S_a$) are commonly used to predict the response of structures to earthquake. Recently, research has been carried out to evaluate the predictive capability of these standard Intensity Measures (IMs) with respect to different types of structures and Engineering Demand Parameter (EDP) commonly used to measure damage. Efforts have been also spent to propose alternative IMs that are able to improve the results of the response predictions. However, most of these IMs are not usually employed in probabilistic seismic demand analyses because of the lack of reliable Ground Motion Prediction Equations (GMPEs). In order to define seismic hazard and thus to calculate demand hazard curves it is essential, in fact, to establish a GMPE for the earthquake intensity. In the light of this need, new GMPEs are proposed here for the elastic input energy spectra, energy-based intensity measures that have been shown to be good predictors of both structural and non-structural damage for many types of structures. The proposed GMPEs are developed using mixed-effects models by empirical regressions on a large number of strong-motions selected from the NGA database. Parametric analyses are carried out to show the effect of some properties variation, such as fault mechanism, type of soil, earthquake magnitude and distance, on the considered IMs. Results of comparisons between the proposed GMPEs and other from the literature are finally shown.