PHD fingers represent one of the largest families of epigenetic readers capable of decoding post-translationally modified or unmodified histone H3 tails. Because of their direct involvement in human pathologies they are increasingly considered as a potential therapeutic target. Several PHD/histone-peptide structures have been determined, however relatively little information is available on their dynamics. Studies aiming to characterize the dynamic and energetic determinants driving histone peptide recognition by epigenetic readers would strongly benefit from computational studies. Herein we focus on the dynamic and energetic characterization of the PHD finger subclass specialized in the recognition of histone H3 peptides unmodified in position K4 (H3K4me0). As a case study we focused on the first PHD finger of autoimmune regulator protein (AIRE-PHD1) in complex with H3K4me0. PCA analysis of the covariance matrix of free AIRE-PHD1 highlights the presence of a "flapping" movement, which is blocked in an open conformation upon binding to H3K4me0. Moreover, binding free energy calculations obtained through Molecular Mechanics/Poisson-Boltzmann Surface Area (MM/PBSA) methodology are in good qualitative agreement with experiments and allow dissection of the energetic terms associated with native and alanine mutants of AIRE-PHD1/H3K4me0 complexes. MM/PBSA calculations have also been applied to the energetic analysis of other PHD fingers recognizing H3K4me0. In this case we observe excellent correlation between computed and experimental binding free energies. Overall calculations show that H3K4me0 recognition by PHD fingers relies on compensation of the electrostatic and polar solvation energy terms and is stabilized by non-polar interactions.