First principle DFT-based molecular dynamics simulations are performed in order to bring new insights into the conformational dynamics of the alanine dipeptide analogue Ac-Ala-NHMe (with methyl group caps at the extremities) immersed in liquid water at ambient temperature. Two simulations have been run for a total of 100 ps, which allows for a relevant statistical sampling of the phase space, at the ab initio level. P-II-beta equilibrium and (P-II-beta)-alpha(R) conformational interconversions are obtained, without a free-energy barrier for the Phi angle and with a rather low barrier of 2-3 kcal/mol for the T angle, easily overcome from solute-solvent energy transfers. We furthermore give first insights into the rather strong zwitterionic character of the peptide bonds of the dipeptide when immersed in the liquid. The structural and zwitterionic properties extracted from first-principle dynamics in the liquid phase will be useful as benchmarks for force field developments.