We present the results of molecular dynamics simulations of small peptide nucleic acid (PNA) molecules, synthetic analogues of DNA, at a lipid bilayer in water. At neutral pH, without any salt, and in the NPngT ensemble, two similar PNA molecules (6-mers) with the same nucleic base sequence but different terminal groups are investigated at the interface between water and a 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) lipid bilayer. The results of our simulations suggest that at low ionic strength of the solution, both PNA molecules adsorb at the lipid-water interface. We calculate the adsorption energy using the free energy perturbation approach and the Bennett acceptance ratio method. Our results suggest that the adsorption energy is equal to -30.36 - 0.25 kT for the PNA molecule with charged terminal groups. For the PNA molecule with neutral terminal groups, the adsorption energy is equal to -55.12 - 0.16 kT. We compare these results with the results obtained using the adaptive biasing force approach with the harmonic constraints. We demonstrate that the free energy change calculated with the latter method overestimates the real adsorption energy by ignoring the conformational contribution of the free energy change. The results suggest that our PNA molecules form several bonds with the lipid water interface, which are stronger in the case of the PNA molecule with neutral terminal groups.