  We report the folding thermodynamics of ccUUCGgg and ccGAGAgg RNA tetraloops
using atomistic molecular dynamics simulations. We obtain a previously
unreported estimation of the folding free energy using parallel tempering in
combination with well-tempered metadynamics. A key ingredient is the use of a
recently developed metric distance, eRMSD, as a biased collective variable. We
find that the native fold of both tetraloops is not the global free energy
minimum using the Amber\c{hi}OL3 force field. The estimated folding free
energies are 30.2kJ/mol for UUCG and 7.5 kJ/mol for GAGA, in striking
disagreement with experimental data. We evaluate the viability of all possible
one-dimensional backbone force field corrections. We find that disfavoring the
gauche+ region of {\alpha} and {\zeta} angles consistently improves the
existing force field. The level of accuracy achieved with these corrections,
however, cannot be considered sufficient by judging on the basis of available
thermodynamic data and solution experiments.
