For both MFCC and MFCC-MBE(2), adding the density-based correction lowers the error significantly. For the db-MFCC scheme, the errors for the 3 10 -helix and the α-helix are reduced to 66 and 60 kJ/mol, respectively, while for the β-strand and the turn, they are reduced to 12 and 30 kJ/mol, respectively. When including two-body contributions in the db-MFCC-MBE(2) scheme, the calculations become virtually exact, with errors between 0.3 and 1.3 kJ/mol in the total energies. This demonstrates that the densitybased correction is able to account for higher-order contributions, that would only appear at third or higher orders in the energy-based expansion.