Density functionals with long-range and/or empirical dispersion corrections, including LC-ωPBE, B97-D, ωB97X-D, M06-2X, B2PLYP-D, and mPW2PLYP-D functionals, are assessed for their ability to describe the conformational preferences of Ac-Ala-NHMe (the alanine dipeptide) and Ac-Pro-NHMe (the proline dipeptide) in the gas phase and in water, which have been used as prototypes for amino acid residues of peptides. For both dipeptides, the mean absolute deviation (MAD) is estimated to be 0.22-0.40 kcal/mol in conformational energy and 2.0-3.2° in torsion angles φ and ψ using these functionals with the 6-311++G(d,p) basis set against the reference values calculated at the MP2/aug-cc-pVTZ//MP2/aug-cc-pVDZ level of theory in the gas phase. The overall performance is obtained in the order B2PLYP-D ≈ mPW2PLYP-D > ωB97X-D ≈ M06-2X > MP2 > LC-ωPBE > B3LYP with the 6-311++G(d,p) basis set. The SMD model at the M06-2X/6-31+G(d) level of theory well reproduced experimental hydration free energies of the model compounds for backbone and side chains of peptides with MADs of 0.47 and 4.3 kcal/mol for 20 neutral and 5 charged molecules, respectively. The B2PLYP-D/6-311++G(d,p)//SMD M06-2X/6-31+G(d) level of theory provides the populations of backbone and/or prolyl peptide bond for the alanine and proline dipeptides in water that are consistent with the observed values.
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