(a) Helix types and fully extended structure (FES). The red, dotted lines denote intra-chain N-H⋅⋅⋅O = C hydrogen bonds. ν denotes the number of peptide units to form a hydrogen bond. (b) Schematic representation of the L-alanine amino acid residue (peptide unit), with the side chain R = CH3. (c) Schematic visualization of the parameters used to construct helices: pitch L, twist Θ, and radius R.
Phonon dispersion relations of the analyzed conformations of the poly-L-alanine chain.
The statistical averages along the thermodynamic integration path determined with Langevin dynamics (black lines) and Nose Hoover dynamics (red lines). As test system a fully extended structure and the SCC-DFTB potential was used. The simulations were performed at T = 300 K. Statistical averages are shown after simulation times of 1 ps (dotted lines), 2.5 ps (dashed lines), and 50 ps (solid lines).
Anharmonic free energy contributions ΔA ah = A ah − A harm at room temperature, as evaluated by thermodynamic integration using different friction parameters γ in the Langevin equations of motion (Eq. (16)). Different simulation lengths are investigated: 103 steps (dotted black line), 104 steps (dashed black line), 105 steps (solid black line), and the SCC-DFTB approach is used (see, Ref. 33). The reference potential is the harmonic potential for a FES in a supercell containing four peptide units. The target potential is the “full” anharmonic potential energy surface. The dashed gray horizontal line denotes the best guess for the free energy difference as determined after 105 simulation steps with γ = 0.01.
Anharmonic corrections, ΔA ah, to the vibrational free energy as determined with DFT-GGA at room temperature denoted in kcal/mol per peptide unit. The anharmonic corrections are referred to the harmonic free energy determined with DFT-GGA at the equilibrium pitch L 0 and twist Θ0, i.e., ΔA ah = A ah − A harm(L 0, Θ0). τsim denotes the number of simulation steps (Δt = 1.5 × 10−15 s) and the remaining statistical error bar is indicated by δΔA ah.
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