Table 5.

Additive Contributions ${\mathbf{ME}}_{\mathbf{A}}({\mathbf{Gly}}_{\mathit{m}}{:\mathrm{Gly}}_{\mathit{n}})$ to the Many-Body Interaction Energies of Glycine Dipeptide Oligomers ${\mathbf{Gly}}_{\mathit{m}}{:\mathrm{Gly}}_{\mathit{n}}$ Calculated by $\omega B97X-\mathbf{D}$/aTZ and Polarizable Force Fields (kcal/mol)^a,b

$\omega \text{B97X}-\mathrm{D}$/aTZ		pGM-perm	pGM-ind	Amoeba13	ff12pol
${\text{Gly:Gly}}_2$
$\alpha \mathrm{R}$	−1.47	−1.43 (0.05)	−1.41 (0.06)	−1.10 (0.38)	−1.04 (0.43)
$\mathrm{a}\beta$	−0.43	−0.42 (0.01)	−0.41 (0.02)	−0.31 (0.12)	−0.36 (0.07)
$\beta$	−0.50	−0.48 (0.02)	−0.47 (0.03)	−0.39 (0.11)	−0.42 (0.08)
${\text{Gly:Gly}}_3$
$\alpha \mathrm{R}$	−2.16	−2.09 (0.07)	−2.08 (0.08)	−1.63 (0.53)	−1.50 (0.66)
$\mathrm{a}\beta$	−0.48	−0.46 (0.02)	−0.45 (0.03)	−0.33 (0.15)	−0.39 (0.09)
$\beta$	−0.59	−0.56 (0.03)	−0.55 (0.04)	−0.44 (0.14)	−0.47 (0.11)
${\text{Gly}}_2{\text{:Gly}}_2$
$\alpha \mathrm{R}$	−3.86	−3.73 (0.14)	−3.69 (0.17)	−2.88 (0.98)	−2.70 (1.16)
$\mathrm{a}\beta$	−1.06	−1.03 (0.03)	−1.01 (0.05)	−0.83 (0.23)	−0.88 (0.17)
$\beta$	−1.17	−1.11 (0.06)	−1.10 (0.07)	−0.92 (0.25)	−0.94 (0.23)
${\text{Gly}}_3{\text{:Gly}}_3$
$\alpha \mathrm{R}$	−6.37	−6.16 (0.22)	−6.12 (0.25)	−4.81 (1.57)	−4.38 (1.99)
$\mathrm{a}\beta$	−1.21	−1.15 (0.06)	−1.13 (0.08)	−0.90 (0.31)	−0.97 (0.24)
$\beta$	−1.43	−1.34 (0.09)	−1.33 (0.10)	−1.11 (0.32)	−1.12 (0.31)
RMSE		0.09	0.10	0.59	0.72
MAE		0.06	0.08	0.42	0.46
max dev		0.22	0.25	1.57	1.99
min dev		0.01	0.02	0.11	0.07

^aThe formula for the additive contributions ${\text{ME}}_{\mathrm{A}}({\text{Gly}}_m{\text{:Gly}}_n)$ to the many-body interaction energies is shown in eq 25.

^bSee Table 2 and text for notation.