TABLE 1.

Comparison of Dipole Moments for Extended Conformations of Ac–X–NHMe in the Training Set Computed by the B3LYP, EPAC, and GDAC Methods^a

X	confb	μB3LYPc	${\mu }_{\text{B3LYP}}^{*}$d	Δe	μEPACf	Δg	μGDACh	Δi
Ala	E	2.92	2.97	0.05	2.95	0.03	2.41	0.51
Val	Eg+g+	2.76	2.62	0.14	2.75	0.00	2.28	0.47
Leu	Eg−t	2.27	2.46	0.19	2.72	0.45	2.14	0.14
Ile	Ett	2.79	2.71	0.08	2.76	0.03	2.32	0.46
Gly	E	3.25	3.13	0.12	3.18	0.07	2.62	0.62
Pro	tCdj	2.65	3.06	0.41	2.80	0.14	2.78	0.13
Cys	Etg+	1.72	2.52	0.80	2.55	0.83	1.32	0.39
Met	Etg+	1.17	2.05	0.88	2.33	1.17	0.99	0.18
His(δ)k	Etg+	2.74	2.39	0.35	2.24	0.50	2.25	0.48
His(ε)k,l	Etg−	4.55	3.83	0.72	3.55	1.00	3.29	1.25
Phe	Etg+	2.71	2.75	0.03	2.68	0.03	2.21	0.50
Tyr	Eg+g+	1.62	2.23	0.61	2.31	0.69	1.37	0.24
Trp	Etg−	4.24	2.69	1.55	2.60	1.64	3.98	0.25
Asn	Etg−	0.82	0.84	0.02	0.77	0.05	0.97	0.14
Gln	Eg−g−	2.88	2.87	0.01	2.51	0.37	2.39	0.49
Ser	Etg+	1.68	1.36	0.33	1.48	0.20	1.32	0.37
Thr	Etg+	1.69	1.44	0.25	1.30	0.39	1.27	0.43
Lys	Eg+t	3.99	3.98	0.01	3.97	0.02	3.61	0.38
Arg	Etg+	5.85	4.59	1.27	4.52	1.33	4.82	1.04
Asp	Etc	2.60	2.25	0.36	2.56	0.04	2.05	0.55
Glu	Eg−g−	2.32	2.19	0.14	2.25	0.07	1.81	0.52
Lys+l	Eg−g−	11.08	10.90	0.18	11.12	0.04	16.52	5.44
Arg+l	Eg−g−	11.99	11.43	0.56	12.37	0.38	19.90	7.91
His+l	Eg−g+	9.61	8.58	1.02	9.72	0.11	12.69	3.08
Asp−l	Ett	8.70	7.98	0.72	8.76	0.06	12.57	3.88
Glu−l	Etg+	9.41	8.79	0.63	9.65	0.24	13.92	4.50
				0.44m		0.38m		1.32m
				0.60n		0.59n		2.34n

^aUnits in Debyes. The 26 representative residues of the training set are listed in Table S4 of the Supporting Information.

^bConformational letter codes. Each code represents the backbone expressed by a capital letter depending on its torsion angles Ф and ψ, and two side-chain torsion angles χ¹ and χ². See the text for definition of torsion angles.³⁸,³⁹

^cDipole moments calculated directly at the B3LYP/6-31G(d,p)//HF/6-31G(d,p) level.

^dDipole moments calculated from atomic charges obtained at the B3LYP/6-31G(d,p)//HF/6-31G(d,p) level.

^eAbsolute differences between ${\mu }_{\text{B3LYP}}^{*}$ and μ_B3LYP values.

^fDipole moments calculated by the EPAC method.

^gAbsolute differences between μ_EPAC and μ_B3LYP values.

^hDipole moments calculated by the GDAC method of Cho et al.²³

ⁱAbsolute differences between μ_GDAC and μ_B3LYP values.

^jPro with the trans prolyl peptide bond and the down puckering.

^kHis(δ) and His(ε) are isomers of the His residue depending on its protonation at N^δ and N^ε, respectively.

^lInitial atomic charges were obtained by a trial-and-error procedure starting from the corresponding values in ref 23 to reproduce the B3LYP/6-31G(d,p) atomic charges for only these residues; see Figure S1 of the Supporting Information.

^mMean values over all residues.

ⁿRms deviations over all residues.