Table 2.

One-Shell and Two-Shell Simulations of Fourier Peak II of the Native S₃ State Samples^a

(A) One-Shell Simulation
sampleb	Mn–Mn interaction			ΔE0 (eV)	Φ (×102)c	ε2 (×104)c
	R (Å)	N	σ2 (Å2)
S3B	2.85	1.27	0.0096	−5.67	0.30	0.50
S3C	2.84	1.33	0.0067	−5.48	0.28	1.04
S3D	2.80	1.29	0.0094	−12.05	0.39	1.17
S3E	2.88	1.05	0.0058	−1.70	0.29	0.57
S3F	2.87	1.14	0.0099	−2.69	0.68	0.55
〈S3〉	2.85	1.22	0.0083
S2	2.73	1.20	0.0025

(B) Two-Shell Simulation
sampleb	Mn–Mn interaction			Mn–Mn interaction			ΔE0 (eV)	Φ (×102)c	ε2 (×104)c
	R (Å)	N	σ2 (Å2)	R (Å)	N	σ2 (Å2)
S3B	2.83	0.64	0.0021	2.97	0.47	0.0021	−3.04	0.13	0.54
S3C	2.82	0.73	0.0010	2.96	0.55	0.0024	−2.24	0.12	0.11
S3D	2.80	0.69	0.0018	2.95	0.62	0.0032	−5.30	0.22	0.65
S3E	2.84	0.58	0.0022	2.95	0.53	0.0026	−0.71	0.23	0.27
S3F	2.83	0.62	0.0046	2.97	0.58	0.0050	−0.64	0.30	0.34
〈S3〉	2.82	0.65	0.0023	2.96	0.55	0.0031
S2	2.71	0.60	0.0010	2.81	0.60	0.0060

^aFit parameters are defined in the text. Data are fit from k = 3.5 to 11.5 Å⁻¹.

^bFive individual S₃ data sets.

^cQuality of fit parameters Φ and ε² are defined in Materials and Methods. 〈S₃〉 is the average of the individual fits presented. One Mn–Mn shell fit is better than a Mn–C fit by a factor of 3–4, and the two-shell Mn–Mn fits are better than one Mn–Mn and one Mn–C fits by a factor of 2–3 (see text for details).