Table 4.

Fit Parameters for Fourier Peak III of the Native S₃ State Samples^a

One-Shell Simulation
sampleb	Mn–Mn interaction			ΔE0 (eV)	Φ (×102)c	ε2 (×104)c
	R (Å)	N	σ 2 (Å2)
S3A	3.42	0.65	0.0056	−5.74	0.16	0.84
S3D	3.41	0.82	0.0076	−6.93	0.39	0.21
〈S3〉	3.42	0.74	0.0066
S2	3.36	0.30	0.0030

Two-Shell Simulation
Mn–Mn Interaction Only
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)
S3A	3.43	0.52	0.0020d	3.58	0.23	0.0020d	−2.29	0.15	0.77
S3D	3.41	0.57	0.0026	3.57	0.37	0.0031	−2.39	0.30	0.36
〈S3〉	3.42	0.55	0.0023	3.58	0.30

Mn–Mn and Mn–Ca Interactions
sampleb	Mn–Mn interaction			Mn–Ca interaction			ΔE0 (eV)	Φ (×102)c	ε2 (×104)c
	R (Å)	N	σ2 (Å2)	R (Å)	N	σ2 (Å2)
S3A	3.43	0.48	0.0020d	3.64	0.27	0.0020d	−1.43	0.10	0.53
S3D	3.40	0.48	0.0023	3.60	0.45	0.0026	−2.50	0.17	0.12
〈S3〉	3.42	0.48	0.0020	3.62	0.36	0.0025
S2	3.38	0.30	0.0020	3.39	0.30	0.0070

^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.

^dParameter is fixed in the fit. 〈S₃〉 is the average of the individual fits presented.