Table 3.

Two-Shell and Four-Shell Simulations of Fourier Peaks II and III of the native S₃ State Samples^a

(A) Mn–Mn Interaction Only
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	2.84	1.24	0.0095	3.39	0.33	0.0044	−6.04	0.28	0.39
S3C	2.84	1.07	0.0048	3.43	0.61	0.0065	−6.17	0.52	0.35
S3D	2.80	1.28	0.0094	3.39	0.93	0.0078	−9.82	0.37	0.33
〈S3〉	2.83	1.20	0.0079	3.40	0.62	0.0062
S2	2.71	1.20	0.0025	3.34	0.30	0.0050

Four-Shell Simulation
sampleb	Mn–Mn interactions			Mn–Mn interactions			ΔE0 (eV)	Φ (×102)c	ε2 (×104)c
	R (Å)	N	σ2 (Å2)	R (Å)	N	σ2 (Å2)
S3B	2.82	0.72	0.0042	3.42	0.28	0.0043	−3.20	0.15	0.21
	2.96	0.55	0.0052	3.58	0.10	0.0090
S3C	2.83	0.73	0.0011	3.43	0.49	0.0056	−2.29	0.17	0.11
	2.96	0.55	0.0029	3.56	0.36	0.0018
S3D	2.80	0.68	0.0015	3.41	0.58	0.0024	−4.84	0.16	0.14
	2.95	0.61	0.0023	3.56	0.38	0.0034
〈S3〉	2.82	0.71	0.0022	3.42	0.45	0.0041
	2.96	0.57	0.0035	3.57	0.28	0.0047

(B) Mn–Mn and Mn–Ca Interactions
Two-Shell Simulation
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)
S3B	2.84	1.04	0.0082	3.45	0.43	0.0045	−6.65	0.21	0.17
S3C	2.84	0.92	0.0040	3.51	0.63	0.0037	−5.61	0.52	0.42
S3D	2.81	1.08	0.0070	3.44	1.07	0.0067	−9.70	0.48	0.42
〈S3〉	2.83	1.01	0.0064	3.47	0.71	0.0050
S2	2.71	1.20	0.0025	3.39	0.40	0.0050

Four-Shell Simulation
sampleb	Mn–Mn interactions				Mn–Mn and Mn–Ca interaction				ΔE0 (eV)	Φ (×102)c	ε2 (×104)c
		R (Å)	N	σ2 (Å2)		R (Å)	N	σ2 (Å2)
S3B	Mn–Mn	2.83	0.70	0.0039	Mn–Mn	3.41	0.29	0.0045	−2.78	0.13	0.18
	Mn–Mn	2.96	0.56	0.0051	Mn–Ca	3.63	0.16	0.0066
S3C	Mn–Mn	2.83	0.73	0.0010	Mn–Mn	3.43	0.49	0.0052	−2.40	0.16	0.11
	Mn–Mn	2.96	0.55	0.0030	Mn–Ca	3.61	0.36	0.0011
S3D	Mn–Mn	2.80	0.68	0.0017	Mn–Mn	3.40	0.48	0.0021	−4.73	0.15	0.13
	Mn–Mn	2.95	0.61	0.0027	Mn–Ca	3.60	0.44	0.0026
〈S3〉	Mn–Mn	2.82	0.70	0.0022	Mn–Mn	3.41	0.42	0.0039
	Mn–Mn	2.96	0.57	0.0036	Mn–Ca	3.61	0.32	0.0034

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

^bThree 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.