Table 1. Results of Investigation of Most Favorable Position for Second Proton, Binding to One of the Sulfide Ions^a.

	first	second		third		fourth		ΔE (kJ/mol)
Structure	S2B	Sb	Other	Fe2	Fe6	Fe3	Fe7	TPSS	TZVPD	B3LYP
S3A(2)	1.36	1.36		1.52	2.40	2.18	1.50	65
S3A(5)	1.36	1.36		1.52	2.42	2.20	1.50	54
S5A(2)	1.36	1.37		1.52	2.27	1.98	1.53	7	9	6
S5A(3)	1.36	1.36		1.52	2.27	1.96	1.54	0	0	0
S1A(Fe1)	1.36	1.39	Fe1 = 2.16	1.51	2.38	2.16	1.50	37
S2A(Fe1)	1.36	1.41	Fe1 = 2.03	1.52	2.24	2.10	1.51	61
S4A(Fe1)	1.36	1.39	Fe1 = 2.17	1.51	2.42	2.13	1.50	63
S4A(S1B)	1.36	1.37		1.52	2.56	2.24	1.50	62
S1B(HCA)	1.36	1.39		1.51	2.51	2.30	1.50	95
S1B(Fe5)	1.36	1.45	Fe5 = 1.87	1.52	2.40	2.20	1.50	88
S3B(S1A)e	1.38	1.37		1.67c	1.68		1.55d	7	4	18
S3B(HCA)	1.36	1.40		1.52	2.63	1.99	1.51	121
S4B(HCA)f	1.36	1.40		1.52	2.37	1.91	1.52	109
S4B(Wat)	1.36	1.39		1.52	2.34	2.11	1.50	116

^aThe first proton binds to S2B(5), and the third and fourth hydrogen atoms bind as bridging hydrides to Fe2/6(5) and Fe3/7(2), as shown in Figure 2. The table shows the S–H or Fe–H distances (Å) of the four hydrogen atoms, as well as the relative energy (ΔE in kJ/mol), calculated either at the TPSS-D3/def2-SV(P), TPSS-D3/def2-TZVPD, or B3LYP-D3/def2-SV(P) levels of theory (the latter two single-point energies on the TPSS/def2-SV(P) structures). All complexes were in the BS4–356 state, unless otherwise stated.

^bThis is the distance to the sulfide ion shown in the first column.

^cFe7 instead of Fe2.

^dA terminal hydride ion, not directed toward the other Fe ion, but instead binding trans to the central carbide ion.

^eChanged to the BS10–147 state.

^fChanged to the BS3–124 state.