Table 4.

Selected bond lengths, partial charges, proton dissociation energies (D_e), and relative energies for [(ImH)₂Zn–S(H)CH₃]²⁺ (top set) and [(ImH)₃Zn–S(H)CH₃]²⁺ (bottom set) as a function of S–Zn–N_n angles. Values from M05-2X/cc-pVDZ calculations.

Bond angles	Bond lengths (Å)			Partial charges (a.u.)				Energies (kJ/mol)
								(S–H) PDE	Relativec
	Zn–S	S–H	Zn–(N)na	Zn	H	S	(ImH)nb		Thiol (Thiolate)
∠SZn(ImH)2			Zn–(ImH)2				(ImH)2
95°	2.565	1.3536	1.943	0.760	0.168	−0.062	0.921	680	36.7 (75.5)
105°	2.460	1.3545	1.948	0.727	0.175	−0.009	0.882	662	10.0 (30.7)
115°	2.398	1.3554	1.957	0.697	0.182	0.034	0.856	651	0.6 (10.1)
120°	2.377	1.3556	1.963	0.689	0.185	0.050	0.840	647	0.5 (6.1)
125°	2.358	1.3560	1.972	0.685	0.188	0.060	0.829	642	3.5 (4.2)
135°	2.327	1.3563	2.009	0.671	0.193	0.080	0.804	627	28.8 (14.5)
Δ(135°−95°)	−0.238	0.0027	0.066	−0.089	0.025	0.142	−0.117	−53
fully optd	2.385	1.3557	1.960	0.699	0.186	0.035	0.842	641	0.0 (0.0)
∠SZn(ImH)3			Zn–(ImH)3				(ImH)3
85°	2.857	1.3513	1.997	0.699	0.129	−0.097	1.125	813	57.8 (129.4)
95°	2.592	1.3522	2.006	0.626	0.143	−0.041	1.106	770	18.9 (47.3)
105°	2.473	1.3527	2.016	0.570	0.155	0.004	1.085	750	1.6 (9.9)
110°	2.436	1.3533	2.024	0.548	0.161	0.021	1.074	741	1.4 (0.9)
115°	2.409	1.3536	2.036	0.543	0.167	0.030	1.062	737	7.0 (3.2)
125°	2.361	1.3546	2.084	0.548	0.179	0.055	0.997	722	49.2 (30.4)
Δ(125°−85°)	−0.496	0.0033	0.087	−0.151	0.050	0.152	−0.128	−91
fully optd	2.454	1.3528	2.020	0.567	0.163	−0.005	1.079	741	0.0 (0.0)

^aaverage Zn–N_n distance,

^btotal charge on the zinc coordinated imidazole ligands,

^cEnergy of the constrained thiol and (thiolate) relative to their fully optimized (ImH)₂ and (ImH)₃ complexes.

^dFully opt numbers are from optimizations with no constraints, in which the average ∠SZn(ImH)₂ = 117.6° and the average ∠SZn(ImH)₃ = 108.0°, for the thiol complexes