Nature of the three-electron bond in H₂S∴SH₂⁺

We have investigated the model system H₂S∴-SH₂⁺, i.e., the sulfur-sulfur bound dimer radical cation of H₂S, using both density functional theory (LDA, BP86, PW91) and traditional ab initio theory (up to CCSD-(T)). Our purpose is to better understand the nature of the three-electron bond. The S-S bond length is 2.886 Å and the bond enthalpy (for 298.15 K) amounts to -40.7 kcal/mol at the BP86/TZ2P level. The best ab initio estimates for the S-S bond strength (our CCSD(T)/6-311++G(2df,2pd)//MP2(full) and literature values) are some 10 kcal/mol weaker than those from nonlocal DFT. It is shown, using an energy decomposition scheme for open-shell systems, that the sulfur-sulfur bond (ΔE = ΔE_2c-3e + ΔE_elst) is nearly 60% provided by the three-electron bond (ΔE^2c-3e) between the unpaired sulfur 3p_x electron on H₂S^+• and the sulfur 3p_x lone pair on H₂S; electrostatic attraction (ΔE_elst) is important, too, with a contribution of somewhat more than 40%. We show furthermore that the three-electron bond (ΔE_2c-3e = Δ_2c-1e + ΔE_pauli) can be conceived as and quantitatively analyzed in terms of a one-electron bond (AE_2c-1e), arising from the β-electron of the H₂S lone pair interacting with the corresponding empty β-spin orbital of H₂^S+•, opposed by the Pauli repulsion (Δ_EPauli) between the α-electrons of the H₂S lone pair and H₂S^+• SOMO.