There is no Hg^+ ion only [Hg-Hg]^2+. The Hg atoms in the ion are equivalent. It is a unique ion!
Hg is [Xe] 4f^14 5d^10 6s^2 and a bizarre phenomenon occurs at Au and Hg. Part is attributed to the Lanthanide Contraction. The 4f^14 e⁻s do not screen effectively as s, p, d e⁻s and so the valence 6s e⁻s experience a much greater Zeff and are contracted. But that is only the beginning of the story. The Schrödinger Wave Equation shows that the ns e⁻s in particular penetrate the core e⁻s and have a finite probability of being at the nucleus (that for Hg has a nuclear charge of 80+). See the radial distribution function for the 6s AO.[1] Near the nucleus the velocity of the 6s e⁻s become comparable to the speed of light (~0.1c?) and from relativity theory they gain mass and hence are further contracted. A strong bond is formed when there is when there is good overlap of AOs and the overlap of the
Hg 6s^1(↑)]^+ + Hg^+6s^1(↓) → [Hg(↑↓)Hg]^2+ is a stable bonding situation. Never mind the +ve charges and the other 78 e⁻s on Hg: we're bonding!! Compare the overlap of two H 1S AOs H(↑↓)H MO (and why He is inert and Hg is a liquid).
