Table 1 Character of the dicationic states shown as red lines in Fig. 4

Geometry	Energy (eV)	Singlet	Triplet
Equilibrium (A: acceptor; D: donor)	33.2	(HOMO)^D(HOMO)^A
	31.0	(HOMO−1)^D(HOMO)^A
	30.8	(HOMO)^D(HOMO−1)^A
	28.7	(HOMO−1)^D(HOMO−1)^A
Proton Transfer (A: H₃O⁺; D: OH⁺)	33.2	(HOMO)^A(HOMO)^D
	32.2	(HOMO−1)^D(HOMO−1)^D
	30.9	(HOMO−1)^D(HOMO)^D
	30.9	(HOMO)^D(HOMO)^D
	33.2		(HOMO)^A(HOMO)^D
	32.6		(HOMO−1)^D(HOMO−2)^D
	32.3		(HOMO)^D(HOMO−2)^D
	28.8		(HOMO)^D(HOMO−1)^D

For the equilibrium geometry, both the singlet and triplet states correspond to H₂O⁺– H₂O⁺ and have the same energy within the quoted accuracy. For the proton transfer geometry, the lowest three singlet and triplet states are OH⁺ – \({{{{\rm{OH}}}}}_{3}^{+}\), the highest, fourth state is OH – \({{{{\rm{OH}}}}}_{3}^{2+}\).

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