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. Author manuscript; available in PMC: 2009 Nov 12.
Published in final edited form as: J Am Chem Soc. 2008 Oct 17;130(45):15002–15021. doi: 10.1021/ja803112w

Table 4.

Reaction free energies in kcal/mol of the individual steps in the proposed mechanism.a

PW91 OPBE B3LYP B3LYP*
2 e− (0.2 eV)b + 2 H+in (pH7)c + 1 → 2 + H2Os +10.55 −14.39 +0.54 +4.79
O2d + H2Op + 1 H+in(pH7) 2 → 3 −28.61 +15.78 +7.64 −3.82
3 → 4 + H+out (pH3)e − 6.21 −11.56 −27.70 −15.45
4 → 5 + H2Op + 2.24 +0.05 +10.64 +2.14
H+in (pH7) + 5 → 6 −2.74 −0.05 −7.14 −4.22
H2Op + 6 → 7 + H+out pH3) + 14.88 +14.50 +12.15 +8.83
7 → 8 + H2Op + 9.96 +8.11 +20.67 +19.55
1 e− (0.2 eV) + 2 H+in (pH7) + 8 → 9 − 31.54 −30.58 −36.86 −35.30
H2Op + 9 → 10 + H+out (pH3) +10.47 +12.60 +7.62 +7.86
10 → 11 + H2Op + H2Os −8.37 −18.99 −9.00 −7.20
1 e− (0.2 eV) + 2 H+in (pH7) + 11 → 12 −19.35 −20.19 −20.96 −23.16
12 → 13 −0.62 +1.74 +0.26 +5.77
H2Op + 13 → 14 + H+out (pH3) +9.17 +7.86 +11.01 +7.97
14 → 1 + H2Op +11.96 +12.27 +4.80 +6.81
Σ 4 e− (0.2 eV) + O2 + 8 H+in (pH7) 1 → 1 4 H+out (pH3) + 2 H2Os −28.21 −22.87 −26.32 − 25.46
Overall rxn: 4 e− (0.2 eV) + O2 + 8 H+in (pH7) → 4 H+out(pH3) + 2 H2Os −27.97 −22.85 −26.37 −25.23
a

See text for explanation of energetics.

b

Relative to the standard hydrogen electrode.

c

Representing the proton taken up on the “inside” of the ba3 molecule, carries its ZPVE.

d

Referenced to 1 M O2 in water rather than to 1 atm pure gas.

e

Representing the proton “pumped” to the “outside” of the ba3 molecule, carries its ZPVE.

p

Indicating a passive water carrying with it a full ZPVE.

s

indicating a “scalar” water also carrying its full ZPVE. See Table 3.