Marcus inverted-region pins: exp at ΔG=−λ is 0; at ΔG=0 is −λ/(4RT); ΔG at max solves to −λ

Exponent evaluations: −(ΔG+λ)²/(4λRT) at ΔG = −λ (inverted-region boundary, rate maximum) equals exactly 0; at ΔG = 0 (thermoneutral) equals exactly −λ/(4·R·T); d(exponent)/d(ΔG) = 0 solves to ΔG = −λ exactly (the maximum-rate condition). …