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The yields of reactions with large driving energies are insensitive to small variations in driving energy

Large energy differentials can provide a margin of safety against errors in modeling. For example, in a mechanosynthetic system, positioning a tip against a workpiece will commonly create a two-state system, S0 = unreacted, S1 = reacted. If the change in the free energy of the reactants (from pre- to post-reaction) is ΔE01, then at equilibrium the probability ratio R01 = P(S0)/P(S1) = exp(ΔE01/kT), and the probability of failure = P(S0) = R01/(1 + R01). If a design calculation estimates ΔE01 = −4kT, then an adverse error of +3kT would drop the probability of success from a calculated 0.98 to an actual 0.73. If the calculated value is a more substantial −14kT, however, an adverse error of +3kT drops the probability merely from 0.99999917 to 0.999983. Reactions that produce a net gain of one covalent bond (for example, radical coupling) commonly reduce free energy by more than 100kT300. Reactions that break weak bonds in order to form strong ones (for example, abstraction of hydrogen from tin to carbon) commonly reduce free energy by more than 30kT300.