As 𝑓′′(𝐸 𝑒𝑞 ) approaches infinity, the transition between the limits of 𝑓′(𝐸 𝑒𝑞 ) approaches a step function between 0 and 1. At the extreme, the point (𝐸 𝑒𝑞 , 𝑓(𝐸 𝑒𝑞 )) would become nondifferentiable, and would be equal to the horizontal asymptote (n = 0). In the reverse scenario, as 𝑓′′(𝐸 𝑒𝑞 ) approaches 0, f' would approach the value of 0.5 across its domain. Hence, the integral of f' from -∞ to 0, and therefore the value of 𝑓(𝐸 𝑒𝑞 ), would approach positive infinity. An initial idea could be that f is of the form 𝑓(∆𝐸 𝑟 ) = 𝑔(∆𝐸 𝑟 )∆𝐸 𝑟 , where g would modify an underlying linear growth. However, if g is some class of sigmoid function, the resulting function would contain a minimum around ΔEr < Eeq and, notably, its value at Eeq would always be identical to its asymptote at negative infinity. This precludes any function 𝑔(∆𝐸 𝑟 ) for which 𝑔(𝐸 𝑒𝑞 ) is defined: the value at 0 would not be defined by the curvature.