The significance of 𝑠(𝐫) and [𝜕𝑠(𝐫) 𝜕𝑁] ⁄ 𝑣 is clearly exposed in eq. 11-13: they both are sufficient to obtain all necessary integrals (eq. 14-18). The abbreviated symbols for various integrals within the alchemical approach have been introduced for the sake of clarity (eq.14eq.18). The results for 𝛥𝐸 𝑁 , 𝛥𝜇 𝑁 and 𝛥𝑁 𝜇 are all parabolic functions of ∆𝑍 with the local hypersoftness function contributing to the variation of each state function in the second order only. The significance of this term for the quantitative results of 𝛥𝐸 𝑁 , 𝛥𝜇 𝑁 and 𝛥𝑁 𝜇 has been