Statistical properties of thermodynamic quantities for cyclodextrin complex formation

Literature values of DeltaG degrees (change in Gibbs free energy), DeltaH degrees (change in enthalpy), and TDeltaS degrees (temperature times change in entropy) for 1:1 complex formation by alpha-, beta-, and gamma-cyclodextrins constitute normally distributed populations with the following statistical parameters (all energy quantities in kcal mol(-1); n is the number of data points; mu is the population mean; sigma is the standard deviation): for alpha-cyclodextrin, n = 512, micro(DeltaG) = -2.85, sigma(DeltaG) = 1.23, micro(DeltaH) = -4.77, sigma(DeltaH) = 2.98, micro(TDeltaS) = -1.96, and sigma(TDeltaS) = 2.72; for beta-cyclodextrin, n = 415, micro(DeltaG) = -3.67, sigma(DeltaG) = 1. 37, micro(DeltaH) = -4.24, sigma(DeltaH) = 2.89, micro(DeltaS) = -0. 56, and sigma(TDeltaS) = 2.63; for gamma-cyclodextrin, n = 42, micro(DeltaG) = -3.71, sigma(DeltaG) = 1.19, micro(DeltaH) = -3.10, sigma(DeltaH) = 3.39, micro(TDeltaS) = +0.69, and sigma(TDeltaS) = 3. 29. The temperature is 298.15 K. The mean DeltaG degrees values correspond to binding constants of 123, 490, and 525 M(-1) for alpha-, beta-, and gamma-cyclodextrins, respectively.