Hence the kinetic rate constants k AB and k BA are solely characterised by the protonation rate constant k p , the pK a value of the acid-base equilibrium, and the sample pH. Since there is no available independent data on the protonation rate constant k p , we treat this quantity as an adjustable parameter. Equations 23 to 26 may be combined with equation 33 to provide an estimate for the decay rate constant R S of 13 C 2 singlet order in 18 O-enriched 1,2-13 C 2 squarate, in the high-pH regime. The singlet relaxation time constant T S is given by the inverse of the rate constant, T S = R -1 S . Evaluation of T S requires estimates of the isotropic shift differences ∆Ω A and ∆Ω B , the 13 C chemical shift anisotropies and dipole-dipole coupling parameters, and the correlation time τ c of the fluctuating interactions. The parameters used for the numerical modelling are given in table III. The pKa value was chosen to equal the known pKa 2 = 3.4 of squaric acid. The chemical shift differences and the CSA parameters are based on the computational chemistry estimates given in appendix A. The dipole-dipole coupling constant is based on the C-C bond length of ∼ 150 pm for the squarate dianion . The rotational correlation time τ C = 100 ps agrees reasonably well with molecular dynamics simulations of the squarate dianion in aqueous solutions . The minor influence of intermolecular interactions, including interactions with dissolved oxygen, is taken into account by a random-field contribution quantified by the parameter ξ erf (1 -κ), recognizing that it is difficult to disentangle the correlation coefficient κ from the mean-square fluctuation amplitude ξ erf . The parameter ξ erf (1 -κ) was chosen to match the experimentally observed T S values at pH = 14.