First-principle calculation of equilibrium cesium ion-pair acidities in tetrahydrofuran

The ion-pair acidities of organic acids in THF are fundamental to synthetic organic chemistry. Although the ion-pair acidities of a number of carbon acids have been experimentally measured by Streitwieser and co-workers, it is important to develop a theoretical method that can accurately predict these quantities because not all the organic acids (e.g., very weak acids or complex synthetic intermediates with multiple acidic positions) are amenable to experimental characterization. In the present study is reported the first theoretical protocol for predicting the cesium ion-pair acidities in THF whose reliability has been tested against almost all the available experimental data. It is found that the root-mean-square error of the current theoretical model equals 1.2 pK units. With the newly developed theoretical method in hand, the structures of cesium ion pairs of different types of carbon acids are then studied. The cesium ion-pair acidities in THF and absolute ionic acidities in DMSO are also systematically compared, which confirms Streitwieser's previous finding that the two scales of acidities have only minor difference. Significantly, from detailed energy analysis the mechanism for the "fortunate" match of the two scales of acidities is found. That is, the combined process of the Cs binding ("micro"-solvation) and the solvation of the ion pair resembles the one-step solvation of a carbanion in DMSO. Finally, it is found that the cesium ion-pair acidities of nitrogen acids in THF have only minor difference from the absolute ionic acidities in DMSO. Consequently, one can easily estimate the cesium ion-pair acidities of almost all types of organic nitrogen acids in THF on the basis of Bordwell's data.