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The pK _as of common chiral Brønsted acids in dimethyl sulfoxide (DMSO) have primarily been interrogated computationally. Cheng found using SMD/M06‐2x/6‐311++G(2df,2p)//B3LYP/6‐31+G(d) method that chiral phosphoric acids and carboxylic acids, derived from BINOL, were the least acidic among those studied, with pK _as of 3.37 and 3.97, respectively, and that bis(sulfonic acid) 8a was the most acidic (Figure 2.2) [17]. In comparison to CPA 6, derived from BINOL, those derived from H₈‐BINOL 12 [18] and SPINOL 13 [19, 20] are less acidic with pK _as of 4.61 and 4.20, respectively. N‐Triflyl chiral phosphoramide 14 [21] is much more acidic with pK _a –3.40. Dicarboxylic acid 7 is slightly less acidic than phosphoric acid, whereas sulfonimide 9 is more acidic. These values broadly agree with experimental values of related compounds [22]. A follow‐up study revealed that 3,3′‐substitution in chiral phosphoric acids enables modulation of acidity by nearly two orders of magnitude: from 2.63 for CPA 6b with 3,5‐(CF₃)₂C₆H₃ groups to 4.20 for CPA 6i with Ph₃Si groups (Figure 2.3).

Figure 2.1. Examples of chiral Brønsted acids.

Figure 2.2. pK_a values of chiral Brønsted acids in DMSO by calculation.

Source: [17].

Figure 2.3. Effect of 3,3′‐substituents of BINOL‐derived phosphoric acid on the pK _a values in DMSO by calculation.

Figure 2.4. Function of chiral phosphoric acid.