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Brønsted acid catalyzed (3⁺ + 2) cycloadditions between hydrazones and alkenes provide a general approach to pyrazolidines. The acidity of the Brønsted acid is crucial for the catalytic efficiency: the less acidic phosphoric acids are ineffective, while highly acidic chiral N-triflylphosphoramides are very efficient and can promote highly enantioselective cycloadditions. The mechanism and origins of catalytic efficiencies and selectivities of these reactions have been explored with density functional theory (M06-2X) calculations. Protonation of hydrazones by N-triflylphosphoramide produces hydrazonium–phosphoramide anion complexes. These ion-pair complexes are very reactive in (3⁺ + 2) cycloadditions with alkenes, producing pyrazolidine products. Alternative 1,3-dipolar (3 + 2) cycloadditions with the analogous azomethine imines are much less favorable due to the endergonic isomerization of hydrazone to …