B(C6F5)3-Catalyzed Formal (n + 3) (n = 5 and 6) Cycloaddition of Bicyclo[1.1.0]butanes to Medium Bicyclo[n.1.1]alkanes

= 5 and 6) cycloaddition of bicyclo[1.1.0]butanes (BCBs) with imidazolidines/hexahydropyrimidines is described. The reaction provides a modular, atom-economical, and efficient strategy to two libraries of synthetically challenging medium-bridged rings, 2,5-diazabicyclo[5.1.1]nonanes and 2,6-diazabicyclo[6.1.1]decanes, in moderate to excellent yields. This reaction also features simple operation, mild reaction conditions, and broad substrate scope. A scale-up experiment and various synthetic transformations of products further highlight the synthetic utility.