Competition between alkenes in intramolecular ketene-alkene [2 + 2] cycloaddition: what does it take to win?

In the course of developing a new synthetic methodology using ketenes in sequential cycloaddition steps, we were faced with a competition problem with molecules containing a ketene tethered to more than one reacting partner. To pinpoint the electronic and tethering requirements for a chemoselective reaction, we undertook a series of ketene-alkene [2 + 2] cycloaddition competition experiments. Those experiments were conducted on molecules containing either two identical alkenes having different tether lengths or two alkenes having the same tether length but being electronically different. We demonstrated that the reaction is much faster for forming five-membered rings than six-membered rings and calculated the Hammett constant rho for intramolecular ketene-alkene [2 + 2] cycloadditions to be -1.39.