Mechanisms of double-bond migration reactions of pentene isomers on different Lewis acids

•Both DBM reactions of n-pentene to cis-2-butene and 2-methyl-1-butene to 2-methyl-2-butene followed AB-AD mechanism on Si-Beta.•n-Pentene was transformed into cis-2-pentene and trans-2-pentene concurrently by AB-AD mechanism on AlCl3@γ-Al2O3 without hydroxyl.•2-methyl-1-butene was transformed into 2-methyl-2-butene by AB-AD mechanism on Si-Beta.•2-methyl-2-butene was transformed into 2-methyl-1-butene by AD-AB mechanism on Si-Beta.•Interconversion of 2-methyl-1-butene and 2-methyl-2-butene followed AB-AD mechanism on AlCl3@γ-Al2O3.