In this article, four series of Diels–Alder (DA) reactions (totally, 68 reactions) have been investigated, including their transition states, by means of ab initio method at MP2/6-311+G(d,p) level and atom-bond electronegativity equalization method (ABEEMσπ) method. The rationalization of stereoselectivities of these DA reactions has been done in the light of the local hard and soft acids and bases (HSAB) criterion. The results show that the finite difference approximation with ab initio method can not always be used to predict the stereoselectivities of these reactions, while ABEEMσπ method can properly be applied to predict the stereoselectivities of these DA reactions. Moreover, we have proposed the generalized Fukui function and local softness which involve the number of the atoms of a molecule. For the first time, we here demonstrate that local HSAB criterion with the generalized local softness can be utilized not only to predict the main products of these DA reactions but also to rationalize the relative magnitudes of the reaction rate constants of these DA reactions. © 2013 Wiley Periodicals, Inc.