As a chemist, I can provide you with a general understanding of the rate-determining step in the Diels-Alder reaction between maleic anhydride and 1,3-butadiene. However, performing quantum chemical calculations requires specialized software and computational resources that I cannot access.The Diels-Alder reaction is a [4+2] cycloaddition reaction between a conjugated diene 1,3-butadiene in this case and a dienophile maleic anhydride . The reaction proceeds through a concerted mechanism, meaning that the formation of new bonds and the breaking of old bonds occur simultaneously in a single step. Therefore, the rate-determining step in the Diels-Alder reaction between maleic anhydride and 1,3-butadiene is the formation of the cyclic transition state, which leads to the formation of the cyclohexene product.Quantum chemical calculations, such as density functional theory DFT or ab initio methods, can be used to study the reaction mechanism, transition state, and activation energy of the Diels-Alder reaction. These calculations can provide insights into the electronic structure, molecular orbitals, and energetics of the reaction, which can help to understand the factors that influence the reaction rate and selectivity.To perform quantum chemical calculations, you would need to use specialized software such as Gaussian, ORCA, or Q-Chem, and have access to computational resources like high-performance computing clusters. Additionally, a deep understanding of computational chemistry methods and techniques is required to interpret the results and draw meaningful conclusions.