Temperature plays a crucial role in the rate and mechanism of a chemical reaction. Generally, an increase in temperature leads to an increase in the reaction rate due to the higher kinetic energy of the reacting molecules, which results in a higher frequency of successful collisions between reactants. Additionally, temperature can also influence the reaction mechanism by altering the energy barriers and relative stability of intermediates and transition states.A case study that demonstrates the effect of temperature on reaction rate and mechanism is the Diels-Alder reaction, a well-known [4+2] cycloaddition reaction between a conjugated diene and a dienophile. This reaction has been extensively studied using quantum chemistry techniques, such as density functional theory DFT and ab initio methods.In the Diels-Alder reaction, the reaction rate and mechanism can be influenced by temperature in the following ways:1. Activation energy: The activation energy is the minimum energy required for the reactants to overcome the energy barrier and form products. As the temperature increases, the fraction of molecules with sufficient energy to overcome the activation energy barrier also increases, leading to a higher reaction rate. Quantum chemistry calculations can be used to determine the activation energy and predict the temperature dependence of the reaction rate.2. Transition state theory: The reaction rate can be described using transition state theory, which involves calculating the partition function for the transition state and reactants. Quantum chemistry techniques can be used to determine the vibrational frequencies and geometries of the transition state and reactants, which are essential for calculating the partition functions. The temperature dependence of the partition functions can then be used to predict the reaction rate at different temperatures.3. Reaction mechanism: The Diels-Alder reaction can proceed through different mechanisms, such as concerted, stepwise, or diradical pathways, depending on the reactants and reaction conditions. Quantum chemistry calculations can be used to determine the relative energies of the intermediates and transition states involved in these mechanisms. As the temperature increases, the relative stability of these species can change, leading to a change in the preferred reaction mechanism.For example, a study by Ess and Houk J. Am. Chem. Soc. 2007, 129, 10646-10647 used DFT calculations to investigate the temperature dependence of the Diels-Alder reaction between 1,3-butadiene and ethylene. They found that at low temperatures, the reaction proceeds through a concerted mechanism with a synchronous transition state. However, as the temperature increases, the reaction becomes more asynchronous, with one carbon-carbon bond forming before the other. This change in mechanism is attributed to the increased thermal energy available to the reacting molecules, which allows them to overcome the higher energy barrier associated with the asynchronous transition state.In conclusion, temperature significantly affects the rate and mechanism of chemical reactions, and quantum chemistry techniques can be used to provide insights into these effects. By understanding the temperature dependence of reaction rates and mechanisms, chemists can better predict and control the outcomes of chemical reactions.