A Frontier Molecular Orbital Theory Approach to Understanding the Mayr Equation and to Quantifying Nucleophilicity and Electrophilicity by Using HOMO and LUMO Energies

Abstract Obtaining the reactivities (such as nucleophilicities and electrophilicities) of molecules is of fundamental importance in chemistry. Mayr and co‐workers have developed the Mayr equation, which has been widely used to quantify nucleophilicity and electrophilicity. Herein we propose a theoretical understanding of the Mayr equation based on frontier molecular orbital (FMO) theory and the Eyring equation of the transition state theory, showing that the nucleophilicity of a molecule is related to the energy of this molecule’s highest occupied molecular orbital (HOMO), while the electrophilicity is related to the energy of the lowest unoccupied molecular orbital (LUMO) of the electrophile. Consequently, we propose a new approach by combining the FMO theory and the Mayr equation to predict the reactivities of new molecules. Ab initio calculation results support these linear relationships between LUMO energies and the Mayr electrophilicities ( E ) and the HOMO energies and the Mayr nucleophilicities ( N ) for sets of electrophiles and nucleophiles, respectively. For each set of nucleophiles or electrophiles, their different reactivities are mainly controlled by the electronic effects of the substituents. If other effects, such as sterics, affect reactivity for a set of electrophiles or nucleophiles, the linear relationships between HOMO levels and N values and LUMO levels and E values cannot be secured. The present approach through combining Mayr equation and the quantitative FMO theory suggests that the Mayr nucleophilicity or electrophilicity of a new molecule, which could be an intermediate of a reaction, unstable reactant, or a hypothetical reactive species, can be obtained through ab initio calculations of the frontier molecular orbital energies, and this will greatly expand the data sets of Mayr nucleophilicities and electrophilicities.