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Homo and lumo3/15/2023 Next, we’ll make use of this LUMO-HOMO energy difference analysis to account for reactivity pattern observed with a set of substrates for Pictet-Spengler reaction. In other words, the nucleophilicity and electrophilicity of substrate/reagent can be assessed by their HOMO and LUMO energies, and whether the reaction will proceed or not could be judged by the difference in energy of the orbitals involved in the reactions. Why LUMO energy could be used to gauge chemical reactivity? Zhi-Xiang Yu’s group provided a theoretical understanding of the Mayr equation based on frontier molecular orbital theory (FMO) 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 (Figure 2). A Frontier Molecular Orbital Theory approach to understanding the Mayr Equation Correlation between LUMO-HOMO energy difference and reactivity Figure 2. These calculated LUMO energy numbers correlate with chemical reactivity of the reagents: the lower the LUMO energy, the more reactive it is as halogenation reagent. TCCA has the lowest LUMO energy of -0.79 eV, DCH LUMO has an intermediate energy of 0.37 eV, and NCS has the highest energy of 1.09 eV. The LUMO lobes of these reagents are distributed around the chlorine atoms, not on the carbonyl carbons, consistent with the fact that they are halogenation reagents rather than acylation reagents. The calculated LUMO orbitals and energies of TCCA, DCH, and NCS are shown in Figure 1. LUMO orbitals and energies of TCCA, DCH and NCS How much stronger? Is there a way to quantify the differences? Figure 1. DCH and TCCA are stronger chlorination reagents than NCS. For example, halogenation of electron-rich aromatic substrates with N-chlorosuccinimide (NCS) usually works, while for electron-deficient ones, we’ll need to use dichlorohydantoin (DCH) or even trichloroisocyanuric acid (TCCA). In organic synthesis, we need to pair substrates and reagents of proper reactivity for the reactions to proceed smoothly.
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