Quantum chemical explanation and APT atomic charge index of substituent orienting effect proposed by DFT calculation and MO Theory

In organic chemistry textbooks, the electron resonance states are used to explain the orienting effect of benzene substituent. However, these resonance states do not exist in the C₆H₅-S + E⁺ electrophilic addition, so the resonance state discussions actually are meaningless. The density functional theory (DFT) calculation shows that the C₆H₅-S + E⁺ addition follows the transition state theory and needs to overcome a barrier. Benzene molecule C₆H₆ has two degenerate highest occupied molecular orbitals (HOMOs), but after becoming substituted benzenes, the two HOMOs split to HOMO and HOMO-1 with different orbital energies and electron distributions. It makes the addition barrier on two or three benzene ring carbons is low, and the addition rate is fast, but the barrier of other carbons is high, and the rate is slow. Therefore, substituent splits the two degenerate HOMOs of benzene molecule, which is the origin of substituent orienting effect. For the substituted benzenes with halogen group -X and electron-releasing group, their HOMO images alone can determine that the two types of substituents are the ortho- and para-orienting groups, but for the substituted benzenes with electron-withdrawing group, their HOMO alone cannot determine whether the substituent is a meta-orienting group. The study found that atomic polar tensor (APT) charges are a good judgment index of substituent orienting effect because based on its physic-chemical model, the charges represent the number of active electrons on the benzene ring carbons. The DFT calculation gives the APT charges of 19 mono-substituted and 12 di-substituted benzenes and some aromatic molecules. The APT charges can all correctly determine their orienting effects, showing that APT atomic charge from quantum theoretical calculation is a good substituent orienting index.