Analysis of Chemical Phenomena by Solving the Constrained Hartree–Fock Equation. II. Relationship between π-Electronic Structure and Its Energy in Benzene

The constrained Hartree–Fock method provides quantum-mechanically acceptable wave functions of an arbitrary electronic structure without changing the molecular geometry. We have applied this method to the analysis of the behavior of π electrons in benzene finding that there are two types of resonance energy, simple resonance between double bonds and super-stabilization due to the topology of benzene, which were estimated as 54 and 168 kJ mol−1, respectively. According to our method, π electrons in benzene were found to have a propensity for uniform distribution. Namely, the D6h distribution of π electrons gives the minimum values concerning both the π-electronic and total energies, which are brought forth by lowering the kinetic energy of π electrons. The origin of delocalization of π electrons in benzene was attributed to relaxation of the kinetic-energy pressure of π electrons.