Analysis of Chemical Phenomena by Solving the Constrained Hartree–Fock Equation. III. Influence of Geometry Change on the Energy of π Electrons in Conjugated Hydrocarbons

The total energy of a conjugated unsaturated hydrocarbon can formally be partitioned into the energy of π electrons and the frame energy. This type of partitioning has been used to study the role of π electrons; to know the relationship between the π-electronic structure and its energy, the molecular geometry has been varied. This paper examines the influences of such geometry change on the energy of π electrons from a basic point of view. It was found that there are four types of geometrical influences which disguise the relationship between the π-electronic structure and its energy. Contrary to this, the constrained Hartree–Fock method was shown to disclose the relationship between π-electronic structure and its energy clearly. Application of the constrained Hartree–Fock method to D6h and D3h benzenes showed that in a D6h benzene π electrons favor the symmetrically uniform distribution independently of the bond length and the partitioning method, while in a D3h benzene the uniform distribution of π electrons is destroyed. Analysis of gradients of partitioned energies with respect to the bond order at a D3h-distorted benzene indicated that π electrons favor a more uniform delocalization, but this is opposed by one- and two-electron potentials.