Bond Orbital Resonance Theory Research Articles

Ground-state properties of benzenoid hydrocarbons by simple bond orbital resonance theory approach

π-electron energies and bond orders of benzenoid hydrocarbons with up to five fused hexagons have been considered by the simple Bond Orbital Resonance Theory (BORT) approach. The corresponding ground states were determined according to four BORT models. In the first three models a diagonalisation of the Huckel-type Hamiltonian was performed in the bases of Kekule, of Kekule and mono-Claus and of Kekule and Claus resonance structures, respectively. In the fourth model a simple BORT ansatz was used. According to this ansatz, the ground state is a linear combination of the positive Kekule structures, all with equal coefficients. It was shown that π-electron energies and bond orders obtained by these models correlate much better with the PPP energies and bond orders than with the Huckel energies and bond orders. This indicates that a simple BORT approach is quite reliable in predicting the more sophisticated PPP results. Concerning the relative performance of the four BORT models, the best results were obtained with the BORT ansatz. The performance deteriorates with the expansion of the basis set. This is attributed to the fact that in these models the improvement of the basis set is not accompanied with the corresponding improvement of the Hamiltonian. Comparing the BORT-ansatz bond orders with the Pauling bond orders, it was shown that BORT-ansatz bond orders correlate much better with the PPP bond orders.

Graphical representation of regular resonance structures and their linear dependence

The configuration interaction (CI) space X n generated by n electrons moving over 2 n orbitals is considered. Linear dependence of regular resonance structures (RRS) in X n is investigated. These structures are defined within the frame-work of the bond orbital resonance theory, and each RRS can be represented as a graph containing mutually disconnected oriented and/or nonoriented bonds. It is shown, using this graphical representation, that the space X n is spanned by the set of all k- and ( k−1)-excited RRS, where k is any of numbers 1,2,…, n. In particular, the set of all nonexcited and singly excited RRS spans X n . It is also shown that the set of all noncrossing RRS spans X n . The set of all ‘positive’ RRS is found to be isomorphic to the set of all ‘negative’ RRS. The spaces X 2 and X 3 are treated in detail, and various complete sets of linearly independent RRS are derived. The results thus obtained are applied to the benzene molecule. It is shown that the benzene SCF ground state can be represented as a linear combination of only three (positive) regular resonance structures.

Butadiene and benzene π‐electron SCF ground states in the bond orbital resonance theory approach

Butadiene and benzene π‐electron SCF ground states in the bond orbital resonance theory approach

Butadiene and benzene π‐electron SCF ground states in the bond orbital resonance theory approach

AbstractButadiene and benzene SCF ground states are analyzed using the bond orbital resonance theory (BORT) approach. The results obtained are compared with the analogous description of these states within the VB approach. It is shown that the structural weights of BORT Kekulé structures are much larger than the structural weights of the corresponding VB Kekulé structures. For example, in the butadiene case the structural weight of the BORT Kekulé structure is over 0.941, while the structural weight of the VB Kekulé structure is only 0.221. In addition, in the BORT approach one has to consider a much smaller number of resonance structures than in the VB approach. This suggests that the description of conjugated systems should be more successful in the BORT than in the VB basis, and that formal Kekulé structures should be interpreted in the BORT and not in the VB sense.

Benzene SCF ground state in the bond orbital resonance theory

The benzene π -electron SCF ground state is treated within the bond orbital resonance theory (BORT) approach. It is shown that this state is a linear combination of only three BORT resonance structures. Two structures are Kekulé BORT structures, and their contribution to the ground state is dominant. The third structure corresponds to the Claus description of the benzene molecule. This simple picture involving only three BORT structures is compared with the VB description which involves 175 VB resonance structures.