RING CURRENT IN ANTHRACENE AND PHENANTHRENE: CORRECTION TO HÜCKEL PARAMETERS

Excessive degeneracy in the ground state of the π-electron energy levels of anthracene was removed using the Hückel method by correcting the Coulomb integral of the four central carbon atoms. A further correction to the resonance integral was proposed based on the ring-current model, which describes the π-ring current flow along the molecule’s perimeter, by introducing a new parameter for the bridge carbon atoms expressed as a fraction of the resonance energy. The solution to the Hamiltonian was obtained based on the symmetry group theory, which provides the advantage of solving the determinant matrix or secular equations in a particular irreducible representation with a relatively small matrix dimension. The results were further analyzed to determine the bond order and bond length. The values of the harmonic oscillator model of aromaticity, GEO, and EN indices of aromaticity and their ratio for the central and outer rings of benzene were used to evaluate the validity of the correction. Applying the same method to phenanthrene as a topological analog of anthracene allows for an interesting comparison of the stabilities of the two molecules.针对蒽（anthracene）的π电子能级基态过度简并问题，本研究通过修正四个中心碳原子的库仑积分（Coulomb integral），采用休克尔方法（Hückel method）消除了该简并。基于环电流模型（ring-current model），本研究提出了共振积分（resonance integral）的进一步修正方案：该模型描述了沿分子周边流动的π环电流，通过引入以共振能分数形式表征的桥碳原子新参数完成修正。哈密顿量（Hamiltonian）的求解基于群论（symmetry group theory）实现，其优势在于可针对特定不可约表示（irreducible representation）以相对较小的矩阵维度求解行列式矩阵（determinant matrix）或久期方程（secular equations）。后续对计算结果展开分析，以确定分子的键级（bond order）与键长（bond length）。本研究采用芳香性简谐振动模型（harmonic oscillator model of aromaticity）的GEO指数、EN芳香性指数，以及苯环中心环与外环的上述指数比值，对修正方案的有效性进行了评估。将该方法应用于蒽的拓扑类似物菲（phenanthrene），可实现两种分子稳定性的富有意义的对比分析。