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以特征矩阵为出发点，根据自相似性原理，结合图论的有关理论对简单分子轨道方法（ＨＭＯ）作了改进．通过对一些由完全相同的重复单元构成的多聚物的讨论，计算出环形和线性多聚物的特征多项式的一般表达式及其态密度．在此基础之上，提出并证实了周期性结构的态密度与边界条件是相关的；得到了构成单元相同的环形和线性多聚物在无限大的情况下有相同态密度的结论；发现了相同单元构成的无限大多聚物的态密度的奇异点可由二聚物的能级确定
Taking the eigenvalue matrix as a starting point, the HMO method is improved based on the self-similarity principle and the theory of graph theory. The general expression of the characteristic polynomials of cyclic and linear polymers and their density of states are calculated by discussing some polymers consisting of identical repeating units. On this basis, it is proposed and confirmed that the state density of periodic structures is related to the boundary conditions. The conclusion is obtained that the same ring and linear polymers with the same constitutional unit have the same state density under the infinite condition. The singularity of the density of states of an infinite macromolecule composed of the same unit can be determined by the energy level of the dimer