不同双原子分子电子态的势能(或振动能谱)的展开性质可能不同, 文章将固定阶数的代数方法(AM)改进为可变阶数的代数方法, 使得该方法可以研究各种不同性质(不同能量展开阶数)的双原子分子电子态, 也可以解决光谱计算中可能出现的“蝴蝶效应”问题。 利用阶数可变的AM方法研究了原来固定阶数的AM方法难以给出正确结果的Ｎ２－ａ′１Σ－ｕ, Ｌｉ＋2－２ ２Σ＋ｇ, ４ＨｅＤ＋－Ｘ 1Σ＋和３９Ｋ ８５Ｒｂ－(２)３Σ＋等不同双核体系的完全振动能谱与离解能, 不但得到了与实验数据精确相符的理论结果, 还正确地预言了许多由于实验条件与技术原因而未能测得的物理数据。 研究表明阶数可变的AM方法能够更广泛地用于研究各类双核电子态体系的完全振动能谱和体系离解能。

The fixed order in the algebraic method (AM) suggested by Sun et al. is changed to be a flexible one in the vibrational energy expansion because the order of diatomic potential energy expansion may not be a constant. The AM with a flexible order was used to tackle the possible “butterfly effect” that may be encountered in spectroscopic computations, and to study the full vibrational levels ｛Ｅν｝ and the dissociation energies Dｅ for Ｎ２－ａ′１Σ－ｕ, Ｌｉ＋2－２ ２Σ＋ｇ, ４ＨｅＤ＋－Ｘ 1Σ＋ and ３９Ｋ ８５Ｒｂ－(２)３Σ＋ electronic systems. The results reproduced all known experimental vibrational energies, and predicted correct dissociation energies and all unknown high-lying levels that may not be given if one uses original AM. The calculations showed that the modified AM can be extended to study the full vibrational spectra for many more diatomic systems.