中文摘要：

对于使用实验数据作为原数据进行的数值计算,由于实验误差的普遍存在,在数值计算过程中可能存在对实验误差的放大效应,使得微小的实验误差对数值计算的结果产生明显影响.因此本文通过在AM（algebraic method）方法中加入用以抵消实验误差的微小变分项δE,从而将AM改进为节点变分的代数方法VAM（variational algebraicmethod）.该方法具有更广泛的适用范围,尤其对处理那些实验数据较少、误差较大、已知的实验振动能级远离体系离解能的双原子体系效果明显.本文利用VAM方法研究了AM方法难以处理的5^1Πu^7Li_2,（6d）^1△9Na2,（7d）^1△9Na2和5^1∑＋NaK等不同碱金属双原子分子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.充分表明了VAM方法的可行性与正确性.此处对数值误差的分析和物理思考对其他精确的数值计算或数值模拟研究也有积极的参考意义.

英文摘要：

The algebraic method （AM） suggested by Sun et. al. is developed into a nodal variational AM （VAM） to offset the possible experimental errors by using an energy variational part 3E after analyzing the error amplification effect. The VAM is used to study the full vibrational levels { Eu } and the dissociation energies De for 5^1Πu^7Li_2,（6d）^1△9Na2,（7d）^1△9Na2 and 5^1∑＋NaK alkali metal diatomic molecular electronic systems. The results reproduce all known experimental vibrational energies, predict correct dissociation energies and all unknown high-lying levels that may not be given if one uses original AM or other numerical methods or experimental methods. These theoretical analyses and results not only show that the VAM is feasible and correct for many diatomic systems, but also provide constructive reference for other numerical calculations or simulations.