论文标题
广义摩尔斯电位的振动水平
Vibrational Levels of a Generalized Morse Potential
论文作者
论文摘要
通用的摩尔斯电势（GMP）是摩尔斯电位（MP）的扩展，其额外的指数项和附加参数可以补偿在相互作用电位的远距离部分中MP的错误行为。由于其他项和参数，与MP不同的情况不同，GMP的振动水平无法分析解决。 We present several numerical approaches for solving the vibrational problem of the GMP based on Galerkin methods, namely the Laguerre Polynomial Method (LPM), the Symmetrized Laguerre Polynomial Method (SLPM) and the Polynomial Expansion method (PEM) and apply them to the vibrational levels of the homonuclear diatomic molecules B$_2$, O$_2$和f $ _2 $，据报道，已经报道了高水平的理论全CI势能表面和实验测量的振动水平。总体而言，LPM产生的GMP的振动状态在光谱精度内收敛于0.01 cm $^{ - 1} $在1到2个数量级之间的数量级，并且比Colbert-Miller离散可变表示（CM-DVR）的方法更快，并且对三种hommonuclecle diat s tene ten of Colbert-Miller iNdiable variable contectation（CM-DVR）方法的基础 /网格函数 /网格点要少得多。
A Generalized Morse Potential (GMP) is an extension of the Morse Potential (MP) with an additional exponential term and an additional parameter that compensate for MP's erroneous behavior in the long range part of the interaction potential. Because of the additional term and parameter, the vibrational levels of the GMP cannot be solved analytically, unlike the case for the MP. We present several numerical approaches for solving the vibrational problem of the GMP based on Galerkin methods, namely the Laguerre Polynomial Method (LPM), the Symmetrized Laguerre Polynomial Method (SLPM) and the Polynomial Expansion method (PEM) and apply them to the vibrational levels of the homonuclear diatomic molecules B$_2$, O$_2$ and F$_2$, for which high level theoretical Full CI potential energy surfaces and experimentally measured vibrational levels have been reported. Overall the LPM produces vibrational states for the GMP that are converged to within spectroscopic accuracy of 0.01 cm$^{-1}$ in between 1 and 2 orders of magnitude faster and with much fewer basis functions / grid points than the Colbert-Miller Discrete Variable Representation (CM-DVR) method for the three homonuclear diatomic molecules examined in this study.
