Diatomic molecules according to the wave mechanics. II. Vibrational levels
Diatomic molecules according to the wave mechanics. II. Vibrational levels
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DOI：
10.1103/physrev.34.57
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发表时间：
1929-07-01
期刊：
影响因子：
--
通讯作者：
Morse, PM
中科院分区：
文献类型：
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作者：
Morse, PM
当假定势能函数具有类似于Heitler和伦敦等人所要求的形式时，得到了描述双原子分子中原子核运动的薛定谔方程的精确解.发现允许的振动能级由公式E（n）= E e+ h ω 0（n+ 1 2）− h ω 0 x（n+ 1 2）2给出，已知该公式相当准确地表达了实验值。在4%的可能误差范围内，分子的标准间距r0与经典振动频率ω 0之间的经验关系为r0 3 ω 0= K，其中K对所有双原子分子和所有电子能级都是相同的常数。利用这一定律和上述解，分析了各种分子的许多电子能级的实验数据，得到了一个常数表，从这个表中可以画出势能曲线。分子转动引起的上述振动能级的变化在一级近似下符合Kratzer公式。
An exact solution is obtained for the Schroedinger equation representing the motions of the nuclei in a diatomic molecule, when the potential energy function is assumed to be of a form similar to those required by Heitler and London and others. The allowed vibrational energy levels are found to be given by the formula E (n)= E e+ h ω 0 (n+ 1 2)− h ω 0 x (n+ 1 2) 2, which is known to express the experimental values quite accurately. The empirical law relating the normal molecular separation r 0 and the classical vibration frequency ω 0 is shown to be r 0 3 ω 0= K to within a probable error of 4 percent, where K is the same constant for all diatomic molecules and for all electronic levels. By means of this law, and by means of the solution above, the experimental data for many of the electronic levels of various molecules are analyzed and a table of constants is obtained from which the potential energy curves can be plotted. The changes in the above mentioned vibrational levels due to molecular rotation are found to agree with the Kratzer formula to the first approximation.