用经典力学计算氢分子的键长键能及力常数

Calculation of Bond-length, Bond-energy and Force Constant of Hydrogen Molecule by Classical Mechanics

氢原子中 1s电子的电子云呈球形 ,电子的最大几率密度分布出现在玻尔半径a0 的球壳内 ,认为几率密度分布及电子云属统计规律 ,意味着已经使用了宏观时标 ,这样就使氢分子体系中能量和时间的作用量远大于普郎克常数 ;根据电子云的交叠 ,用经典力学计算了基态氢分子的结构常数 ,获得键长、键能及力常数的表达式分别为Re=2a0 ,De=ze/4 2a0 ,k=ze/2 2a30 ,采用原子单位 (a .u .)时z、e及a0 均为 1,获得Re=1 414a .u .,De=0 177a .u .,k =0 3 5 4a .u .,这些数值与实验值的相对误差分别 <1% ,<2 %和<4% ;成键模型直观 ,物理意义明确 。

The 1s electron cloud in hydrogen atom has the largest probability density distribution around a spherical shell with Bohr radius a 0. The author thinks the probability density distribution and electron cloud belong in fact,to statistic regularity, and imply a macro-time scale is used, therefore in hydrogen molecule the product of energy and time is far larger than Planck Constant. Based on the overlap of electron cloud, the ground state hydrogen molecule structural parameters are calculated with the classical mechanics, and the hydrogen molecule bond-length R e, bonding-energy D e and force constant k are represented R-e=2a-0,D-e=ze/42a-0,k=ze/22a+3-0,respectively. When atomic-unit is used, z,e and a 0 are all 1,and there is R e=1.414 a.u.,D e=0.177 a.u., k=0.354 a.u.. Compared with experimental values, the respective errors are less than 1%, 2% and 4%. In this calculation, hydrogen molecule chemical bonding model is concise and has clear physical meaning, and no any artificial parameters are introduced.