Solving the Schroedinger Equation of Hydrogen Molecule with the Free-Complement Variational Theory: Essentially Exact Potential Curves and Vibrational Levels of the Ground and Excited States of Σ symmetry
Solving the Schroedinger Equation of Hydrogen Molecule with the Free-Complement Variational Theory: Essentially Exact Potential Curves and Vibrational Levels of the Ground and Excited States of Σ symmetry
复制标题
用自由补变分理论求解氢分子薛定谔方程：Σ对称基态和激发态的本质精确势能曲线和振动能级
DOI：
10.1039/c8cp05949g
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发表时间：
2019
影响因子：
3.3
通讯作者：
and Hiroshi Nakatsuji
中科院分区：
文献类型：
--
作者：
Yusaku I. Kurokawa;Hiroyuki Nakashima;and Hiroshi Nakatsuji
对氢分子的Schrödinger方程进行了基本准确和系统的求解，计算了1Σg、1Σu、3Σg和3Σu对称态的电子基态和激发态的势能曲线。其基本理论是变分自由补理论，是求解原子分子Schrödinger方程的精确通用理论。结果基本准确，绝对能量在μ-hart位以上是正确的。此外，所有的波函数沿势曲线在每个核距上都满足正确的正交性和哈密顿正交性，这使得在所有计算的电子态之间进行系统的分析和讨论成为可能。值得注意的是，目前报道的许多H2的精确计算都不满足这些条件。基于目前基本准确的势曲线，我们计算并分析了与所有电子态相关的振动能级。其中具有双阱势的激发态表现出一些有趣的振动态特征。这些结果值得未来天文学研究的进一步研究。
The Schrödinger equation of hydrogen molecules was solved essentially exactly and systematically for calculating the potential energy curves of the electronic ground and excited states of the 1Σg, 1Σu, 3Σg, and 3Σu symmetries. The basic theory is the variational free complement theory, which is an exact general theory for solving the Schrödinger equation of atoms and molecules. The results are essentially exact with the absolute energies being correct beyond μ-hartree digits. Furthermore, all of the present wave functions satisfy correct orthogonalities and Hamiltonian-orthogonalities to each other at every nuclear distance along the potential curve, which makes systematic analyses and discussions possible among all the calculated electronic states. It is noteworthy that these conditions were not satisfied in many of the accurate calculations of H2 reported so far. Based on the present essentially exact potential curves, we calculated and analyzed the vibrational energy levels associated with all the electronic states. Among them, the excited states having double-well potentials showed some interesting features of the vibrational states. These results are worthy of future investigations in astronomical studies.