Electronic quantum motions in hydrogen molecule ion

Ciann Dong Yang, Hung Jen Weng

研究成果: Article同行評審

8 引文 斯高帕斯(Scopus)


The hydrogen molecule ion is a two-center force system expressed under the prolate spheroidal coordinates, whose quantum motions and quantum trajectories have never been addressed in the literature before. The momentum operators in this coordinate system are derived for the first time from the Hamilton equations of motion and used to construct the Hamiltonian operator. The resulting Hamiltonian comprises a kinetic energy T and a total potential V Total consisting of the Coulomb potential and a quantum potential. It is shown that the participation of the quantum potential and the accompanied quantum forces in the force interaction within H2+ is essential to develop an electronic motion consistent with the prediction of the probability density function |ψ|2. The motion of the electron in H2+ can be either described by the Hamilton equations derived from the Hamiltonian H = TK + VTotal or by the Lagrange equations derived from the Lagrangian H = TK - V Total. Solving the equations of motion with different initial positions, we show that the solutions yield an assembly of electronic quantum trajectories whose distribution and concentration reconstruct the σ and π molecular orbitals in H2+.

頁(從 - 到)2980-2999
期刊International Journal of Quantum Chemistry
出版狀態Published - 2011 十月

All Science Journal Classification (ASJC) codes

  • 原子與分子物理與光學
  • 凝聚態物理學
  • 物理與理論化學


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