The focus of our investigation is to evaluate one of the four contributing terms to the coulombic potential energy of an H<sub>2</sub> molecule. Specifically, we are interested in the term describing the e...The focus of our investigation is to evaluate one of the four contributing terms to the coulombic potential energy of an H<sub>2</sub> molecule. Specifically, we are interested in the term describing the electronic interaction of the charge distribution of one of the hydrogen atoms with the proton of the second atom. Quantum mechanics provides the charge distribution;hence, the evaluation of this term is a semi-classic quantum physics issue. For states other than the ground state the charge distributions are not spherically symmetric;they are functions of the radial and the angular coordinates. For the excited states we develop exact analytic expressions conducive to the potential energies. Because of the functional complexities of the wave functions, the evaluation of the core integrals is carried out utilizing symbolic capabilities of Mathematica [1]. Plots of these energies vs. the distance between the two protons reveal global features.展开更多
文摘The focus of our investigation is to evaluate one of the four contributing terms to the coulombic potential energy of an H<sub>2</sub> molecule. Specifically, we are interested in the term describing the electronic interaction of the charge distribution of one of the hydrogen atoms with the proton of the second atom. Quantum mechanics provides the charge distribution;hence, the evaluation of this term is a semi-classic quantum physics issue. For states other than the ground state the charge distributions are not spherically symmetric;they are functions of the radial and the angular coordinates. For the excited states we develop exact analytic expressions conducive to the potential energies. Because of the functional complexities of the wave functions, the evaluation of the core integrals is carried out utilizing symbolic capabilities of Mathematica [1]. Plots of these energies vs. the distance between the two protons reveal global features.
