Hydrogen molecule, bond length molecular orbitals

We shall examine the simplest possible molecular orbital problem, calculation of the bond energy and bond length of the hydrogen molecule ion Hj. Although of no practical significance, is of theoretical importance because the complete quantum mechanical calculation of its bond energy can be canied out by both exact and approximate methods. This pemiits comparison of the exact quantum mechanical solution with the solution obtained by various approximate techniques so that a judgment can be made as to the efficacy of the approximate methods. Exact quantum mechanical calculations cannot be carried out on more complicated molecular systems, hence the importance of the one exact molecular solution we do have. We wish to have a three-way comparison i) exact theoretical, ii) experimental, and iii) approximate theoretical. 

Consider atomic hydrogen and its components. In its most common isotopic form, it has one proton and one electron. The mass ratio of these two components is nearly 2000 1. Why are the two parts so different in mass Protons are so massive that they, individually and therefore in assemblages, may be assumed to be stationary. From this the concept of molecular and geometric structure arises bond lengths and angles require fixed positions. The mass of the electron is so low that we should consider electrons inherently delocalized. From this the concept of orbitals and electronic structure unavoidably arises we should not talk about dots and lines that describe fixed electrons. At least as importantly, atoms, molecules, and all the chemical-based reality from legumes to lepidoptera... 

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