Hydrogen atom, calculations Schrodinger model

Exact solutions to the electronic Schrodinger equation are not possible for many-electron atoms, but atomic HF calculations have been done both numerically and within the LCAO model. In approximate work, and for molecular applications, it is desirable to use basis functions that are simple in form. A polyelectron atom is quite different from a one-electron atom because of the phenomenon of shielding", for a particular electron, the other electrons partially screen the effect of the positively charged nucleus. Both Zener (1930) and Slater (1930) used very simple hydrogen-like orbitals of the form... 

The modern theory of chemical bonding begins with the article The Atom and the Molecule published by the American chemist G. N. Lewis in 1916 [1], In this article, which is still well worth reading, Lewis for the first time associates a single chemical bond with one pair of electrons held in common by the two atoms "After a brief review of Lewis model we turn to a quantum-mechanical description of the simplest of all molecules, viz. the hydrogen molecule ion H J. Since this molecule contains only one electron, the Schrodinger equation can be solved exactly once the distance between the nuclei has been fixed. We shall not write down these solutions since they require the use of a rather exotic coordinate system. Instead we shall show how approximate wavefunctions can be written as linear combinations of atomic orbitals of the two atoms. Finally we shall discuss so-called molecular orbital calculations on the simplest two-electron atom, viz. the hydrogen molecule. 

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