Orbitals ofthe Hydrogen Atom

So called Ilydrogenic atomic orbitals (exact solutions for the hydrogen atom) h ave radial nodes (values of th e distance r where the orbital s value goes to zero) that make them somewhat inconvenient for computation. Results are n ot sensitive to these nodes and most simple calculation s use Slater atom ic orbitals ofthe form... 

The wave functions (6.8) are known as atomic orbitals, for / = 0, 1,2, 3, etc., they are referred to as s, p, d, f, respectively, with the value of n as a prefix, i.e. Is, 2s, 2p, 3s, 3p, 3d, etc., From the explicit forms ofthe wave functions we can calculate both the sizes and shapes of the atomic orbitals, important properties when we come to consider molecule formation and structure. It is instructive to examine the angular parts of the hydrogen atom functions (the spherical harmonics) in a polar plot but noting from (6.9) that these are complex functions, we prefer to describe the angular wave functions by real linear combinations of the complex functions, which are also acceptable solutions of the Schrodinger equation. This procedure may be illustrated by considering the 2p orbitals. From equations (6.8) and (6.9) the complex wave functions are... 

Bohr, bohr radius ( o) - The radius ofthe lowest orbit in the Bohr model of the hydrogen atom, defined as where e is the permit-... 

Because ofthe factor exp (—0.5r ), the density distribution p is concentrated on the nucleus. The authors compare this density distribution with the corresponding Hartree-Fock density (appropriate for the potential used), and even with the density distribution related to the hydrogenlike atom (after neglecting l/ri2 in the Hamiltonian, the wave function becomes an antisymmetrized product of the two hydrogen-Uke orbitals). In the latter case, the electrons do not see each other, and the corresponding density distribution is too concentrated on the nucleus. As soon as the term l/ri2 is restored, the electrons immediately move apart, and p on the nucleus decreases by about 30%. The second result is also interesting the Hartree-Fock density is very close to ideal-it is almost the same curve. ... 

---