An Introduction to the Electronic Structure of Atoms and Molecules

Dr. Richard F.W. Bader 
Professor of Chemistry / McMaster University / Hamilton, Ontario

1.  The Nature of the Problem
2.  The New Physics
3. The Hydrogen Atom
  The Quantization of Energy
  The Probability Distribution of the Hydrogen Atom
  Angular Momentum of an Electron in an H Atom
  Some Useful Expressions
4.  Many-Electron Atoms
5.  Electronic Basis for the Properties of the Elements
6.  The Chemical Bond
7.  Ionic and Covalent Binding
8.  Molecular Orbitals
Table of Contour Values

Some Useful expressions

Listed below are a number of equations which give the dependence of  and  on the quantum numbers n, l and m. They refer not only to the hydrogen atom but also to any one-electron ion in general with a nuclear charge of Z. Thus He+ is a one-electron ion with Z = 2, Li+2 another example with Z = 3.

  The average distance between the electron and the nucleus expressed in atomic units of length is:

Note that  is proportional to n2 for l = 0 orbitals, and deviates only slightly from this for l ¹ 0. The value of decreases as Z increases because the nuclear attractive force is greater. Thus  for He+ would be only one half as large as  for H.