Relativistic effects have been found to play a crucial role in the description of the electronic structure of heavy elements. Ab initio quantum mechanical methods which are based upon many-electron extensions of Dirac's relativistic single-particle wave equation have proven to be extremely effective in properly describing the electronic structure of molecules which contain heavy atoms, though these methods are prohibitively expensive for most systems of chemical interest. These notes begin with a review of Dirac's equation for a single particle, and some many-electron extensions of this equation. Next, many of the most widely used relativistic quantum chemical techniques are discussed. Finally, the major effects of special relativity on atomic electronic structure are explored and quantified, and the consequences of these effects on molecular structure and chemical behavior are discussed.
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