A relativistic consistent quantum-theoretical description of electronic bound states in atoms was first introduced in atomic physics as early as the late 1920s and has been pushed forward since that time. It was believed, however, that effects stemming from Einstein’s theory of relativity were of little or even no importance to chemistry. This changed in the 1970s when it was recognized by Pyykkö, Pitzer, Desclaux, Grant and others that several ‘unusual’ features in heavy-element chemistry and spectroscopy can only be explained in terms of so-called relativistic effects. Relativistic effects denote the deviation of results obtained in a theoretical framework which is in accordance with Einstein’s theory of special relativity from nonrelativistic Schrödinger quantum mechanics. Since then, the development of quantum chemical methods for the description of relativistic electronic structures has made huge progress — particularly since the late 1980s.
Current relativistic electronic structure theory is now in a mature and welldeveloped state. We are in possession of sufficiently detailed knowledge on relativistic approximations and relativistic Hamiltonian operators which will be demonstrated in the course of this book. Once a relativistic Hamiltonian has been chosen, the electronic wave function can be constructed using methods well known from nonrelativistic quantum chemistry, and the calculation of molecular properties can be performed in close analogy to the standard nonrelativistic framework. In addition, the derivation and efficient implementation of quantum chemical methods based on (quasi-)relativistic Hamiltonians have facilitated a very large amount of computational studies in heavy element chemistry over the last two decades. Relativistic effects are now well understood, and many problems in contemporary relativistic quantum chemistry are technical rather than fundamental in nature.