First-Quantized Dirac-Based Many-Electron Theory

First-Quantized Dirac-Based Many-Electron Theory 

In the molecular sciences it is most appropriate to adopt a pragmatic attitude toward the Dirac equation in order to set up a theory which closely resembles nonrelativistic many-electron theory. We will see that we can afford a number of approximations designed such that the numerical effect on physical observables still resembles that of a truly relativistic many-electron theory. Hence, we proceed from the fundamental physical principles of Einstein s special theory of relativity to approximations of different degree. As a matter of fact this is exactly the program of relativistic quantum chemistry that we shall start to develop in this chapter. 

Quantum mechanical calculations in the molecular sciences do not necessarily involve a variation of the number of particles (especially not through pair creation and annihilation processes). This even holds true in the case of particle exchange processes as the reactants involved can be described in a fixed-particle-number framework. For example, a reductant can be treated together with the molecule to be reduced as a whole system such that the number of electrons remains constant during the reduction process. Also, the energy of liberated electrons can be considered zero, and thus such electrons can be neglected from one step to the next in a reaction sequence. This is, for instance, useful for ionization processes, where the released electron is considered to be at rest and features zero energy at infinite distance so that it makes no contribution to the Hamiltonian of the ionized system. There is therefore a need to proceed from QED to a computationally more appropriate albeit less 

Relativistic Quantum Chemistry. Markus Reiher and Alexander Wolf 

The Hamiltonian of the two-electron atom already features all pair-interaction operators that are required to describe a system with an arbitrary number of electrons and nuclei. Hence, the step from one to two electrons is much larger than from two to an arbitrary number of electrons. For the latter we are well advised to benefit from the development of nonrelativistic quantum chemistry, where the many-electron Hamiltonian is exactly known, i.e., where it is simply the sum of all kinetic energy operators according to Eq. (4.48) plus all electrostatic Coulombic pair interaction operators. 

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I 8 First-Quantized Dirac-Based Many-Electron Theory... 

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