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Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science by Mark F. Horstemeyer

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6.5 PRIOR TO DENSITY FUNCTIONAL THEORY (DFT)

Our understanding so far of the electronic structure of matter is based on the theoretical methods of quantum mechanics and statistical mechanics. Now the history of the DFT is presented that deals with the developments that led up to the numerical methods related to quantum theory. Thus, our starting point is the Hamiltonian for the system of electrons and nuclei. Here the relativistic effects, magnetic effects, and quantum electrodynamics are not included:

c06ue005

can be simplified to

c06e013 (6.13)

where electrons are denoted by a lowercase subscript and the charge Zi and mass Mi are taken as unit. It is required to include the effects of many body terms: electron–electron Coulomb interaction, electron–ion interaction, ion–ion interaction, and the kinetic terms from both the electrons and ions. The key issue of the electronic structure theory is the development of methods to treat electronic correlations with sufficient accuracy that one can predict the diverse array of phenomena exhibited by matter. Schrödinger’s equation is the basic quantum mechanical equation that represents the fundamental many body theory. There is only one term in the Schrödinger equation that can be regarded as “small” that involves the inverse nuclei mass. If we set the mass ...

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