Mathematical Models in First-Principles Calculations for Materials Science
The mathematical models used in first-principles calculations aresummarized, and the uses of mathematics in various industries are introduced. The different approximations used to obtain the Hartree-Fock equation from the Schrödinger equation for multi-atom systems are summarized, and difficulties in solving the Hartree-Fock equation in a self-consistent way are presented. Novel algorithms are needed in order to reduce computational costs of large systems.
KeywordsFirst-principles calculations Hartree-Fock molecular orbital SCF DFT computer simulation materials science electron correlation
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