Mathematical Models in First-Principles Calculations for Materials Science

Chapter
Part of the Mathematics for Industry book series (MFI, volume 5)

Abstract

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.

Keywords

First-principles calculations Hartree-Fock molecular orbital SCF DFT computer simulation materials science electron correlation 

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Copyright information

© Springer Japan 2014

Authors and Affiliations

  1. 1.Advanced Materials LaboratoriesSony CorporationAtsugiJapan

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