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Title: Density-functional theory of material design: fundamentals and applications-I

Journal Article · · Oxford open materials science
ORCiD logo [1]; ORCiD logo [2]
  1. Iowa State Univ., Ames, IA (United States)
  2. Indian Inst. of Technology (IIT), Kanpur (India)
+ Show Author Affiliations

This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in its extensive use for materials design and discovery and has thus ushered in the new field of computational material science. In this article, we start with an introduction to Schrödinger equation and methods of its solutions. After presenting exact results for some well-known systems, difficulties encountered in solving the equation for interacting electrons are described. How these difficulties are handled using the variational principle for the energy to obtain approximate solutions of the Schrödinger equation is discussed. The resulting Hartree and Hartree–Fock theories are presented along with results they give for atomic and solid-state systems. We then describe Thomas–Fermi theory and its extensions which were the initial attempts to formulate many-electron problem in terms of electronic density of a system. Having described these theories, we introduce modern DFT by discussing Hohenberg–Kohn theorems that form its foundations. We then go on to discuss Kohn–Sham (KS) formulation of DFT in its exact form. Next, local density approximation (LDA) is introduced and solutions of KS equation for some representative systems, obtained using the LDA, are presented. We end part-I of the review describing the contents of part-II.

Research Organization:
Ames Laboratory (AMES), Ames, IA (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
AC02-07CH11358
OSTI ID:
1842211
Report Number(s):
IS-J 10,693
Journal Information:
Oxford open materials science, Vol. 1, Issue 1; ISSN 2633-6979
Publisher:
Oxford University PressCopyright Statement
Country of Publication:
United States
Language:
English

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Related Subjects

36 MATERIALS SCIENCE
Schrödinger equation
density functional theory
Kohn–Sham equation
variational method
Hartree–Fock theory
local-density approximation