Open AccessO(N) complexity algorithms for First-Principles Electronic Structure Calculations
Author(s) -
JeanLuc Fattebert
Publication year - 2007
Language(s) - English
Resource type - Reports
DOI - 10.2172/1036851
Subject(s) - eigenvalues and eigenvectors , hamiltonian (control theory) , schrödinger equation , eigenfunction , subspace topology , operator (biology) , physics , quantum , electronic structure , mathematics , quantum mechanics , chemistry , mathematical analysis , mathematical optimization , biochemistry , repressor , transcription factor , gene
The fundamental equation governing a non-relativistic quantum system of N particles is the time-dependant Schroedinger Equation [Schroedinger, 1926]. In 1965, Kohn and Sham proposed to replace this original many-body problem by an auxiliary independent-particles problem that can be solved more easily (Density Functional Theory). Solving this simplified problem requires to find the subspace of dimension N spanned by the N eigenfunctions {Psi}{sub i} corresponding to the N lowest eigenvalues {var_epsilon}{sub i} of a non-linear Hamiltonian operator {cflx H} determined from first-principles. From the solution of the Kohn-Sham equations, forces acting on atoms can be derived to optimize geometries and simulate finite temperature phenomenon by molecular dynamics. This technique is used at LLNL to determine the Equation of State of various materials, and to study biomolecules and nanomaterials