O(N) complexity algorithms for First-Principles Electronic Structure Calculations

Fattebert, J. L.

Lawrence Livermore National Laboratory

关键词: Electronic Structure;    Lawrence Livermore National Laboratory;    Schroedinger Equation;    Dimensions;    75 Condensed Matter Physics, Superconductivity And Superfluidity;   

DOI  :  10.2172/1036851
RP-ID  :  UCRL-TR-228407
RP-ID  :  W-7405-ENG-48
RP-ID  :  1036851

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来源: UNT Digital Library

【 摘 要 】

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.