Finite-element method for electronic structure

Journal Article · Wed Mar 15 00:00:00 EST 1989 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.39.5819· OSTI ID:6315369

White, S R; Wilkins, J W; Teter, M P

We discuss the use of the finite-element method in electronic-structure calculations. Products of orthogonal or nonorthogonal one-dimensional (1D) finite-element shape functions are used to form 3D basis functions on a cubic grid. The strict locality of these functions means that the matrix for any local operator is very sparse, making calculation times proportional to the number of basis functions (N) possible. The completeness of the basis can be increased globally by decreasing the grid spacing and locally by increasing the number of basis functions per site. We discuss algorithms, including the highly efficient multigrid method, for solving the Poisson equation and for the ground state of the single-particle Schroedinger equation in O(N) time. Results are presented for test calculations of H, H/sub 2//sup +/, He, and H/sub 2/ using as many as 500 000 basis functions.

• Research Organization: Laboratory of Atomic and Solid State Physics, Clark Hall, Cornell University, Ithaca, New York 14853-2501
• OSTI ID: 6315369
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Vol. 39:9
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
HELIUM
ELECTRONIC STRUCTURE
HYDROGEN
HYDROGEN IONS 2 PLUS
ALGORITHMS
ATOMS
FINITE ELEMENT METHOD
GROUND STATES
LOCALITY
MOLECULES
POISSON EQUATION
SCHROEDINGER EQUATION
CATIONS
CHARGED PARTICLES
DIFFERENTIAL EQUATIONS
ELEMENTS
ENERGY LEVELS
EQUATIONS
FLUIDS
GASES
HYDROGEN IONS
IONS
MATHEMATICAL LOGIC
MOLECULAR IONS
NONMETALS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
RARE GASES
WAVE EQUATIONS
640302* - Atomic
Molecular & Chemical Physics- Atomic & Molecular Properties & Theory