Comparison of optimization methods for electronic-structure calculations

Journal Article · Thu Jun 15 00:00:00 EDT 1989 · Phys. Rev. B: Condens. Matter; (United States)

DOI:https://doi.org/10.1103/PhysRevB.39.12899· OSTI ID:6036198

Garner, J; Das, S G; Min, B I; Woodward, C; Benedek, R

The performance of several local-optimization methods for calculatingelectronic structure is compared. The fictitious first-order equation of motionproposed by Williams and Soler is integrated numerically by three procedures:simple finite-difference integration, approximate analytical integration (theWilliams-Soler algorithm), and the Born perturbation series. These techniquesare applied to a model problem for which exact solutions are known, the Mathieuequation. The Williams-Soler algorithm and the second Born approximationconverge equally rapidly, but the former involves considerably lesscomputational effort and gives a more accurate converged solution. Applicationof the method of conjugate gradients to the Mathieu equation is discussed.

• Research Organization: Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439(US)
• DOE Contract Number: W-31-109-ENG-38
• OSTI ID: 6036198
• Journal Information: Phys. Rev. B: Condens. Matter; (United States), Vol. 39:17
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
ELECTRONIC STRUCTURE
CALCULATION METHODS
ANNEALING
EQUATIONS OF MOTION
FINITE DIFFERENCE METHOD
HAMILTONIAN FUNCTION
MATHIEU EQUATION
NUMERICAL SOLUTION
PERTURBATION THEORY
SERIES EXPANSION
SIMULATION
DIFFERENTIAL EQUATIONS
EQUATIONS
FUNCTIONS
HEAT TREATMENTS
ITERATIVE METHODS
PARTIAL DIFFERENTIAL EQUATIONS
656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-)