Abstract

Iterative diagonalization of the Hamiltonian matrix is required to solve very large electronic-structure problems. Present algorithms are limited in their convergence rates at low wave numbers by stability problems associated with large changes in the Hartree potential, and at high wave numbers with large changes in the kinetic energy. A new method is described which includes the effect of density changes on the potentials and properly scales the changes in kinetic energy. The use of this method has increased the rate of convergence by over an order of magnitude for large problems.

Keywords

Hamiltonian (control theory)Kinetic energyPhysicsRate of convergenceConvergence (economics)Schrödinger equationStability (learning theory)Statistical physicsApplied mathematicsQuantum mechanicsMathematicsComputer scienceMathematical optimization

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Publication Info

Year
1989
Type
article
Volume
40
Issue
18
Pages
12255-12263
Citations
1080
Access
Closed

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Michael P. Teter, Michael C. Payne, Douglas C. Allan (1989). Solution of Schrödinger’s equation for large systems. Physical review. B, Condensed matter , 40 (18) , 12255-12263. https://doi.org/10.1103/physrevb.40.12255

Identifiers

DOI
10.1103/physrevb.40.12255