On the Convergence of the Self-Consistent Field Iteration in Kohn--Sham Density Functional Theory
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By analyzing the second-order Taylor expansion of the KS total energy functional and estimating the relationship between the Hamiltonian and the part of the Hessian which is not used in the SCF iteration, this paper is able to prove global convergence from an arbitrary initial point and local linear converge from an initial point sufficiently close to the solution of theKS equation.Abstract:
It is well known that the self-consistent field (SCF) iteration for solving the Kohn--Sham (KS) equation often fails to converge, yet there is no clear explanation. In this paper, we investigate the SCF iteration from the perspective of minimizing the corresponding KS total energy functional. By analyzing the second-order Taylor expansion of the KS total energy functional and estimating the relationship between the Hamiltonian and the part of the Hessian which is not used in the SCF iteration, we are able to prove global convergence from an arbitrary initial point and local linear convergence from an initial point sufficiently close to the solution of the KS equation under the assumptions that the gap between the occupied states and unoccupied states is sufficiently large and the second-order derivatives of the exchange correlation functional are uniformly bounded from above. Although these conditions are very stringent and are almost never satisfied in reality, our analysis is interesting in the sense th...read more
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References
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Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set
Georg Kresse,Jürgen Furthmüller +1 more
TL;DR: A detailed description and comparison of algorithms for performing ab-initio quantum-mechanical calculations using pseudopotentials and a plane-wave basis set is presented in this article. But this is not a comparison of our algorithm with the one presented in this paper.
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Modern quantum chemistry : introduction to advanced electronic structure theory
Attila Szabo,Neil S. Ostlund +1 more
TL;DR: In this paper, modern in-depth approaches to the calculation of the electronic structure and properties of molecules Hartree-Fock approximation, electron pair approximation, much more Largely self-contained, only prerequisite is solid course in physical chemistry Over 150 exercises 1989 edition
Book
Electronic Structure: Basic Theory and Practical Methods
TL;DR: In this paper, the Kohn-Sham ansatz is used to solve the problem of determining the electronic structure of atoms, and the three basic methods for determining electronic structure are presented.
Journal ArticleDOI
The Geometry of Algorithms with Orthogonality Constraints
TL;DR: The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms and developers of new algorithms and perturbation theories will benefit from the theory.
Journal ArticleDOI
A black-box self-consistent field convergence algorithm: One step closer
TL;DR: The present algorithm is benchmarked against the direct inversion iterative subspace method based on the commutator of the density and Fock matrices developed by Pulay (DIIS), and it is shown how EDIIS can detect the presence and determine the value of fractional occupations in KS-DFT.