TY - GEN

T1 - Optimization of functionals of orthonormal functions in the absence of unitary invariance

AU - Klüpfel, Peter

AU - Klüpfel, Simon

AU - Tsemekhman, Kiril

AU - Jónsson, Hannes

PY - 2012

Y1 - 2012

N2 - We discuss the optimization of a functional with respect to sets of orthonormal functions where unitary invariance does not apply. This problem arises, for example, when density functionals with explicit self-interaction correction are used for systems of electrons. There, unitary invariance cannot be used to reformulate the minimization of the energy with respect to each of the functions as an eigenvalue problem as can be done for the commonly used GGA-DFT and Hartree-Fock theory. By including optimization with respect to unitary transformations as an explicit step in the iterative minimization procedure, fast convergence can, nevertheless, be obtained. Furthermore, by working with two sets of orthonormal functions, the optimal functions and a set of eigenfunctions, the implementation of the extended functional form in existing software becomes easier. The additional computations arising from the lack of unitary invariance can largely be carried out in parallel.

AB - We discuss the optimization of a functional with respect to sets of orthonormal functions where unitary invariance does not apply. This problem arises, for example, when density functionals with explicit self-interaction correction are used for systems of electrons. There, unitary invariance cannot be used to reformulate the minimization of the energy with respect to each of the functions as an eigenvalue problem as can be done for the commonly used GGA-DFT and Hartree-Fock theory. By including optimization with respect to unitary transformations as an explicit step in the iterative minimization procedure, fast convergence can, nevertheless, be obtained. Furthermore, by working with two sets of orthonormal functions, the optimal functions and a set of eigenfunctions, the implementation of the extended functional form in existing software becomes easier. The additional computations arising from the lack of unitary invariance can largely be carried out in parallel.

KW - electrons

KW - functional optimization

KW - orthonormal functions

UR - http://www.scopus.com/inward/record.url?scp=84857480995&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-28145-7_3

DO - 10.1007/978-3-642-28145-7_3

M3 - Conference contribution

AN - SCOPUS:84857480995

SN - 9783642281440

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 23

EP - 33

BT - Applied Parallel and Scientific Computing - 10th International Conference, PARA 2010, Revised Selected Papers

T2 - 10th International Conference on Applied Parallel and Scientific Computing, PARA 2010

Y2 - 6 June 2010 through 9 June 2010

ER -