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Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations
Eric Cancès1, Katarzyna Pernal
1CERMICS, Ecole des Ponts and INRIA, 6 & 8 Avenue Blaise Pascal, 77455 Marne-la-Vallée Cedex 2, France. cances@cermics.enpc.fr
The Journal of Chemical Physics
|April 10, 2008
Summary
Projected gradient algorithms efficiently optimize some density matrix functionals but struggle with BBk functionals due to their nature. This research explores computational chemistry optimization methods for N-representable density matrices.
Area of Science:
- Computational quantum chemistry
- Mathematical optimization techniques
Background:
- N-representable one-electron reduced density matrices are crucial in electronic structure theory.
- Optimizing functionals defined on these matrices is computationally challenging.
Purpose of the Study:
- To develop and evaluate projected gradient algorithms for optimizing functionals on N-representable density matrices.
- To assess the efficiency of these algorithms for different types of functionals.
Main Methods:
- Implementation of projected gradient algorithms.
- Application to Hartree-Fock, Muller-Buijse-Baerends, and BBk functionals.
- Analysis of convergence rates and computational efficiency.
Main Results:
- Projected gradient algorithms demonstrate high efficiency for Hartree-Fock and Muller-Buijse-Baerends functionals.
- Slow convergence was observed for BBk functionals (k=1,2,3).
- The inefficiency with BBk functionals is attributed to their non-proper functional nature.
Conclusions:
- Projected gradient algorithms are effective for certain density matrix functionals.
- The BBk functionals present unique challenges for optimization due to their mathematical properties.
- Further research may be needed to develop specialized algorithms for non-proper density matrix functionals.
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