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Plane-wave pseudopotential implementation of explicit integrators for time-dependent Kohn-Sham equations in
André Schleife1, Erik W Draeger, Yosuke Kanai
1Condensed Matter and Materials Division, Lawrence Livermore National Laboratory, Livermore, California 94550, USA.
The Journal of Chemical Physics
|December 20, 2012
Summary
Explicit integrators for real-time Kohn-Sham equation propagation were evaluated. The fourth-order Runge-Kutta method demonstrated conditional stability and accuracy for large-scale simulations.
Area of Science:
- Computational Physics
- Quantum Chemistry
- Materials Science
Background:
- Accurate real-time propagation of time-dependent Kohn-Sham equations is crucial for simulating quantum systems.
- Assessing numerical integrators is essential for efficient large-scale electronic structure calculations.
Purpose of the Study:
- To compare the stability and accuracy of explicit integrators for time-dependent Kohn-Sham equations.
- To identify suitable algorithms for large-scale real-time electronic structure simulations.
Main Methods:
- Implementation and assessment of four explicit integration algorithms (Euler, finite-difference, Runge-Kutta).
- Utilized a plane-wave pseudopotential framework with the adiabatic approximation for exchange-correlation functional.
- Performed simulations for a single sodium atom and a sodium atom in bulk magnesium oxide.
Main Results:
- First-order Euler and second-order finite-difference schemes showed instability.
- The fourth-order Runge-Kutta scheme exhibited conditional stability and accuracy.
- Demonstrated excellent parallel scalability for hundreds of electrons on over a thousand processors.
Conclusions:
- The fourth-order Runge-Kutta method is a suitable choice for large-scale simulations using real-time propagation of time-dependent Kohn-Sham equations.
- Explicit integrators, particularly the fourth-order Runge-Kutta, enable efficient and accurate quantum system simulations.
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