ODE integration schemes for plane-wave real-time time-dependent density functional theory.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Real-time time-dependent density functional theory (RT-TDDFT) is crucial for simulating electronic dynamics.
• Accurate and efficient numerical integration schemes are essential for RT-TDDFT.
• Plane-wave basis sets are commonly used in density functional theory (DFT) calculations.

Purpose of the Study:

• To implement and assess various integration schemes for RT-TDDFT using a plane-wave basis.
• To compare the accuracy, stability, and computational cost of different methods.
• To identify superior integration schemes for electronic structure simulations.

Main Methods:

• Implementation of Crank-Nicolson and explicit integration schemes (Adams-Bashforth, Adams-Bashforth-Moulton, Runge-Kutta).
• Utilizing a plane-wave basis set within the RT-TDDFT framework.
• Investigating a graphene monolayer system to evaluate performance.

Main Results:

• Adams-Bashforth and Adams-Bashforth-Moulton methods (orders 4 and 5) demonstrated higher accuracy than Crank-Nicolson and Runge-Kutta.
• These methods showed favorable stability and serial computational cost.
• Parallel runtime scaling confirmed the efficiency of the proposed methods.

Conclusions:

• Higher-order Adams-Bashforth and Adams-Bashforth-Moulton methods are recommended for RT-TDDFT simulations requiring low error.
• These schemes offer an efficient and accurate approach for propagating time-dependent Kohn-Sham equations.
• The developed integration schemes are available as an extension to the Quantum ESPRESSO code.