Fast Real-Time Time-Dependent Density Functional Theory Calculations with the Parallel Transport Gauge

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Real-time time-dependent density functional theory (RT-TDDFT) simulations require very small time steps (attosecond or smaller) due to rapid electron wave function oscillations.
• This limitation restricts the study of ultrafast dynamics and the range of applicable systems.

Purpose of the Study:

• To develop a method for accelerating RT-TDDFT calculations.
• To enable the study of ultrafast dynamics with larger time steps.

Main Methods:

• Optimizing gauge choice using the parallel transport formalism to reduce electron wave function oscillations.
• Combining the parallel transport gauge with implicit integrators for accelerated RT-TDDFT.
• Implementing the scheme within a Schrödinger representation for broad software compatibility.

Main Results:

• The new method allows for significantly larger time steps (10-100 attoseconds) compared to standard explicit integrators.
• RT-TDDFT calculations using this method are over 10 times faster in wall clock time.
• Demonstrated applicability for absorption spectrum, ultrashort laser pulse, and Ehrenfest dynamics calculations.

Conclusions:

• The parallel transport gauge combined with implicit integrators offers a substantial acceleration for RT-TDDFT.
• This advancement broadens the applicability of RT-TDDFT for simulating ultrafast dynamics in materials like silicon.