Calculation of phonons in real-space density functional theory

Area of Science:

• Computational Materials Science
• Condensed Matter Physics
• Quantum Chemistry

Background:

• Phonon calculations are crucial for understanding material properties.
• Existing methods often face limitations in efficiency or applicability.
• Real-space approaches offer potential advantages for complex systems.

Purpose of the Study:

• To present an accurate and efficient real-space formulation for phonon calculations.
• To enable the treatment of diverse material systems (insulators, metals) and dimensionalities.
• To develop a robust implementation for practical applications.

Main Methods:

• Utilized Kohn-Sham density functional theory within a real-space finite-difference framework.
• Derived expressions for the dynamical matrix and Sternheimer equation using specific approximations (local functional, norm-conserving pseudopotentials).
• Implemented the formulation using a high-order finite-difference method.

Main Results:

• Developed a formulation applicable to insulating and metallic systems of any dimensionality.
• Successfully treated semi-infinite and bulk systems with both orthogonal and nonorthogonal cells.
• Demonstrated excellent agreement between computed phonon dispersion curves and density of states with established plane-wave results.

Conclusions:

• The proposed real-space formulation provides an accurate and efficient method for phonon calculations.
• The implementation is versatile, applicable to a wide range of materials and system types.
• This work advances the capability of real-space density functional theory for materials simulations.