Hybrid functionals and GW approximation in the FLAPW method | JoVE Visualize

Area of Science:

Computational Materials Science
Condensed Matter Physics
Quantum Chemistry

Background:

Density-functional theory (DFT) and many-body perturbation theory are crucial for understanding material properties.
Hybrid functionals and the GW approximation are advanced methods within these theories.
Numerical implementations, particularly within the full-potential linearized augmented-plane-wave (FLAPW) method, are computationally demanding.

Purpose of the Study:

To present recent advances in the numerical implementation of hybrid functionals and the GW approximation.
To detail the use of the mixed product basis for efficient calculations.
To introduce computational cost reduction techniques for these advanced electronic structure methods.

Main Methods:

Utilized the full-potential linearized augmented-plane-wave (FLAPW) method.
Employed a mixed product basis for wave function products, enabling efficient representation of nonlocal potentials and screened interactions.
Developed techniques for calculating the GW self-energy (imaginary frequency axis with analytic continuation or direct frequency convolution) and optimizing hybrid-functional calculations (exploiting symmetries, sparse Coulomb matrices, analytic expansions, and nested convergence schemes).

Main Results:

Demonstrated efficient numerical implementations of hybrid functionals and GW approximation within the FLAPW framework.
Showcased significant reductions in computational cost through various optimization strategies.
Presented CPU timings for prototype semiconductors and illustrative results for GdN and ZnO, validating the implemented methods.

Conclusions:

The presented numerical advances and computational tricks considerably reduce the cost of hybrid-functional and GW calculations.
These optimized implementations within the FLAPW method provide a versatile and efficient approach for electronic structure studies.
The findings pave the way for more accessible and accurate theoretical investigations of materials properties.