Efficient real space formalism for hybrid density functionals.

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Mechanics

Background:

• Generalized Kohn-Sham density functional theory (DFT) is crucial for electronic structure calculations.
• Hybrid exchange-correlation functionals offer improved accuracy but can be computationally expensive.
• Existing methods often rely on Fast Fourier Transforms (FFT), which have limitations with boundary conditions.

Purpose of the Study:

• To present an efficient real-space formalism for hybrid exchange-correlation functionals in DFT.
• To enable accurate and computationally competitive electronic structure calculations without FFT limitations.
• To provide a framework for ab initio molecular dynamics with hybrid functionals.

Main Methods:

• Developed an efficient representation of the real-space finite-difference Laplacian matrix using Kronecker products.
• Implemented the formalism for unscreened and range-separated hybrid functionals.
• Validated accuracy and efficiency against established planewave codes for various systems.

Main Results:

• Achieved a highly competitive time to solution, comparable to FFT schemes, without boundary condition restrictions.
• Demonstrated up to an order-of-magnitude speedup for the real-space method.
• Successfully applied the framework to study liquid water structure via ab initio molecular dynamics, showing good agreement with literature.

Conclusions:

• The developed real-space formalism offers an efficient and flexible approach for DFT calculations with hybrid functionals.
• This method overcomes limitations of FFT-based approaches, particularly regarding boundary conditions.
• The formalism opens new avenues for accurate and fast electronic structure investigations and molecular dynamics simulations.