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Fast and accurate Coulomb calculation with Gaussian functions.
László Füsti-Molnár1, Jing Kong
1Q-CHEM Inc., Pittsburgh, Pennysylvania 15213, USA.
The Journal of Chemical Physics
|March 4, 2005
Summary
A new Fourier transform Coulomb method significantly accelerates density functional theory (DFT) calculations. This advancement makes large-scale DFT simulations, crucial for understanding molecular behavior, more computationally affordable and efficient.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Materials Science
Background:
- Coulomb interaction is a significant bottleneck in Density Functional Theory (DFT) calculations.
- Previous methods like Continuous Fast Multipole Method (CFMM) and J-engine have improved efficiency.
- Q-Chem has been a hub for developing advanced Coulomb calculation techniques.
Purpose of the Study:
- To introduce and evaluate an improved Fourier transform Coulomb method for DFT.
- To demonstrate the computational speedup and accuracy of the new method.
- To show the combined performance of multiple Coulomb calculation methods for large systems.
Main Methods:
- Implementation of an improved Fourier transform Coulomb method in Q-Chem.
- Utilizing an accurate numerical integration scheme with O(N^2) scaling.
- Benchmarking against existing efficient Coulomb calculation codes (CFMM and J-engine).
Main Results:
- The Fourier transform Coulomb method achieves O(N^2) scaling with basis size, improving upon O(N^4).
- Benchmark calculations show several-fold speedup in Coulomb energy calculations compared to CFMM and J-engine.
- The new method maintains accuracy while significantly reducing computational cost.
Conclusions:
- The Fourier transform Coulomb method offers substantial performance gains for the Coulomb part of DFT.
- Combining CFMM, J-engine, and the Fourier transform method provides optimal performance for large-scale DFT.
- These advancements enable affordable DFT calculations for systems with thousands of basis functions.