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Linear-scaling multipole-accelerated Gaussian and finite-element Coulomb method
Mark A Watson1, Yuki Kurashige, Takahito Nakajima
1Department of Applied Chemistry, School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan. mark@qcl.t.u-tokyo.ac.jp
The Journal of Chemical Physics
|February 13, 2008
Summary
A new linear-scaling Gaussian and finite-element Coulomb (GFC) method, enhanced with the fast multipole method (FMM), rapidly computes electronic Coulomb potentials. This approach achieves significant speedups for large systems without compromising accuracy.
Area of Science:
- Computational Chemistry
- Quantum Chemistry
- Materials Science
Background:
- The Gaussian and finite-element Coulomb (GFC) method enables electronic Coulomb potential computation.
- Large systems present computational bottlenecks for the standard GFC method.
Purpose of the Study:
- To develop a linear-scaling implementation of the GFC method.
- To accelerate the computation of electronic Coulomb potentials for large-scale systems.
Main Methods:
- Implemented a linear-scaling version of the GFC method.
- Integrated the fast multipole method (FMM) to solve the Poisson equation boundary condition.
- Evaluated performance on one-dimensional polyalanine chains and three-dimensional diamond fragments.
Main Results:
- The GFC method with FMM shows significant computational savings for small- to medium-sized systems.
- Achieved over 100-fold speedups for systems with >1000 basis functions compared to exact boundary treatment.
- Demonstrated effectiveness and accuracy for both 1D and 3D molecular fragments.
Conclusions:
- The linear-scaling GFC method with FMM is an effective approach for rapid electronic Coulomb potential calculation.
- This method overcomes previous computational limitations for large molecular systems.
- The approach maintains high accuracy while providing substantial performance gains.
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