# Real-Space Finite Difference Method for O(N) First-Principles Molecular Dynamics with Plane Waves Accuracy

Wednesday, August 1, 2007 - 4:00pm - 4:30pm

EE/CS 3-180

Jean-Luc Fattebert (Lawrence Livermore National Laboratory)

Representing the electronic structure in Density Functional Theory (DFT)

by a set of localized wave functions discretized on a real-space mesh

essentially leads to a linear scaling of the computational cost with

the size of the physical system.

This can be achieved by formulating the DFT energy functional

in terms of general non-orthogonal orbitals which are then optimized

under localization constraints (spatial confinement).

Multigrid preconditioning and a block version of Anderson's

extrapolation scheme are used to accelerate convergence towards the

ground state.

For localization regions --- constraints --- large enough,

one can reduce truncation error to a value smaller than discretization

error and achieve the level of accuracy of a Plane Waves calculation.

Accuracy is improved by allowing for flexible localization regions that

can adapt to the system.

This also reduces problems with local minima and enables energy

conserving Born-Oppenheimer molecular dynamics simulations.

Our implementation of this approach scales on hundreds of processors and

becomes competitive with Plane Waves codes around 500 atoms.

References:

[1] J.-L. Fattebert and F. Gygi, Phys. Rev. B 73, 115124 (2006)

[2] J.-L. Fattebert and F. Gygi, Comput. Phys. Comm. 162, 24 (2004)

This work was performed under the auspices of the U.S. Department of

Energy by University of California Lawrence Livermore National

Laboratory under contract No. W-7405-Eng-48.

by a set of localized wave functions discretized on a real-space mesh

essentially leads to a linear scaling of the computational cost with

the size of the physical system.

This can be achieved by formulating the DFT energy functional

in terms of general non-orthogonal orbitals which are then optimized

under localization constraints (spatial confinement).

Multigrid preconditioning and a block version of Anderson's

extrapolation scheme are used to accelerate convergence towards the

ground state.

For localization regions --- constraints --- large enough,

one can reduce truncation error to a value smaller than discretization

error and achieve the level of accuracy of a Plane Waves calculation.

Accuracy is improved by allowing for flexible localization regions that

can adapt to the system.

This also reduces problems with local minima and enables energy

conserving Born-Oppenheimer molecular dynamics simulations.

Our implementation of this approach scales on hundreds of processors and

becomes competitive with Plane Waves codes around 500 atoms.

References:

[1] J.-L. Fattebert and F. Gygi, Phys. Rev. B 73, 115124 (2006)

[2] J.-L. Fattebert and F. Gygi, Comput. Phys. Comm. 162, 24 (2004)

This work was performed under the auspices of the U.S. Department of

Energy by University of California Lawrence Livermore National

Laboratory under contract No. W-7405-Eng-48.