Sunday, March 25, 2012

Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase

Joost VandeVondele, Urban Borštnik, and Jürg Hutter Journal of Chemical Theory and Computation 2012, ASAP. (Paywall)

This paper presents orbital-based self-consistent field calculations on three-dimensional dihydrogen and water clusters containing up to two million atoms. The main new feature is the use of a mathematical technique called the matrix sign function to express the density matrix and the inverse overlap matrix. This is combined with more conventional linear techniques: a static mixing approach to solve the self-consistent equation, parallel sparse matrix multiplication, use of plane waves and Fast Fourier Transforms to compute the Coulomb energy, and use of energy functions that do not require Hartree-Fock exchange.

The method is implemented in the open source CP2K/Quickstep software package.

The LDA-DFT/minimial basis set energy of one million dihydrogen molecules is computed in 8 minutes of wall clock time using 46,656 cores of an Cray XT5. For comparison, an LDA-DFT/double zeta single point calculation on a 96,000-atom water cluster (736,000 basis functions) requires 16 h using  46,656 cores.  Results for NDDO and DFT tight binding energy functions are also presented.

It will be very interesting to see how this method performs with heterogeneous systems and GGA functionals.

Acknowledgement: Thanks to Noel O'Boyle and Michael Banck for alerting me to this article.

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