We propose progressive down-sampling of wave vectors in the Brillouin zone integrations occurring in the second-order many-body or M�ller-Plesset perturbation (MP2) method for extended systems of one-dimensional periodicity.  Higher-lying unoccupied and lower-lying occupied Bloch orbitals are subject to down-sampling by an exponentially increasing factor, making the total number of Bloch orbitals included in the MP2 lattice sums grow only logarithmically with respect to the number of basis functions per unit cell.  The quadrature weights of two-electron integrals entering the MP2 energy and quasiparticle energy expressions are proposed.  A combined use of this new down-sampling and the modulo scheme proposed earlier can speedup the MP2/6-31G** calculation of polyacetylene typically by a factor of 20 with an error in the correlation energy within a few percent relative to the conventional calculation.  Similar combinations can reproduce the MP2 quasiparticle energy bands accurately at a fraction of the usual computational cost.

Fast many-body perturbation method for extended systems by progressive down-sampling of wave vectors

241st National Meeting (2011)

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