  The calculation of the MP2 correlation energy for extended systems can be
viewed as a multi-dimensional integral in the thermodynamic limit, and the
standard method for evaluating the MP2 energy can be viewed as a trapezoidal
quadrature scheme. We demonstrate that existing analysis neglects certain
contributions due to the non-smoothness of the integrand, and may significantly
underestimate finite-size errors. We propose a new staggered mesh method, which
uses two staggered Monkhorst-Pack meshes for occupied and virtual orbitals,
respectively, to compute the MP2 energy. We demonstrate that the staggered mesh
method circumvents a significant error source in the standard method, in which
certain quadrature nodes are always placed on points where the integrand is
discontinuous. Numerical results indicate that the staggered mesh method can be
particularly advantageous for quasi-1D systems, as well as quasi-2D and 3D
systems with certain symmetries.
