  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. 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. One
significant advantage of the proposed method is that there are no tunable
parameters, and the additional numerical effort needed can be negligible
compared to the standard MP2 calculation. 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.
