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The calculation of the MP2 correlation energy for extended systems can beviewed as a multi-dimensional integral in the thermodynamic limit, and thestandard method for evaluating the MP2 energy can be viewed as a trapezoidalquadrature scheme. We demonstrate that existing analysis neglects certaincontributions due to the non-smoothness of the integrand, and may significantlyunderestimate finite-size errors. We propose a new staggered mesh method, whichuses two staggered Monkhorst-Pack meshes for occupied and virtual orbitals,respectively, to compute the MP2 energy. The staggered mesh method circumventsa significant error source in the standard method, in which certain quadraturenodes are always placed on points where the integrand is discontinuous. Onesignificant advantage of the proposed method is that there are no tunableparameters, and the additional numerical effort needed can be negligiblecompared to the standard MP2 calculation. Numerical results indicate that thestaggered mesh method can be particularly advantageous for quasi-1D systems, aswell as quasi-2D and 3D systems with certain symmetries.

Staggered mesh method for correlation energy calculations of solids: Second order M{\o}ller-Plesset perturbation theory