Achieving linear scaling for the electronic quantum coulomb problem

The computation of the electron-electron Coulomb interaction is one of the limiting factors in ab initio electronic structure calculations. The computational requirements for calculating the Coulomb term with commonly used analytic integration techniques between Gaussian functions prohibit electronic structure calculations of large molecules and other nanosystems. Here, it is shown that a generalization of the fast multipole method to Gaussian charge distributions dramatically reduces the computational requirements of the electronic quantum Coulomb problem. Benchmark calculations on graphitic sheets containing more than 400 atoms show near linear scaling together with high speed and accuracy.