Linear scaling second-order Moller-Plesset theory in the atomic orbital basis for large molecular systems

We have used Almlof and Haser's Laplace transform idea to eliminate the ene rgy denominator in second-order perturbation theory (MP2) and obtain an ene rgy expression in the atomic orbital basis. We show that the asymptotic com putational cost of this method scales quadratically with molecular size. We then define atomic orbital domains such that selective pairwise interactio ns can be neglected using well-defined thresholding criteria based on the p ower law decay properties of the long-range contributions. For large molecu les, our scheme yields linear scaling computational cost as a function of m olecular size. The errors can be controlled in a precise manner and our met hod reproduces canonical MP2 energies. We present benchmark calculations of polyglycine chains and water clusters containing up to 3040 basis function s. (C) 1999 American Institute of Physics. [S0021-9606(99)30108-2].