We have developed the adaptive density partitioning technique (ADPT) in the auxiliary plane wave method, in which a part of the density is expanded to plane waves, for the fast evaluation Of Coulomb matrix. Our partitioning is based on the error estimations and allows us to control the accuracy and efficiency. Moreover, we can drastically reduce the core Gaussian products that are left in Gaussian representation (its analytical integrals is the bottleneck in this method). For the taxol molecule with 6-31G** basis, the core Gaussian products accounted only for 5% in submicrohartree error. (c) 2005 Elsevier B.V. All rights reserved.