FAST ASSEMBLY OF THE COULOMB MATRIX - A QUANTUM-CHEMICAL TREE CODE

Fast methods based on a representation of the electron charge density in a Hermite Gaussian basis are introduced for constructing the Coulom b matrix encountered in Hartree;Fock and density functional theories. Simplifications that arise from working in a Hermite Gaussian basis ar e discussed, translations of such functions are shown to yield rapidly convergent expansions valid in both the near- and far-field, and the corresponding truncation errors are derived in compact form. The relat ionship of such translations to hierarchical multipole methods is poin ted out and a quantum chemical tree code related to the Barnes-Hut met hod is developed. Novel methods are introduced for the independent thr esholding of ''bra'' and ''ket'' distributions as well as for screenin g out insignificant multipole interactions. Recurrence relations for c omputing the Cartesian multipole tensor are used to efficiently calcul ate far-field electrostatic interactions using high-order expansions. Application of the quantum chemical tree code to assembly of the Coulo mb matrix for HF/3-21G calculations on sequences of polyglycine cr-hel ices and water clusters demonstrate scalings as favorable as N-1.6, wh ere N is the number of basis functions. Comparisons with a commercial electronic structure program indicate that our method is highly compet itive. Speed is obtained without sacrificing precision, truncation err ors are controlled with a single parameter, and the method performs eq ually well with a contracted or uncontracted LCAO basis. (C) 1996 Amer ican Institute of Physics.