Linear scaling computation of the Fock matrix. IV. Multipole accelerated formation of the exchange matrix

A new method for the multipole evaluation of contracted Cartesian Gaussian-based electron repulsion integrals is described, and implemented in linear scaling methods for computation of the Hartree - Fock exchange matrix. The new method, which relies on a nonempirical multipole acceptability criterion [J. Chem. Phys. 109, 8764 (1998)], renders the work associated with integral evaluation independent of the basis set contraction length. Benchmark calculations on a series of three-dimensional water molecule clusters and graphitic sheets with highly contracted basis sets indicate that the new method is up to 4.6 times faster than a well optimized direct integral evaluation routine. For calculations involving lower levels of contraction a factor of 2 speedup is typically observed. Importantly, the method achieves these large gains in computational efficiency while maintaining numerical equivalence with standard direct self consistent field theory. copyright 1999 American Institute of Physics