A QUANTITATIVE STUDY OF THE SCALING PROPERTIES OF THE HARTREE-FOCK METHOD

Although it is usually stated that the Hartree-Fock method formally scales as N4, where N is the number of basis functions employed in the calculation, it is also well known that mathematical bounds computed with the Schwarz inequality can be used to screen and eliminate four-center two-electron integrals smaller than a certain threshold. In this work, quantitative data is presented to illustrate the effects of this integral screening on the scaling properties of the Hartree-Fock (HF) method. Calculations are performed on a range of carbon-hydrogen model systems, two-dimensional graphitic sheets, and three-dimensional diamond pieces, to determine the effective scaling exponent a of the computational expense. The data obtained in this paper for calculations including over 250 carbon atoms and 1500 basis functions shows two significant trends: (1) in the asymptotic limit of large molecules, a is found to be approximately 2.2-2.3, and (2) for molecules of modest size, a is still very much less than 4. Therefore, integral screening is quantitatively shown to substantially reduce the Hartree-Fock scaling from its formal value of N 4. © 1995 American Institute of Physics.