New method for approximate Hartree–Fock calculations using density approximations and coulomb field corrections. I

A method is proposed that reduces the computational effort of HF calculations considerably by reducing the number of two‐electron integrals that have to be calculated. The following concepts are used: (i) approximation of the electron density by only few functions for the Coulomb part of the HF matrix; (ii) modification of this approximate density, to improve its Coulomb field; (iii) in the exchange part, a basis function χ is replaced by a function \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \chi $\end{document} consisting of fewer Gaussian lobes; (iv) the error caused by this replacement is reduced by a modification of the densities \documentclass{article}\pagestyle{empty}\begin{document}$ \tilde \chi _i \tilde \chi _j $\end{document} in the exchange integrals. The computation time of the integral part is reduced by a factor 6 for molecules containing five first‐row atoms as, e.g., CF 4 , if one uses a 7 S /3 P basis set contracted to (5, 1, 1/3). The integral time increases roughly with n 3 , if n is the number of Gaussian lobes.