An Efficient Hartree–Fock Implementation Based on the Contraction of Integrals in the Primitive Basis

A new approach to implement the restricted closed-shell Hartree–Fock equation is proposed. In the ansatz presented, the explicit transformation of integrals from the primitive to the atomic-orbital basis is omitted. Instead, the density matrix is transformed to the primitive basis, in which it is contracted with the untransformed integrals. Obtained is the two-electron part of the Fock matrix, which is transformed back to the atomic orbital basis. The remaining steps of the self-consistent field algorithm are then performed as usual. The program presented here incorporates the most important standard techniques, such as integral prescreening, convergence acceleration (via the direct inversion of the iterative subspace ansatz), and the differential density scheme. Test calculations on standard Hartree–Fock problems were compared to the commercially available MOLPRO and TURBOMOLE program packages. Except in a few special cases, the performance of the program presented here is superior, in comparison to those two programs. Accelerations by up to a factor of 5 were found, with respect to MOLPRO calculations, and up to 3 for TURBOMOLE (in the latter case, up to 55 for generalized contracted basis sets). The program structure is independent of the type of radial contraction; however, the best results are obtained for generalized radial contraction basis sets of low contraction. The program is written in C++ and utilizes code generation engines to automatically generate the routines for the integration and density contraction. Streaming SIMD extensions are used explicitly.