A mathematical and computational review of Hartree-Fock SCF methods in Quantum Chemistry

We present here a review of the fundamental topics of Hartree-Fock theory in Quantum Chemistry. From the molecular Hamiltonian, using and discussing the Born-Oppenheimer approximation, we arrive to the Hartree and Hartree-Fock equations for the electronic problem. Special emphasis is placed in the most relevant mathematical aspects of the theoretical derivation of the final equations, as well as in the results regarding the existence and uniqueness of their solutions. All Hartree-Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. Then, the discretization of the one-electron orbitals space is reviewed and the Roothaan-Hall formalism introduced. This leads to a exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing in algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (specially those related to the design of linear-scaling methods) are commented and linked to the issues discussed. The whole work is intentionally introductory and rather self-contained, so that it may be useful for non experts that aim to use quantum chemical methods in interdisciplinary applications. Moreover, much material that is found scattered in the literature has been put together here to facilitate comprehension and to serve as a handy reference.Comment: 64 pages, 3 figures, tMPH2e.cls style file, doublesp, mathbbol and subeqn package

Laser spectroscopy of the 1S-2S transition in hydrogen and deuterium: Determination of the 1S Lamb shift and the Rydberg constant.

We have observed the narrow 1S-2S transition in hydrogen and deuterium with high resolution using Doppler-free two-photon absorption of continuous-wave 243-nm light. The transition frequencies were measured by direct comparison with accurately calibrated lines in the spectrum of the Te2130 molecule. We find the 1S-2S interval to be 2 466 061 414.1(8) MHz in hydrogen and 2 466 732 408.5(7) MHz in deuterium. By combining these results with recent measurements of the Rydberg constant we obtain the values 8172.6(7) and 8183.7(6) MHz for the 1S Lamb shifts in hydrogen and deuterium, respectively. These are the most precise measurements of the 1S Lamb shifts in these atoms and they are in excellent agreement with the theoretical values of 8173.03(9) and 8184.08(12) MHz. Alternatively, if the 1S Lamb shift is supposed known from theory, our measurements determine the Rydberg constant as R=109 737.315 73(3) cm-1. © 1989 The American Physical Society