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

Design, construction and operation of the ProtoDUNE-SP Liquid Argon TPC

The ProtoDUNE-SP detector is a single-phase liquid argon time projection chamber (LArTPC) that was constructed and operated in the CERN North Area at the end of the H4 beamline. This detector is a prototype for the first far detector module of the Deep Underground Neutrino Experiment (DUNE), which will be constructed at the Sandford Underground Research Facility (SURF) in Lead, South Dakota, U.S.A. The ProtoDUNE-SP detector incorporates full-size components as designed for DUNE and has an active volume of 7 × 6 × 7.2 m3. The H4 beam delivers incident particles with well-measured momenta and high-purity particle identification. ProtoDUNE-SP's successful operation between 2018 and 2020 demonstrates the effectiveness of the single-phase far detector design. This paper describes the design, construction, assembly and operation of the detector components

TDDFT and quantum-classical dynamics: A universal tool describing the dynamics of matter

Time-dependent density functional theory (TDDFT) is currently the most efficient approach allowing to describe electronic dynamics in complex systems, from isolated molecules to the condensed phase. TDDFT has been employed to investigate an extremely wide range of time-dependent phenomena, as spin dynamics in solids, charge and energy transport in nanoscale devices, and photoinduced exciton transfer in molecular aggregates. It is therefore nearly impossible to give a general account of all developments and applications of TDDFT in material science, as well as in physics and chemistry. A large variety of aspects are covered throughout these volumes. In the present chapter, we will limit our presentation to the description of TDDFT developments and applications in the field of quantum molecular dynamics simulations in combination with trajectory-based approaches for the study of nonadiabatic excited-state phenomena. We will present different quantum-classical strategies used to describe the coupled dynamics of electrons and nuclei underlying nonadiabatic processes. In addition, we will give an account of the most recent applications with the aim of illustrating the nature of the problems that can be addressed with the help of these approaches. The potential, as well as the limitations, of the presented methods is discussed, along with possible avenues for future developments in TDDFT and nonadiabatic dynamics