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

TRPC4/TRPC5 channels mediate adverse reaction to the cancer cell cytotoxic agent (-)-Englerin A

(-)-Englerin A (EA) is a natural product which has potent cytotoxic effects on renal cell carcinoma cells and other types of cancer cell but not non-cancer cells. Although selectively cytotoxic to cancer cells, adverse reaction in mice and rats has been suggested. EA is a remarkably potent activator of ion channels formed by Transient Receptor Potential Canonical 4 and 5 proteins (TRPC4 and TRPC5) and TRPC4 is essential for EA-mediated cancer cell cytotoxicity. Here we specifically investigated the relevance of TRPC4 and TRPC5 to the adverse reaction. Injection of EA (2 mg.kg⁻¹ i.p.) adversely affected mice for about 1 hour, manifesting as a marked reduction in locomotor activity, after which they fully recovered. TRPC4 and TRPC5 single knockout mice were partially protected and double knockout mice fully protected. TRPC4/TRPC5 double knockout mice were also protected against intravenous injection of EA. Importance of TRPC4/TRPC5 channels was further suggested by pre-administration of Compound 31 (Pico145), a potent and selective small-molecule inhibitor of TRPC4/TRPC5 channels which did not cause adverse reaction itself but prevented adverse reaction to EA. EA was detected in the plasma but not the brain and so peripheral mechanisms were implicated but not identified. The data confirm the existence of adverse reaction to EA in mice and suggest that it depends on a combination of TRPC4 and TRPC5 which therefore overlaps partially with TRPC4-dependent cancer cell cytotoxicity. The underlying nature of the observed adverse reaction to EA, as a consequence of TRPC4/TRPC5 channel activation, remains unclear and warrants further investigation

The CARMENES search for exoplanets around M dwarfs High-resolution optical and near-infrared spectroscopy of 324 survey stars

The CARMENES radial velocity (RV) survey is observing 324 M dwarfs to search for any orbiting planets. In this paper, we present the survey sample by publishing one CARMENES spectrum for each M dwarf. These spectra cover the wavelength range 520–1710 nm at a resolution of at least R >80 000, and we measure its RV, Hα emission, and projected rotation velocity. We present an atlas of high-resolution M-dwarf spectra and compare the spectra to atmospheric models. To quantify the RV precision that can be achieved in low-mass stars over the CARMENES wavelength range, we analyze our empirical information on the RV precision from more than 6500 observations. We compare our high-resolution M-dwarf spectra to atmospheric models where we determine the spectroscopic RV information content, Q, and signal-to-noise ratio. We find that for all M-type dwarfs, the highest RV precision can be reached in the wavelength range 700–900 nm. Observations at longer wavelengths are equally precise only at the very latest spectral types (M8 and M9). We demonstrate that in this spectroscopic range, the large amount of absorption features compensates for the intrinsic faintness of an M7 star. To reach an RV precision of 1 m s−1 in very low mass M dwarfs at longer wavelengths likely requires the use of a 10 m class telescope. For spectral types M6 and earlier, the combination of a red visual and a near-infrared spectrograph is ideal to search for low-mass planets and to distinguish between planets and stellar variability. At a 4 m class telescope, an instrument like CARMENES has the potential to push the RV precision well below the typical jitter level of 3–4 m s−1

The CARMENES search for exoplanets around M dwarfs HD147379 b: A nearby Neptune in the temperate zone of an early-M dwarf

We report on the first star discovered to host a planet detected by radial velocity (RV) observations obtained within the CARMENES survey for exoplanets around M dwarfs. HD 147379 (V = 8.9 mag, M = 0.58 ± 0.08 M⊙), a bright M0.0 V star at a distance of 10.7 pc, is found to undergo periodic RV variations with a semi-amplitude of K = 5.1 ± 0.4 m s−1 and a period of P = 86.54 ± 0.06 d. The RV signal is found in our CARMENES data, which were taken between 2016 and 2017, and is supported by HIRES/Keck observations that were obtained since 2000. The RV variations are interpreted as resulting from a planet of minimum mass mP sin i = 25 ± 2 M⊕, 1.5 times the mass of Neptune, with an orbital semi-major axis a = 0.32 au and low eccentricity (e < 0.13). HD 147379 b is orbiting inside the temperate zone around the star, where water could exist in liquid form. The RV time-series and various spectroscopic indicators show additional hints of variations at an approximate period of 21.1 d (and its first harmonic), which we attribute to the rotation period of the star.FEDER/ERF FICTS-2011-02 fundsMajor Research Instrumentation Programme and DFG Research Unit FOR2544 “Blue Planets around Red StarsEuropean Research Council (ERC-279347), Deutsche Forschungsgemeinschaft (RE 1664/12-1, RE 2694/4-1), Bundesministerium für Bildung und Forschung (BMBF-05A14MG3, BMBF-05A17MG3), Spanish Ministry of Economy and Competitiveness (MINECO, grants AYA2015-68012-C2-2-P, AYA2016-79425-C3-1,2,3-P, AYA2015-69350-C3-2-P, AYA2014-54348-C03- 01, AYA2014-56359-P, AYA2014-54348-C3-2-R, AYA2016-79425-C3-3-P and 2013 Ramòn y Cajal program RYC-2013-14875), Fondo Europeo de Desarrollo Regional (FEDER, grant ESP2016-80435-C2-1-R, ESP2015-65712-C5- 5-R), Generalitat de Catalunya/CERCA programme, Spanish Ministerio de Educación, Cultura y Deporte, programa de Formación de Profesorado Universitario (grant FPU15/01476), Deutsches Zentrum für Luft- und Raumfahrt (grants 50OW0204 and 50OO1501), Office of Naval Research Global (award no. N62909-15-1-2011), Mexican CONACyT grant CB-2012-183007

The CARMENES search for exoplanets around M dwarfs High-resolution optical and near-infrared spectroscopy of 324 survey stars

The CARMENES radial velocity (RV) survey is observing 324 M dwarfs to search for any orbiting planets. In this paper, we present the survey sample by publishing one CARMENES spectrum for each M dwarf. These spectra cover the wavelength range 520–1710 nm at a resolution of at least R >80 000, and we measure its RV, Hα emission, and projected rotation velocity. We present an atlas of high-resolution M-dwarf spectra and compare the spectra to atmospheric models. To quantify the RV precision that can be achieved in low-mass stars over the CARMENES wavelength range, we analyze our empirical information on the RV precision from more than 6500 observations. We compare our high-resolution M-dwarf spectra to atmospheric models where we determine the spectroscopic RV information content, Q, and signal-to-noise ratio. We find that for all M-type dwarfs, the highest RV precision can be reached in the wavelength range 700–900 nm. Observations at longer wavelengths are equally precise only at the very latest spectral types (M8 and M9). We demonstrate that in this spectroscopic range, the large amount of absorption features compensates for the intrinsic faintness of an M7 star. To reach an RV precision of 1 m s−1 in very low mass M dwarfs at longer wavelengths likely requires the use of a 10 m class telescope. For spectral types M6 and earlier, the combination of a red visual and a near-infrared spectrograph is ideal to search for low-mass planets and to distinguish between planets and stellar variability. At a 4 m class telescope, an instrument like CARMENES has the potential to push the RV precision well below the typical jitter level of 3–4 m s−1

CARMENES: high-resolution spectra and precise radial velocities in the red and infrared

SPIE Astronomical Telescopes + Instrumentation (2018, Austin, Texas, United States

The CARMENES search for exoplanets around M dwarfs. First visual-channel radial-velocity measurements and orbital parameter updates of seven M-dwarf planetary systems

Stars and planetary system