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

Three applications of path integrals: equilibrium and kinetic isotope effects, and the temperature dependence of the rate constant of the [1,5] sigmatropic hydrogen shift in (Z)-1,3-pentadiene

Recent experiments have confirmed the importance of nuclear quantum effects even in large biomolecules at physiological temperature. Here we describe how the path integral formalism can be used to describe rigorously the nuclear quantum effects on equilibrium and kinetic properties of molecules. Specifically, we explain how path integrals can be employed to evaluate the equilibrium (EIE) and kinetic (KIE) isotope effects, and the temperature dependence of the rate constant. The methodology is applied to the [1,5] sigmatropic hydrogen shift in pentadiene. Both the KIE and the temperature dependence of the rate constant confirm the importance of tunneling and other nuclear quantum effects as well as of the anharmonicity of the potential energy surface. Moreover, previous results on the KIE were improved by using a combination of a high level electronic structure calculation within the harmonic approximation with a path integral anharmonicity correction using a lower level method.Comment: 9 pages, 4 figure

The RR Lyrae Distance Scale

We review seven methods of measuring the absolute magnitude M_V of RR Lyrae stars in light of the Hipparcos mission and other recent developments. We focus on identifying possible systematic errors and rank the methods by relative immunity to such errors. For the three most robust methods, statistical parallax, trigonometric parallax, and cluster kinematics, we find M_V (at [Fe/H] = -1.6) of 0.77 +/- 0.13, 0.71 +/- 0.15, 0.67 +/- 0.10. These methods cluster consistently around 0.71 +/- 0.07. We find that Baade-Wesselink and theoretical models both yield a broad range of possible values (0.45-0.70 and 0.45-0.65) due to systematic uncertainties in the temperature scale and input physics. Main-sequence fitting gives a much brighter M_V = 0.45 +/- 0.04 but this may be due to a difference in the metallicity scales of the cluster giants and the calibrating subdwarfs. White-dwarf cooling-sequence fitting gives 0.67 +/- 0.13 and is potentially very robust, but at present is too new to be fully tested for systematics. If the three most robust methods are combined with Walker's mean measurement for 6 LMC clusters, V_{0,LMC} = 18.98 +/- 0.03 at [Fe/H] = -1.9, then mu_{LMC} = 18.33 +/- 0.08.Comment: Invited review article to appear in: `Post-Hipparcos Cosmic Candles', A. Heck & F. Caputo (Eds), Kluwer Academic Publ., Dordrecht, in press. 21 pages including 1 table; uses Kluwer's crckapb.sty LaTeX style file, enclose

Recent advances in electronic structure theory and their influence on the accuracy of ab initio potential energy surfaces

Recent advances in electronic structure theory and the availability of high speed vector processors have substantially increased the accuracy of ab initio potential energy surfaces. The recently developed atomic natural orbital approach for basis set contraction has reduced both the basis set incompleteness and superposition errors in molecular calculations. Furthermore, full CI calculations can often be used to calibrate a CASSCF/MRCI approach that quantitatively accounts for the valence correlation energy. These computational advances also provide a vehicle for systematically improving the calculations and for estimating the residual error in the calculations. Calculations on selected diatomic and triatomic systems will be used to illustrate the accuracy that currently can be achieved for molecular systems. In particular, the F+H2 yields HF+H potential energy hypersurface is used to illustrate the impact of these computational advances on the calculation of potential energy surfaces

Observational and Physical Classification of Supernovae

This chapter describes the current classification scheme of supernovae (SNe). This scheme has evolved over many decades and now includes numerous SN Types and sub-types. Many of these are universally recognized, while there are controversies regarding the definitions, membership and even the names of some sub-classes; we will try to review here the commonly-used nomenclature, noting the main variants when possible. SN Types are defined according to observational properties; mostly visible-light spectra near maximum light, as well as according to their photometric properties. However, a long-term goal of SN classification is to associate observationally-defined classes with specific physical explosive phenomena. We show here that this aspiration is now finally coming to fruition, and we establish the SN classification scheme upon direct observational evidence connecting SN groups with specific progenitor stars. Observationally, the broad class of Type II SNe contains objects showing strong spectroscopic signatures of hydrogen, while objects lacking such signatures are of Type I, which is further divided to numerous subclasses. Recently a class of super-luminous SNe (SLSNe, typically 10 times more luminous than standard events) has been identified, and it is discussed. We end this chapter by briefly describing a proposed alternative classification scheme that is inspired by the stellar classification system. This system presents our emerging physical understanding of SN explosions, while clearly separating robust observational properties from physical inferences that can be debated. This new system is quantitative, and naturally deals with events distributed along a continuum, rather than being strictly divided into discrete classes. Thus, it may be more suitable to the coming era where SN numbers will quickly expand from a few thousands to millions of events.Comment: Extended final draft of a chapter in the "SN Handbook". Comments most welcom

Deficiency of Vasodilator-Stimulated Phosphoprotein (VASP) Increases Blood-Brain-Barrier Damage and Edema Formation after Ischemic Stroke in Mice

Background: Stroke-induced brain edema formation is a frequent cause of secondary infarct growth and deterioration of neurological function. The molecular mechanisms underlying edema formation after stroke are largely unknown. Vasodilator-stimulated phosphoprotein (VASP) is an important regulator of actin dynamics and stabilizes endothelial barriers through interaction with cell-cell contacts and focal adhesion sites. Hypoxia has been shown to foster vascular leakage by downregulation of VASP in vitro but the significance of VASP for regulating vascular permeability in the hypoxic brain in vivo awaits clarification. Methodology/Principal Findings: Focal cerebral ischemia was induced in Vasp2/2 mice and wild-type (WT) littermates by transient middle cerebral artery occlusion (tMCAO). Evan’s Blue tracer was applied to visualize the extent of blood-brainbarrier (BBB) damage. Brain edema formation and infarct volumes were calculated from 2,3,5-triphenyltetrazolium chloride (TTC)-stained brain slices. Both mouse groups were carefully controlled for anatomical and physiological parameters relevant for edema formation and stroke outcome. BBB damage (p,0.05) and edema volumes (1.7 mm360.5 mm3 versus 0.8 mm360.4 mm3; p,0.0001) were significantly enhanced in Vasp2/2 mice compared to controls on day 1 after tMCAO. This was accompanied by a significant increase in infarct size (56.1 mm3617.3 mm3 versus 39.3 mm3610.7 mm3, respectively; p,0.01) and a non significant trend (p.0.05) towards worse neurological outcomes. Conclusion: Our study identifies VASP as critical regulator of BBB maintenance during acute ischemic stroke. Therapeutic modulation of VASP or VASP-dependent signalling pathways could become a novel strategy to combat excessive edema formation in ischemic brain damage

Impairment of Vowel Articulation as a Possible Marker of Disease Progression in Parkinson's Disease

Purpose: The aim of the current study was to survey if vowel articulation in speakers with Parkinson’s disease (PD) shows specific changes in the course of the disease. Method: 67 patients with PD (42 male) and 40 healthy speakers (20 male) were tested and retested after an average time interval of 34 months. Participants had to read a given text as source for subsequent calculation of the triangular vowel space area (tVSA) and vowel articulation index (VAI). Measurement of tVSA and VAI were based upon analysis of the first and second formant of the vowels /a/, /i/and /u / extracted from defined words within the text. Results: At first visit, VAI values were reduced in male and female PD patients as compared to the control group, and showed a further decrease at the second visit. Only in female Parkinsonian speakers, VAI was correlated to overall speech impairment based upon perceptual impression. VAI and tVSA were correlated to gait impairment, but no correlations were seen between VAI and global motor impairment or overall disease duration. tVSA showed a similar reduction in the PD as compared to the control group and was also found to further decline between first and second examination in female, but not in male speakers with PD. Conclusions: Measurement of VAI seems to be superior to tVSA in the description of impaired vowel articulation and its further decline in the course of the disease in PD. Since impairment of vowel articulation was found to be independent fro

Glatiramer acetate reduces the risk for experimental cerebral malaria: a pilot study

<p>Abstract</p> <p>Background</p> <p>Cerebral malaria (CM) is associated with high mortality and morbidity caused by a high rate of transient or persistent neurological sequelae. Studies on immunomodulatory and neuroprotective drugs as ancillary treatment in murine CM indicate promising potential. The current study was conducted to evaluate the efficacy of glatiramer acetate (GA), an immunomodulatory drug approved for the treatment of relapsing remitting multiple sclerosis, in preventing the death of C57Bl/6J mice infected with <it>Plasmodium berghei </it>ANKA.</p> <p>Methods and Results</p> <p>GA treatment led to a statistically significant lower risk for developing CM (57.7% versus 84.6%) in treated animals. The drug had no effect on the course of parasitaemia. The mechanism of action seems to be an immunomodulatory effect since lower IFN-gamma levels were observed in treated animals in the early course of the disease (day 4 post-infection) which also led to a lower number of brain sequestered leukocytes in treated animals. No direct neuro-protective effect such as an inhibition of apoptosis or reduction of micro-bleedings in the brain was found.</p> <p>Conclusion</p> <p>These findings support the important role of the host immune response in the pathophysiology of murine CM and might lead to the development of new adjunctive treatment strategies.</p

The Lipopolysaccharide from Capnocytophaga canimorsus Reveals an Unexpected Role of the Core-Oligosaccharide in MD-2 Binding

Capnocytophaga canimorsus is a usual member of dog's mouths flora that causes rare but dramatic human infections after dog bites. We determined the structure of C. canimorsus lipid A. The main features are that it is penta-acylated and composed of a “hybrid backbone” lacking the 4′ phosphate and having a 1 phosphoethanolamine (P-Etn) at 2-amino-2-deoxy-d-glucose (GlcN). C. canimorsus LPS was 100 fold less endotoxic than Escherichia coli LPS. Surprisingly, C. canimorsus lipid A was 20,000 fold less endotoxic than the C. canimorsus lipid A-core. This represents the first example in which the core-oligosaccharide dramatically increases endotoxicity of a low endotoxic lipid A. The binding to human myeloid differentiation factor 2 (MD-2) was dramatically increased upon presence of the LPS core on the lipid A, explaining the difference in endotoxicity. Interaction of MD-2, cluster of differentiation antigen 14 (CD14) or LPS-binding protein (LBP) with the negative charge in the 3-deoxy-d-manno-oct-2-ulosonic acid (Kdo) of the core might be needed to form the MD-2 – lipid A complex in case the 4′ phosphate is not present