Time-dependent density functional study of the electronic potential energy curves and excitation spectrum of the oxygen molecule

Orbital energies, ionization potentials, molecular constants, potential energy curves, and the excitation spectrum of O(2) are calculated using time-dependent density functional theory (TDDFT) with Tamm-Dancoff approximation (TDA). The calculated negative highest occupied molecular orbital energy (-epsilon(HOMO)) is compared with the energy difference ionization potential for five exchange correlation functionals consisting of the local density approximation (LDAxc), gradient corrected Becke exchange plus Perdew correlation (B(88X)+P(86C)), gradient regulated asymptotic correction (GRAC), statistical average of orbital potentials (SAOP), and van Leeuwen and Baerends asymptotically correct potential (LB94). The potential energy curves calculated using TDDFT with the TDA at internuclear distances from 1.0 to 1.8 A are divided into three groups according to the electron configurations. The 1pi(u) (4)1pi(g) (2) electron configuration gives rise to the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) states; the 1pi(u) (3)1pi(g) (3) electron configuration gives rise to the c (1)Sigma(u) (-), C (3)Delta(u), and A (3)Sigma(u) (+) states; and the B (3)Sigma(u) (-), A (1)Delta(u), and f (1)Sigma(u) (+) states are determined by the mixing of two or more electron configurations. The excitation spectrum of the oxygen molecule, calculated with the aforementioned exchange correlation functionals, shows that the results are quite sensitive to the choice of functional. The LDAxc and the B(88X)+P(86C) functionals produce similar spectroscopic patterns with a single strongly absorbing band positioned at 19.82 and 19.72 eV, respectively, while the asymptotically corrected exchange correlation functionals of the SAOP and the LB94 varieties yield similar excitation spectra where the computed strongly absorbing band is located at 16.09 and 16.42 eV, respectively. However, all of the exchange correlation functionals yield only one strongly absorbing band (oscillator strength greater than 0.1) in the energy interval of 0-20 eV, which is assigned to a X (3)Sigma(g) (-) to (3)Sigma(u) (-) transition. Furthermore, the oxygen molecule has a rich spectrum in the energy range of 14-20 eV and no spin allowed absorption bands are predicted to be observed in the range of 0-6 eV

Braids, posets and orthoschemes

In this article we study the curvature properties of the order complex of a graded poset under a metric that we call the ``orthoscheme metric''. In addition to other results, we characterize which rank 4 posets have CAT(0) orthoscheme complexes and by applying this theorem to standard posets and complexes associated with four-generator Artin groups, we are able to show that the 5-string braid group is the fundamental group of a compact nonpositively curved space.Comment: 33 pages, 16 figure

Combinatorial Stokes formulas via minimal resolutions

We describe an explicit chain map from the standard resolution to the minimal resolution for the finite cyclic group Z_k of order k. We then demonstrate how such a chain map induces a "Z_k-combinatorial Stokes theorem", which in turn implies "Dold's theorem" that there is no equivariant map from an n-connected to an n-dimensional free Z_k-complex. Thus we build a combinatorial access road to problems in combinatorics and discrete geometry that have previously been treated with methods from equivariant topology. The special case k=2 for this is classical; it involves Tucker's (1949) combinatorial lemma which implies the Borsuk-Ulam theorem, its proof via chain complexes by Lefschetz (1949), the combinatorial Stokes formula of Fan (1967), and Meunier's work (2006).Comment: 18 page

The Greater Boston Housing Report Card 2021 Pandemic Housing Policy: From Progress to Permanence

The COVID-19 pandemic brought so many intense social, economic and public health challenges it is easy to think that the pandemic has "changed everything" with respect to housing. This year's edition of the Greater Boston Housing Report Card suggests the opposite: The region's most difficult long-term housing challenges are not only still with us, but have been compounded by recent events, and bold federal, state and local policy changes are as badly needed as ever.This report includes extensive economic and housing data from the five counties that comprise the Greater Boston region and includes analysis and policy recommendations in three general areas: economic health, housing stability, and housing supply and sustainability

Optimal bounds for a colorful Tverberg--Vrecica type problem

We prove the following optimal colorful Tverberg-Vrecica type transversal theorem: For prime r and for any k+1 colored collections of points C^l of size |C^l|=(r-1)(d-k+1)+1 in R^d, where each C^l is a union of subsets (color classes) C_i^l of size smaller than r, l=0,...,k, there are partition of the collections C^l into colorful sets F_1^l,...,F_r^l such that there is a k-plane that meets all the convex hulls conv(F_j^l), under the assumption that r(d-k) is even or k=0. Along the proof we obtain three results of independent interest: We present two alternative proofs for the special case k=0 (our optimal colored Tverberg theorem (2009)), calculate the cohomological index for joins of chessboard complexes, and establish a new Borsuk-Ulam type theorem for (Z_p)^m-equivariant bundles that generalizes results of Volovikov (1996) and Zivaljevic (1999).Comment: Substantially revised version: new notation, improved results, additional references; 12 pages, 2 figure

Jubilee mugs:the monarchy and the Sex Pistols

With rare exceptions sociologists have traditionally had little to say about the British monarchy. In the exceptional cases of the Durkheimian functionalism of Shills and Young (1953), the left humanism of Birnbaum (1955), or the archaic state/backward nation thesis of Nairn (1988), the British nation has been conceived as a homogenous mass. The brief episode of the Sex Pistols' Jubilee year song 'God Save the Queen' exposed some of the divisions within the national 'mass', forcing a re-ordering of the balance between detachment and belonging to the Royal idea. I argue that the song acted as a kind of 'breaching experiment'. Its wilful provocation of Royalist sentiment revealed the level of sanction available to the media-industrial complex to enforce compliance to British self-images of loyal and devoted national communicants

Draper Station Analysis Tool

Draper Station Analysis Tool (DSAT) is a computer program, built on commercially available software, for simulating and analyzing complex dynamic systems. Heretofore used in designing and verifying guidance, navigation, and control systems of the International Space Station, DSAT has a modular architecture that lends itself to modification for application to spacecraft or terrestrial systems. DSAT consists of user-interface, data-structures, simulation-generation, analysis, plotting, documentation, and help components. DSAT automates the construction of simulations and the process of analysis. DSAT provides a graphical user interface (GUI), plus a Web-enabled interface, similar to the GUI, that enables a remotely located user to gain access to the full capabilities of DSAT via the Internet and Webbrowser software. Data structures are used to define the GUI, the Web-enabled interface, simulations, and analyses. Three data structures define the type of analysis to be performed: closed-loop simulation, frequency response, and/or stability margins. DSAT can be executed on almost any workstation, desktop, or laptop computer. DSAT provides better than an order of magnitude improvement in cost, schedule, and risk assessment for simulation based design and verification of complex dynamic systems

Bromine counts from XRF scanning as an estimate of the marine organic carbon content of sediment cores

XRF sediment core scanning technology is increasingly used to quantify sediment composition. The overall good correlation between biophilic halogen bromine (Br) and sedimentary total organic carbon (TOC) potentially allows the fast estimation of down core TOC profiles by XRF scanning. In order to test this approach we present data from the Arabian Sea and a Mediterranean brine basin, comparing XRF core scanning Br data with discrete sample TOC analyses. Overall, Br counts and TOC show a clear correlation, except when stable carbon isotope and C/N data indicate intervals characterized by enhanced input of terrestrial organic matter. Hence, solid phase Br is exclusively associated with marine organic matter (MOC) and can be used as a direct estimate of this parameter after a calibration is established. High pore water Br in the brine core steepens the Br/TOC correlation but after salt correction shows a nearly identical gradient to that of the Arabian Sea cor