Structural manifestation of the delocalization error of density functional approximations: C(4N+2) rings and C(20) bowl, cage, and ring isomers.

The ground state structure of C(4N+2) rings is believed to exhibit a geometric transition from angle alternation (N < or = 2) to bond alternation (N > 2). All previous density functional theory (DFT) studies on these molecules have failed to reproduce this behavior by predicting either that the transition occurs at too large a ring size, or that the transition leads to a higher symmetry cumulene. Employing the recently proposed perspective of delocalization error within DFT we rationalize this failure of common density functional approximations (DFAs) and present calculations with the rCAM-B3LYP exchange-correlation functional that show an angle-to-bond-alternation transition between C(10) and C(14). The behavior exemplified here manifests itself more generally as the well known tendency of DFAs to bias toward delocalized electron distributions as favored by Huckel aromaticity, of which the C(4N+2) rings provide a quintessential example. Additional examples are the relative energies of the C(20) bowl, cage, and ring isomers; we show that the results from functionals with minimal delocalization error are in good agreement with CCSD(T) results, in contrast to other commonly used DFAs. An unbiased DFT treatment of electron delocalization is a key for reliable prediction of relative stability and hence the structures of complex molecules where many structure stabilization mechanisms exist.

Performance of density functionals for calculating barrier heights of chemical reactions relevant to astrophysics

The performance of 39 different LDA, GGA, meta-GGA, and hybrid density functionals has been evaluated, for calculating forward and reverse barrier heights of 10 gas-phase reactions involving hydrogen. The reactions are all relevant to astrochemistry. Special focus is put on the applicability of DFT for calculating the rates of corresponding surface hydrogenation reactions that are relevant to the chemistry of ice-coated interstellar grains. General trends in the performance of the density functionals for reactions involving H atoms, H-2, and OH are discussed. The OH+CO reaction is shown to be a very problematic case for DFT. The best overall performance is found for the hybrid density functionals, such as MPW1K, B97-1, B97-2, and B1B95. For several reactions, the HCTH GGA functionals and the VS98 and OLAP3 meta-GGA functionals also give results that are almost as good as those of the hybrid functionals.

Economies of scaling: More evidence that allometry of metabolism is linked to activity, metabolic rate and habitat

Organismal metabolic rates influence many ecological processes, and the mass-specific metabolic rate of organisms decreases with increasing body mass according to a power law. The exponent in this equation is commonly thought to be the three-quarter-power of body mass, determined by fundamental physical laws that extend across taxa. However, recent work has cast doubt as to the universality of this relationship, the value of 0.75 being an interspecies 'average' of scaling exponents that vary naturally between certain boundaries. There is growing evidence that metabolic scaling varies significantly between even closely related species, and that different values can be associated with lifestyle, activity and metabolic rates. Here we show that the value of the metabolic scaling exponent varies within a group of marine ectotherms, chitons (Mollusca: Polyplacophora: Mopaliidae), and that differences in the scaling relationship may be linked to species-specific adaptations to different but overlapping microhabitats. Oxygen consumption rates of six closely related, co-occurring chiton species from the eastern Pacific (Vancouver Island, British Columbia) were examined under controlled experimental conditions. Results show that the scaling exponent varies between species (between 0.64 and 0.91). Different activity levels, metabolic rates and lifestyle may explain this variation. The interspecific scaling exponent in these data is not significantly different from the archetypal 0.75 value, even though five out of six species-specific values are significantly different from that value. Our data suggest that studies using commonly accepted values such as 0.75 derived from theoretical models to extrapolate metabolic data of species to population or community levels should consider the likely variation in exponents that exists in the real world, or seek to encompass such error in their models. This study, as in numerous previous ones, demonstrates that scaling exponents show large, naturally occurring variation, and provides more evidence against the existence of a universal scaling law. © 2012 Elsevier B.V.

Parker Morris and the economies of the Fordist house

The Parker Morris report of 1961 attempted, through the application of scientific principles, to define the minimum living space standards needed to accommodate household activities. But while early modernist research into ideas of existenzminimum were the work of avant-garde architects and thinkers, this report was commissioned by the British State. This normalization of scientific enquiry into space can be considered not only a response to new conditions in the mass production of housing – economies of scale, prefabrication, system-building and modular coordination – but also to the post-war boom in consumer goods. The domestic interior was assigned a key role as a privileged site of mass consumption as the production and micro-management of space in Britain became integral to the development of a planned national economy underpinned by Fordist principles. The apparently placeless and scale-less diagrams executed by Gordon Cullen to illustrate Parker Morris emblematize these relationships. Walls dissolve as space flows from inside to outside in a homogenized and ephemeral landscape whose limits are perhaps only the boundaries of the nation state and the circuits of capital.

Direct Observation of Density-Gradient Effects in Harmonic Generation from Plasma Mirrors

High-order harmonics and attosecond pulses of light can be generated when ultraintense, ultrashort laser pulses reflect off a solid-density plasma with a sharp vacuum interface, i.e., a plasma mirror. We demonstrate experimentally the key influence of the steepness of the plasma-vacuum interface on the interaction, by measuring the spectral and spatial properties of harmonics generated on a plasma mirror whose initial density gradient scale length L is continuously varied. Time-resolved interferometry is used to separately measure this scale length. 

Systematic construction of models for the exchange hole of density functional theory.

Dans ce travail, nous étendons le nombre de conditions physiques actuellement con- nues du trou d’échange exact avec la dérivation de l’expansion de quatrième ordre du trou d’échange sphérique moyenne exacte. Nous comparons les expansions de deux- ième et de quatrième ordre avec le trou d’échange exact pour des systèmes atomiques et moléculaires. Nous avons constaté que, en général, l’expansion du quatrième ordre reproduit plus fidèlement le trou d’échange exact pour les petites valeurs de la distance interélectronique. Nous démontrons que les ensembles de base de type gaussiennes ont une influence significative sur les termes de cette nouvelle condition, en étudiant com- ment les oscillations causées par ces ensembles de bases affectent son premier terme. Aussi, nous proposons quatre modèles de trous d’échange analytiques auxquels nous imposons toutes les conditions actuellement connues du trou d’échange exact et la nou- velle présentée dans ce travail. Nous évaluons la performance des modèles en calculant des énergies d’échange et ses contributions à des énergies d’atomisation. On constate que les oscillations causeés par les bases de type gaussiennes peuvent compromettre la précision et la solution des modèles.

Extent and limitations of density functional theory in describing magnetic systems

The performance of density-functional theory to solve the exact, nonrelativistic, many-electron problem for magnetic systems has been explored in a new implementation imposing space and spin symmetry constraints, as in ab initio wave function theory. Calculations on selected systems representative of organic diradicals, molecular magnets and antiferromagnetic solids carried out with and without these constraints lead to contradictory results, which provide numerical illustration on this usually obviated problem. It is concluded that the present exchange-correlation functionals provide reasonable numerical results although for the wrong physical reasons, thus evidencing the need for continued search for more accurate expressions.

Development and applications of density matrix functional theory of generalized Hubbard Models

In dieser Doktorarbeit wird eine akkurate Methode zur Bestimmung von Grundzustandseigenschaften stark korrelierter Elektronen im Rahmen von Gittermodellen entwickelt und angewandt. In der Dichtematrix-Funktional-Theorie (LDFT, vom englischen lattice density functional theory) ist die Ein-Teilchen-Dichtematrix γ die fundamentale Variable. Auf der Basis eines verallgemeinerten Hohenberg-Kohn-Theorems ergibt sich die Grundzustandsenergie Egs[γgs] = min° E[γ] durch die Minimierung des Energiefunktionals E[γ] bezüglich aller physikalischer bzw. repräsentativer γ. Das Energiefunktional kann in zwei Beiträge aufgeteilt werden: Das Funktional der kinetischen Energie T[γ], dessen lineare Abhängigkeit von γ genau bekannt ist, und das Funktional der Korrelationsenergie W[γ], dessen Abhängigkeit von γ nicht explizit bekannt ist. Das Auffinden präziser Näherungen für W[γ] stellt die tatsächliche Herausforderung dieser These dar. Einem Teil dieser Arbeit liegen vorausgegangene Studien zu Grunde, in denen eine Näherung des Funktionals W[γ] für das Hubbardmodell, basierend auf Skalierungshypothesen und exakten analytischen Ergebnissen für das Dimer, hergeleitet wird. Jedoch ist dieser Ansatz begrenzt auf spin-unabhängige und homogene Systeme. Um den Anwendungsbereich von LDFT zu erweitern, entwickeln wir drei verschiedene Ansätze zur Herleitung von W[γ], die das Studium von Systemen mit gebrochener Symmetrie ermöglichen. Zuerst wird das bisherige Skalierungsfunktional erweitert auf Systeme mit Ladungstransfer. Eine systematische Untersuchung der Abhängigkeit des Funktionals W[γ] von der Ladungsverteilung ergibt ähnliche Skalierungseigenschaften wie für den homogenen Fall. Daraufhin wird eine Erweiterung auf das Hubbardmodell auf bipartiten Gittern hergeleitet und an sowohl endlichen als auch unendlichen Systemen mit repulsiver und attraktiver Wechselwirkung angewandt. Die hohe Genauigkeit dieses Funktionals wird aufgezeigt. Es erweist sich jedoch als schwierig, diesen Ansatz auf komplexere Systeme zu übertragen, da bei der Berechnung von W[γ] das System als ganzes betrachtet wird. Um dieses Problem zu bewältigen, leiten wir eine weitere Näherung basierend auf lokalen Skalierungseigenschaften her. Dieses Funktional ist lokal bezüglich der Gitterplätze formuliert und ist daher anwendbar auf jede Art von geordneten oder ungeordneten Hamiltonoperatoren mit lokalen Wechselwirkungen. Als Anwendungen untersuchen wir den Metall-Isolator-Übergang sowohl im ionischen Hubbardmodell in einer und zwei Dimensionen als auch in eindimensionalen Hubbardketten mit nächsten und übernächsten Nachbarn. Schließlich entwickeln wir ein numerisches Verfahren zur Berechnung von W[γ], basierend auf exakten Diagonalisierungen eines effektiven Vielteilchen-Hamilton-Operators, welcher einen von einem effektiven Medium umgebenen Cluster beschreibt. Dieser effektive Hamiltonoperator hängt von der Dichtematrix γ ab und erlaubt die Herleitung von Näherungen an W[γ], dessen Qualität sich systematisch mit steigender Clustergröße verbessert. Die Formulierung ist spinabhängig und ermöglicht eine direkte Verallgemeinerung auf korrelierte Systeme mit mehreren Orbitalen, wie zum Beispiel auf den spd-Hamilton-Operator. Darüber hinaus berücksichtigt sie die Effekte kurzreichweitiger Ladungs- und Spinfluktuationen in dem Funktional. Für das Hubbardmodell wird die Genauigkeit der Methode durch Vergleich mit Bethe-Ansatz-Resultaten (1D) und Quanten-Monte-Carlo-Simulationen (2D) veranschaulicht. Zum Abschluss wird ein Ausblick auf relevante zukünftige Entwicklungen dieser Theorie gegeben.

A comparative analysis by means of quantum molecular similarity measures of density distributions derived from conventional ab initio and density functional methods

A procedure based on quantum molecular similarity measures (QMSM) has been used to compare electron densities obtained from conventional ab initio and density functional methodologies at their respective optimized geometries. This method has been applied to a series of small molecules which have experimentally known properties and molecular bonds of diverse degrees of ionicity and covalency. Results show that in most cases the electron densities obtained from density functional methodologies are of a similar quality than post-Hartree-Fock generalized densities. For molecules where Hartree-Fock methodology yields erroneous results, the density functional methodology is shown to yield usually more accurate densities than those provided by the second order Møller-Plesset perturbation theory