Moduli spaces of convex projective structures on surfaces

We introduce explicit parametrisations of the moduli space of convex projective structures on surfaces, and show that the latter moduli space is identified with the higher Teichmüller space for SL₃(R) defined in [V.V. Fock, A.B. Goncharov, Moduli spaces of local systems and higher Teichmüller theory, math.AG/0311149]. We investigate the cluster structure of this moduli space, and define its quantum version.     

Steady‐State and Pseudo‐Steady‐State Photocrystallographic Studies on Linkage Isomers of [Ni(Et4dien)(η2‐O,ON)(η1‐NO2)]: Identification of a New Linkage Isomer

At temperatures below 150 K, the photoactivated metastable endo‐nitrito linkage isomer [Ni(Et₄dien)(η²‐O,ON)(η¹‐ONO)] (Et₄dien=N,N,N′,N′‐tetraethyldiethylenetriamine) can be generated with 100 % conversion from the ground state nitro‐(η¹‐NO₂) isomer on irradiation with 500 nm light, in the single crystal by steady‐state photocrystallographic techniques. Kinetic studies show the system is no longer metastable above 150 K, decaying back to the ground state nitro‐(η¹‐NO₂) arrangement over several hours at 150 K. Variable‐temperature kinetic measurements in the range of 150–160 K show that the rate of endo‐nitrito decay is highly dependent on temperature, and an activation energy of E_act=+48.6(4) kJ mol^?1 is calculated for the decay process. Pseudo‐steady‐state experiments, where the crystal is continually pumped by the light source for the duration of the X‐ray experiment, show the production of a previously unobserved, exo‐nitrito‐(η¹‐ONO) linkage isomer only at temperatures close to the metastable limit (ca. 140–190 K). This exo isomer is considered to be a transient excited‐state species, as it is only observed in data collected by pseudo‐steady‐state methods.     

Local Transient Unfolding of Native State PAI‐1 Associated with Serpin Metastability

The metastability of the native fold makes serpin (serine protease inhibitor) proteins prone to pathological conformational change, often by insertion of an extra β‐strand into the central β‐sheet A. How this insertion is made possible is a hitherto unresolved question. By the use of advanced hydrogen/deuterium‐exchange mass spectrometry (HDX‐MS) it is shown that the serpin plasminogen activator inhibitor 1 (PAI‐1) transiently unfolds under native condition, on a second‐to‐minute time scale. The unfolding regions comprise β‐strand 5A as well as the underlying hydrophobic core, including β‐strand 6B and parts of helices A, B, and C. Based thereon, a mechanism is proposed by which PAI‐1 makes transitions through progressively more unfolded states along the reaction coordinate to the inactive, so‐called latent form. Our results highlight the profound utility of HDX‐MS in detecting sparsely populated, transiently unfolded protein states.     

Pressure-energy correlations in liquids. V. Isomorphs in generalized Lennard-Jones systems

This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble. Paper IV [N. Gnan et al., J. Chem. Phys. 131, 234504 (2009)] showed that strongly correlating liquids have "isomorphs," which are curves in the phase diagram along which structure, dynamics, and some thermodynamic properties are invariant in reduced units. In the present paper, using the fact that reduced-unit radial distribution functions are isomorph invariant, we derive an expression for the shapes of isomorphs in the WU phase diagram of generalized Lennard-Jones systems of one or more types of particles. The isomorph shape depends only on the Lennard-Jones exponents; thus all isomorphs of standard Lennard-Jones systems (with exponents 12 and 6) can be scaled onto a single curve. Two applications are given. One tests the prediction that the solid-liquid coexistence curve follows an isomorph by comparing to recent simulations by Ahmed and Sadus [J. Chem. Phys. 131, 174504 (2009)]. Excellent agreement is found on the liquid side of the coexistence curve, whereas the agreement is less convincing on the solid side. A second application is the derivation of an approximate equation of state for generalized Lennard-Jones systems by combining the isomorph theory with the Rosenfeld-Tarazona expression for the temperature dependence of the potential energy on isochores. It is shown that the new equation of state agrees well with simulations.     

Coupled-cluster theory in a projected atomic orbital basis

We present a biorthogonal formulation of coupled-cluster (CC) theory using a redundant projected atomic orbital (PAO) basis. The biorthogonal formulation provides simple equations, where the projectors involved in the definition of the PAO basis are absorbed in the integrals. Explicit expressions for the coupled-cluster singles and doubles equations are derived in the PAO basis. The PAO CC equations can be written in a form identical to the standard molecular orbital CC equations, only with integrals that are related to the atomic orbital integrals through different transformation matrices. The dependence of cluster amplitudes, integrals, and correlation energy contributions on the distance between the participating atomic centers and on the number of involved atomic centers is illustrated in numerical case studies. It is also discussed how the present reformulation of the CC equations opens new possibilities for reducing the number of involved parameters and thereby the computational cost.     

Homogenität,Kovarianz und Relativität

Zusammenfassung Es werden zwei Begriffe: Homogenität des Raumzeitkontinuums und Kovarianz der Gleichungen, wie sie in der Relativitätstheorie gebraucht werden, definiert und erläutert. Es wird gezeigt, doss die beiden Begriffe wesentlich verschieden sind und in Form nichtäquivalenter mathematischer Bedingungen ihren Ausdruck finden. Trotzdem werden beide Begriffe sowohl von Einstein, als auch in der Literatur über Relativitätstheorie mit einem und demselben Wort Relativität bezeichnet. Der Missgebrauch des Wortes Relativität bedeutet nicht nur einen terminologischen Fehler, sondern spricht auch von einem ungenügenden Verständnis der Grundidee der Relativitätstheorie, besonders der sog. allgemeinen Relativitätstheorie. Versteht man unter Relativität Homogenität des Raumes, so ist in der sog. allgemeinen Relativitätstheorie überhaupt keine Relativität vorhanden. Versteht man dagegen unter Relativität Kovarianz der Gleichungen, so steckt in jener Theorie nicht mehr Relativität, wie z. B. in den unrelativistischen Bewegungsgleichungen, welche ebensogut eine allgemein-kovariante Formulierung gestatten (Lagrangesche Gleichungen 2-ter Art). Die Bezeichnung allgemeine Relativitätstheorie ist daher irrefuhrend. Die geniale Theorie Einsteins ist eine reine Gravitationstheorie. , No 4, . 131, 1955. (RhilosophischeFragen No 4, S. 131, Moskau 1955. Ins Deutsche über setzt vom Verfasser).     

Effective handling of a large configuration state function expansion for an MCSCF state and improved efficiency for two-electron integral transformations in MCSCF

Effective solutions for two difficulties which may be present in MCSCF calculation are discussed: (i) We show how the large configuration state function state expansion case may be handled simply and effectively without the introduction of extraneous projection operators or Lagrange multipliers; (ii) we present a simplified two-electron integral transformation procedure which significantly reduces the operation count (and hence computational efficiency is increased) for second order and particularly for third order MCSCF procedures. The procedures we introduce use some freedom available in the orthogonal complement Cl space and the virtual orbital space to simplify MCSCF calculations.