Linear-scaling Møller-Plesset Perturbation Theory for the Calculation of Electron Correlation in Large Molecules

Die Berechnung der Elektronenkorrelation mit konventionellen ab-initio-Methoden ist aufgrund des starken Anstiegs des Rechenaufwands mit der Systemgröße auf kleine Moleküle beschränkt. Die Møller-Plesset-Störungstheorie zweiter Ordnung (MP2), welche in Bezug auf den Rechenaufwand die günstigste Korrelationsmethode darstellt, zeigt bereits einen Anstieg des Rechenaufwandes mit der fünften Potenz der Systemgröße, so dass dieser bei Verdopplung der Systemgröße auf das 32-fache ansteigt. Um die Anwendbarkeit des MP2-Verfahrens auf große Moleküle zu erweitern, wurde eine linear skalierende Methode entwickelt, bei der sich der Rechenaufwand direkt proportional zur Systemgröße verhält. Grundlage ist der in den 1990er Jahren von Almlöf und Häser entwickelte Laplace- Ansatz, mit dem die Kopplung an kanonische Molekülorbitale aufgehoben werden kann. Kanonische Molekülorbitale erstrecken sich typischerweise über das gesamte Molekül und lassen somit keine Reduktion des Skalenverhaltens zu. Dagegen ermöglichen die von Natur aus lokalen Atomorbitale (AO) oder auch lokalisierte Molekülorbitale die Reduktion auf ein lineares Skalenverhalten. Die Verwendung rigoroser Integralschranken, die durch eine Kombination aus einer Cauchy-Schwarz- und einer multipolbasierten Abschätzung realisiert wurden, erlaubt eine Vorselektion signifikanter Beiträge und somit eine vollständige numerische Kontrolle der Genauigkeit. Durch eine Neuformulierung der AO-MP2-Gleichung mit Hilfe halbtransformierter Zweielektronenintegrale und die Entwicklung eines Indizierungsschemas für dünn besetzte Vierindexmatrizen konnte eine effiziente Implementierungder AO-MP2-Methode umgesetzt werden, welche Berechnungen der MP2-Energie für Systeme mit mehr als 1000 Atomen gestattet. Mit Hilfe der linear skalierenden AO-MP2-Methode konnte die Wechselwirkungsenergie eines katalytisch aktiven Ribonukleinsäuremoleküls (Ribozym) berechnet werden. Die Ursache für die katalytische Wirkung ist in der Literatur kontrovers diskutiert: Neben der Erniedrigung der Aktivierungsenergie werden eine bevorzugte Bildung eines Reaktandenkomplexes durch deren hydrophoben Charakter sowie die Bildung einer reaktiven Reaktandenkonformationen diskutiert. Die Berechnungen mit der AO-MP2-Methode zeigen eine stärkere Wechselwirkung zwischen Ribozym und Übergangszustandals zwischen Ribozym und den Reaktanden. Zudem wurde eine gute Übereinstimmung mit der experimentell beobachteten relativen Geschwindigkeitskonstanten gefunden, so dass die Ursache der katalytischen Wirkung in der Erniedrigung der Aktivierungsbarriere in der RNA-Kavität zu sein scheint. Weiterhin erlauben die Berechnungen eine genaue Aufschlüsselung der Wechselwirkungsbeiträgeeinzelner Fragmente, womit Vorhersagen zur Änderung der katalytischen Aktivität aufgrund gezielter Mutationen am Ribozym möglich werden. Zusammenfassend liefert die linear skalierende AO-MP2-Methode einen wertvollen Beitrag zur Berechnung der Korrelationsenergie großer Moleküle, deren Berücksichtigung für eine zuverlässige Beschreibung zahlreicher biochemischer Systeme essentiell ist.The calculation of electron correlation employing conventional ab-initio methods is restricted to small-sized molecules due to the strong increase of the computational effort with the molecular size. Although the Møller-Plesset second order pertubation theory (MP2) represents the most favorable correlation method, the computational effort already scales with the fifth order ofthe system size. This means that by doubling the system size the computational effort becomes 32 times as large. In order to enhance the applicability of the MP2 method onto larger molecules, a linear-scaling method was developed, whose computational effort increases directly proportional to the system size. The new formulation is based on the Laplace ansatz introduced in the 1990s by Almlöf and Häser avoid the use of canonical molecular orbitals. These canonical MOs are typically delocalized over the entire molecule and inhibit a reduction of the scaling behavior. In contrast, the use of inherently local atomic orbitals (AO) or localized molecular orbitals open the way to a linear-scaling behavior. A combination of Cauchy-Schwarz and multipole-based integral bounds allows a rigorous preselection of significant contributions, so that the numerical accuracy is fully controllable. A reformulation of the AO-MP2 equation using half-transformed two-electron integrals and the development of an indexing scheme for sparce matrices permit an efficient implementation of the linear-scaling AO-MP2 method. In this way, it is for the first time possible to calculate wavefunction-based correlation energies for systems containing more than 1000 atoms without any empirical assumptions. The new linear-scaling AO-MP2 method was employed to study the catalytic activity of an RNA molecule (ribozyme). As dispersion-type interactions play an important role in such biomolecular systems, it is crucial to take electron correlation into account for a reliable description. The question arises whether the catalytic activity is based on the lowering of the activation energy or on hydrophobic effects which favor the formation of the reactant complex. The AO-MP2 calculations show that the interaction between the ribozyme and the transition state is much stronger as the interaction between the ribozyme and the reactants. Therefore, the results suggest that the catalytic effect results from a lowering of the activation barrier of the reaction within the RNA cavity. This calculated decrease in the activation energy evoked by the interaction with the ribozyme is in agreement with the experimentally observed rate enhancement. To providea detailed understanding of the catalytic mechanism, the contributions of individual RNA fragments to the interaction energy were investigated. Overall, the linear-scaling AO-MP2 method is a valuable approach to calculate the correlation energy of large molecules. It provides an opportunity for an accurate description of dipersion-type interactions, which is crucial for many chemical and biochemical systems, as it was demonstrate by means on studies of a catalytically active RNA system

Annihilation Event

Annihilation Event has no singular origin, but many strands and streams. This is a project about copies, prints, scans, derivations, reconstructions, casts, and virtual models.The 6 day programme in the Lethaby Gallery will bring together a contrary group of artists, archivists, archaeologists, historians, technical experts and theorists from all over Europe. The scheduled events will operate as an experiment, an exchange, a chance to inhabit the Lethaby with a constellation of objects, machines, speculative processes and performances, an unprecedented opportunity for collisions and collusions.In particle physics, annihilation is the process that occurs when a subatomic particle collides with its respective antiparticle to produce other particles. A particle collision is a useful metaphor for the unruly and generative process of transdiciplinary exchange, of bringing disciplines and generations into contact: the productive ground of cultural participation. That exchange is something that we see at the root, or the radical, of art school present and future. Our 3D imaging project has produced a ruin of the Granary building and in that sense has un-formed our inherited institutional structures. What we are figuring out here relies not so much on the shell of a building, but on its infrastructures, connections and collectives built by affiliation: a facilitation of workflows.Rather than new critiques, it is new cartographies that we need.Cartographies not of the Empire, but of the lines of flight out of it.How is it to be done? We need maps. Not maps of what is off the map, but navigation maps. Maritime maps. Orientation tools. That do not try to explain or represent what lies inside the different archipelagos of desertion, but tell us how to reach them

Terrestrial Very-Long-Baseline Atom Interferometry Workshop (TVLBAI 2023)

This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions

Terrestrial Very-Long-Baseline Atom Interferometry: Workshop Summary

Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions