ExoMol molecular line lists - XXVII: spectra of C2H4

A new line list for ethylene, $^{12}$C$_2$$^1$H$_4$ is presented. The line list is based on high level ab initio potential energy and dipole moment surfaces. The potential energy surface is refined by fitting to experimental energies. The line list covers the range up to 7000 cm$^{-1}$ (1.43 $\mu$m) with all ro-vibrational transitions (50 billion) with the lower state below 5000 cm$^{-1}$ included and thus should be applicable for temperatures up to 700 K. A technique for computing molecular opacities from vibrational band intensities is proposed and used to provide temperature dependent cross sections of ethylene for shorter wavelength and higher temperatures. When combined with realistic band profiles (such as the proposed three-band model), the vibrational intensity technique offers a cheap but reasonably accurate alternative to the full ro-vibrational calculations at high temperatures and should be reliable for representing molecular opacities. The C$_2$H$_4$ line list, which is called MaYTY, is made available in electronic form from the CDS

Symmetries and deformations in the spherical shell model

23 pages, 7 figures, 2 tables, to be published in a special edition of Physica Scripta to commemorate the 40e anniversary of the Nobel Prize of Bohr, Mottelson and Rainwater. Some figures may appear in colour only in the online journalpour commémorer le 40me anniversaire du prix Nobel de Bohr, Mottelson et Rainwater.International audienceWe discuss symmetries of the spherical shell model that make contact with the geometric collective model of Bohr and Mottelson. The most celebrated symmetry of this kind is SU(3), which is the basis of Elliott's model of rotation. It corresponds to a deformed mean field induced by a quadrupole interaction in a single major oscillator shell N and can be generalized to include several major shells. As such, Elliott's SU(3) model establishes the link between the spherical shell model and the (quadrupole component of the) geometric collective model. We introduce the analogue symmetry induced by an octupole interaction in two major oscillator shells N-1 and N, leading to an octupole-deformed solution of the spherical shell model. We show that in the limit of large oscillator shells (large N) the algebraic octupole interaction tends to that of the geometric collective model

Construction of SO(5)>SO(3) spherical harmonics and Clebsch-Gordan coefficients

The SO(5)>SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1,1)xSO(5) basis. We present a computer code for explicit construction of the SO(5)>SO(3) spherical harmonics and use them to compute the Clebsch-Gordan coefficients needed for collective model calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients it becomes possible to compute the matrix elements of collective model observables by purely algebraic methods.Comment: LaTeX (RevTeX), 15 pages; to be published in Computer Phys. Comm

Unified description of vibronic transitions with coherent states

Vibronic (vibrational-electronic) transition is one of the fundamental processes in molecular physics. Indeed, vibronic transition is essential both in radiative and nonradiative photophysical or photochemical properties of molecules such as absorption, emission, Raman scattering, circular dichroism, electron transfer, internal conversion, etc. A detailed understanding of these transitions in varying systems, especially for (large) biomolecules, is thus of particular interest. Describing vibronic transitions in polyatomic systems with hundreds of atoms is, however, a difficult task due to the large number of coupled degrees of freedom. Even within the relatively crude harmonic approximation, such as for Born-Oppenheimer harmonic potential energy surfaces, the brute-force evaluation of Franck-Condon intensity profiles in a time-independent sum-over-states approach is prohibitive for complex systems owing to the vast number of multi-dimensional Franck-Condon integrals. The main goal of this thesis is to describe a variety of molecular vibronic transitions, with special focus on the development of approaches that are applicable to extended molecular systems. We use various representations of Fermi’s golden rule in frequency, time and phase spaces via coherent states to reduce the computational complexity. Although each representation has benefits and shortcomings in its evaluation, they complement each other. Peak assignment of a spectrum can be made directly after calculation in the frequency domain but this sum-over-states route is usually slow. In contrast, computation is considerably faster in the time domain with Fourier transformation but the peak assignment is not directly available. The representation in phase space does not immediately provide physically-meaningful quantities but it can link frequency and time domains. This has been applied to, herein, for example (non-Condon) absorption spectra of benzene and electron transfer of bacteriochlorophyll in the photosynthetic reaction center at finite temperature. This work is a significant step in the treatment of vibronic structure, allowing for the accurate and efficient treatment of complex systems, and provides a new analysis tool for molecular science.Absorption von Licht und der darauf folgende Elektronentransfer in photosynthetischen Systemen sind entscheidende Prozesse in unserem Alltag. Die Verbesserung von Kontrolle und Effizienz dieser Prozesse ist eine Herausforderung im Hinblick auf die weltweite Nahrungs- und Energieversorgung. Diese Art von Prozessen wird jedoch dadurch kompliziert, dass Absorption, Emission und Lichtstreuung verschiedene strahlungslose molekulare Übergänge wie Ladungswanderung, innere Umwandlung und Interkombinationsübergänge nach sich ziehen können. Ein genaues Verständnis dieser Prozesse auf molekularer Ebene in verschiedenen Systemen ist daher von besonderem Interesse. Molekulare Übergangsprozesse werden durch Wechselwirkungen zwischen Kernen, Elektronen, der Umgebung und äußeren Feldern (z. B. elektromagnetischen) bestimmt. Das Zusammenspiel von vibratorischen und elektronischen (vibronischen) Freiheitsgraden der Moleküle spielt typischerweise eine bedeutende Rolle in molekularen (vibronischen) Übergängen. Ein molekularer vibronischer Übergang wird für gewöhnlich durch Fermis goldene Regel (FGR), die sich aus der zeitabhängigen Störungstheorie ableitet, als eine das absolute Quadrat von Übergangsmomenten enthaltende Übergangsgeschwindigkeitskonstante beschrieben. Laut dem Ausdruck für die Übergangsgeschwindigkeitskonstante in der Basis der Born-Oppenheimer-Wellenfunktionen ist einer der Schlüsselbeiträge zu vibronischen Übergängen der Franck-Condon-Faktor (FCF). Der FCF ist definiert als das Absolutquadrat des Überlappungsintegrals zwischen zu verschiedenen elektronischen Zuständen gehörenden Schwingungswellenfunktionen. Die theoretische Beschreibung vibronischer Übergänge großer polyatomarer Systeme (mehr als 100 Atome) ist jedoch wegen der hohen Dimensionalität eine schwierige Aufgabe. Sogar in einer relativ groben harmonischen Näherung wie den harmonischen Born-Oppenheimerschen Potentialhyperflächen ist die theoretische brute-force-Berechnung der FC-Intensitätsprofile durch eine Summenbildung über die zeitunabhängigen Zustände für komplexe Systeme wegen der gewaltig großen Zahl multi-dimensionaler FC-Integrale ungeeignet. Das Hauptziel dieser Arbeit ist die Beschreibung einer Vielzahl molekularer vibronischer Übergänge, insbesondere der Entwicklung von Herangehensweisen, die auf ausgedehnte molekulare Systeme anwendbar sind. Wir haben verschiedene Darstellungen von FGR in Frequenz-, in Zeit- und, zur Verringerung des Rechenaufwandes über kohärente Zustände, in Phasenräumen verwendet. Jede Darstellung hat Vor- und Nachteile in ihrer Auswertung, aber alle ergänzen einander. Die Signalzuordnung des Spektrums zu verschiedenen Quantenzustandsübergängen kann direkt nach der Berechnung in der Frequenzdomäne vorgenommen werden, doch ist dieser Weg über die Summierung von Zuständen normalerweise zeitintensiv. Im Gegensatz dazu ist die Berechnung über Fouriertransformation in der Zeitdomäne schneller, aber eine Zuordnung der Signale zu verschiedenen Quantenzustandsübergängen ist nicht direkt möglich. Die Darstellung im Phasenraum liefert nicht sofort physikalisch bedeutsamen Größen, kann aber Frequenz- und Zeitdomäne verknüpfen. Folglich können wir die molekularen Übergangsspektren effizient berechnen, einschließlich thermischer und Nicht-Condon-Effekte. Zusätzlich zur Effizienzsteigerung sind wir in der Lage, die einzelnen Dynamiken der Schwingungsfreiheitsgrade während der elektronischen Übergänge für relativ große Systeme zu analysieren. Unsere Methode ist nicht nur auf molekularer Übergänge anwendbar, sondern auf jedes physikalische Problem, das eine Näherung über harmonische Oszillatoren enthält, beispielsweise Nichtgleichgewichtsdynamiken dissipativer Systeme

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In Memory of Vladimir Gerdt

Center for Computational Methods in Applied Mathematics of RUDN, Professor V.P. Gerdt, whose passing was a great loss to the scientific center and the computer algebra community. The article provides biographical information about V.P. Gerdt, talks about his contribution to the development of computer algebra in Russia and the world. At the end there are the author’s personal memories of V.P. Gerdt.Настоящая статья - мемориальная, она посвящена памяти руководителя научного центра вычислительных методов в прикладной математике РУДН, профессора В.П. Гердта, чей уход стал невосполнимой потерей для научного центра и всего сообщества компьютерной алгебры. В статье приведены биографические сведения о В.П. Гердте, рассказано о его вкладе в развитие компьютерной алгебры в России и мире. В конце приведены личные воспоминания автора о В.П. Гердте

Polarised Raman spectroscopy as a quantitative probe of interfacial molecular orientation

Raman scattering is a ubiquitous phenomenon that can be used to great effect to study molecules near interfaces. It has traditionally been used as an analytical tool to identify materials, but by using polarised light, the degree of order within that material can be assessed simultaneously. This thesis seeks to enhance this technique by accurately quantifying interfacial molecular orientation from peak intensities in polarised Raman spectra. This requires a joint modelling and experimental approach. The experimental system, previously developed in our group, obtains surface selectivity through total internal reflection (TIR) of an incident laser beam at the interface under investigation. The evanescent wave generated by TIR causes Raman scattering by the molecules of interest. This system enables investigation of molecular layers at solid-air, solid-liquid and solid-solid interfaces. A numerical model is constructed to predict Raman scattering intensities based on a generalised experimental geometry, the Raman tensor of the vibrational mode under investigation and the orientation of the scattering molecule. A local field correction is implemented for incident as well as emitted radiation. The scattered intensity is calculated with Lorentz reciprocity and integration over the microscope objective that collects the Raman signal. The modelling outcomes are fitted to experimental Raman scattering intensities to deduce molecular orientation. The electrodynamic model of the scattering process is complemented with Raman tensors, polarisabilities and molecular radii obtained by ab initio computation. The novel methodology is validated with isotropic scatterers and a supported monolayer of zinc arachidate. Analysis of Raman spectra of zinc arachidate in a contact under static load reveals a variation in alkyl chain tilt of (4.8±0.5)° per 100 MPa around (27±4)° at 500 MPa. The exact tilt angle depends on the intensity and fitting metrics used. The model further allows quantitative interpretation of Raman spectra as well as optimisation of experimental design. Limitations as well as future applications of this approach are discussed

Computer Science for Continuous Data:Survey, Vision, Theory, and Practice of a Computer Analysis System

Building on George Boole's work, Logic provides a rigorous foundation for the powerful tools in Computer Science that underlie nowadays ubiquitous processing of discrete data, such as strings or graphs. Concerning continuous data, already Alan Turing had applied "his" machines to formalize and study the processing of real numbers: an aspect of his oeuvre that we transform from theory to practice.The present essay surveys the state of the art and envisions the future of Computer Science for continuous data: natively, beyond brute-force discretization, based on and guided by and extending classical discrete Computer Science, as bridge between Pure and Applied Mathematics