Performance of density functional theory in computing nonresonant vibrational (hyper)polarizabilities

A set of exchange‐correlation functionals, including BLYP, PBE0, B3LYP, BHandHLYP, CAM‐B3LYP, LC‐BLYP, and HSE, has been used to determine static and dynamic nonresonant (nuclear relaxation) vibrational (hyper)polarizabilities for a series of all‐trans polymethineimine (PMI) oligomers containing up to eight monomer units. These functionals are assessed against reference values obtained using the Møller–Plesset second‐order perturbation theory (MP2) and CCSD methods. For the smallest oligomer, CCSD(T) calculations confirm the choice of MP2 and CCSD as appropriate for assessing the density functionals. By and large, CAM‐B3LYP is the most successful, because it is best for the nuclear relaxation contribution to the static linear polarizability, intensity‐dependent refractive index second hyperpolarizability, static second hyperpolarizability, and is close to the best for the electro‐optical Pockels effect first hyperpolarizability. However, none of the functionals perform satisfactorily for all the vibrational (hyper)polarizabilities studied. In fact, in the case of electric field‐induced second harmonic generation all of them, as well as the Hartree–Fock approximation, yield the wrong sign. We have also found that the Pople 6–31+G(d) basis set is unreliable for computing nuclear relaxation (hyper)polarizabilities of PMI oligomers due to the spurious prediction of a nonplanar equilibrium geometry. © 2013 Wiley Periodicals, Inc.     

Theoretical Modelling of Photoswitching of Hyperpolarisabilities in Ruthenium Complexes

Static excited‐state polarisabilities and hyperpolarisabilities of three Ru^II ammine complexes are computed at the density functional theory (DFT) and several correlated ab initio levels. Most accurate modelling of the low energy electronic absorption spectrum is obtained with the hybrid functionals B3LYP, B3P86 or M06 for the complex [Ru^II(NH₃)₅(MeQ⁺)]³⁺ (MeQ⁺=N‐methyl‐4,4′‐bipyridinium, 3 ) in acetonitrile. The match with experimental data is less good for [Ru^II(NH₃)₅L]³⁺ (L=N‐methylpyrazinium, 2 ; N‐methyl‐4‐{E,E‐4‐(4‐pyridyl)buta‐1,3‐dienyl}pyridinium, 4 ). These calculations confirm that the first dipole‐ allowed excited state (FDAES) has metal‐to‐ligand charge‐transfer (MLCT) character. Both the solution and gas‐phase results obtained for 3 by using B3LYP, B3P86 or M06 are very similar to those from restricted active‐space SCF second‐order perturbation theory (RASPT2) with a very large basis set and large active space. However, the time‐dependent DFT λ_max predictions from the long‐range corrected functionals CAM‐B3LYP, LC‐ωPBE and wB97XB and also the fully ab initio resolution of identity approximate coupled‐cluster method (gas‐phase only) are less accurate for all three complexes. The ground state (GS) two‐state approximation first hyperpolarisability β_2SA for 3 from RASPT2 is very close to that derived experimentally via hyper‐Rayleigh scattering, whereas the corresponding DFT‐based values are considerably larger. The β responses calculated by using B3LYP, B3P86 or M06 increase markedly as the π‐conjugation extends on moving along the series 2 → 4 , for both the GS and FDAES species. All three functionals predict substantial FDAES β enhancements for each complex, increasing with the π‐conjugation, up to about sevenfold for 4 . Also, the computed second hyperpolarisabilities γ generally increase in the FDAES, but the results vary between the different functionals.     

Darstellung und Reaktionen von 4-Selenoxoimidazolidinen

Zusammenfassung 2,5-gleichsubstituierte, C-peralkylierte 4-Selenoxoimidazolidine (1–5) lassen sich glatt aus Ketoncyanhydrinen, NH₃, H₂Se und den den Cyanhydrinen zugrunde liegenden Ketonen darstellen.Durch Umsetzung von -Aminonitrilen (-Aminoacetonitril, -Aminoisobutyronitril und -Aminobenzylcyanid) mit Aldehyden oder Ketonen und H₂Se können auch in 2- und 5-Stellung unterschiedlich substituierte 4-Selenoxoimidazolidine (1, 7–17) synthetisiert werden. Es werden die Salzbildung (Ag⁺, Cd⁺⁺), die saure Hydrolyse, die Hydrierung mit LiAlH₄ und die Oxydation mit H₂O₂/NaOH am Beispiel von C-peralkylierten 4-Selenoxoimidazolidinen beschrieben.Die aminkatalysierte Einwirkung von Schwefel auf ein 2,2-dialkyliertes 5-Phenyl-4-selenoxoimidazolidin führt zum entsprechenden Imidazolin-³-thion-(5).

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Identically 2.5-substituted, C-peralkylated 4-selenoxoimidazolidines (1–5) may be obtained readily from ketone cyanohydrins, ammonia, selenium hydride and the ketones corresponding to the cyanohydrins.4-Selenoxoimidazolines, differently substituted in 2- and 5-positions may also be synthesised by the reaction of -aminonitriles, e.g. -aminoacetonitrile, -aminoisobutyronitrile or -aminobenzylcyanide, with aldehydes or ketones. Salt formation (Ag⁺, Cd⁺⁺), acid hydrolysis, reduction with LiAlH₄ as well as oxidation with NaOH/H₂O₂ have been described in the case of C-peralkylated 4-selenoxomidazolidines.

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65. Mitt.:F. Asinger, H. Offermanns, P. Müller undH. Andree, Mh. Chem.99, 2059 (1968).

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Teil der Dissertation vonH. Berding, Techn. Hochschule Aachen, 1966.     

On the Atomic Photoeffect in Non-relativistic QED

In this paper we present a mathematical analysis of the photoelectric effect for one-electron atoms in the framework of non-relativistic QED. We treat photo-ionization as a scattering process where in the remote past an atom in its ground state is targeted by one or several photons, while in the distant future the atom is ionized and the electron escapes to spacial infinity. Our main result shows that the ionization probability, to leading order in the fine-structure constant, α, is correctly given by formal time-dependent perturbation theory, and, moreover, that the dipole approximation produces an error of only sub-leading order in α. In this sense, the dipole approximation is rigorously justified.     

Determination of Soot Particle Size in a Premixed Flame: a Static and Dynamic Light Scattering Study

In this contribution we report upon our static and dynamic light scattering experiments to characterize soot particles in flames. We studied sooting laminar premixed flame with acetylene as fuel mixed with air as oxidizer. The air equivalence ratio of the combustion was larger than one. We used a Kaskan type burner with circular geometry and a stabilizing flow of nitrogen around the flame. We focused on the determination of the size of the soot particles in the center of the flame as a function of height above burner. In addition we investigated the influence of the mixing ratio of the gases on the size of the particles. Our results show that static light scattering is better suited than dynamic light scattering for a fast and reliable characterization of soot particles in flames. The latter needs detailed a priori information about the flame to allow the unique determination of sizes from the diffusion measurements. The soot particles grow monotonously with height above burner and with decreasing air equivalence ratio. The aggregates have a fractal dimension lower than two.