High-precision evaluation of the Vibrational spectra of long-range molecules

Vibrational spectra of long-range molecules are determined accurately and to arbitrary accuracy with the Canonical Function Method. The energy levels of the $0^-_g$ and $1_u$ electronic states of the $^{23}{\rm Na}_2$ molecule are determined from the Ground state up to the continuum limit. The method is validated by comparison with previous results obtained by Stwalley et al. using the same potential and Trost et al. whose work is based on the Lennard-Jones potential adapted to long-range molecules.Comment: 19 pages, 5 figures and 6 tables. To be published in the G. Herzberg memorial issue, Can. J. Physics Vol. 79 (2001

Petrology of some oceanic island basalts: PRIMELT2.XLS software for primary magma calculation

PRIMELT2.XLS software is introduced for calculating primary magma composition and mantle potential temperature (TP) from an observed lava composition. It is an upgrade over a previous version in that it includes garnet peridotite melting and it detects complexities that can lead to overestimates in TP by >100°C. These are variations in source lithology, source volatile content, source oxidation state, and clinopyroxene fractionation. Nevertheless, application of PRIMELT2.XLS to lavas from a wide range of oceanic islands reveals no evidence that volatile-enrichment and source fertility are sufficient to produce them. All are associated with thermal anomalies, and this appears to be a prerequisite for their formation. For the ocean islands considered in this work, TP maxima are typically ~1450–1500°C in the Atlantic and 1500–1600°C in the Pacific, substantially greater than ~1350°C for ambient mantle. Lavas from the Galápagos Islands and Hawaii record in their geochemistry high TP maxima and large ranges in both TP and melt fraction over short horizontal distances, a result that is predicted by the mantle plume model

Low-Temperature Photoluminescence Spectroscopy of Solvent-Free PCBM Single-Crystals

PCBM ([6,6]-phenyl-C61-butyric acid methyl ester) is a highly soluble C60 derivative that is extensively used in organic solar cells, enabling power conversion efficiencies above 10%. Here we report, for the first time to the best of our knowledge, the photoluminescence of high-quality solvent-free PCBM crystals between room temperature and 4 K. Interestingly, the PL spectra of these crystals become increasingly structured as the temperature is lowered, with extremely well-resolved emission lines (and a minimum line width of ∼1.3 meV at 1.73 eV). We are able to account for such a structured emission by means of a vibronic coupling model including Franck–Condon, Jahn–Teller and Herzberg–Teller effects. Although optical transitions are not formally forbidden from the low-lying excited states of PCBM, the high symmetry of the electronically active fullerene core limits the intensity of the 0–0 transition, such that Herzberg–Teller transitions which borrow intensity from higher-lying states represent a large part of the observed spectrum. Our simulations suggest that the emissive state of PCBM can be considered as a mixture of the T1g and Hg excited states of C60 and hence that the Hg state plays a larger role in the relaxed excited state of PCBM than in that of C60

Herzberg Circuit and Berry's Phase in Chirality-based Coded Qubit in a Triangular Triple Quantum Dot

We present a theoretical proposal for the Herzberg circuit and controlled accumulation of Berry's phase in a chirality-based coded qubit in a triangular triple quantum dot molecule with one electron spin each. The qubit is encoded in the two degenerate states of a three spin complex with total spin $S=1/2$. Using a Hubbard and Heisenberg model the Herzberg circuit encircling the degeneracy point is realized by adiabatically tuning the successive on-site energies of quantum dots and tunnel couplings across a pair of neighbouring dots. It is explicitly shown that encircling the degeneracy point leads to the accumulation of the geometrical Berrys phase. We show that only triangular but not linear quantum dot molecule allows for the generation of Berry's phase and we discuss a protocol to detect this geometrical phase

On-the-fly ab initio semiclassical evaluation of absorption spectra of polyatomic molecules beyond the Condon approximation

To evaluate vibronic spectra beyond the Condon approximation, we extend the on-the-fly ab initio thawed Gaussian approximation by considering the Herzberg-Teller contribution due to the dependence of the electronic transition dipole moment on nuclear coordinates. The extended thawed Gaussian approximation is tested on electronic absorption spectra of phenyl radical and benzene: Calculated spectra reproduce experimental data and are much more accurate than standard global harmonic approaches, confirming the significance of anharmonicity. Moreover, the extended method provides a tool to quantify the Herzberg-Teller contribution: we show that in phenyl radical, anharmonicity outweighs the Herzberg-Teller contribution, whereas in benzene, the Herzberg-Teller contribution is essential, since the transition is electronically forbidden and Condon approximation yields a zero spectrum. Surprisingly, both adiabatic harmonic spectra outperform those of the vertical harmonic model, which describes the Franck-Condon region better. Finally, we provide a simple recipe for orientationally averaging spectra, valid beyond Condon approximation, and a relation among the transition dipole, its gradient, and nonadiabatic coupling vectors.Comment: Final form available via open access in J. Phys. Chem. Lett.: https://pubs.acs.org/doi/10.1021/acs.jpclett.8b00827. Last 11 pages contain the Supporting Informatio

Experimental energy levels and partition function of the 12^{12}C2_2 molecule

The carbon dimer, the $^{12}$C$_2$ molecule, is ubiquitous in astronomical environments. Experimental-quality rovibronic energy levels are reported for $^{12}$C$_2$, based on rovibronic transitions measured for and among its singlet, triplet, and quintet electronic states, reported in 42 publications. The determination utilizes the Measured Active Rotational-Vibrational Energy Levels (MARVEL) technique. The 23,343 transitions measured experimentally and validated within this study determine 5,699 rovibronic energy levels, 1,325, 4,309, and 65 levels for the singlet, triplet, and quintet states investigated, respectively. The MARVEL analysis provides rovibronic energies for six singlet, six triplet, and two quintet electronic states. For example, the lowest measurable energy level of the \astate\ state, corresponding to the $J=2$ total angular momentum quantum number and the $F_1$ spin-multiplet component, is 603.817(5) \cm. This well-determined energy difference should facilitate observations of singlet--triplet intercombination lines which are thought to occur in the interstellar medium and comets. The large number of highly accurate and clearly labeled transitions that can be derived by combining MARVEL energy levels with computed temperature-dependent intensities should help a number of astrophysical observations as well as corresponding laboratory measurements. The experimental rovibronic energy levels, augmented, where needed, with {\it ab initio} variational ones based on empirically adjusted and spin-orbit coupled potential energy curves obtained using the \Duo\ code, are used to obtain a highly accurate partition function, and related thermodynamic data, for $^{12}$C$_2$ up to 4,000 K.Comment: ApJ Supplements (in press), 48 page

Asymptotic optimal designs under long-range dependence error structure

We discuss the optimal design problem in regression models with long-range dependence error structure. Asymptotic optimal designs are derived and it is demonstrated that these designs depend only indirectly on the correlation function. Several examples are investigated to illustrate the theory. Finally, the optimal designs are compared with asymptotic optimal designs which were derived by Bickel and Herzberg [Ann. Statist. 7 (1979) 77--95] for regression models with short-range dependent error.Comment: Published in at http://dx.doi.org/10.3150/09-BEJ185 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

The LYRA Instrument Onboard PROBA2: Description and In-Flight Performance

The Large Yield Radiometer (LYRA) is an XUV-EUV-MUV (soft X-ray to mid-ultraviolet) solar radiometer onboard the European Space Agency PROBA2 mission that was launched in November 2009. LYRA acquires solar irradiance measurements at a high cadence (nominally 20 Hz) in four broad spectral channels, from soft X-ray to MUV, that have been chosen for their relevance to solar physics, space weather and aeronomy. In this article, we briefly review the design of the instrument, give an overview of the data products distributed through the instrument website, and describe the way that data are calibrated. We also briefly present a summary of the main fields of research currently under investigation by the LYRA consortium