Generating M-Indeterminate Probability Densities by Way of Quantum Mechanics

Probability densities that are not uniquely determined by their moments are said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether or not a density is M-indeterminate, or how to generate an M-indeterminate density, is a challenging problem with a long history. Quantum mechanics is inherently probabilistic, yet the way in which probability densities are obtained is dramatically different in comparison with standard probability theory, involving complex wave functions and operators, among other aspects. Nevertheless, the end results are standard probabilistic quantities, such as expectation values, moments and probability density functions. We show that the quantum mechanics procedure to obtain densities leads to a simple method to generate an infinite number of M-indeterminate densities. Different self-adjoint operators can lead to new classes of M-indeterminate densities. Depending on the operator, the method can produce densities that are of the Stieltjes class or new formulations that are not of the Stieltjes class. As such, the method complements and extends existing approaches and opens up new avenues for further development. The method applies to continuous and discrete probability densities. A number of examples are given.

     

The effects of oxygenation on the optical properties of dimethyl-dithienothiophenes: comparison between experiments and first-principles calculations

Modifications of the optical properties of dimethyl-dithienothiophenes due to the oxygen functionalization of the central sulfur atom are investigated. We have measured the absorption, photoluminescence (PL) and PL excitation spectra, the PL quantum efficiencies, and the PL decay times. These experimental results are interpreted and compared with first-principles time-dependent density-functional theory calculations, which predict, for the considered systems, excitation and emission energies with an accuracy of 0.1 eV. It is found that the oxygenation strongly changes optical and photophysical properties. These effects are related to the modifications of the energetically lowest-unoccupied molecular orbital and the energetically second highest occupied one, which change the relative position of the two lowest singlet and triplet excited states.     

Computational study of the reaction of N(2D) atoms with CH2F radicals: an example of a barrier-free reaction involving very high internal energies

The singlet potential-energy surface for the N(2D)+CH2F(2A') reaction has been studied employing both second-order M?ller-Plesset and density-functional theories. The energies of the involved species have been refined using the Gaussian-2, complete basis set, and coupled-cluster singles and doubles (triples) methods. The reaction proceeds through the formation of an initial intermediate, which does not involve any activation barrier. Based on the energy profile for the singlet potential-energy surface, the preferred product should be the most exothermic one, namely, HCN+HF, followed by HNC+HF and FCN+H2. This result seems in contradiction with a computational study of the kinetics of the title reaction in terms of the statistical theories, which leads to the prediction that the production of HNC+HF should be the dominant channel. Consequently, a limited molecular-dynamics study has been carried out, concluding that in fact the system behaves in a nonstatistical way. According to the molecular-dynamics study, the most exothermic channel, HCN+HF, should be the dominant one. An analysis of the possible role of the singlet surface in the reaction of N(4S) with CH2F(2A') has also been carried out. The computational study shows that the microcanonical coefficients for the nonadiabatic channels are much smaller than the competing adiabatic ones. Therefore, the reaction of N(4S) with CH2F(2A') should proceed on the triplet surface without spin change.     

Headspace solid-phase microextraction method for determining 3-alkyl-2-methoxypyrazines in musts by means of polydimethylsiloxane-divinylbenzene fibres

A method for determining 2-methoxypyrazine, 3-methyl-, 3-ethyl-, 3-isopropyl-, 3-sec.-butyl- and 3-isobutyl-2-methoxypyrazine in musts is described. It involves headspace solid-phase microextraction (SPME) and determination by capillary gas chromatography using nitrogen–phosphorous detection. Pyrazines were satisfactorily separated under isothermal conditions, and quantification was carried out using 3-isopropyl-2-ethoxypyrazine as the internal standard. Ionic strength, time and temperature were studied in order to make SPME as efficient as possible. The developed method enabled detection limits at the 0.1 ng l⁻¹ levels for some of the analytes. The method was successfully applied to identify and quantify different 3-alkyl-2-methoxypyrazines in experimental musts of Cabernet Sauvignon and Merlot. Their evolution during the ripening was also monitored.     

Theoretical modeling of vibroelectronic quantum states in complex molecular systems: solvated carbon monoxide, a test case

In this paper we extend the perturbed matrix method by explicitly including the nuclear degrees of freedom, in order to treat quantum vibrational states in a perturbed molecule. In a previous paper we showed how to include, in a simple way, nuclear degrees of freedom for the calculation of molecular polarizability. In the present work we extend and generalize this approach to model vibroelectronic transitions, requiring a more sophisticated treatment.