A comparative study of optic phonon-like excitations in liquid mixtures and molten salts

We report a study of collective excitations in an equimolar Lennard–Jones liquid mixture KrAr and a molten salt NaCl within the parameter-free generalized collective modes (GCM) approach. It is shown that the high-frequency propagating modes in liquid KrAr and molten NaCl correspond to optic phonon-like excitations, caused by fast mass-concentration (charge in NaCl) fluctuations. Dispersion curves for optic collective excitations are discussed.     

On‐Surface Synthesis of Ethynylene‐Bridged Anthracene Polymers

Engineering low‐band‐gap π‐conjugated polymers is a growing area in basic and applied research. The main synthetic challenge lies in the solubility of the starting materials, which precludes advancements in the field. Here, we report an on‐surface synthesis protocol to overcome such difficulties and produce poly(p‐anthracene ethynylene) molecular wires on Au(111). To this aim, a quinoid anthracene precursor with =CBr₂ moieties is deposited and annealed to 400 K, resulting in anthracene‐based polymers. High‐resolution nc‐AFM measurements confirm the nature of the ethynylene‐bridge bond between the anthracene moieties. Theoretical simulations illustrate the mechanism of the chemical reaction, highlighting three major steps: dehalogenation, diffusion of surface‐stabilized carbenes, and homocoupling, which enables the formation of an ethynylene bridge. Our results introduce a novel chemical protocol to design π‐conjugated polymers based on oligoacene precursors and pave new avenues for advancing the emerging field of on‐surface synthesis.     

Single particle nature of the yrast line at high angular momentum in 152Dy

Linear polarization and Doppler shift recoil-distance decay curves for γ-ray transitions deexciting very high spin yrast states up to spin 36? in ¹⁵²Dy were measured with a delayed-promt γ-γ coincidence technique via the reactions ¹²²Sn (³⁴S, 4n) and ¹²⁴Sn(³²S, 4n), at 150 MeV incident beam energy. The deduced experimental transition probabilities are consistent with those obtained for non-rotational nuclei indicating that the yrast angular momentum originates mainly from the alignment of individual particle spins.     

Analysis and prediction of absorption band shapes, fluorescence band shapes, resonance Raman intensities, and excitation profiles using the time-dependent theory of electronic spectroscopy

A general method for the simulation of absorption (ABS) and fluorescence band shapes, resonance-Raman (rR) spectra, and excitation profiles based on the time-dependent theory of Heller is discussed. The following improvements to Heller's theory have been made: (a) derivation of new recurrence relations for the time-dependent wave packet overlap in the case of frequency changes between the ground and electronically excited states, (b) a new series expansion that gives insight into the nature of Savin's preresonance approximation, (c) incorporation of inhomogeneous broadening effects into the formalism at no additional computational cost, and (d) derivation of a new and simple short-time dynamics based equation for the Stokes shift that remains valid in the case of partially resolved vibrational structure. Our implementation of the time-dependent theory for the fitting of experimental spectra and the simulation of model spectra as well as the quantum mechanical calculation of the model parameters is discussed. The implementation covers all electronic structure approaches which are able to deliver ground- and excited-state energies and transition dipole moments. The technique becomes highly efficient if analytic gradients for the excited-state surface are available. In this case, the computational cost for the simultaneous prediction of ABS, fluorescence, and rR spectra is equal to that of a single excited-state geometry optimization step while the limitations of the short-time dynamics approximation are completely avoided. As a test case we discuss the well-known case of the strongly allowed 1 (1)A(g) --> 1 (1)B(u) transition in 1,3,5 trans-hexatriene in detail using method ranging from simple single-reference treatments to elaborate multireference electronic structure approaches. At the highest computational level, the computed spectra show the best agreement that has so far been obtained with quantum chemical methods for this problem.     

Toward a Clarity of the Extreme Value Theorem

We apply a framework developed by C. S. Peirce to analyze the concept of clarity, so as to examine a pair of rival mathematical approaches to a typical result in analysis. Namely, we compare an intuitionist and an infinitesimal approaches to the extreme value theorem. We argue that a given pre-mathematical phenomenon may have several aspects that are not necessarily captured by a single formalisation, pointing to a complementarity rather than a rivalry of the approaches.     

On the dimension of the space of ℝ-places of certain rational function fields

We prove that for every n ∈ ? the space M(K(x ₁, …, x _n ) of ?-places of the field K(x ₁, …, x _n ) of rational functions of n variables with coefficients in a totally Archimedean field K has the topological covering dimension dimM(K(x ₁, …, x _n )) ≤ n. For n = 2 the space M(K(x ₁, x ₂)) has covering and integral dimensions dimM(K(x ₁, x ₂)) = dim_? M(K(x ₁, x ₂)) = 2 and the cohomological dimension dim _G M(K(x ₁, x ₂)) = 1 for any Abelian 2-divisible coefficient group G.