Diffusion of vibrationally excited molecules

A treatment is presented for the effect of intermolecular vibrational energy transfer on the diffusion coefficient of vibrationally excited molecules. An analytic treatment based on random walk statistics and a Monte Carlo type calculation have been performed. Both methods yield very similar results which correlate well with existing experimental studies. A hard sphere collision model is treated extensively with comparisons made to other internmolecular potentials. The results support the involvement of long range energy transfer in V → V interactions. The effect of temeprature on the diffusion coefficient of vibrationally excited molecules is calculated, with applications to the CO^*₂CO₂ system.     

The Threshold Photoelectron Spectrum of Fulvenone: A Reactive Ketene Derivative in Lignin Valorization

Unveiling reaction mechanisms by isomer-selective detection of reactive intermediates requires advanced spectroscopic knowledge. We study the photoionization of fulvenone (c-C₅H₄=C=O), a reactive ketene species relevant in catalytic pyrolysis of lignin, which was generated by pyrolysis of 2-methoxy acetophenone. The high-resolution threshold photoelectron spectrum (TPES) with vacuum ultraviolet synchrotron radiation revealed well-resolved vibrational transitions, assigned to ring deformation modes of the cyclopentadiene moiety. The adiabatic ionization energy was determined to be 8.25±0.01 eV and is assigned to the ²A₂← ¹A₁ transition. A broad and featureless band arising at 9 eV is associated with the ²B₁← ¹A₁ excitation. A conical intersection is responsible for the ultrafast relaxation of the fulvenone cation from the into the state resulting in a featureless and lifetime broadened band. These insights will increase the detection capabilities for fulvenone and thereby help to elucidate reaction mechanisms in lignin catalytic pyrolysis.     

Molecular transport junctions: asymmetry in inelastic tunneling processes

Inelastic electron tunneling spectroscopy (IETS) measurements are usually carried out in the low-voltage ("Ohmic", i.e., linear) regime where the elastic conduction/voltage characteristic is symmetric to voltage inversion. Inelastic features, normally observed in the second derivative d(2)I/dV(2) are also symmetric (in fact antisymmetric) in many cases, but asymmetry is sometimes observed. We show that such asymmetry can occur because of different energy dependences of the two contact self-energies. This may be attributed to differences in contact density of states (different contact material) or different energy dependence of the coupling (STM-like geometry or asymmetric positioning of molecular vibrational modes in the junction). The asymmetry scales with the difference between the energy dependence of these self-energies and disappears when this dependence is the same for the two contacts. Our nonequilibrium Green function approach goes beyond proposed WKB scattering theory in properly accounting for Pauli exclusion, as well as providing a path to generalizations, including consideration of phonon dynamics and higher-order perturbation theory.     

Inelastic electron tunneling spectroscopy in molecular junctions: peaks and dips

We study inelastic electron tunneling through a molecular junction using the nonequilibrium Green's function formalism. The effect of the mutual influence between the phonon and the electron subsystems on the electron tunneling process is considered within a general self-consistent scheme. Results of this calculation are compared to those obtained from the simpler Born approximation and the simplest perturbation theory approaches, and some shortcomings of the latter are pointed out. The self-consistent calculation allows also for evaluating other related quantities such as the power loss during electron conduction. Regarding the inelastic spectrum, two types of inelastic contributions are discussed. Features associated with real and virtual energy transfer to phonons are usually observed in the second derivative of the current I with respect to the voltage Phi when plotted against Phi. Signatures of resonant tunneling driven by an intermediate molecular ion appear as peaks in the first derivative dI/dPhi and may show phonon sidebands. The dependence of the observed vibrationally induced lineshapes on the junction characteristics, and the linewidth associated with these features are also discussed.     

Non radiative transition probabilities in the statistical limit

In this paper we derive a general computational scheme for the calculation of the non radiative decay probability of a polyatomic molecule in the statistical limit. Within the framework of the Harmonic Approximation the relaxation rate of any polyatomic molecule can be expressed in terms of an infinite sum where each term consists of a medium distribution function and an intramolecular term. In the statistical limit the medium induced vibrational relaxation widths do not affect the non radiative decay characteristics. Numerical calculations are reported for the T ₁S ₀ intersystem crossing in the benzene molecule.     

Current-induced light emission and light-induced current in molecular-tunneling junctions

The interaction of metal-molecule-metal junctions with light is considered within a simple generic model. We show, for the first time, that light-induced current in unbiased junctions can take place when the bridging molecule is characterized by a strong charge-transfer transition. The same model shows current-induced light emission under potential bias that exceeds the molecular excitation energy. Results based on realistic estimates of molecule-lead coupling and molecule-radiation field interaction suggest that both effects should be observable.     

The Maximum Number of Edges in Geometric Graphs with Pairwise Virtually Avoiding Edges

Let G be a geometric graph on n vertices that are not necessarily in general position. Assume that no line passing through one edge of G meets the relative interior of another edge. We show that in this case the number of edges in G is at most 2n?3.     

From Exact Systems to Riesz Bases in the Balian�CLow Theorem

We look at the time–frequency localization of generators of lattice Gabor systems. For a generator of a Riesz basis, this localization is described by the classical Balian–Low theorem. We establish Balian–Low type theorems for complete and minimal Gabor systems with a frame-type approximation property. These results describe how the best possible localization of a generator is limited by the degree of control over the coefficients in approximations given by the system, and provide a continuous transition between the classical Balian–Low conditions and the corresponding conditions for generators of complete and minimal systems. Moreover, this holds for the non-symmetric generalizations of these theorems as well.     

Carbohydrate hydration: heavy water complexes of α and β anomers of glucose, galactose, fucose and xylose

The singly and doubly hydrated complexes of the α and β anomers of a systematically varied set of monosaccharides, O-phenyl D-gluco-, D-galacto-, L-fuco- and D-xylopyranoside, have been generated in a cold molecular beam and probed through infrared-ultraviolet double resonance ion-dip (IRID) spectroscopy coupled with quantum mechanical calculations. A new 'twist' has been introduced by isotopic substitution, replacing H(2)O by D(2)O to separate the carbohydrate (OH) and hydrate (OD) vibrational signatures and also to relieve spectral congestion. The new spectroscopic and computational results have exposed subtle aspects of the intermolecular interactions which influence the finer details of their preferred structures, including the competing controls exerted by co-operative hydrogen bonding, bi-furcated and OH-π hydrogen bonding, stereoelectronic changes associated with the anomeric effect, and dispersion interactions. They also reassert the operation of general 'working rules' governing conformational change and regioselectivity in both singly and doubly hydrated monosaccharides.