Wave packet dynamics in an harmonic potential disturbed by disorder: Entropy, uncertainty, and vibrational revivals.

We investigate the quantum and classical wave packet dynamics in an harmonic oscillator that is perturbed by a disorder potential. This perturbation causes the dispersion of a Gaussian wave packet, which is reflected in the coordinate-space and the momentum-space Shannon entropies, the latter being a measure for the amount of information available on a system. Regarding the sum of the two quantities, one arrives at an entropy that is related to the coordinate-momentum uncertainty. Whereas in the harmonic case, this entropy is strictly periodic and can be evaluated analytically, this behavior is lost if disorder is added. There, at selected times, the quantum mechanical probability density resembles that of a classical oscillator distribution function, and the entropy assumes larger values. However, at later times and dependent on the degree of disorder and the chosen initial conditions, quantum mechanical revivals occur. Then, the observed effects are reversed, and the entropy may decrease close to its initial value. This effect cannot be found classically.

A time-resolved photoelectron imaging study on isolated tolane: observation of the biradicalic 1Au state.

Tolane (diphenylacetylene, C14H10) was studied by picosecond time-resolved photoionisation and photoelectron imaging in a supersonic jet. The low-energy part of the 1B1u← S0 REMPI spectrum is very similar to an earlier LIF spectrum, however additional bands were observed at higher energies above the fluorescence cut-off. For a number of bands the dynamics were investigated via pump-probe photoionisation and photoelectron spectroscopy. Around the 1B1u origin the lifetimes are in the ns range, but they drop to some 10 ps at higher excitation energies. For the short-lived bands at higher energies a sequential two-step relaxation to a long-lived electronic state was observed proceeding via an intermediately populated state with a lifetime of 100-200 ps. By comparison with previous quantum chemical calculations we assign this state as the biradicalic trans-bent1Au state that is ionised in a two-photon process.

Pentadiynylidene and Its Methyl-Substituted Derivates: Threshold Photoelectron Spectroscopy of R1-C5-R2 Triplet Carbon Chains.

Mass-selective threshold photoelectron spectroscopy in the gas phase was employed to characterize the dialkynyl triplet carbenes pentadiynylidene (HC5H), methylpentadiynylidene (MeC5H), and dimethylpentadiynylidene (MeC5Me). Diazo compounds were employed as precursors to generate the carbenes by flash pyrolysis. The R1-C5-R2 carbon chains were photoionized by vacuum ultraviolet (VUV) synchrotron radiation in photoelectron photoion coincidence (PEPICO) experiments. High-level ab initio computations were carried out to support the interpretation of the experiments. For the unsubstituted pentadiynylidene (R1 = R2 = H) the recorded spectrum yields an adiabatic ionization energy (IEad) of 8.36 ± 0.03 eV. In addition, a second carbene isomer, 3-(didehydrovinylidene)cyclopropene, with a singlet electronic ground state, was identified in the spectrum based on the IEad of 8.60 ± 0.03 eV and Franck-Condon simulations. We found that multireference computations are required to reliably calculate the IEad for this molecule. CASPT2 computations predicted an IEad = 8.55 eV, while coupled-cluster computations significantly overestimate the IE. The cyclic isomer is most likely formed from another isomer of the precursor present in the sample. Stepwise methyl-substitution of the carbene leads to a reduction of the IE to 7.77 ± 0.04 eV for methylpentadiynylidene and 7.27 ± 0.06 eV for dimethylpentadiynylidene. The photoionization and dissociative photoionization of the precursors is investigated as well.

Mechanistical Insights into the Bioconjugation Reaction of Triazolinediones with Tyrosine.

The bioconjugation at tyrosine residues using cyclic diazodicarboxamides, especially 4-substituted 3 H-1,2,4-triazole-3,5(4 H)-dione (PTAD), is a highly enabling synthetic reaction because it can be employed for orthogonal and site-selective (multi)functionalizations of native peptides and proteins. Despite its importance, the underlying mechanisms have not been thoroughly investigated. The reaction can proceed along four distinctive pathways: (i) the SEAr path, (ii) along a pericyclic group transfer pathway (a classical ene reaction), (iii) along a stepwise reaction path, or (iv) along an unusual higher order concerted pericyclic mechanism. The product mixtures obtained from reactions of PTAD with 2,4-unsubstituted phenolate support the SEAr mechanism, but it remains unclear if other mechanisms also take place. In the present work, the various mechanisms are compared using high-level quantum chemistry approaches for the model reaction of 4 H,3 H-1,2,4-triazole-3,5(4 H)-dione (HTAD) with p-cresol and p-cresolate. In a protic solvent (water), the barriers of the SEAr mechanism and the ene reaction are similar but still too high to explain the available experimental observations. This is only possible if the SEAr reaction of cresolate with HTAD is taken into account for which nearly vanishing barriers are computed. This satisfactorily explains measured conversion rates in buffered aqueous solutions and the strong activation effects observed upon addition of bases.

Communication: Adiabatic and non-adiabatic electron-nuclear motion: Quantum and classical dynamics.

Using a model for coupled electronic-nuclear motion we investigate the range from negligible to strong non-adiabatic coupling. In the adiabatic case, the quantum dynamics proceeds in a single electronic state, whereas for strong coupling a complete transition between two adiabatic electronic states takes place. It is shown that in all coupling regimes the short-time wave-packet dynamics can be described using ensembles of classical trajectories in the phase space spanned by electronic and nuclear degrees of freedom. We thus provide an example which documents that the quantum concept of non-adiabatic transitions is not necessarily needed if electronic and nuclear motion is treated on the same footing.

Femtosecond dynamics of diphenylpropynylidene in ethanol and dichloromethane.

Carbon chains with an odd number of C atoms are reactive intermediates with a high biradical character. Here we report a joint experimental and computational investigation of the dynamics of diphenylpropynylidene, C6H5-C3-C6H5, in dichloromethane and ethanol. The biradical is generated by ultraviolet light from 1,3-diphenyldiazopropyne. Electron paramagnetic resonance spectra are recorded to elucidate the spin multiplicity and geometry of the biradical. In both solvents a triplet ground state at 4 K is verified. Transient absorption spectra provide insight into the fate of the biradical. A study in deaerated dichloromethane permits us to follow the photophysics of diphenylpropynylidene and to extract time constants for its vibrational as well as electronic relaxation. In the presence of oxygen, a more complex photochemistry is observed that permits us to derive a model for the reaction of the biradical with O2. In ethanol, the spectra recorded in the presence and absence of O2 are very similar, which can be explained by the similarity of the chromophores of the reaction products.

Methylbismuth: an organometallic bismuthinidene biradical.

We report the generation, spectroscopic characterization, and computational analysis of the first free (non-stabilized) organometallic bismuthinidene, BiMe. The title compound was generated in situ from BiMe3 by controlled homolytic Bi-C bond cleavage in the gas phase. Its electronic structure was characterized by a combination of photoion mass-selected threshold photoelectron spectroscopy and DFT as well as multi-reference computations. A triplet ground state was identified and an ionization energy (IE) of 7.88 eV was experimentally determined. Methyl abstraction from BiMe3 to give [BiMe2]• is a key step in the generation of BiMe. We reaveal a bond dissociation energy of 210 ± 7 kJ mol-1, which is substantially higher than the previously accepted value. Nevertheless, the homolytic cleavage of Me-BiMe2 bonds could be achieved at moderate temperatures (60-120 °C) in the condensed phase, suggesting that [BiMe2]• and BiMe are accessible as reactive intermediates under these conditions.