Does really Born–Oppenheimer approximation break down in charge transfer processes? An exactly solvable model

Effects of deviation from the Born–Oppenheimer approximation (BOA) on the non-adiabatic transition probability for the transfer of a quantum particle in condensed media are studied within an exactly solvable model. The particle and the medium are modeled by a set of harmonic oscillators. The dynamic interaction of the particle with a single local mode is treated explicitly without the use of BOA. Two particular situations (symmetric and non-symmetric systems) are considered. It is shown that the difference between the exact solution and the true BOA is negligibly small at realistic parameters of the model. However, the exact results differ considerably from those of the crude Condon approximation (CCA) which is usually considered in the literature as a reference point for BOA (Marcus–Hush–Dogonadze formula). It is shown that the exact rate constant can be smaller (symmetric system) or larger (non-symmetric one) than that obtained in CCA. The non-Condon effects are also studied.     

Structure and Decay of Gaseous Organic Radical Cations Studied by Their Radiative Decay,Exemplified by the 1,3-Pentadiyne Cation

The radiative decay of over a hundred open-shell organic radical cations has now been established. As a result, the spectral structure of such cations in their ground and excited electronic states can be probed with resolutions of the order of ? 1 cm^?1. This is achieved by means of emission and laser-induced fluorescence techniques. The analysis of the emission and excitation spectra provides the vibrational frequencies of many of the totally symmetric fundamentals of the cations in the two electronic states. In order to study the relaxation behavior of these cations under “isolated conditions”, the lifetimes and fluorescence quantum fields can be obtained by means of photoelectron-photon coincidence measurements. These data yield the radiative and non-radiative rate constants as a function of the internal energy of the cations. The structural and decay information obtained from each of these techniques is illustrated using the 1,3-pentadiyne radical cation as example.     

Radical Anion Intermediates in Organic Chemistry

Radical anions are reactive intermediates in a variety of organic reactions. They make possible several unique synthetic conversions and provide an opportunity for investigating structural relationships. Examples of such reactions are given and current mechanistic views are discussed.     

Substituent Effects in P- and As-centered Radical Cations

The first vertical ionization potentials of isostructural P(III) and As(III) compounds EX₃ (E = P, As) whose highest occupied molecular orbital is preferentially localized on the lone electron pairs of atom E depend on the inductive, resonance, and polarization effects of substituents X. Hyperconjugation in fragments like As^{+ ·}-C-H is the only resonance effect in radical cations As^{+ ·}X₃. The same effect in similar P-centered radical cations is weaker.     

Substituent Effects in S- and Se-Centered Radical Cations

The first ionization potentials of molecules XZY and 1,4-XC₆H₄ZR (X, Y are inorganic, organo- metallic, or organic substituents; Z = S, Se), as well as the energies of charge-transfer bands in the electronic spectra of tetracyanoethylene complexes of these molecules are determined by the inductive, resonance, and polarization effects of substituents X and Y. Z-Centered radical cations formed both from individual molecules in the gas phase and from those incorporated in tight radical ion pairs in solutions are closely allied in their electronic structure. The resonance parameters ⁺ _R of organosilicon, organogermanium, and organotin substituents bound to the radical cation center Z+^· were determined.     

A Closer Look at Spontaneous Mirror Symmetry Breaking in Aldol Reactions

The aldol reaction between acetone and 4‐nitrobenzaldehyde run in the nominal absence of any enantioselective catalyst was monitored by chiral HPLC with the aid of an internal standard. The collected data show the presence of a detectable initial enantiomeric excess of the aldol product in the early stages of the reaction in about 50 % of the experiments. Only a small fraction of the reaction contained the non‐racemic aldol product after 24 h. This temporary emergence of natural optical activity could be the signature of a coupled reaction network that leads to a spontaneous mirror‐symmetry‐breaking process, which originates at very low conversions (i.e., strongly depends on events taking place at the very first stages of the process). The reaction is not autocatalytic in the aldol product, which rules out a simple Frank‐type reaction network as the source of the observed symmetry breaking. On the other hand, the isolation and characterisation of a double‐aldol adduct suggested a reaction network that involved both indirect autocatalysis and indirect mutual inhibition between the enantiomers of the reaction product.     

Mirror Symmetry Breaking by Chirality Synchronisation in Liquids and Liquid Crystals of Achiral Molecules

Spontaneous mirror symmetry breaking is an efficient way to obtain homogeneously chiral agents, pharmaceutical ingredients and materials. It is also in the focus of the discussion around the emergence of uniform chirality in biological systems. Tremendous progress has been made by symmetry breaking during crystallisation from supercooled melts or supersaturates solutions and by self‐assembly on solid surfaces and in other highly ordered structures. However, recent observations of spontaneous mirror symmetry breaking in liquids and liquid crystals indicate that it is not limited to the well‐ordered solid state. Herein, progress in the understanding of a new dynamic mode of symmetry breaking, based on chirality synchronisation of transiently chiral molecules in isotropic liquids and in bicontinuous cubic, columnar, smectic and nematic liquid crystalline phases is discussed. This process leads to spontaneous deracemisation in the liquid state under thermodynamic control, giving rise to long‐term stable symmetry‐broken fluids, even at high temperatures. These fluids form conglomerates that are capable of extraordinary strong chirality amplification, eventually leading to homochirality and providing a new view on the discussion of emergence of uniform chirality in prebiotic systems.     

A New Radical Allylation Reaction of Dithiocarbonates

A radical allylation reaction without tin: The xanthate group in aliphatic xanthates can be replaced by an allyl unit [Eq. (a)]. This radical chain reaction is propagated by ethyl radicals generated by extrusion of sulfur dioxide from ethanesulfonyl radicals, which are themselves derived from allyl ethyl sulfone.     

Spectroscopic and Electrochemical Evaluation of Salt Effects on Electron‐Transfer Equilibria between Donor/Acceptor and Ion‐Radical Pairs in Organic Solvents

Addition of “inert” tetrabutylammonium hexafluorophosphate (Bu₄NPF₆) to a solution of TMDO/DDQ in dichloromethane (where TMDO= 2,2,6,6‐tetramethylbenzo[1,2‐d;4,5‐d]bis[1,3]‐dioxole, donor, and DDQ= diclorodicyano‐p‐benzoquinone, acceptor) is accompanied by drastic changes in the electronic spectrum, which are related to the appearance of the DDQ ^{? .} and TMDO ^+. ion radicals and a decrease in the concentration of the neutral molecules and the charge‐transfer complex [ TMDO,DDQ ]. These changes point to a considerable rise (of about three orders of magnitude) in the apparent electron‐transfer equilibrium constant (K_ET) for this donor/acceptor pair upon increasing the electrolyte concentration from 0 to 0.5 M . Accordingly, the ion‐radical fractions and K_ET values are higher in dichloromethane, at high electrolyte concentrations, than in acetonitrile (where the effect of Bu₄NPF₆ is less pronounced). Similar trends of the apparent equilibrium constants are observed for the tetramethyl‐p‐phenylenediamine/tetracyanoethylene pair. Electron‐transfer equilibrium constants for both donor/acceptor dyads obtained from spectral measurements are related to those derived from the redox potentials of the reactants. The effects of media variations on the electron‐transfer equilibria are discussed within the ion‐pairing and ionic‐activity frameworks.     

Bonding in C2 and Be2: Broken symmetry and correlation in DFT solutions

Summary The solution of both Hartree-Fock (HF) and Kohn-Sham (KS) equations is based on the variational principle. Exact wavefunctions would obey the same symmetry restrictions contained in the total hamiltonian. However, the variational principle does not guarantee these symmetry restrictions and the HF and KS solutions are not necessarily symmetric in spin and space. Spatial and spin symmetry broken solutions with lower energies than their restricted analogues are examined for C₂ and Be₂, in the context of the KS formalism. Comparison with UHF solutions shows that KS instabilities are far less pronounced. The main differences between HF and KS solutions are related to effects of electron correlation.     

Bond‐Forming Reactions of Small Triply Charged Cations with Neutral Molecules

Time‐of‐flight mass spectrometry reveals that atomic and small molecular triply charged cations exhibit extensive bond‐forming chemistry, following gas‐phase collisions with neutral molecules. These experiments show that at collision energies of a few eV, I³⁺ reacts with a variety of small molecules to generate molecular monocations and molecular dications containing iodine. Xe³⁺ and CS₂³⁺ react in a similar manner to I³⁺, undergoing bond‐forming reactions with neutrals. A simple model, involving relative product energetics and electrostatic interaction potentials, is used to account for the observed reactivity.     

Single‐Electron Self‐Exchange between Cage Hydrocarbons and Their Radical Cations in the Gas Phase

We show that the radical cations of adamantane (C₁₀H₁₆^.+, 1 H^.+) and perdeuteroadamantane (C₁₀D₁₆^.+, 1 D^.+) are stable species in the gas phase. The radical cation of adamantylideneadamantane (C₂₀H₂₈^.+, 2 H^.+) is also stable (as in solution). By using the natural ¹³C abundances of the ions, we determine the rate constants for the reversible isergonic single‐electron transfer (SET) processes involving the dyads 1 H^.+/ 1 H, 1 D^.+/ 1 D and 2 H^.+/ 2 H. Rate constants for the reaction 1 H^.++ 1 D? 1 H+ 1 D^.+ are also determined and Marcus’ cross‐term equation is shown to hold in this case. The rate constants for the isergonic processes are extremely high, practically collision‐controlled. Ab initio computations of the electronic coupling (H_DA) and the reorganization energy (λ) allow rationalization of the mechanism of the process and give insights into the possible role of intermediate complexes in the reaction mechanism.     

The Reactivity of Primary Free Radicals and Radical Ions,Mass Transfer,and Electrosorption—The Fundamental Factors for Selectivity in Electrochemical Syntheses of Organic Compounds

In many cases the electrolytic synthesis of organic compounds is rather unselective. This is because the primary radical ions and/or radicals are very often so reactive that they are able to react competitively with several of the different species present in the electrolyte. The aim is to increase the selectivity by rationally altering the process parameters; this demands a knowledge, inter alia, of electrosorption effects and of the relationships between mass transfer and chemical reaction, at or in front of the electrodes (in the so-called reaction layer). Four examples will be used to illustrate this theme:

• 1 The anodic synthesis of triarylsulfonium salts,
• 2 The addition of anodically generated N₃-radicals to olefins, producing “monomeric” 1,2-diazides and “dimeric” 1,4-diazides,
• 3 The cathodic synthesis of optically active 1-(2-pyridyl)ethanol,
• 4 The synthesis of 1,2- and 1,4-diol ethers by anodic oxidation of vinyl compounds in alcoholic solutions.