Point group symmetries of the molecular orbitals of HD+ beyond the Born–Oppenheimer approximation

The isotope shifts of the electronic states of HD⁺ are calculated, for the first time, within an adiabatic MO-LCAO theory. A typical heteronuclear C_∞v correlation diagram comes out, obeying conservation of point group orbital symmetries and noncrossing rule.     

Atoms in molecules: beyond Born–Oppenheimer paradigm

This contribution presents the first atoms in molecules study that goes beyond the Born–Oppenheimer paradigm employing the newly developed two-component quantum theory of atoms in molecules (TC-QTAIM). The LiH, LiD, and LiT systems containing quantum instead of clamped hydrogen nuclei are used as typical examples. The computational analysis that is done on non-adiabatic wavefunctions derived from the fully variational multicomponent molecular orbital approach (FV-MC-MO) results in hydrogen atomic basins without any clamped nucleus. The topological analysis of the Γ-field, the field that replaces the usual one-electron density used in the orthodox topological analysis, reveals delicate differences among the considered systems. The calculation of basin properties also demonstrates that the TC-QTAIM differentiates among atomic basins containing isotopes. Since the nuclear dynamics is contained intrinsically in non-adiabatic wavefunctions, the nuclear contribution to both topological analysis and basin properties naturally emerges from the TC-QTAIM analysis resolving the long-standing obstacle of consistent incorporation of nuclear dynamics within the context of the orthodox QTAIM. Also, a similar analysis is done on non-adiabatic wavefunctions describing excited instead of ground nuclear vibrations of the considered systems demonstrating the fact that TC-QTAIM is capable of being employed for both ground and excited nuclear vibrational states.     

Temperature dependence of photoinduced electron transfer in hydrogen-bonded donor–acceptor systems

We have studied the temperature dependence of photoinduced electron transfer (PET) reactions in three hydrogen-bonded donor–acceptor systems in the range 220–298 K. For the hydrogen-bonded system in the normal region, the PET rate constant was found to increase with increase in temperature. For the two systems in the inverted region, the rate constants were nearly independent of temperature. We have analyzed the results using electron transfer theories.     

Comparison Between a Generalized Electronic Diabatic Approach and the Born–Oppenheimer Separation Scheme in Inertial Frames

We discuss a generalized electronic diabatic (GED) approach to diagonalize the exact Hamiltonian of an n-electron system which embeds an external background of positive charges. This Hamiltonian, denoted by _e(q,), is defined in an inertial frame, and it contains a quantum part (the electrons with coordinates q) and a classical part (the external charges in a three-dimensional configuration ). We derive a GED basis set { _k (q)} using an operator _e(q,⁰) for a single configuration ⁰, and then show that these are also eigenfunctions for any other _e(q,); only the ordering of eigenvalues may depend on (i.e., k=k()). The GED functions can also be used to represent the eigenstates of a fully quantum-mechanical system of electrons and nuclei. We discuss briefly the differences between the present procedure and the standard Born–Oppenheimer (BO) technique in the clamped-nuclei approximation. As illustration, we show how chemical changes emerge as transitions among diabatic states mediated by an electromagnetic field.     

Franck–Condon factors in curvilinear coordinates: the photoelectron spectrum of ammonia

An approach to the calculation of Franck–Condon factors in curvilinear coordinates is outlined. The approach is based on curvilinear normal coordinates, which allows for an easy extension of Duschinsky’s transformation to the case of curvilinear coordinates, and on the power series expansion of the kinetic energy operator. Its usefulness in the case of molecules undergoing large displacements of their equilibrium nuclear configurations upon excitation is then demonstrated by an application to the vibrational structure of the photoelectron spectrum of ammonia, using an anharmonic potential only for the symmetric stretching and bending coordinates of the radical cation.     

Long-range electron and excitation energy transfer in donor–bridge–acceptor systems

Donor–bridge–acceptor (D-B-A) systems, either as supermolecules or on surfaces, have been extensively studied with respect to long-range electron (ET) and excitation energy (EET) transfer. In more recent years, the main research objective has been to develop knowledge on how to construct molecular-based devices, with predetermined electron transfer properties, intended for application in electronics and photovoltaics. At present, such construction is in general hampered for several reasons. Most importantly, the property of a D-B-A system is not a simple linear combination of properties of the individual components, but depends on the specific building blocks and how they are assembled. An important example is the ability of the bridge to support the intended transfer process. The mediation of the transfer is characterized by an attenuation factor, β, often viewed as a bridge specific constant but which also depends on the donor and the acceptor, i.e. the same bridge can either be poorly or strongly conducting depending on the donor and acceptor. This review gives an account of the experimental exploration of the attenuation factor β in a series of bis(porphyrin) systems covalently linked by bridges of the oligo(phenyleneethynylene) (OPE) type. Attenuation factors for ET as well as for both singlet and triplet EET are discussed. A report is also given on the dependence of the transfer efficiency on the energy-gap between the donor and bridge states relevant for the specific transfer process. The experimental variation of β with varying donor and acceptor components is shown for a range of conjugated bridges by representative examples from the literature. The theoretical rationalization for the observed variation is briefly discussed. Based on the Gamow tunneling model, the observed variations in β-values with varying donors and acceptors for the same bridges is simulated successfully simultaneously as the observed energy-gap dependence is modelled.     

Gauging away the electron–electron interaction by the local phase of complex wave functions in two-electron systems

The electron–electron interaction is eliminated in the expectation values of the electronic Hamiltonian for two-electron systems. The part of the Hamiltonian referring to the repulsive interaction is gauged away by the local phase of the complex wave functions, much like a gauge field transformation, thereby leading to a one-electron Hamiltonian. Despite the appearance of complex wave functions, the expectation values of the total momentum operator vanish and Löwdin’s criterion holds for the stationary states.     

Theoretical study of proton transfer in ammonia–hydrogen halides in the presence of methanol

In this work, the effect of solvent (methanol, CH₃OH) molecules on proton transfer (PT) between ammonia and hydrogen halides was studied. We performed MP2 and B3LYP calculations on HX–NH₃–(CH₃OH) _n clusters for three hydrogen halides, HF, HCl, and HBr, with the number of methanol molecules varying from none to three (n = 0–3). The results showed that stepwise association of methanol molecules with the gas-phase complex can eventually facilitate ionization within the complex, producing the $ {\text{NH}}_{4}^{ + } {\text{X}}^{ - } - \left( {{\text{CH}}_{ 3} {\text{OH}}} \right)_{\text{n}} $ cluster. We found that PT occurs on addition of from one (for HBr) to three (for HF) methanol molecules. The interaction energy $ E_{\text{int}} $ and $ \Updelta E_{\text{add}} $ for the complexes were calculated and basis set superposition error (BSSE) correction was also performed. Atoms-in-molecule and natural-bond-orbital analysis were used to study the properties of the hydrogen bonds in the complexes.     

Franck–Condon breakdown in core-level photoelectron spectroscopy of chemisorbed CO

The photon energy dependence of the vibrational fine structure in the C1s and O1s X-ray photoelectron main lines of chemisorbed CO on Ni(100) and Ru(0001) has been measured from 6 to 150 eV above the core-level thresholds. Significant deviations from the behavior in gas-phase CO are found. A strong dominance of the adiabatic peak towards threshold is found for the C1s, but not the O1s, lines. In the C1s lines, we observe a broad maximum of vibrational excitation 5 eV above the shape resonance. At high photon energies, Franck–Condon behavior is observed in both the C1s and O1s lines. This behavior is discussed in terms of the adsorbate electronic structure and the dynamic metallic screening upon core ionization.     

Where does the electron go? Electron distribution and reactivity of peptide cation radicals formed by electron transfer in the gas phase

We report the first detailed analysis at correlated levels of ab initio theory of experimentally studied peptide cations undergoing charge reduction by collisional electron transfer and competitive dissociations by loss of H atoms, ammonia, and N-C alpha bond cleavage in the gas phase. Doubly protonated Gly-Lys, (GK + 2H) (2+), and Lys-Lys, (KK + 2H) (2+), are each calculated to exist as two major conformers in the gas phase. Electron transfer to conformers with an extended lysine chain triggers highly exothermic dissociation by loss of ammonia from the Gly residue, which occurs from the ground ( X ) electronic state of the cation radical. Loss of Lys ammonium H atoms is predicted to occur from the first excited ( A ) state of the charge-reduced ions. The X and A states are nearly degenerate and show extensive delocalization of unpaired electron density over spatially remote groups. This delocalization indicates that the captured electron cannot be assigned to reduce a particular charged group in the peptide cation and that superposition of remote local Rydberg-like orbitals plays a critical role in affecting the cation-radical reactivity. Electron attachment to ion conformers with carboxyl-solvated Lys ammonium groups results in spontaneous isomerization by proton-coupled electron transfer to the carboxyl group forming dihydroxymethyl radical intermediates. This directs the peptide dissociation toward NC alpha bond cleavage that can proceed by multiple mechanisms involving reversible proton migrations in the reactants or ion-molecule complexes. The experimentally observed formations of Lys z (+*) fragments from (GK + 2H) (2+) and Lys c (+) fragments from (KK + 2H) (2+) correlate with the product thermochemistry but are independent of charge distribution in the transition states for NC alpha bond cleavage. This emphasizes the role of ion-molecule complexes in affecting the charge distribution between backbone fragments produced upon electron transfer or capture.     

PANI–TiC nanocomposite film for the direct electron transfer of hemoglobin and its application for biosensing

A novel polyaniline and titanium carbide (PANI–TiC) nanocomposite was synthesized by an in situ chemical oxidative polymerization method, and a hydrogen peroxide (H₂O₂) biosensor was fabricated by PANI–TiC with hemoglobin (Hb)-modified glassy carbon electrode (GCE). Scanning electron microscope and energy dispersive X-ray spectroscopy showed the morphology and ingredient of PANI–TiC. Electrochemical investigation of the biosensor showed a pair of well-defined, quasi-reversible redox peaks with E _pa?=??0.318 V and E _pc?=??0.356 V (vs SCE) in 0.1 M, pH 7.0 sodium phosphate-buffered saline at the scan rate of 150 mV s^?1. Transfer rate constant (k _s) was 2.01 s^?1. The Hb/PANI–TiC/GCE showed a good electrochemical catalytic response for the reduction of H₂O₂ with the linear range from 0.5 to 285.5 μM and the detection limit of 0.2 μM (S/N?=?3). The apparent Michaelis–Menten constant (K _m) was estimated to be 1.21 μM. Therefore, the PANI–TiC as a novel matrix opened up a further possibility for study on the design of enzymatic biosensors with potential applications.     

Theoretical studies on the influence of molecular interactions on the mechanism of electron transfer in photosynthetic reaction center of Rps.viridis

Based on the QM/MM optimized X-ray crystal structure of the photosynthetic reaction center (PRC) of purple bacteria Rhodopseudomonas (Rps.) viridis, quantum chemistry density functional method (DFT, B3LYP/6-31G) has been performed to study the interactions between the pigment molecules and either the surrounded amino acid residues or water molecules that are either axially coordinated or hydrogen bonded with the pigment molecules, leading to an explanation of the mechanism of the primary electron-transfer (ET) reactions in the PRC. Results show that the axial coordination of amino acid residues greatly raises the ELUMO of pigment molecules and it is important for the possibility of ET to take place. Different hydrogen bonds between amino acid residues, water molecules and pigment molecules decrease the ELUMO of the pigment molecules to different extents. It is crucial for the ET taking place from excited P along L branch and sustains that the ET is a one-step reaction without through accessory bacterioc     

Dynamic relaying properties of a β-turn peptide in long-range electron transfer

The relay stations play a significant role in long-range charge hopping transfer in proteins. Although studies have clarified that many more protein structural motifs can function as relays in charge hopping transfers by acting as intermediate charge carriers, the relaying properties are still poorly understood. In this work, taking a β-turn oligopeptide as an example, we report a dynamic character of a relay with tunable relaying properties using the density functional theory calculations. Our main finding is that a β-turn peptide can serve as an effective electron relay in facilitating long-range electron migration and its relay properties is vibration-tunable. The vibration-induced structural transient distortions remarkably affect the lowest occupied molecular orbital (LUMO) energy, vertical electron affinity and electron-binding mode of the β-turn oligopeptide and the singly occupied molecular orbital (SOMO) energy of the corresponding electron adduct and thus the relaying properties. Different vibration modes lead to different structural distortions and thus have different effects on the relaying properties and ability of the β-turn peptide. For the relaying properties, there approximately is a linear negative correlation of electron affinity with the LUMO energy of the β-turn or the SOMO energy of its electron adduct. Besides, such relaying properties also vary in the vibration evolution process, and the electron-binding modes may be tunable. As an important addition to the known static charge relaying properties occurring in various protein structural motifs, this work reports the dynamic electron-relaying characteristics of a β-turn oligopeptide with variable relaying properties governed by molecular vibrations which can be applied to different proteins in mediating long-range charge transfers. Clearly, this work reveals molecular vibration effects on the electron relaying properties of protein structural motifs and provides new insights into the dynamics of long-range charge transfers in proteins. © 2018 Wiley Periodicals, Inc.     

Tunneling transfer of an electron in oxidation of the HS− ion by an I 3 − complex in aqueous solution

Methods of chemical kinetics have been used in a study of the mechanism of hydrogen sulfide oxidation by iodine. It has been shown that the stage of electron transfer from HS^– to the I ₃ ^/– complex proceeds through a tunneling mechanism. A proposed twinkling model of the reaction mechanism provides an explanation for the observed experimental facts: the dependence of the rate constant on the acidity, viscosity, and ionic strength of the solution; the inverse temperature dependence of the reaction rate constant; the dependence of the reaction rate constant on the concentrations of iodide ion and maleic acid, which are not involved directly in the reaction.B. P. Konstantinov Institute of Nuclear Physics, Russian Academy of Sciences, Gatchina 188350. Translated from Izvestiya Akademii Nauk, Seriya Khimicheskaya, No. 3, pp. 522–536, March, 1992.     

Phase diagram of the face-centred cubic Blume–Emery–Griffiths model in the cluster variation method tetrahedron approximation

Abstract

The critical behaviour of the Blume–Emery–Griffiths model is analysed utilizing the cluster variation method in the tetrahedron approximation in order to include the effects of four-body correlations and to obtain an accurate determination of critical surfaces. The model has a very rich phase diagram and recently its interest has increased for it exhibits a reentrant phenomenon. In this paper the Blume–Emery–Griffiths model is proposed to describe the reentrant isotropic-nematic transition in lyotropic liquid crystals. Our results are compared with experimental data with a good success.     

Photoinduced electron transfer reactions in the 10-methylacridinium cation–benzyltrimethylsilane system: steady-state and flash photolysis studies

The mechanism of the photoinduced reaction of the lowest excited singlet state of the 10-methylacridinium (AcrMe⁺) cation with benzyltrimethylsilane (BTMSi) in acetonitrile has been investigated by means of steady-state and time-resolved methods. A variety of stable products was found after irradiation (365 nm) of the reaction mixture under aerobic and oxygen-free conditions. The stable products were identified and analyzed using UV–Vis spectrophotometry, high performance liquid chromatography (HPLC), and mass spectrometry (MS). Based on Stern–Volmer plots of the AcrMe⁺ fluorescence quenching by BTMSi (using fluorescence intensity and lifetime measurements), the rate constants were determined to be k _q = 1.24 (± 0.02) × 10¹⁰ M⁻¹ s⁻¹ and k _q = 1.23 (± 0.02) × 10¹⁰ M⁻¹ s⁻¹, i.e., close to the diffusion-controlled limit in acetonitrile, indicating the dynamic quenching mechanism. The quenching process was shown to occur via an electron-transfer reaction leading to the formation of acridinyl radicals (AcrMe^•) and C₆H₅CH₂Si(CH₃)₃ ^•+ radical cations. Based on stationary and flash photolysis experiments, a detailed mechanism of the secondary reactions is proposed and discussed. The AcrMe^• radical was shown to decay by two processes. The fast decay, observed on the nanosecond timescale, was attributed to the back-electron transfer occurring within the initial radical ion pair. The slow decay on the microsecond timescale was explained by recombination reactions of radicals which escaped from the radical pair, including benzyl radicals formed via C–Si bond cleavage in the C₆H₅CH₂Si(CH₃)₃ ^•+ radical cation.     

Effect of beta-alkylthioethyl substitution in 1,3-dithianes: quasianchimeric assistance in photoinduced electron transfer?

Nanosecond laser flash photolysis (LFP) experiments show that the rates of ET quenching of triplet benzophenone by 2-alkyldithianes significantly decrease with bulkier substitution. Introduction of sulfur at the beta-position of the flexible alkyl chain reverses this trend, whereas such substitution at the alpha-position has negligible effect. This is rationalized in terms of the three electron two center bonds, favorable due to the formation of five-membered cyclic radical cations in the case of beta-substitution, which is supported by DFT computations.     

Is there any group additive rules in the calculation of electron correlation energies of long straight chain alkane molecules?

According to the definition in the text, the correlation energy of 1s2C of carbon atoms, the primary and secondary C-H bonding electron pairs in some CH3, CH2 fragments and CH3(CH2)mCH3 (m=1-5) linear alkane molecules are calculated and analyzed. The transferability of the correlation energies of these electron pairs in the linear alkanes is investigated. The results indicate that the correlation energy of 1s2C is perfectly transferable in the respective methyl and methylene groups, while the correlation energies of the primary and secondary C-H bonding electron pairs are approximately transferable in methyl and methylene groups. The analysis of the results of group correlation energy shows that both of the correlation energies of methyl and methylene groups are transferable in these linear alkanes. The correlation energies of methylene group in CH3(CH2)mCH3 (m=1-5) molecules are slightly decreasing showing a converging trend to a "standard" methylene group in linear alkanes. The excellent fitting relationship between the total correlation energy and the number of methylene groups of the linear alkanes shows that the total correlation energy is a linear function of the number of methylene groups, which means that the total correlation energies of large linear alkanes can be reproduced and predicted by counting the numbers of methylene groups. In this way, total correlation energy of large linear alkane molecule can be approximately calculated using this simple group additive scheme with substantial saving in computational time.     

Orientational effects of β-cyclodextrins on electron transfer between metal complexes in solution

The kinetics of the electron transfer reaction between pentammine-(4,4bipyridine)ruthenium(II) and cyclohexyldiamine-N,N,N,N-tetraacetatocobaltate(III) has been studied in unsubstituted and substituted -cyclodextrin solutions. The increased ion-pairing and the decreased electron transfer rates that result when the ruthenium complex are encapsulated by cyclodextrins are interpreted in terms of hydrogen bonding between cyclodextrin and the metal complexes markedly stabilizing the ionpair.Presented at the Symposium 76^th CSC Congress, Sherbrooke, Quebec, May 30–June 3, 1993, honoring Professor Donald Patterson on the occasion of his 65^th birthday.