A quantum chemical study of interchain hopping model of negatively charged solitons in polyacetylene

Phonon-assisted interchain hopping of negatively charged solitons in polyacetylene has been studied using a local chemical reaction model CH + CH₄ → CH₄ + CH. Quantum chemical characteristics of the electron transfer process have been analyzed in terms of the dynamic electron density and the mutual polarization moment. The CH stretching vibrational motion of CH₄, which is a local model of the sp³ defect, has been found to play a significant role for the electron transfer. The excitation of the corresponding vibrational mode of the sp³ defect would promote the interchain hopping of the charged soliton. The electron transfer process has also been studied in terms of the “regional” density functional theory. It has been shown that the driving force of the electron transfer is represented by the regional chemical potentials.     

Length dependence of the optical transition energies of the exactly solvable Hubbard model for linear polyenes

Some accurate results on the length dependence of the excitation energies from the ground state to ionic excited states in the Hubbard model of linear polyenes are obtained based on the method of Lieb and Wu. To this end, it is first shown that singly ionic excited states with “plus” alternancy symmetry in the Hubbard model are described by the wave functions in which the two electron operator [∑(?)ⁿCC] is acted on (N ? 2)-electron covalent eigenstates. Then by solving the Lieb-Wu equations the exact excitation energies of the lowest ionic state, which corresponds to the E state in this model, are calculated for systems with up to 50 electrons. The result, together with a correction for the end effect, indicates that the excitation energies do not decrease as 1/N but converge to the limiting value more rapidly when the number of electrons N becomes large.     

Electron transfer reactivity of O2+O system in low-spin coupling: Ab Initio study at electron correlation level

The electron transfer reactivity of the O₂+O system in low-spin coupling is studied at the second-order unrestricted Møller–Plesset (full)/6-311+G* basis set level by using different transition state structures. The properties and stabilities of the encounter complexes are compared for the five selected coupling structures: two T type, collinear, parallel, and crossing. The activation barriers and the coupling matrix elements are also calculated. The results indicate that the structures of the encounter complexes directly affect the electron transfer mechanism and rate. These encounter complexes are structurally unstable, the contact distances between the acceptor O₂ and the donor O are generally large, the interaction is weak, and the structures are floppy. The electronic transmission factor for the reacting system, O₂+O, is less than unity; thus, the electron transfer reaction is nonadiabatic in nature. Analysis of the dependence of relevant kinetic parameters on various influencing factors has shown that the effect of the solvent medium on the coupling matrix element is small but that on the electron transfer rate is very large. Among the five selected transition state structures, the electron transfer is more likely to take place via T₁-type and P-type structures. In the low-spin coupling the favorable electronic states for two reacting species are ¹∑(O₂) and X²Π_g(O) instead of X³∑(O₂) and X²π_g(O), which are favorable for the high-spin (quartet state) coupling mechanism. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 989–998, 1999     

Free-energy correlation for catalysis of outer sphere electron-transfer reactions by noncoordinated pyridine derivatives

Recent experimental data concerning the rate constants and their free energy of the outer sphere electron-transfer reactions, as catalyzed by noncoordinated pyridine derivatives in aqueous solution, are examined for possible correlation. For the electron transfer reactions between V or Eu and the bipyridyl derivatives, such as N,N'-dimethyl-4,4′-bipyridyl (paraquat) or diquat, the data are correlated quite well by the Marcus equation. The electron exchange rate constant, 5 × 10⁷M^?1·s^?1, for an organic radical ion and its parent molecule obtained from semiquinones or their related compounds can be applied to these pyridine derivatives. However, in some cases such as electron transfer from paraquat or diquat cation radical to Co(en), positive departures from the Marcus model are observed. These positive departures are interpreted in terms of interaction between the molecular orbitals of electron donors and electron acceptors in the transition state.     

Intermolecular Electron Spin Transfer between Naphthalene π-Systems Separated by a Variable Number of Spirobonded Cyclobutane Rings,An. ESR and ENDOR Study

The radical anions of the compounds N1N, N3N and N5N , in which two naphthalen π-systems are separated by 1, 3 and 5 spirobonded cyclobutane rings, respectively, and tha tof the reference compound N1 , containing one naphthalene π-system and one cyclobutane ring, have been studied by ESR and ENDOR spectroscopy under a variety of experimental conditions. The intramolecular electrons spin transfer between the two π-moieties in N3N and N5N is slow on the hyperfine time-scale, irrespective of the applied conditions. It is also slow in N1N , except for media of high solvating power. In such media, with a slight reduction of N1N to its radical anion, a paramagnetic species is observed, the hyperfine data for which are consistent with N1N to its radical anion, a paramagnetic species is observed, the hyperfine data of which are consistent with N1N , undergoing a fast intramolecular electron spin tansfer. The ESR and ENDOR spectra of this species are superimposed on those characteristic of a slow transfer. It is suggested that the fast and slow transfer involve the syn- and anti-conformations, respectively, since the distance, r, between the two naphthalene π-systems of N1N is considerably shorter in the former than in the latter (r = 740 vs. 880 Pm for the distance between the centres of the π-systems). Glassy solutions of exhaustively reduced N1N display signals of the dianion triplet state, whereas no such signals are found for N3N and N5N . The zero-field splitting parameter, D , is 4.7 mT, corresponding to r ≈ 480 pm.     

Crossed-Molecular beam studies of the state-to-state reaction dynamics of charge transfer at low and intermediate energy

The microscopic, state-to-state reaction dynamics of charge transfer reactions are reviewed for the two system N(N₂, N₂)N and Ar⁺(N₂, Ar)N. The crossed molecular beam method demonstrates that the symmetric, molecular case proceeds by two mechanisms at low collision energy (< 0.7 eV). One of these involves an orbiting complex in which the total available energy is redistributed, essentially statistically. The second mechanism is a direct mechanism which involves nearly rectilinear trajectories and corresponds to exactly resonant charge transfer at low energy (0.7 eV) and charge transfer accompanied by vibrational excitation at higher energy (> 10 eV). The orbiting mechanism is dominant at low energies and disappears entirely with increasing collision energy. The unsymmetric, nearly resonant charge transfer reaction is direct at all energies. At very low collision energy (0.6 eV) and moderate collision energy (> 1.5 eV) the dominant reaction channel is the generation of N₂⁺(X² g, v = 1) with little rotational excitation. At 0.6 eV substantial angular scattering (including back-scattering) is observed; above 1.5 eV the trajectories are essentially rectilinear. At intermediate energies (0.8 < E < 1.3 eV) a very different mechanism is observed. All the energetically accessible vibrational states of N are formed, each with a preferred scattering angle at a given energy. Related experiments and theoretical models which rationalize some, but not all, of these results are described. The most intriguing puzzle is the “energy window” in which quantum-state specific, angular-specific reactive scattering is observed.     

Kinetics and thermochemistry of electron attachment to SF6

Thermochemical analysis of the electron capture process of SF₆ leads to a rate constant for the reverse process \documentclass{article}\pagestyle{empty}\begin{document}$ {\rm SF}_6^ - \mathop \to \limits^2 {\rm SF}_6 + e^ -,k_2 = 1.5 \times 10^{13 - 31.4/\theta } {\rm s}^{{\rm - 1}} $\end{document}, where θ = 2.303RT, in kcal/mol. The electron affinity of 32±3 kcal/mol is deduced from the observed bimolecularity of the capture process down to 0.1 torr Ar bath gas and estimated entropies of SF₆ and SF. The capture process is discussed from the view point of the formation of a metastable SF electron (SF₆·e) Langevin complex which appears to have a lifetime of about 2 × 10^?13 s. Curve crossing from the SF₆·e complex to vibrationally excited (SF)* appears to have a normal rate and A factor. This is interpreted to indicate near-resonant coupling between the orbiting electron and the vibronic motions of SF₆, together with similarity in structure of SF₆ and SF. It is shown that the apparent slowness of thermal electron ejection from SF is a result of an unfavorable equilibrium constant rather than a slow rate.     

Convergence accelerator approach for the evaluation of some three‐electron integrals containing explicit rij factors

A simplified analysis is presented for the evaluation of the three‐electron one‐center integrals of the form ∫rrrrrred r ₁d r ₂d r ₃, for the cases i, j, k, ≥−2, l=−2, m≥−1, n≥−1. These integrals arise in the calculation of lower bounds for energy levels and certain relativistic corrections to the energy when Hylleraas‐type basis sets are employed. Convergence accelerator techniques are employed to obtain a reasonable number of digits of precision, without excessive CPU requirements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 93–99, 1999     

Evaluation of two‐center,three‐ and four‐electron integrals over Slater‐type orbitals in elliptical coordinates

An algorithm for evaluation of two‐center, three‐electron integrals with the correlation factors of the type rr and rrr as well as four‐electron integrals with the correlation factors rrr and rrr in the Slater basis is presented. This problem has been solved here in elliptical coordinates, using the generalized and modified form of the Neumann expansion of the interelectronic distance function r for k ≥ ?1. Some numerical results are also included. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Charge stripping C

Measurements of the translational energy loss accompanying the charge-stripping reactions M⁺+N→M²⁺+N+e⁻ and M²⁺+N→M³⁺+N+e⁻ have been performed for C, C and C, C respectively. The energy nesessary to remove the second electron from Buckminsterfullerene was determined, Q=IE(C→C=12.25±0.5 eV.     

Ionic atmosphere effects on the energetics of thermal and optical electron-exchange reactions: Application to ferrocenium-ferrocene self exchange

A treatment of ionic-atmosphere effects upon symmetrical electron-transfer reactions resulting from added electrolyte is outlined. Relationships are derived on the basis of the extended Debye-Huckel model for the increase in the activation free energy, ΔG_ia*, associated with reorganization of the ionic atmosphere for homogeneous-phase reactions involving a pair of spherical reactants with varying internuclear distance R. Similar relationships apply to the energetics of symmetrical optical electron transfer, since the increase in the optical transition energy, ΔE, should equal the corresponding ionic atmosphere reorganization energy, E; under the anticipated linear response conditions, E = 4ΔG_ia*. The predicted ΔG_ia* (and hence ΔE) values increase sharply with increasing R, as a consequence of the diminished “sharing” of the ionic cloud surrounding the donor and acceptor sites under these conditions. Outer-sphere electrochemical reactions, featuring a single “near-isolated” reactant, are predicted to feature substantially larger ΔG_ia* values than for homogeneous processes proceeding with the reaction partners in contact. The influence of more specific “ionic atmosphere” effects upon ΔG_ia*, especially involving reactant-electrolyte ion pairing, is also discussed. Unlike that of the nonspecific ionic atmosphere, the nuclear reorganization process associated with counterion transport between donor and acceptor sites coupled with electron transfer is nonlinear in nature, so that E ≠ 4ΔG_ia*. Some recent experimental data for electrolyte effects upon the rate constants for ferrocenium-ferrocene self exchange and related systems are examined in the light of these considerations.     

The formation of highly excited H in the reaction H2+(v) + H2 → H + H

A quasiclassical trajectory surface hopping method has been used to study H(v) + H₂ → H + H for v = 0, 3, 7, 10, 13, and 17 with an emphasis on determining the H internal energy and angular momentum distributions for high v. For v = 13 and 17, significant cross sections are found for producing H at energies above its dissociation energy. An average metastable H lifetime of 11.5 ps for v = 13 and 4.7 ps for v = 17 is found, but there is also a much longer lived component to the lifetime distributions that is more important for v = 13 than for v = 17. Some of the longer lived metastables correspond to high angular momentum orbiting states of H, but other sources of metastability are also present.     

Conformational Analysis and Chromic Acid Oxidation. Oxidation Rates and Equilibrium Constants of Epimeric Alcohols

The linear free energy relationship of Sicher for relative reactivity towards chromic acid oxidation (ΔΔG) as a function of thermodynamic stability (ΔG) has been reexamined with 23 pairs of epimeric alcohols. The plot of ΔG vs. ΔG has a slope of 0.8, a correlation coefficient of 0.97 and a standard deviation of 0.23 kcal/mol on ΔΔG_Ox. The limitations of the relationship and the exceptions are discussed.     

Hydrogen Generation by Visible Light Irradiation of Aqueous Solutions of Metal Complexes. An approach to the photochemical conversion and storage of solar energy

We describe a photochemical system for the generation of hydrogen by water reduction under visible light or sunlight irradiation of aqueous solutions containing the following components: a photosensitizer, the Ru (bipy) complex, for visible light absorption; a relay species, the Rh (bipy) complex, which mediates water reduction by intermediate storage of electrons via a reduced state; an electron donor, triethanolamine (TEOA) which provides the electrons for the reduction process and a redox catalyst, colloïdal platinum, which facilitates hydrogen formation. The conditions for efficient hydrogen production and the influence of the concentration of the components have been investigated; the metal complexes act as catalysts with high turnover numbers; excess bipyridine facilitates the reaction. The process contains two catalytic cycles: a ruthenium cycle and a rhodium cycle. The Ru cycle involves oxidative quenching of the *Ru(bipy) excited state by Rh(bipy) forming Ru(bipy) which is converted back to Ru(bipy) by oxidation of the electron donor TEOA, which is thus consumed. The Rh cycle comprises a complicated set of transformations of the initial Rh(bipy) complex. The reduced rhodium complex formed in the quenching process undergoes a series of transformations involving the Rh(bipy) complex and hydridorhodium-bipyridine species, from which hydrogen is generated by reaction with the protons of water. In view of the storage of two electrons in the reduced rhodium species, the process is formally a dielectronic water reduction. The properties and eventual participation of [Rh(III)(bipy)₂LL′]ⁿ⁺(L,L′ = H₂O, OH^?) species are investigated. It is concluded that at neutral pH in presence of excess bipyridine, the cycle involving regeneration of the Rh(bipy) complex is predominant. A number of experiments have been performed with modified systems. Hydrogen evolution is observed with other photosensitizers (like proflavin), other relay species (like Rh(dimethylbipy) or Co(II)-bipyridine complexes), other donor species, or in absence of the platinum catalyst. It also occurs in absence of photosensitizer by sunlight of UV. irradiation of Rh(bipy) or by visible light irradiation of iridium (III)-bibyridine complexes. These systems deserve further investigations. The present photochemical hydrogen generating system represents the reductive component of a complete water splitting process. Its role in solar energy conversion and in photochemical fuel production is discussed.     

Role of angular electron pair correlation in stabilizing C

A pseudo‐potential that was successfully employed in an earlier study by the Compton group is used to describe the binding of a single electron to a C₆₀ molecule to form C. Then, the interaction of a second electron with the C anion is treated in two manners. First, as performed in the earlier Compton study, a mean‐field (i.e., Hartree–Fock) approach is used to estimate the C‐to‐C energy difference for the singlet state of the dianion and, much as in the earlier study, this dianion is predicted to be unstable by ∼0.4 eV. Second, for this same singlet state, a configuration interaction wave function is employed that allows for the angular correlation of the two excess electrons, allowing them to avoid one another by moving on opposite sides of the C₆₀ skeleton. The energy of the dianion is lowered by 0.3 eV when angular correlation is included, suggesting that the singlet dianion is unstable with respect to electron loss by only ∼0.1 eV. A Coulomb barrier (>1 eV high) and angular momentum barriers then combine to trap electrons of singlet C from detaching, thus producing the very long observed lifetimes. In addition, the energy of the lowest triplet state of C is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

The role of d orbitals in tetrahedral hybrid orbitals of oxy-ions

The hybrid orbitals of tetrahedral oxy-ions containing some d character have been calculated by maximum overlap method. The d characters of hybrid orbitals increase in the order of SiO, PO, SO, ClO, and decrease in order of GeO, AsO, SeO, BrO. The bond strengths are also obtained for these ions. The hybrid Orbital of VO, CrO, and MnO are of the type d³s as the result of calculation.     

Internal energy deposition in doubly charged tungsten hexacarbonyl on charge exchange at high energy with atomic and molecular targets

Charge exchange of W(CO) in the course of 7 keV collisions with various targets results in singly charged ions which are highly internally excited. The distribution of internal energies estimated by the degree to which consecutive fragmentations by CO loss occur is broad and includes very high energies (up to 15 eV). This result is inconsistent with exclusive operation of long-range electron transfer e.g. by either a curve crossing or Demkov mechanism; rather it suggests that direct excitation to a high-energy repulsive state of the products also occurs perhaps by an electronic excitation mechanism. The nature of the internal energy distribution suggests mechanistic analogies with simple collisional activation. Different target gases give rise to different average internal energy depositions monatomics and diatomics yielding higher energy depositions than do polyatomic targets. There is an approximate correlation between energy deposition and target ionization energy which is consistent with the proposed excitation mechanism considering the shapes of the potential energy surfaces. When the detailed internal energy distributions are compared characteristic differences are seen for individual targets. The efficiencies of the various targets at producing charge exchange were also compared. Large differences were found with the polyatomic targets having the greatest efficiencies. In addition a rough correlation was observed between the extent of charge exchange and target ionization energy and this is interpreted in terms of greater contributions from the long-range electron transfer process for targets of lower ionization energy. All the results are also consistent with contributons from more violent collisions which involve electron transfer at relatively small internuclear distances where the shapes of the potential surfaces are strongly dependent on distance.     

Molecular Ions of Transient Species: Vinyl-Alcohol Cation

Vinyl alcohol 1 was prepared by thermolysis of cyclobutanol and its photoelectron spectrum was determined. I = 9.18 eV and I = 9.52 eV were found, the vibrations progression (? = 1400 cm^?1) for this lowest energy transition 1(X)→1⁺(X?) indicating significant skeletal changes in the ion. The question of the relative stability of the syn ( 1 )- vs. anti-ions ( 1 ) is discussed in the light of theoretical calculations. The energy of the second π-state of 1 ⁺ is estimated at 13.6–14.1 eV above the ground state of 1 .     

Application of the field‐theoretic method of Bohm and Pines to a study of the metal–insulator transition in doped dielectric media

A treatment based on the field‐theoretic formalism of Bohm and Pines is presented which reproduces theoretically the essential features of the Mott–Edwards–Sienko relation, na∼¼, for the location of the metal–insulator transition in doped dielectric media, where n_c is the critical electron concentration and a is the effective radius. The model allows a study to be made of the dopant electronic wave function from the localized insulating state through to the metallic regime. The effective interparticle interaction shows Friedel oscillations and, at short range, is close to the Thomas–Fermi form. The doping dependence of the electronic hyperfine interaction, total dielectric constant, and ionization energy for a disordered collection of s‐state one‐electron atoms in a structureless dielectric medium are derived and both are found to be in satisfactory qualitative agreement with experiment. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 111–120, 1999     

Structure and stability of B6, B,and B clusters

We investigated various isomers of B₆, B, and B clusters with ab initio [Hartree–Fock (HF), MP2)] and density functional theory (DFT) methods. Ten B₆ isomers, 6 B isomers, and 6 B isomers are determined to be local minima on their potential energy hypersurfaces by the HF, B3LYP, B3PW91, and MP2 methods. Fourteen of these structures are first reported. The most stable neutral B₆ cluster is the capped pentagonal pyramid (C_5v), in agreement with the results reported previously. Hexagon B (C_2h) isomer and fan‐shaped B (C_2v) isomer are found to be the most stable on the cationic and anionic energy hypersurfaces, respectively. Natural bond orbital analysis suggests that there are three‐centered bonds in the most stable B₆ neutral and ionic clusters. The multicentered bonds are responsible for the special stability of the lowest‐energy isomer. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 94: 269–278, 2003