Delocalization Properties Research Articles

Local Aromaticity of [n]Acenes, [n]Phenacenes, and [n]Helicenes (n= 1−9)

The local aromaticity of the six-membered rings in three series of benzenoid compounds, namely, the [n]acenes, [n]phenacenes, and [n]helicenes for n = 1-9, has been assessed by means of three probes of local aromaticity based on structural, magnetic, and electron delocalization properties. For [n]acenes our analysis shows that the more reactive inner rings are more aromatic than the outer rings. For [n]phenacenes, all indicators of aromaticity show that the external rings are the most aromatic. From the external to the central ring, the local aromaticity varies in a damped alternate way. The trends for the [n]helicene series are the same as those found for [n]phenacenes. Despite the departure from planarity in [n]helicenes, only a very slight loss of aromaticity is detected in [n]helicenes as compared to the corresponding [n]phenacenes. Finally, because of magnetic couplings between superimposed six-membered rings in the higher members of the [n]helicenes series, we have demonstrated that the NICS indicator of aromaticity artificially increases the local aromaticity of their most external rings.

Electrochemical and ESR study on the transformation processes of α-hydroxy-quinones

The electrochemical analysis by cyclic voltammetry and double potential step chronoamperometry of two α-hydroxyquinones (2-hydroxy-1,4-naphthoquinone and perezone) in acetonitrile, reveals that in the first electron transfer process, self-protonation reactions are present. One of the products of this reduction is the deprotonated original quinone. This last intermediate is reduced by a monoelectronic process in the second reduction step, generating a radical dianion. The radical dianions formed can be detected by EC-ESR coupled experiments and the spectra characteristics were explained in terms of the electron delocalization properties of the analyzed compounds. Upon the addition of a base (tetrabutylammonium hydroxide), the ESR signal increases in intensity and hyperfine coupling analysis is better resolved, proving the radical nature of such species. The oxidation properties of the deprotonated quinone of 2-hydroxy-1,4-naphthoquinone were also studied under these basic conditions. The results provide insights into the proposal of a dimerization process occurring in this oxidation process.

Complexed nitrogen heterosuperbenzene: the coordinating properties of a remarkable ligand.

Tetra-peri-(tert-butyl-benzo)-di-peri-(pyrimidino)-coronene 1, the parent compound of the nitrogen heterosuperbenzene family N-HSB, is employed as a novel monotopic ligand in the formation of [Pd(eta3-C3H5)(1)]PF6 2 and [Ru(bpy)2(1)](PF6)2 (where bpy = 2,2'-bipyridine 3a and d8-2,2'-bipyridine 3b). These N-coordinated complexes are fully characterized by 1H NMR and IR spectroscopy and ESI-MS. Metal coordination has a profound effect on both the absorption and the emission properties of 1. Pd(II) coordination causes a red-shift in the low-energy absorptions, a decrease in the intensity of the n-pi absorptions, and a quenching of the emission. Ru(II) coordination causes absorption throughout the visible region and creates two new complexes that join an elite group of compounds known as "black" absorbers. 3a and 3b possess two discernible 1MLCT bands. The one of exceptionally low energy (lambda(max) = 615 nm) has an associated (3)MLCT emission (lambda(max) = 880 nm) due to the unprecedented electron delocalization and acceptor properties of the rigid aromatic N-HSB 1. Both Ru(II) complexes are near-IR emitters with unusually protracted emission lifetimes of 320 ns at 77 K. They are photochemically inert, and their electrochemical properties are consistent with the presence of a low-lying pi orbital on 1. The first two reversible reductions (E(1/2) (CH3CN), -0.54 V, -1.01 V vs SCE) are due to the stepwise reduction of 1 and are anodically shifted as compared to [Ru(bpy)3]2+. Temperature- and concentration-dependent NMR studies on 2 and 3a suggest extensive aggregation is occurring in solution.

The Baum–Connes assembly map, delocalization and the Chern character

For a discrete group Γ, we explicitly describe the rational Baum–Connes assembly map μ ∗ Γ⊗id C in “homological degree ⩽2” and show that in this domain it factors through the algebraic K-theory of the complex group ring of Γ. We also state and prove a delocalization property for μ ∗ Γ , namely expressing it rationally in terms of the Novikov assembly map. Finally, we give a handicrafted construction of the delocalized equivariant Chern character (in the analytic language) and prove that it coincides with the equivariant Chern character of Lück (Invent. Math. 149 (2002) 123–152) (defined in the topological framework).

Reaction Monitoring of Imine Synthesis Using Raman Spectroscopy

Laser-induced Raman spectroscopy has been utilized to demonstrate its feasibility for studying the kinetics of imine formation in chloroform solvent. The imine formation, by the nucleophilic addition of primary amine to the carbonyl group of ketone, has been monitored at ten minute intervals for eight hours. The intensity of the C=O stretching mode at 1684 cm - 1 was measured to determine the rate constant of the reaction. In order to correct the sample-to-sample fluctuations in Raman peak area, this peak was normalized to the C-Cl bending peak at 666 cm - 1 . By the peak area change during the course of reaction, the second order rates at three different temperatures have been determined. The substituent effects on the π conjugations of imine product have also been investigated. On the basis of Raman frequency shifts, the delocalization properties of the aromatic system modified by substitution of a hydrogen atom with -Cl and -CH 3 O groups could be clearly understood.

Structures and Stabilities of Three-Membered Rings Containing a Hypervalent Atom

We investigated the structures and the stabilities of the three-membered rings (X = Si, P, S; Y = CH2, NH, O; n = 2 or 3) containing a hypervalent atom (X) and disclosed their origins by developing and applying an electron-pair bond model for hypervalent molecules. For the rings containing a pentacoordinated Si or P atom, the (ap, eq) isomers with the ring bonds in the apical and equatorial positions are local minima, while the (eq, eq) isomers with both ring bonds in the equatorial positions are the transition states of pseudorotation reactions due to the high ring strains. In contrast, the (ap, eq) and (eq, eq) isomers for the rings containing a tetracoordinated P or S atom are both local minima. The tetracoordinated species are less strained than the pentacoordinated ones because of the effect of the lone pair on X giving rise to less antibonding properties of the electron delocalization between the geminal ring bonds on X. Moreover, the more strained (eq, eq) isomers are surprisingly more stable than ...

Cu-O network-dependent core-hole screening in low-dimensional cuprates: A theoretical analysis

We analyze the influence of the dimensionality on the Cu 2p_3/2 core level X-ray photoemission spectra of undoped cuprates. Both exchange splitting and delocalization properties are described within one framework using a multi-band Hubbard model. The spectral intensity is calculated by means of the Mori-Zwanzig projection technique for a CuO_4 plaquette ('zero'-dimensional), an infinite CuO_3 chain (one-dimensional), and an infinite CuO_2 plane (two-dimensional). The results are compared to the spectra of Bi_2CuO_4, Sr_2CuO_3, and Sr_2CuO_2Cl_2. Our analysis allows to distinguish between effects of the Cu-O geometry and effects from material-specific properties.

Theory of core-level XPS on undoped cuprates

We analyze the influence of the dimensionality on the Cu 2p 3/2 core level X-ray photoemission spectra of undoped cuprates. Both exchange splitting and delocalization properties are described within one framework using a multi-band Hubbard model. The spectral intensity is calculated by means of the Mori–Zwanzig projection technique for a CuO 4 plaquette (‘zero’ dimensional), an infinite CuO 3 chain (one dimensional), and an infinite CuO 2 plane (two dimensional). The results are compared to the spectra of Bi 2 CuO 4, Sr 2 CuO 3 , and Sr 2CuO 2Cl 2. Our analysis allows to distinguish between effects of the Cu–O geometry and effects from material-specific properties.

Intramolecular charge delocalization and nonlinear optical properties from vibrational spectra

The vibrational method for the evaluation of molecular hyperpolarizabilities of polyconjugated molecules is used in order to account for the modulation of second order hyperpolarizability (γ) induced by the effect of charge delocalization.

Electrons and nuclei of C 6H 6 and C 6D 6; a combined Feynman path integral – ab initio approach

We have linked an ab initio approach of the Hartree–Fock (HF) type to the Feynman path integral quantum Monte Carlo (PIMC) formalism in order to study C 6H 6 and C 6D 6 under consideration of the quantum character of the nuclei and electrons. The combination of the statistical Monte Carlo approach with an electronic Hamiltonian offers the possibility to study the influence of the quantum and classical (=thermal) nuclear degrees of freedom on electronic expectation values. The PIMC technique has been used to derive the finite-temperature properties of the nuclei of both π rings. We discuss the temperature ( T) dependence of the energy of the C 6H 6 and C 6D 6 nuclei, their spatial delocalization properties as well as the radial and angular distribution functions. The nuclear configurations generated by the PIMC formalism have been used as input for ab initio HF calculations. Electronic expectation values have been derived as ensemble averages over 6000 different nuclear configurations which are populated in thermal equilibrium. As a result of the large quantum effects of the C 6H 6 and C 6D 6 nuclei, we derive ensemble averaged electronic expectation values which differ sizeable from the corresponding single-configuration quantities at the energy minimum. This difference is mainly caused by nuclear quantum effects; thermal degrees of freedom are of minor importance only. The electronic origin of the potential energy part of the total vibrational energy is emphasized. It is largely determined by the raise in the electron–core attraction under the influence of the spatial uncertainty of the nuclei. The all-quantum approach yields a temperature and isotope dependence of bare electronic quantities already in the framework of the Born–Oppenheimer approximation (BOA). The principal findings of the all-quantum study have been used to reconsider certain solid state problems. We mention theoretical difficulties to reproduce Compton profiles and consider metal–insulator transitions of the Mott type as well as superconductivity. On the basis of the present all-quantum results we have to emphasize, that there is no unambiguous justification to adopt an observed isotope shift in the superconducting transition temperature T c as an indicator of an electron–phonon-coupled superconducting pairing mechanism.

Inverted Bond and Its Effect on the Strains of [1.1.1]Propellane Frameworks

Abstract The delocalization of σ electrons from a normal bond to a geminal “inverted” bond was shown to be strongly bonding due to the orbital phase property. The bonding property of the geminal delocalization was predicted to increase with bond inversion. The central bond between the bridgehead atoms in the [1.1.1]propellane frameworks (1) is inverted to relax the ring strains as the row of the elements is high in the periodical table. The strain decreases in the order of 1a (M = C) > 1b (M = Si) > 1c (M = Ge) > 1d (M = Sn).

Evidence for a partial breakdown of the molecular orbital picture in the ionization spectra of large saturated hydrocarbons

The x-ray photoionization spectra of large saturated hydrocarbons have been investigated by means of one-particle Green’s function calculations. These spectra saturate overall rather quickly to their asymptotic form with increasing system size. The results obtained indicate a severe breakdown of the molecular orbital picture of ionization above a binding energy threshold of about 23 eV, for n-alkane chains ranging from n-propane to n-nonane, or cycloalkane compounds such as cyclobutane, cyclopentane, and cyclohexane. In spite of the fast multiplication of satellite solutions, shake-up lines remain confined above that threshold, as a result of the delocalization properties of one-electron canonical states. The ring closure is shown to emphasize the dispersion of photoionization intensity into satellites. Conformational changes, on the other hand, have only marginal effects on the convoluted correlation bands.

Formation of satellite bands in the ionization spectra of extended systems.

The ionization spectra of hydrogen clusters converging onto a polymer limit have been investigated by means of one-particle Green's-function calculations. This study focuses on the construction of well-organized correlation bands of shake-up satellites at the expense of the lines in the main (primary) band. Two series of chains have been studied, belonging, in regards to their fundamental Hartree-Fock band gap, to the categories of insulating and semiconducting polymers. Evidence is given for a limitation of the contamination by shake-up lines with the delocalization properties of one-particle canonical states in an insulating situation, whereas a nearly complete fragmentation of main bands into satellites can be expected with polymers of the semiconducting type, as a result of multistates interactions. The onset of this contamination, marking in the ionization spectrum a bifurcation between the one-particle and correlation regimes, can be evaluated from a zeroth-order estimate for the energy threshold of a shake-up transition. Electronic correlation in the neutral ground-state wave function is also shown to increase the breakdown of the one-particle picture of ionization. \textcopyright{} 1996 The American Physical Society.

Excited-State Distortions and Electron Delocalization in Mixed-Valence Dimers: Vibronic Analysis of the Near-IR Absorption and Resonance Raman Profiles of [Fe2(OH)3(tmtacn)2]2+

The near-IR transition associated with valence delocalization in the class III mixed-valence dimer [Fe(2)(OH)(3)(tmtacn)(2)](2+) is studied using variable-temperature (VT) electronic absorption and resonance Raman (RR) spectroscopies to gain insight into the properties of electron delocalization in this dimer. Laser excitation into this absorption band leads to dominant resonance Raman enhancement of totally-symmetric [Fe(2)(OH)(3)](2+) core vibrational modes at 316 and 124 cm(-)(1), descriptions of which are calculated from a normal coordinate analysis. Vibronic analysis of the near-IR resonance Raman excitation profiles and VT-absorption bandshapes using an anharmonic excited-state model provides a description of the geometric distortions accompanying this excitation. The excited-state distortion is dominated by expansion of the [Fe(2)(OH)(3)](2+) core along the Fe.Fe axis, reflecting the significant Fe-Fe sigma --> sigma character of this transition. The ground-state sigma-interaction between the two metals has been identified as the orbital pathway for valence delocalization, and the sigma --> sigma distortion analysis is used to quantify the structural dependence of the electronic-coupling matrix element, H(AB), associated with this pathway. The dominant role of totally-symmetric nuclear coordinates in the absorption and RR spectroscopies of [Fe(2)(OH)(3)(tmtacn)(2)](2+) is also discussed in relation to the Q(-) vibrational coordinate and the vibronic spectroscopies of other class II and class III mixed-valence dimers. It is shown that intensity contributions from the Q(-) coordinate to the absorption and RR spectra of [Fe(2)(OH)(3)(tmtacn)(2)](2+) are small relative to those of the totally-symmetric coordinates due to the inefficient change-in-curvature mechanism by which the Q(-) coordinate gains intensity, compared to the efficient excited-state displacement mechanism allowed for totally-symmetric coordinates. This is in contrast with the dominance of the Q(-) coordinate over other totally-symmetric coordinates observed in intervalence transfer (IT) absorption and RR spectroscopies of class II mixed-valence complexes.

Geminal Delocalization of σ-Electrons and Inverted Tetrahedral Configurations of the Bridgehead Carbons in Bicyclo[1.1.0]butane Frameworks

The origin of the inverted tetrahedral configurations of the bridgehead carbons in bicyclo[1.1.0]butane has been investigated in a theoretical manner. The delocalization of σ-electrons between the central C1−C3 bond and the side C1−C2 bonds was found to be bonding to relax the angle strains, while the delocalization between the geminal C−C bonds is antibonding in propane and cyclopropane, etc. The bonding property of the geminal delocalization was shown to be related to the inversion of the configurations. Inverted and normal tetrahedral bridgehead configurations in the bicyclo[1.1.0]butane frameworks were designed by controlling the geminal delocalization and confirmed by ab initio molecular orbital calculations.

Quantum delocalization of nuclei and electrons: cyclobutadiene

A Feynman path integral method for evaluating the quantum delocalization of atomic nuclei is combined with a scheme for calculating electronic delocalization parameters in the correlated electronic ground state. As model system we have selected the cyclobutadiene molecule whose π-electronic structure is discussed in the Pariser-Parr-Pople and Hubbard approaches. The dynamics of the electrons are described by the charge fluctuations as well as by the probabilities P( n) of finding n = 0, 1, 2 π-electrons at the respective atomic site. For both Hamiltonians we have compared the π-electron delocalization properties in the fermionic state | Ψ fe〉 with those realized in the so-called hard core bosonic state | Ψ hcb〉. The negative sign in | Ψ fe〉 leads to a suppression of the charge fluctuations in comparison to their | Ψ hcb〉 va dynamics of the electrons are attenuated by the quantum delocalization of the atomic nuclei. Details of this overall effect depend both on the nature of the π-Hamiltonian and on the nature of the electronic wavefunction.

Do the extended states in random dimer chains survive under perturbations?

We study the delocalization properties of the resonant extended states in the random dimer model (RDM) with various perturbations added. The divergent localization length ξ is found to display a power-law decay ξ ∝ W α as a function of the disorder W in the dimer or the background energies, with an exponent α around 2 depending on the location of the resonant state. For randomness in the dimer structure the exponent becomes α p = 1 and for the case of an applied electric field it reaches higher values α e > 2. These effects on the resonant states are discussed in connection with the electronic transport properties of realistic disordered systems.

Preparation and properties of a metal dithiolene conductor, partially oxidized salt of tetra(n-butyl)ammonium bis(5,6-dithio-benzo[ d]-l,3-dithiole-2-thione) nickelate, (n-Bu 4N) 0.29[Ni(dmbit) 2

The title compound, the partially oxidized salt of tetra(n-butyl)ammonium bis(5,6-dithio-benzo[d]-1,3-dithiole-2- thione) nickelate ( 11), was crystallized electrochemically and its d.c. conductivity has been measured down to 10 K. It shows a metallic behavior from 300 to 220±20 K at which it has the maximum conductivity of 1.35±0.35 S/cm. Below 42 K it shows another metallic behavior again down to 20 K. The UV spectral evolution of ligand precursors caused by the incorporation of sulfur atoms has been discussed in relation to π-electron delocalization and conduction property. Cyclic voltammetry, IR and magnetic susceptibility have also been measured and discussed including the other related compounds.

.sigma.-Electrons in silanes and phosphines: geminal bond interaction, angle strain, and delocalizability

Bond-to-bond delocalization of σ-electrons in silanes and phosphanes was analyzed. σ-Electrons in the Si-Si and P-P bonds were numerically shown to delocalize more than those in the C-C bonds and C-C than π-electrons in C=C bonds. The delocalization between the geminal bonds is antibonding as was previously reported for the C-C bonds. As the bond angle is acute, the antibonding property increases in the silanes and decreases in the phosphanes. This implies that the three-membered ring is more strained in the silanes and less strained in the phosphanes. The concept of antibonding delocalization was substantiated. The correlation between the antibonding property of the geminal delocalization and angle strain was confirmed

Effect of charge fluctuations on the phonon dispersion and electron-phonon interaction in La2CuO4.

In this paper we propose a formulation of the electronic density response that is well suited to investigate the influence of localization and delocalization properties of the electrons on the phonon dispersion and the electron-phonon interaction. The formalism is applied to study nonlocal, long-range, electron-phonon-interaction effects of the charge-fluctuation type in high-temperature superconductors, using ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ as an example. Some important features in the experimental phonon spectrum can be understood within such an approach. We discuss the modification of the usual picture of electron pairing, taking into account these nonlocal effects. In this context the symmetric apical oxygen breathing mode at the Z point is of special importance. In this vibration, nonlocal electron-phonon-interaction effects of the charge-fluctuation type are shown to generate in the metallic phase of ${\mathrm{La}}_{2}$${\mathrm{CuO}}_{4}$ an interplane charge transfer that is blocked completely in the insulating phase if a strictly two-dimensional electronic structure is assumed. Very recently we became aware of unpublished experimental results where this previously undetected mode appears, unusually broad, as the highest ${\mathrm{\ensuremath{\Lambda}}}_{1}$ mode at the Z point, in agreement with our theoretical predictions for the insulating phase. Finally, our considerations point towards a simple structure that could be very effective for high-temperature superconductivity.