Bond length alternation in infinitely long conjugated polyacenes

This paper concludes that whereas linear polyacenes are stable to distortions that preserve mirror symmetry with respect to the plane which is the perpendicular bisector of their interior bonds, they are unlikely to be stable with respect to distortions that do not preserve this symmetry.     

Bond length alternation and energy band gap of polyyne

The bond length alternation (BLA) and energy band gap of polyyne are investigated by various first-principles theories, including Hartree-Fock, MP2, hybrid, and nonhybrid density functional theories. Both solid-state calculations utilizing periodic boundary conditions on polymers and molecular quantum mechanical calculations on extra-long oligomers were performed with consistent results. By validation on similar linear conjugated polymers, polyacetylene and polydiacetylene, the combination of hybrid-DFT schemes, B3LYP//BHandHLYP or B3LYP//KMLYP, is shown to give the best predictions for both geometry and band gap of polyyne based on available experimental data. We conclude that the best estimate of the BLA of polyyne is about 0.13 A and that of the band gap is about 2.2 eV.     

Bond order bond polarizability model for fullerene cages and nanotubes

It is still a challenge to accurately calculate the polarizabilities of large fullerene cages and nanotubes. In this paper, a simple bond order bond polarizability relationship for carbon was found, which allowed us to apply the bond polarizability model to any pentagon isolation rule (PIR) fullerene (cage or nanotube). Following this approach, the following simple equation, alpha=1.262n, was obtained relating the static dipole polarizability (alpha) of PIR fullerenes (cages or closed nanotubes) to their number (n) of carbon atoms. Furthermore, it was shown that the polarizabilities of C60 and C70, calculated on the basis of this model, are in excellent agreement with those obtained experimentally and by density-functional theory calculations.     

Microextraction,capillary electrophoresis,and mass spectrometry for forensic analysis of azo and methine basic dyes from acrylic fibers

Designed experiments based on a simplex mixture design were employed to explore the effects of three solvent components (water, formic acid, and aqueous acetic acid), extraction time, and extraction temperature for the automated microextraction of basic (cationic) dyes from acrylic fibers. Extractions were conducted by an automated liquid handling system, and dye extraction was evaluated using a UV/visible microplate reader. Highest extraction efficiency for two subclasses of basic dyes (methine and azo) from acrylic fibers was achieved with an extraction solvent containing 88% formic acid/12% water. Cationic dyes were analyzed by capillary electrophoresis using a 45 mM ammonium acetate buffer in acetonitrile–water at pH 4.7. The utility of microextraction combined with capillary electrophoresis–mass spectrometry for analysis of extracts from trace fibers was demonstrated by the detection and characterization of three basic dyes extracted from a 2-mm length of single acrylic fiber.     

Theory and method for calculating resonance Raman scattering from resonance polarizability derivatives

We present a method to calculate both normal Raman-scattering (NRS) and resonance Raman-scattering (RRS) spectra from the geometrical derivatives of the frequency-dependent polarizability. In the RRS case, the polarizability derivatives are calculated from resonance polarizabilities by including a finite lifetime of the electronic excited states using time-dependent density-functional theory. The method is a short-time approximation to the Kramers, Heisenberg, and Dirac formalism. It is similar to the simple excited-state gradient approximation method if only one electronic excited state is important, however, it is not restricted to only one electronic excited state. Since the method can be applied to both NRS and RRS, it can be used to obtain complete Raman excitation profiles. To test the method we present the results for the S2 state of uracil and the S4, S3, and S2 states of pyrene. As expected, the results are almost identical to the results obtained from the excited-state gradient approximation method. Comparing with the experimental results, we find in general quite good agreement which enables an assignment of the experimental bands to bands in the calculated spectrum. For uracil the inclusion of explicit waters in the calculations was found to be necessary to match the solution spectra. The calculated resonance enhancements are on the order of 10(4)-10(6), which is in agreement with experimental findings. For pyrene the method is also able to distinguish between the three different electronic states for which experimental data are available. The neglect of anharmonicity and solvent effects in the calculations leads to some discrepancy between theory and experiment.     

Bond alternation in ring-shaped molecules: The stability of the Peierls instability

We investigate the phenomenon of bond alternation in ring molecules of the type (CH)_2n, which occurs due to the Peierls instability. We prove that the energy-minimizing configuration of bond lengths always has period two when n is odd. When n is even, a new instability may destroy the periodicity two as long as n is not too large. We also analyze the corresponding problem for the Heisenberg antiferromagnetic “spin-Peierls” system and prove that instabilities other than period two never occur there. © 1996 John Wiley & Sons, Inc.     

Bond alternation in infinite polyene: Peierls distortion reduced by electron correlation

The formation of the bond-alternating structure in polyene is investigated both within the one-particle (Hartree-Fock) picture and including electron correlation effects by perturbation theory. An off-diagonal charge-density wave of the equi-distant structure is identified at the Hartree-Fock level as precursor of the bond-alternate state which is found by subsequent lattice optimization. The valence-shell correlation energy is calculated by using second-order Møller-Plesset perturbation theory. It is found to be finite also in the metallic one-dimensional chain and a comparison with results obtained for the acetylene unit shows that this method recovers ~-70–75% of the total valence-shell correlation. Correlation effects are shown to reduce the Peierls distortion and the corresponding energy barrier but the bond alternation persists also if the results are extrapolated to the case of full correlation.     

Bond length alternation in cyclic polyenes. VII. Valence bond theory approach

The problem of bond length alternation in linear extended ϕ-electron systems with conjugated double bonds is examined using the valence bond theory applied to a simple model of cyclic polyenes C_NH_N with N = 4v and N = 4v + 2 sites as described by the Pariser-Parr-Pople Hamiltonian. Overlap enhanced atomic orbitals are employed in order to achieve the optimal treatment with only two Kekulé structures. The predicted bond length alternation and its magnitude are in good agreement with earlier molecular orbital based calculations and with experiment. Special attention is given to the discussion of the origin of bond length alternation in long polyenic chains and to the role of the resonance energy leading to stabilization of undistorted, symmetric structures for small aromatic (N = 4v + 2) cycles. © 1996 John Wiley & Sons, Inc.     

Bond length alternation in cyclic polyenes. III. Alternant molecular orbital method

The bond length alternation problem in cyclic polyene models as described by the Pariser–Parr–Pople Hamiltonian and an empirical quasiharmonic π-core potential is investigated using the one-parameter alternant molecular orbital (AMO) method. It is shown that in contrast to the unrestricted Hartree–Fock (UHF) results, which lead to symmetric equidistant structures, the one-parameter AMO results yield bond length alternating structures similar to those obtained with the restricted HF approach. The correlation energy recovered by the AMO method is examined for the symmetric polyenes in the whole range of coupling constants for both the Pariser–Parr–Pople and Hubbard Hamiltonians and compared with exact full configuration interaction (FCI) results. For the first member of the cyclic polyene series we also compared the FCI and AMO correlation energies for different nuclear framework distortions. This comparison indicates that in contrast to the UHF results the fraction of the correlation energy recovered by the AMO approach is very uniform over the range of nuclear distortions considered. The AMO results thus strongly indicate the dimerization in the polyenic chains.     

Bond length alternation in cyclic polyenes. V. Local finite-order perturbation theory approach

The finite-order many-body perturbation theory using the localized Wannier orbital basis is applied to the problem of bond length alternation in the Pariser–Parr–Pople model of cyclic polyenes C_N H_N, N = 4v + 2, which may be regarded as a simplified model of polyacetylene. Both the Møller–Plesset and the Epstein–Nesbet-type partitionings of the model Hamiltonian are employed. The localized orbital basis enables an efficient truncation of the perturbation theory summations over the intermediate states as well as an elimination of energetically unimportant diagrams, thus enabling one to obtain the fourth-order Møller–Plesset-perturbation energies with a relatively small computational effort even for large polyenes. The results obtained with the second-, third-, and fourth-order Møller–Plesset and with the third-order Epstein–Nesbet perturbation theories yield very similar bond length distortions (about 0.05 Å) and stabilization energies per site (about 0.04 eV) as obtained earlier with the RHF , one-parameter AMO , and delocalized orbital perturbation theories. The effects of truncation and diagram elimination in the fourth-order Møller–Plesset perturbation theory and the abnormal behavior of the second-order Epstein–Nesbet perturbation theory results in the localized Wannier basis near the instability threshold of the RHF solutions are discussed.     

Bond length alternation in cyclic polyenes. II. Unrestricted hartree–fock method

The problem of bond length alternation in cyclic polyene models as described by the Pariser–Parr–Pople π-electron Hamiltonian, together with an empirical quasi harmonic σ-core potential is investigated using the unrestricted Hartree–Fock wave function employing different spatial orbitals for different spins. It is shown that in contrast to the restricted Hartree–Fock method, which favors bond alternation in large cyclic polyenes, the unrestricted Hartree–Fock method stabilizes the symmetric structures with equidistant internuclear separation. An assessment of the amount of correlation error recovered by the unrestricted Hartree–Fock procedure is examined and the qualitatively different behavior of the cyclic polyene models when described by restricted and unrestricted Hartree–Fock wave functions is discussed from this viewpoint.     

Bond length alternation in cyclic polyenes. I. Restricted Hartree–Fock method

The problem of bond length alternation in cyclic polyene models as described by the Pariser–Parr–Pople π-electron Hamiltonian and its relationship to the singlet stability problem for symmetry adapted Hartree–Fock solutions for these systems is investigated using the restricted Hartree–Fock method. The σ-energy contribution is approximated by a quasiharmonic empirical potential. It is shown that the restricted Hartree–Fock energies favor the cyclic polyene distortion and an estimate of the distortion and of the stabilization energy for infinite linear polyenes is obtained.     

Two-step resonance energy transfer between dyes in layered silicate films

Single- and two-step fluorescence resonance energy transfer (FRET) was investigated between laser dyes rhodamine 123 (R123), rhodamine 610 (R610), and oxazine 4 (Ox4). The dye molecules played the role of molecular antennas and energy donors (ED, R123), energy acceptors (EA, Ox4), or both (R610). The dye cations were embedded in the films based on layered silicate laponite (Lap) with the thickness of several μm. Optically homogeneous films were prepared directly from dye/Lap colloids. Dye concentration in the films was high enough for FRET to occur but sufficiently low to prevent the formation of large amounts of molecular aggregates. The films were characterized by absorption and fluorescence spectroscopies, and their optical properties were compared with colloid precursors and dye aqueous solutions. The phenomenon of FRET was confirmed by means of steady-state and time-resolved fluorescence spectroscopies. Significant quenching of ED emission in favor of the luminescence from EA molecules was observed. FRET led to the decrease in the lifetimes of excited states of ED molecules. Molecular orientation of dye molecules was determined by polarized absorption and fluorescence spectroscopies. Almost parallel orientation with respect to silicate surface (～30°) was determined for all fluorescent species of the dyes. Theoretical model on relationship between anisotropy and molecular orientation of the fluorophores fits well with measured data. The analysis of anisotropy measurements confirmed the significant role of FRET in the phenomenon of light depolarization.