Valence Effective Hamiltonian Method Research Articles

Valence Electronic Structure of π-Conjugated Materials: Simulation of the Ultraviolet Photoelectron Spectra with Semiempirical Hartree−Fock Approaches

A detailed understanding of the electronic structure of π-conjugated materials can be reached by means of two widely available semiempirical quantum-chemical methods: Austin model 1 (AM1) and intermediate neglect of differential overlap (INDO). This is illustrated by calculating the ultraviolet photoelectron spectra (UPS) of π-conjugated oligomers and polymers and comparing the theoretical data to experimental spectra. The approach is applied here to a series of compounds with varying molecular topology and chemical constitution: oligomers of p-phenylenevinylene and various derivatives, fluorinated derivatives of polyisothianaphthene, and 4,4‘-bis(m-tolyphenylamino)biphenyl (TPD). The AM1- and INDO-calculated UPS spectra are also compared to data obtained with the valence effective Hamiltonian method, which is known to provide reliable results for the simulation of UPS spectra of these types of molecules. An easily applicable procedure is proposed to obtain the best fit to the experimental spectra from the AM1 and INDO molecular orbital energies. Both techniques accurately reproduce the lower energy part of the spectrum, which contains the most important part of the π electronic structure; INDO is also found to perform well for the inner part of the UPS spectrum, which mainly corresponds to the σ electronic states.

First-principles calculation of bulk susceptibility for second-harmonic generation in crystalline C60

The hyperpolarizabilities for electric dipole second-harmonic generation (SHG) due to the bilinear combination of an electric field and either the electric-field gradient (μeeq) or the associated magnetic field (τeem), and for electric quadrupole SHG quadratic in the electric field (μqee) have been calculated for the C60 molecule at pump photon energies from 0.5 to 2.2 eV using the valence effective Hamiltonian method with a minimal STO-3G basis; magnetic dipole SHG quadratic in the electric field (τmee) is zero by symmetry in C60. The coefficients exhibit resonances at photon energies near 1.9 for μeeq, 1.4 for μqee, and 2.0 eV for τeem. They are combined with empirical local-field factors and a theoretical local field-gradient tensor to calculate the composite susceptibility χ(2) for SHG from crystalline C60 in the same energy range. The susceptibility shows several resonances that arise from those in μeeq, μqee, and τeem. The results are able to reproduce the magnitudes and signs reported experimentally, subject to a sensitive dependence on photon energy near resonances.

Photoelectron spectrum of poly(methyl-n-propylsilane): a valence band theoretical interpretation

The results of a theoretical investigation of the photoelectron spectrum of poly(methyl-n-propylsilane) are reported. The simulation of the UPS spectrum has been obtained from band structure calculations performed using the valence effective Hamiltonian method (VEH). The theoretical spectrum is fully consistent with the experimental UPS spectrum, and an excellent quantitative agreement is observed when the energies of the main peaks of both spectra are compared. A complete analysis of the contributions to the main peaks, together with a detailed interpretation of all the photoemission bands observed in the experimental spectrum have also been performed.

Theoretical study of torsion and its effect on the structural and electronic properties of cyano-substituted poly ( p-phenylene vinylene) and its derivatives

We report the results of a theoretical study on torsion and its effect on the structural and electronic properties of cyano-substituted poly ( p-phenylene vinylene) and its dimethoxy and dimethyl ring-substituted derivatives. Geometries, inter-ring torsion potentials, and potentials associated with torsion of the ring substituents are calculated using the semiempirical quantum-chemical Austin model 1 method. The evolution of the bandgap, ionization potential, and electron affinity is evaluated using the pseudopotential valence effective Hamiltonian method.

Theoretical Investigation of the Magnetic Dipole and Electric Quadrupole Contributions to the Second-Harmonic Generation in C60 and C70

Abstract We develop the Valence Effective Hamiltonian method to calculate the magnetic dipole (MD) and electric quadrupole (EQ) contributions to the hyperpolarizability β of molecular systems. For both the C60 and C70 molecules, we find that the MD contribution leads to a β value which is several times larger than that of the EQ contribution. Taking into account the local field correction factor for C60 in solid state, we calculate x (2) susceptibility values that are in excellent agreement with recent experimental data.

Theoretical study of the interaction between sodium and oligomers of poly( p-phenylenevinylene) and poly( p-phenylene)

The semi-empirical Austin Model 1 and the non-empirical pseudo-potential valence effective Hamiltonian (VEH) methods as well as the local spin density (LSD) approximation technique have been applied to the investigation of the doping-induced electronic and geometrical changes in some conjugated molecules related to poly( p-phenylene) and poly( p-phenylenevinylene) (PPV): biphenyl, stilbene and a phenyl-capped dimer of PPV. The theoretical results are compared with experimental valence band spectra, as recorded by ultraviolet photoelectron spectroscopy (UPS). The experimental UPS studies show that two ingap states are detected upon doping with alkali metals. The energy splitting between the two in-gap states increases as the molecule size decreases. The results of the LSD calculations agree very well with the experimental results, while the VEH method overestimates the energy splitting for the small molecules. The LSD modelling also indicates a destabilization of several high binding energy valence levels, due to the presence of counter-ions, in agreement with experiment.

Electronic structure of polyparaphenylene vinylene copolymers: The relationship to light-emitting characteristics

We investigate theoretically the electronic structure of regular and statistical copolymer chains containing segments of poly(p-phenylene vinylene) (PPV) and its dimethoxy-substituted derivative, poly(2,5-dimethoxy-1,4-phenylene vinylene) (DMeOPPV). Such copolymers have recently been shown to present remarkable electroluminescence properties. The calculations on the copolymer chains are performed on the basis of the negative factor counting technique coupled to the valence effective Hamiltonian method. The eigenfunctions of the upper occupied and lower unoccupied levels are calculated explicitly using the inverse iteration technique, and the degree of localization is determined via the inverse participation number approach. It is shown that the electronic structure of PPV/DMeOPPV copolymers is strongly affected by both the concentrations and relative locations of the parent polymer moieties along the chains. The appearance of clusters of dimethoxy-substituted units leads to energy gaps that are smaller than those of the parent polymers and to a spatial localization of the upper occupied levels within the DMeOPPV clusters, while the lower unoccupied levels remain smoothly delocalized over the unsubstituted regions. Our results thus indicate that electron–hole recombination processes should take place preferentially at the interfaces between PPV and DMeOPPV segments. The evolution of the PPV/DMeOPPV copolymer band gaps as a function of the concentration in dimethoxy substituted rings is compared to experimental photoluminescence and absorption data.

Evolution of the electronic structure in a conjugated polymer series: polyacetylene, poly(p-phenylene), and poly(p-phenylenevinylene)

Poly(p-phenylenevinylene) can be loosely viewed as a regular copolymer of polyacetylene and poly(p-phenylene). The electronic structure of polyacetylene, poly(p-phenylene), and poly(p-phenylenevinylene) have been studied using UV photoelectron spectroscopy and quantum chemical calculations based upon the valence effective Hamiltonian method. Excellent agreement between theory and experiment allows for a detailed description of the evolution of the electronic structure in this polymer series

Theoretical study on the effect of backbone conformation on the electronic structure of poly(di-n-butylsilane)

We present the results of valence effective Hamiltonian (VEH) calculations on the electronic structure of poly(di-n-butylsilane) in its all-trans and 7/3 conformations. The band structure of all-trans conformation is analyzed in detail and the effects of the backbone conformation on the electronic and optical properties are studied. The VEH results for the 2/1 and 7/3 conformations are in excellent quantitative agreement with photoemission and UV-absorption data and show the reliability of the VEH method to deal with organopolysilanes.

Electronic structure and nonlinear optical properties of the fullerenes C60 and C70: A valence-effective-Hamiltonian study.

Based on the geometries optimized by the AM1 semiempirical technique (Austin Model 1 of Dewar et al.), we exploit the valence-effective-Hamiltonian (VEH) method to study the electronic structures of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$. The valence-electronic density of states (DOS) calculated is found to be in excellent agreement with the high-resolution energy-distribution curves obtained from synchrotron-photoemission experiments in terms of both positions and relative intensities of the peaks. The maximum difference in peak position between theory and experiment is 0.4 eV. This shows that the VEH method provides a very reasonable description of these two fullerenes. We then apply the VEH-SOS (sum-over-states) approach to study the nonlinear optical response of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$. We obtain that the off-resonance third-order susceptibility ${\mathrm{\ensuremath{\chi}}}^{(3)}$ is on the order of ${10}^{\mathrm{\ensuremath{-}}12}$ esu. Our results are fully consistent with the electric-field-induced second-harmonic generation and third-harmonic-generation (THG) measurements by Wang and Cheng and the degenerate-four-wave-mixing measurements by Kafafi et al., but about three to four orders of magnitude lower than the data reported by Blau et al. and by Yang et et al. The static ${\mathrm{\ensuremath{\chi}}}^{(3)}$ values of ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ are compared to those of polyacetylene. We also investigate the dynamic nonlinear optical response by calculating the THG spectrum. We find that the lowest two-photon and three-photon resonances occur at almost the same frequency for ${\mathrm{C}}_{60}$, because of the symmetry of the molecule.

Influence of polymerization irregularities on the electronic properties of polythiophene

The results of quantum chemical calculations on the electronic structure of chains of poly(2,5-thienylene), i.e., polythiophene, along which some of the α–α′(2–5′) linkages are replaced randomly by α–β′(2–4′) linkages are presented. The randomness in the α–β′ linkage positions is taken into account via the negative factor counting technique, on the basis of Fock matrices calculated by the valence effective Hamiltonian method. The eigenfunctions of the upper occupied levels are explicitly calculated using the inverse iteration technique and the degree of localization is determined via the inverse participation number approach. It is shown that a random distribution in the α–β′ linkages leads to a localization of the upper occupied levels within segments containing exclusively α–α′ linkages; more extended levels start to appear some 0.3 eV below the HOMO level for α–β′ linkage concentrations of about 6%. On the contrary, when the α–β′ linkages occur regularly, delocalization remains effective even for the upper occupied levels.

Effects of geometrical disorder on the electronic structure of alkyl-substituted polythiophenes

In this work, the role of structure disorder on the alkyl-substituted polythiophene electronic spectrum is investigated. A series of AM1 calculations is carried out to estimate the total energy as a function of torsion angle of alkyl-thiophene dimers. The dependence of torsion energy on the radical length and substitution position are studied. The calculated torsion barriers are used to simulate the out-of-plane disordered twisting of thiophene rings within a simple statistical model. Electronic structure calculations on long disordered thiophene chains are performed by the combination of Valence Effective Hamiltonian method and the Negative Factor Counting technique. Thermally induced disorder on alkyl-substituted polythiophenes is shown to explain irreversible changes on infrared spectrum of the polymer upon heating and cooling cycles.

Electronic structure of polysilane oligomers

We present the results of valence effective Hamiltonian (VEH) nonempiricalcalculations on the ele electronic structure of linear oligosilanes, H(SiH 2) nH containing up to 8 silicon atoms. The one-electron energy level distributions calculated for these systems are discussed in terms of their bonding nature and indicate that the HOMO and LUMO levels correspond to Si Si θ bonding and antibonding molecular orbitals, respectively. The VEH results are found to be in excellent agreement with photoemission and UV absorption experimental data and illustrate the importance of backbone conformation. These studies show the reliability of the VEH method to deal with organopolysilanes.

Conjugated heterocyclic copolymers: Correlation between electronic structures and conducting properties

The theoretical electronic characteristics of two conjugated regular copolymers, poly(1,4-phenylene-2′,5′-thienylene) (PT 2–5) and poly(1,4-phenylene-2′,6′-pyridinediyl) (PP 2–6), were determined using the valence effective Hamiltonian (VEH) method. The VEH method allows one to calculate ionization potential, bandgap, bandwidth and electron affinity in relation to the molecular composition and geometry of the polymeric repeating unit. The crystalline organization of the two copolymers was studied by X-ray diffraction analysis and compared to that of the well-ordered corresponding homopolymer, polyparaphenylene. The d.c. conductivity properties of the products chemically doped with iodine or arsenic pentafluoride were then correlated with the electronic and crystalline structural data. Good overall agreement was found between the conductivity levels upon doping and the electronic properties from VEH calculations. In addition, the conductivity seemed to be partly governed by the crystallinity ratio of the polymeric system when the less oxidizing iodine dopant was used. In this case, the lower the crystallinity ratio, the higher the concentration of iodine required to produce a conductivity enhancement.

Influence of molecular architecture on electronic and transport properties in sulfur-containing heterocyclic conducting polymers

We investigate a series of thiophene-based conjugated polymers built from monomers with extended π-electron delocalization. The polymers are polythiophene, polythieno[3,2-b]thiophene and polydithieno[3,2-b;2',3'-d]thiophene. In order to obtain a better understanding of the evolution of the transport properties in this family of compounds, we present spectroscopic studies, including infrared, UV-visible and emission data, structural investigations and conductivity measurements, and compare them with theoretical parameter such as bandgaps and bandwidths as calculated by the Valence Effective Hamiltonian method. Polymer growth is optimized to prevent at best morphological differences between the three polymers.

Valence effective Hamiltonian method for molecular fragments

The valence effective Hamiltonian method has been applied to the calculation of the electronic structures of molecular fragments. With increasing fragment size, charge densities and isolated orbital energies rapidly converge to those determined from a full molecule calculation.

Combination of MOMM and VEH methods to calculate electronic properties of polymers

AbstractA Molecular‐Orbital‐Based Molecular Mechanics method (MOMM) has been employed to calculate the structures of cyclopentadiene, pyrrole, furan, thiophene, dibenzocyclopentadiene (fluorene), dibenzopyrrole, dibenzofuran, and dibenzothiophene. The dimer structures of the above compounds have also been calculated using the same method to derive the unit cells of polycyclopentadiene, polypyrrole, polyfuran, polythiophene, polydibenzocyclopentadiene, polydibenzopyrrole, polydibenzofuran, and polydibenzothiophene. The band structures, densities of states, ionization potentials, band gaps, reduction potentials, and oxidation potentials of these polymers then have been calculated by using the Valence Effective Hamiltonian method (VEH). The structural effects on electronic properties are discussed.

Valence effective Hamiltonian technique for nitrogen containing polymers: Electronic structure of polypyrrole, pyrolized polyacrylonitrile, paracyanogen, polymethineimine, and derivatives

We present the parametrization of nitrogen for use in the valence effective Hamiltonian (VEH) technique. We describe five different parametrization schemes and discuss the quality of the results each of them affords. The VEH method is then applied to the study of the electronic structure of nitrogen containing polymers of interest with regard to the conducting polymers area. These polymers include polypyrrole, poly-β-dimethylpyrrole, poly-N-methylpyrrole, pyrolized polyacrylonitrile, paracyanogen (polypyrazinopyrazine), and polymethineimine [CH=N]x. Parameters related to the conductivity properties upon doping such as ionization potentials, bandgaps, and bandwidths, are discussed in detail.

Electronic properties of sulfur containing conjugated polymers

Valence effective Hamiltonian (VEH) calculations are performed on a number of sulfur containing organic conjugated polymers of interest to the conducting polymers area. Theoretical results for parameters related to conductivity such as ionization potentials, bandwidths, and bandgaps are presented. Systems considered include various derivatives of poly (p-phenylene sulfide), polybenzothiophene, and polythiophene, as well as potentially interesting compounds such as polythieno [3,2-b] thiophene and polyvinylene sulfide. The electronic structure description afforded by the VEH method for sulfur containing polymers is demonstrated to be of the same quality as that presented previously for hydrocarbon polymers. In particular, for ionization potentials, good agreement with available experimental data on poly (p-phenylene sulfide) and polybenzothiophene is obtained, after scaling downward the VEH values by a 1.9 eV polarization correction. The comparison between the theoretical and experimental XPS spectra for polybenzothiophene is excellent with use of the same energy scaling factor previously employed for polyacetylene, poly(p-phenylene), and poly(p-phenylene sulfide). These results, in conjuction with previous results obtained on hydrocarbon polymers, lend confidence in the predictive capabilities of this purely theoretical technique. Calculations show that polyvinylene sulfide, as yet unsynthesized, should display very promising characteristics as a conducting polymer.

Valence effective Hamiltonian study of the electronic structure of poly(p-phenylene) and poly(p-phenylene sulfide)

The parametrization of atomic potentials for sulfur is presented in the framework of the valence effective Hamiltonian (VEH) technique for polymers. The VEH method is applied to band structure and density of states calculations on poly(p-phenylene) and poly(p-phenylene sulfide), compounds of interest with regard to the conducting polymers area. The quality of the electronic structure description afforded by the VEH technique is demonstrated via a comparison of experimental XPS spectra for these polymers with spectra predicted theoretically. The ionization potential of poly(p-phenylene sulfide) is predicted to be 0.7 eV higher than poly(p-phenylene) in good agreement with experimental estimates.