Linear Polyacenes Research Articles

Graph theoretical procedure for obtaining analytical expressions of eigenspectra of linear chains and cycles with alternant vertex weights and same edge weight: Application to some complicated graphs

AbstractA graph theoretical procedure for obtaining eigenvalues of linear chains and cycles having alternant vertex weights (h1, h2, h1, h2, h1, h2, …) and the same edge weight (k) have been developed. The eigenvalues of some complicated graphs, such as graphs of linear polyacenes, methylene‐substituted linear polyacenes and cylindrical polyacene strips, stack graphs, and reciprocal graphs have been shown to be generated in closed analytical forms by this procedure. Many such graphs represent chemically important molecules or radicals. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Semiempirical calculation of electronic spectra of organic compounds by using the improved method of new- γ electron repulsion integral

Electronic spectra of organic compounds were calculated by incorporating the improved method of New- γ for the two-center electron repulsion integral into two semiempirical molecular orbital methods (CNDO/S and INDO/S). In this method we improved the previously reported New- γ approximation by determining a parameter k for each bond. This method significantly improved the calculated wavelengths of linear polyenes obtained by using New- γ. We further improved this by determining an expression for a variable k in which k is a function of the bond length of C–C. This variable method well reproduced experimental electronic spectra of linear polyenes, toluene, xylene, styrene, and polyacenes. These results show that this variable method can be applied to the C–C bond in other organic compounds, such as polycyclic aromatic hydrocarbons (PAHs).

Approximate Calculations of Ionization Potential in Electronic Cluster Models

A simple formulation of generalized Koopmans' theorem is suggested for multiconfigurational wave functions. In a coupled cluster approximation (CCD variant), π-electron estimates have been obtained for the first ionization potential in a series of linear polyenes and polyacenes. The calculated data satisfactorily reproduce the electron correlation effects characteristic of the ionized states of molecules.

Ab initio calculations of zero-field splitting parameters in linear polyacenes

Abstract The results of ab initio calculations of zero-field splitting (ZFS) parameters are presented for the linear polyacenes from benzene to pentacene. We show how the electron spin–spin (SS) parameters can be efficiently obtained from restricted high-spin open-shell wave functions (ROHF), and present calculations of these, comparing with the results of a recent multi-configurational self-consistent field approach. The SS parameters are obtained from electron SS coupling strengths evaluated as expectation values over the wave functions and from state-to-state spin–orbit (SO) interactions. The results for the two lowest triplet states of naphthalene demonstrate that excellent values can be obtained even using moderate basis sets in the wave function, indicating that this technique can be used to obtain reliable ZFS parameters of aromatic compounds. Electron correlation is, however, not negligible; by accounting for full π-electron correlation the ZFS parameters are in considerably better agreement with experiment than the ROHF results. The ROHF method still reproduced the qualitative trend in the polyacene series in which the ZFS parameters are reduced with increasing size of the π-conjugation. We confirm that the SS coupling contributions completely determine the D and E parameters for the lowest triplet state of the linear polyacenes and that the SO coupling contributions are small. Geometry optimization of the lowest triplet state was found to be fairly significant for the calculated D and E values; these were reduced by about 30% and 40%, respectively, when the geometry was changed from the ground-state singlet to the triplet-excited state optimized geometry, with the latter values being in better agreement with experiment. The present calculations predict that the second triplet state of naphthalene is very unusual, as it has a negative zero-field splitting, implying an altered ordering of the spin sublevels compared to what is common in aromatic systems.

Fast evaluation of a linear number of local exchange matrices

A fast method is described for evaluating multiple exchange matrices in a Gaussian atomic orbital basis. For insulators, it is asymptotically linear scaling, and is a generalization of the linear scaling exchange (LinK) method, which was formulated for a single exchange matrix [J. Chem. Phys. 109 (1998) 1663]. It is employed to evaluate exchange-type contractions of all derivative density matrices with two-electron integrals for a series of linear alkanes, linear polyacenes, and water clusters using STO-3G, 3-21G, and 6-31G* basis sets. Significant computational savings are obtained for molecules with as few as 10 non-hydrogen atoms.

Möbius strip versus linear and cyclic polyacenes: a Hückel and semiempirical investigation

The electronic structure of finite and infinite linear, cyclic and Mobius strip polyacenes has been investigated by adopting Huckel and semiempirical schemes. Using the Huckel approach, it turns out that the Mobius belting process modifies the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gap in such a way its evolution with chain length is similar to the linear polyacenes rather than their cyclic analogs. These results are corroborated at the Austin model 1 (AM1) level, where the geometry relaxation effects are taken into account. The optimized AM1 structures show that the Mobius defect is localized and extends over a third of the ring. With respect to the Huckel approach, accounting for geometry distortion at the AM1 levels results in an increase in the HOMO–LUMO gap of the Mobius strip relative to the linear and cyclic finite-size structures. On the other hand, when including electron-hole correlation at the configuration interaction singles/Zerner's intermediate neglect of differential overlap level the behavior with system size of the first excitation energy of cyclic and Mobius polyacenes differs from their linear analogs and leads to smaller singlet excitation energies.

Hexagonal chains with minimal total π-electron energy

The total π-electron energy of a conjugated molecule (within the framework of HMO approximation) can be calculated by its molecular graph. For the acyclic molecules, the extremal problem of some important types of conjugated molecules have been solved previously. This Letter for the first time deals with a type of cyclic conjugated molecule–benzenoid chains (hexagonal chains). We prove that in the set of all hexagonal chains with n hexagons, the linear polyacene has the minimal energy. Furthermore, a sharp lower bound of total π-electron energies of the hexagonal chain is also obtained.

Linear, cyclic, and Möbius strip polyacenes: The influence of the topology on the size‐dependent HOMO–LUMO energy gap

AbstractThe electronic structure of finite and infinite linear, cyclic, and Möbius strip polyacenes has been investigated by adopting simple Hückel methodology without and with variable β resonance integrals and the more involved MNDO scheme. Using the Hückel approach, it turns out that the linear polyacenes and the Möbius ladder molecules exhibit HOMO–LUMO gap which monotonously decrease with chain length while their cyclic analogs have a sawtooth behavior. The originality of the approach is to combine band structure and MO approaches to get analytical forms of the energy levels. These results are corroborated at the MNDO levels where the geometry relaxation effects are taken into account. The optimized MNDO structures show that the Möbius defect is localized and extends over approximately one‐third of the ladder. Accounting for geometry distortion at the MNDO level results in an increase of the gap of the Möbius strip relative to the linear and cyclic finite size structures, but the similar results for the two methods confirm that the topology is the main factor acting on HOMO–LUMO energy gaps. © 2001 John Wiley & Sons, Inc. Int J Quant Chem, 2001

Global and Local Aromaticity of Linear and Angular Polyacenes

Ab initio (B3LYP/6-311G∗∗) optimisation of seven linear and five angular polyacenes gave us an opportunity to study aromaticity in terms of HOMA index and its components EN and GEO, the energy of the carbon skeleton of these hydrocarbons was calculated from CC bond lengths. Independently, the Cohen–Benson group additivity values were used to estimate the thermochemical aromatic stabilisation energy (ASE). For individual rings the NICS values were computed and compared with HOMA. An increase of size of both linear and angular polyacenes is associated with a substantial decrease in their aromaticity, with a greater decrease for the linear polyacenes. This is well documented by both HOMA and Cohen–Benson ASE.

Characteristic polynomials of linear polyacenes and their subspectrality

Coefficients of characteristic polynomials (CP) of linear polyacenes (LP) have been shown to be obtainable from Pascal’s triangle by using a graph factorisation and squaring technique. Strong subspectrality existing among the members of the linear polyacene series has been shown from the derivation of the CP’s. Thus it has been shown that the entire eigenspectrum of ann-ring LP is included in that of (2n + 1)-ring LP. Correspondence between the eigenspectra of linear chains and LP’s is brought out by a recently developed vertex-alternation and squaring algorithm.

Revisiting superdelocalizability. Mathematical stability of reactivity indices

Superdelocalizability, S r, defined by Fukui et al. as a variant of reactivity indices in the Huckel molecular orbital scheme for conjugated hydrocarbon molecules is reinvestigated with particular emphasis on its behavior for infinitely large π-electronic systems. Surprisingly, almost all the S r values of polyacetylene are found to diverge with the size of molecule, while all the S r values of comb polyene converge to certain values. Similarly, the S r values of linear polyacene diverge, while those of zigzag polyacene converge. Whether the superdelocalizability for a series of periodic polymers converges or diverges can be predicted, respectively, if the density of states of the infinitely large π-electron network is shown to have non-zero or zero gap at the Fermi level. The behavior of atom-atom polarizability defined by Coulson et al. is also checked and discussed.

Probing the Limits of Resonance Stabilization. The Case of Linear Polyacenes

The gas-phase basicity and proton affinity of pentacene have been determined by means of Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometry. AM1 semiempirical calculations for neutral and protonated linear polyacenes ranging from benzene to pentaicosacene were carried out. The influence of successive annellations (up to 25 rings) on structures, heats of formation, and proton affinities was investigated. Extrapolated values for an infinite linear polyacene have been derived. AM1-calculated electronic structures (HOMO and LUMO energies) for the studied linear polyacenes have been compared with the available experimental ionization potentials and electron affinities.

Synthesis and characterization of polyacene precursors

Polyacenes are one-dimensional analogs of graphite and are predicted to have high conductivities without chemical doping.. The acid-catalyzed condensation of 1,2-bis(methoxymethyl)benzene gives a network polymer with idealized structure that corresponds to a linear polyacene precursor, that after elimination of H2, should yield polyacenes with extended π electron systems. In contrast, the polymerization, of 1,4-bis(methoxymethyl)benzene and 1,3-bis(methoxymethyl)benzene are expected to result in networks with a proportionately higher polybenzyl content. Based on TGA and IR studies, we propose that polyacene precursors are formed in the polymerization of the ortho substituted monomer, while the meta and para-substituted monomers contain a higher fraction of the less stable polybenzyl structure. Samples heated in an inert atmosphere show conversion of the acene precursors to partially graphitized products.

Theoretical studies of the molecular second-order hyperpolarizabilities of polycyclic aromatics

Semiempirical-FF calculations were performed for the second-order hyperpolarizabilities 〈γ〉 of a series of polycyclic aromatics to examine the structure–optical–propertyrelationship. First, 〈γ〉 of the unsubstituted PAHs were presented. For linear polyacenes, 〈γ〉 and total resonance energy were found to be increased while the HOMO-LUMO gap and resonance energy per electron decreased as the number of six-membered rings increased. For nonlinear PAHs, the chain topology should be taken into consideration. An empirical formula was given to relate the computed 〈γ〉 and linear polarizabilities 〈α〉. 〈γ〉 of mono- and di-substituted PAHs were then presented to examine the substituent effects on 〈γ〉. © 1995 John Wiley & Sons, Inc.

Semi-empirical calculations of the nonlinear optical properties of polycyclic aromatic compounds

A systematic study of factors influencing nonlinear optical properties, in particular the second hyperpolarizability 〈γ〉, is conducted for a series of polycyclic aromatic hydrocarbons (PAHs). The HOMO-LUMO gap, polarizability 〈α〉, first hyperpolarizability 〈β〉, and second hyperpolarizability 〈γ〉 of polycyclic aromatic compounds are computed by using semi-empirical MNDO-FF calculation implemented in the MOPAC package. For linear polyacenes, the linear and nonlinear properties and total resonance energy are found to increase while the HOMO-LUMO gap and resonance energy per electron decrease as the number of six-membered rings increases. For nonlinear PAHs, the chain topology should be taken into account. An empirical formula is given to relate the computed 〈γ〉 and 〈α〉.

Graph factorization: A new mode of application of a vertex‐alternation scheme

AbstractLinear chains where the vertex weights change sign alternantly but are equal in magnitude were able to be reduced to smaller chains by a procedure analogous to that given by Coulson and Rushbrooke. The algorithm for constructing the reduced chains has been stated and proved. The results have been utilized, in conjunction with McClelland's graph‐factorization method using reflection (σ) planes, to reduce the HMO secular determinants of some chemical graphs to an extent beyond the ability of group theory. McClelland's σ‐plane algorithm, used repetitively where possible, produces factors whose sizes (nM) are equal to those (nG) of the group‐theoretic factor blocks. For linear polyacenes (LP), however, a new observation has been made: If the LP has an even number of fused rings, nM = nG; but when the LP has an odd number of fused rings, McClelland's process is effective in further reduction, i.e., nM < nG. In any case, however, the vertex alternation procedure reported in the present paper brings about further reduction. To demonstrate the utility of the present method, a sample calculation of the LUMO eigenvector graph theoretically has been shown for p‐benzoquinone and the result has been utilized to obtain an inductive effect HMO parameter of the methyl group from the charge‐transfer bands of some molecular complexes of methylated p‐benzoquinones.© 1993 John Wiley & Sons, Inc.

Semiempirical calculations of molecular polarizabilities and hyperpolarizabilities of polycyclic aromatic compounds

AbstractThe correlation of 2D conjugation and the nonlinear properties of a series of polycyclic aromatic compounds were studied by performing semiempirical calculations using the MOPAC package. For linear polyacenes, both linear and nonlinear properties are found to be increased as the number of six‐membered rings increases. In general, the polarizabilities, 〈α〉, and second hyperpolarizabilities, 〈γ〉, are found to correlate very well with total resonance energies. In the case of first hyperpolarizabilities, 〈β〉, symmetry is the dominating factor. © 1992 John Wiley & Sons, Inc.

Role of the semiconductor/insulator interface in the characteristics of π-conjugated-oligomer-based thin-film transistors

Thin-film transistors (TFT) were made with various π-conjugated oligomers, including an oligothiophene series (from tetrhienyl up to octithienyl) and two linear polyacenes, tetracene and pentacene. Furthermore, various inorganic and organic insulators have been used. The devices were characterized by measuring the drain current as a function of the source-drain bias for various source-gate voltages, which allow the determination of the field-effect mobility, μ FET. As expected, μ FET increases as the conjugation length of the oligomer increases. Importantly, the mobility also appears to be very dependent on the nature of the isolating layer, which shows that the charge transport of the device is predominantly governed by the properties of the semiconductor-insulator interface.

Mixed-valence, conjugated quinone and imide anion radicals. An ESR investigation

Anion radicals of linear polyacene diquinones and diimides were produced electrochemically and studied by ESR. The odd electron of substituted 1,4,8,11-pentacenetrone anion radicals is localized (in a naphthoquinoid unit) and hops from one quinone to the other. The hopping rate was measured. The anion radicals of similarly sized anthracenetetracarboxylic acid 2,3:6,7-diimides have a delocalized odd electron, and there is relatively high electron density on the bridge. The results are compared to other unconjugated two-electrophore anion radicals

Two-dimensional model of charge transfer excitons in polyacene crystals

A two-dimensional analog of the Merrifield model of the coupling between Frenkel and charge transfer (CT) excitations of a molecular crystal is proposed and applied for the calculation of the band structure of the CT excitons in the crystals of linear polyacenes. The solutions are compared with those obtained within the previously used linear model and the limitations of the latter are discussed. Some possible applications of the new approach for the interpretation of experimental data are suggested.