Reaction energetics on long‐range corrected density functional theory: Diels–Alder reactions

The possibility of quantitative reaction analysis on the orbital energies of long‐range corrected density functional theory (LC‐DFT) is presented. First, we calculated the Diels–Alder reaction enthalpies that have been poorly given by conventional functionals including B3LYP functional. As a result, it is found that the long‐range correction drastically improves the reaction enthalpies. The barrier height energies were also computed for these reactions. Consequently, we found that dispersion correlation correction is also crucial to give accurate barrier height energies. It is, therefore, concluded that both long‐range exchange interactions and dispersion correlations are essentially required in conventional functionals to investigate Diels–Alder reactions quantitatively. After confirming that LC‐DFT accurately reproduces the orbital energies of the reactant and product molecules of the Diels–Alder reactions, the global hardness responses, the halves of highest occupied molecular orbital (HOMO)‐lowest unoccupied molecular orbital (LUMO) energy gaps, along the intrinsic reaction coordinates of two Diels–Alder reactions were computed. We noticed that LC‐DFT results satisfy the maximum hardness rule for overall reaction paths while conventional functionals violate this rule on the reaction pathways. Furthermore, our results also show that the HOMO‐LUMO gap variations are close to the reaction enthalpies for these Diels–Alder reactions. Based on these results, we foresee quantitative reaction analysis on the orbital energies. © 2012 Wiley Periodicals, Inc.     

Comparison of DFT methods for molecular orbital eigenvalue calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.     

Koopmans-like approximation in the Kohn-Sham method and the impact of the frozen core approximation on the computation of the reactivity parameters of the density functional theory

A Koopmans-like approximation is introduced in the spin-polarized version of the Kohn-Sham (KS) density functional theory to obtain a relation between KS orbital energies and vertical ionization potential and electron affinity. Expressions for reactivity indexes (like electronegativity, hardness, electrophilicity, and excitation energies) include KS frontier orbital energies and additional contributions associated with the self-interaction correction. Those reactivity parameters were computed with different exchange-correlation functionals to test the approach for a set of small molecules. The results show that the present approximation provides a better way to estimate hardness, electronegativity, and electrophilicity than just the use of frontier orbital energy values. However KS HOMO and LUMO energy gap gives a better agreement with excitation energies.     

Scanning‐Tunneling‐Spectroscopy‐Directed Design of Tailored Deep‐Blue Emitters

Frontier molecular orbitals can be visualized and selectively set to achieve blue phosphorescent metal complexes. For this purpose, the HOMOs and LUMOs of tridentate Pt^II complexes were measured using scanning tunneling microscopy and spectroscopy. The introduction of electron‐accepting or ‐donating moieties enables independent tuning of the frontier orbital energies, and the measured HOMO–LUMO gaps are reproduced by DFT calculations. The energy gaps correlate with the measured and the calculated energies of the emissive triplet states and the experimental luminescence wavelengths. This synergetic interplay between synthesis, microscopy, and spectroscopy enabled the design and realization of a deep‐blue triplet emitter. Finding and tuning the electronic “set screws” at molecular level constitutes a useful experimental method towards an in‐depth understanding and rational design of optoelectronic materials with tailored excited state energies and defined frontier‐orbital properties.     

Long‐range corrected density functionals combined with local response dispersion: A promising method for weak interactions

Density functional theory, in general, is considered to underestimate the weak van der Waals type of intermolecular interactions. We optimized parameters of the local response dispersion (LRD) method applied to the long‐range corrected exchange‐correlation functionals (LC‐BOP12+LRD and LCgau‐BOP+LRD) on the interaction energy for the complexes in the recently compiled S66 database and found to be comparable with the high‐level wave function‐based methods reported in ?ezá? et al. (J. Chem. Theory Comput. 2011 , 7, 2427). Our calculations with the S66 intermolecular complexes at equilibrium geometries suggests that the LC‐BOP12+LRD and LCgau‐BOP+LRD are well‐balanced and lower cost alternatives to the methods reported in the database. Further, test on the S66X8 database (with eight nonequilibrium points) and the HBC6 and NBC10 database shows LC+LRD method with newly optimized parameters is a promising candidate for dealing such weak interactions. Finally, the new parameterized LC+LRD method was tested on X40 benchmark halogenated complexes.Copyright © 2013 Wiley Periodicals, Inc.     

A semiempirical long-range corrected exchange correlation functional including a short-range Gaussian attenuation (LCgau-B97)

We applied an improved long‐range correction scheme including a short‐range Gaussian attenuation (LCgau) to the Becke97 (B97) exchange correlation functional. In the optimization of LCgau‐B97 functional, the linear parameters are determined by least squares fitting. Optimizing μ parameter (0.2) that controls long‐range portion of Hartree‐Fock (HF) exchange to excitation energies of large molecules (Chai and Head‐Gordon, J Chem Phys 2008, 128, 084106) and additional short‐range Gaussian parameters (a = 0.15 and k = 0.9) that controls HF exchange inclusion ranging from short‐range to mid‐range (0.5–3 Å) to ground state properties achieved high performances of LCgau‐B97 simultaneously on both ground state and excited state properties, which is better than other tested semiempirical density functional theory (DFT) functionals, such as ωB97, ωB97X, BMK, and M0x‐family. We also found that while a small μ value (～0.2) in LC‐DFT is appropriate to the local excitation and intramolecular charge‐transfer excitation energies, a larger μ value (0.42) is desirable in the Rydberg excitation‐energy calculations. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

Tuning of the electronic properties of H‐passivated armchair graphene nanoribbons by mild border oxidation: Theoretical study on periodic models

We report the results of a DFT study of the electronic properties, intended as highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, of periodic models of H‐passivated armchair graphene nanoribbons (a‐GNRs) as that synthetized by bottom‐up technique, functionalized by vicinal dialdehydic groups. This material can be obtained by border oxidation in mild and easy to control conditions with ¹Δ_g O₂ as we reported in our previous paper (Ghigo et al., ChemPhysChem 2015, 16, 3030). The calculations show that the two models of border oxidized a‐GNRs (model A, 0.98 nm and model B, 1.35 nm wide) present LUMO and HOMO energies lowered by an extend roughly linearly dependent on the amount of oxygen chemically bound. The frontier orbital energy variations dependence on the % wt of oxygen bound are, for model A: ?0.12 eV for the LUMO and ?0.05 eV for the HOMO; for model B: ?0.15 eV (HOMO) and ?0.06 eV (LUMO). © 2016 Wiley Periodicals, Inc.     

二茂铁及其衍生物的电化学特性与结构理论研究

研究了二茂铁及其衍生物(甲酰二茂铁,乙酰二茂铁,甲醇二茂铁和乙酸二茂铁)的电化学行为,运用结构理论给出了二茂铁D5点群群轨道能级图与二茂铁衍生物的前线轨道能级图,得出在二茂铁分子结构中1e2(dx2-y2,dxy)与3a1(dz2,4s)分别属于分子前线轨道中的HOMO和LUMO。同时用密度泛函理论(DFT)在LANL2DZ基组水平上对其结构进行了全优化,得到了二茂铁及其衍生物前线最高被占轨道(HOMO)能量值,Fe原子净电荷,对其电化学行为与前线轨道能级相对大小进行了验证。     

Assessment of substituent effects on the parameters of 35Cl nuclear quadrupole resonance in para‐substituted benzene‐sulphenyl chloride via quantum chemical calculations

In this research, substituent effects on the parameters of ³⁵Cl nuclear quadrupole resonance (NQR) in para‐substituted benzene‐sulphenyl chloride were studied at M062X/6‐311G(d,p) theory level. The ³⁵Cl NQR parameters of the quadrupole coupling constant (QCC) and electric‐field gradient (EFG) tensor, as well as an asymmetric parameter, were shown to be correlated with Hammett constant following their calculations. The frontier orbital energy levels, HOMO‐LUMO gaps, hardness, electrophilicity, and chemical potential values of these molecules were calculated as well. natural bond orbital (NBO) analysis was applied for calculating natural populations at chlorine atoms.     

Effects of different basis sets and donor‐acceptor groups on linear and second‐order nonlinear optical properties and molecular frontier orbital energies

The calculation of molecular hyperpolarizability, molecular frontier orbital energies of some donor‐acceptor oxadiazoles ( 5a – f , 8a – f , and 9a – f ) have been investigated using ab initio methods and different basis sets. Ab initio optimizations were performed at the Hartree–Fock (HF) and density functional (Beckee‐3–Lee–Yang–Parr; B3LYP) levels of theory with 6‐31G basis set. The polarizability (<α>), anisotropy of polarizability (Δα), and ground‐state dipole moment (μ), first hyperpolarizability (β), and molecular frontier orbital (HOMO, highest occupied molecular orbital and LUMO, lowest unoccupied molecular orbital) energies of 5a – f , 8a – f , and 9a – f have been calculated at the HF and B3LYP methods with 6‐31G, 6‐31G(d), 6‐31+G(d), 6‐31++G(d,p), 6‐311G, 6‐311G(d), 6‐311+G(d), and 6‐311++G(d,p) basis sets. Also, the molecular hardness (η) and electronegativity (χ) parameters have been obtained using molecular frontier orbital energies. The <α>, Δα, μ, β, HOMO, LUMO energies, η and χ parameters have been investigated as dependence on the choice of method and basis set. The variation graphics of <α>, Δα, μ, β, η, and χ parameters using HF and B3LYP methods with different basis sets are presented. We have examined the frontier molecular orbital pictures of 5a – f , 8a – f , and 9a – f using B3LYP/6‐31++G(d,p) level. The 5a – f , 8a – f , and 9a – f display significant linear, second‐order molecular nonlinearity, and molecular parameters and provide the basis for future design of efficient nonlinear optical materials having the 1,3,4‐oxadiazole core. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Comparative study of the electronic structure of pregnanolones by ab initio theory

Pregnanedione (5β‐pregnane, 3,20‐dione), pregnanolone (3β‐hydroxy‐5β‐pregnan‐20‐one), and epipregnanolone (3α‐hydroxy‐5β‐pregnan‐20‐one) result from the 5β‐reduction of progesterone [4‐pregnene, 3‐20‐dione (P)]. These P metabolites induce anesthesia and smooth muscle relaxation (nongenomic actions). In the present study, geometries and electronic structure of these steroids were assessed by ab initio calculations using the 6‐31G* basis set. Consequently, bond distances, valence angles, and dihedral angles were measured. In addition total energy, frontier orbitals, i.e., highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), dipole moment, and electrostatic potentials were calculated. Total energy was higher for P, followed by pregnanedione. Pregnanolones, the hydroxylated progestins, showed the lower energies. Concerning frontier orbitals, P showed the highest HOMO energy and the lowest LUMO energy. Pregnanedione showed lower HOMO and LUMO energy values than pregnanolone and epipregnanolone. P showed both HOMO and LUMO located at the A ring, including the π bond at C4, C5, and the carbonyl at C3. The HOMO in pregnanedione was included mostly in the A ring and the C3 carbonyl group, while the LUMO was shared by the carbonyl groups at C3 and C20. The frontier orbitals of pregnanolone and epipregnanolone were quite similar. The HOMO in both steroids included the B, C, and D rings and the carbonyl at C20. The LUMO was also similar in both pregnanolones including mostly the carbonyl at C20. The dipole moment was shorter for P and pregnanedione and directed toward the acetyl side chain at C17. Pregnanolone and epipregnanolone showed the dipole moment vector larger and directed toward the A ring. The electrostatic potentials were related mostly with the lone pairs of electrons from the oxygens. By the total energy and frontier orbitals energies of the hormones studied, it is concluded that the metabolism of progesterone toward its 5β‐reduced metabolites might be rationalized from the theoretical chemistry point of view. Besides, the importance of the A/B ring cis configuration, dipole moment, and electrostatic potential are highlighted as possible improving elements of molecular interactions to explain the nongenomic biological action of 5β‐reduced progestins. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 433–440, 1999     

The effect of conjugated spacer on novel carbazole derivatives for dye‐sensitized solar cells: Density functional theory/time‐dependent density functional theory study

The ground‐state structure and frontier molecular orbital of D‐π‐A organic dyes, CFT1A, CFT2A, and CFT1PA were theoretically investigated using density functional theory (DFT) on B3LYP functional with 6‐31G(d,p) basis set. The vertical excitation energies and absorption spectra were obtained using time‐dependent DFT (TD‐DFT). The adsorptions of these dyes on TiO₂ anatase (101) were carried out by using a 38[TiO₂] cluster model using Perdew–Burke–Ernzerhof functional with the double numerical basis set with polarization (DNP). The results showed that the introduction of thiophene–thiophene unit (T–T) as conjugated spacer in CFT2A could affect the performance of intramolecular charge transfer significantly due to the inter‐ring torsion of T–T being decreased compared with phenylene–phenylene (P–P) spacer of CFP2A in the researhcers' previous report. It was also found that increasing the number of π‐conjugated unit gradually enhanced charge separation between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of these dyes, leading to a high‐efficiency photocurrent generation. The HOMO–LUMO energy gaps were calculated to be 2.51, 2.37, and 2.50 eV for CFT1A, CFT2A, and CFT1PA respectively. Moreover, the calculated adsorption energies of these dyes on TiO₂ cluster were ～14 kcal/mol, implying that these dyes strongly bind to TiO₂ surface. Furthermore, the electronic HOMO and LUMO shapes of all dye–TiO₂ complexes exhibited injection mechanism of electron via intermolecular charge‐transfer transition. © 2012 Wiley Periodicals, Inc.     

Computational study of substituent effect in para substituted platinabenzene complexes

The electronic structure and properties of the platinabenzene and para substituted platinabenzenes have been investigated using the hybrid density functional mpw1pw91 theory. The substituent effect in structure parameters, frontier orbital energies, aromaticity indexes, and hyperpolarizability has been studied. The calculations show that, in all molecules HOMO → LUMO transition makes the major contribution in the most intense electronic transition.     

Electronic Structure Insights into the Solvation of Magnesium Ions with Cyclic and Acyclic Carbonates

A computational framework to rank the solvation behavior of Mg²⁺ in carbonates by using molecular dynamics simulations and density functional theory is reported. Based on the binding energies and enthalpies of solvation calculated at the M06‐2X/6‐311++G(d,p) level of theory and the free energies of solvation from ABF‐MD simulations, we find that ethylene carbonate (EC) and the ethylene carbonate:propylene carbonate (EC:PC) binary mixture are the best carbonate solvents for interacting with Mg²⁺. Natural bond orbital and quantum theory of atoms in molecules analyses support the thermochemistry calculations with the highest values of charge transfer, perturbative stabilization energies, electron densities, and Wiberg bond indices being observed in the Mg²⁺(EC) and Mg²⁺(EC:PC) complexes. The plots of the noncovalent interactions indicate that those responsible for the formation of Mg²⁺ carbonate complexes are strong‐to‐weak attractive interactions, depending on the regions that are interacting. Finally, density of state calculations indicate that the interactions between Mg²⁺ and the carbonate solvents affects the HOMO and LUMO states of all carbonate solvents and moves them to more negative energy values.     

Orbital energies and negative electron affinities from density functional theory: Insight from the integer discontinuity

Orbital energies in Kohn-Sham density functional theory (DFT) are investigated, paying attention to the role of the integer discontinuity in the exact exchange-correlation potential. A series of closed-shell molecules are considered, comprising some that vertically bind an excess electron and others that do not. High-level ab initio electron densities are used to calculate accurate orbital energy differences, Deltavarepsilon, between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO), using the same potential for both. They are combined with accurate vertical ionization potentials, I(0), and electron affinities, A(0), to determine accurate "average" orbital energies. These are the orbital energies associated with an exchange-correlation potential that averages over a constant jump in the accurate potential, of magnitude Delta(XC)=(I(0)-A(0))-Deltavarepsilon, as given by the discontinuity analysis. Local functional HOMO energies are shown to be almost an order of magnitude closer to these average values than to -I(0), with typical discrepancies of just 0.02 a.u. For systems that do not bind an excess electron, this level of agreement is only achieved when A(0) is set equal to the negative experimental affinity from electron transmission spectroscopy (ETS); it degrades notably when the zero ground state affinity is instead used. Analogous observations are made for the local functional LUMO energies, although the need to use the ETS affinities is less pronounced for systems where the ETS values are very negative. The application of an asymptotic correction recovers the preference, leading to positive LUMO energies (but bound orbitals) for these systems, consistent with the behavior of the average energies. The asymptotically corrected LUMO energies typically agree with the average values to within 0.02 a.u., comparable to that observed with the HOMOs. The study provides numerical support for the view that local functionals exhibit a near-average behavior based on a constant jump of magnitude Delta(XC). It illustrates why a recently proposed DFT expression involving local functional frontier orbital energies and ionization potential yields reasonable estimates of negative ETS affinities and is consistent with earlier work on the failure of DFT for charge-transfer excited states. The near-average behavior of the exchange-correlation potential is explicitly illustrated for selected systems. The nature of hybrid functional orbital energies is also mentioned, and the results of the study are discussed in terms of the variation in electronic energy as a function of electron number. The nature of DFT orbital energies is of great importance in chemistry; this study contributes to the understanding of these quantities.     

α‐Oligofurans: A Computational Study

Recently, α‐oligofurans have emerged as interesting and promising organic electronic materials that have certain advantages over α‐oligothiophenes. In this work, α‐oligofurans were studied computationally, and their properties were compared systematically with those of the corresponding oligothiophenes. Although the two materials share similar electronic structures, overall, this study revealed important differences between α‐oligofurans and α‐oligothiophenes. Twisting studies on oligofurans revealed them to be significantly more rigid than oligothiophenes in the ground state and first excited state. Neutral α‐oligofurans have more quinoid character, higher frontier orbital energies, and higher HOMO–LUMO gaps than their α‐oligothiophene counterparts. The theoretical results suggest that oligofurans (and subsequently polyfuran) have lower ionization potentials than the corresponding oligothiophenes (and polythiophene), which in turn predicts that oligofurans can be lightly doped more easily than oligothiophenes. Oligofuran dications (8 F²⁺–14 F²⁺) of medium‐sized and longer chain lengths show a polaron‐pair character, and the polycations of α‐oligofurans cannot accommodate high positive charges as easily as their thiophene analogues.     

New Conjugated Oligothiophenes Containing the Unique Arrangement of Internal Adjacent [All]‐S,S‐Oxygenated Thiophene Fragments

The quest for obtaining conjugated oligothiophene‐containing molecules with narrower HOMO–LUMO gaps and higher oxidation and reduction potentials is the subject of this study. Molecules containing the bithiophene tetraoxide ( 2 ) and the terthiophene hexaoxide ( 3 ) moieties were prepared and studied. They were obtained by transferring oxygen atoms to the corresponding dibromo oligothiophenes with the HOF ? CH₃CN complex and then cross‐coupling them with either thiophene‐ or acetylene tin derivatives. The photophysical and electrochemical studies of the products revealed that this particular class of mixed thiophenes is characterized by significantly smaller frontier orbital gaps and higher oxidation and reduction potentials compared with any other arrangement of oligothiophenes including various [all]‐S,S‐oxygenated thiophene derivatives.     

On Koopmans' theorem in density functional theory

This paper clarifies why long-range corrected (LC) density functional theory gives orbital energies quantitatively. First, the highest occupied molecular orbital and the lowest unoccupied molecular orbital energies of typical molecules are compared with the minus vertical ionization potentials (IPs) and electron affinities (EAs), respectively. Consequently, only LC exchange functionals are found to give the orbital energies close to the minus IPs and EAs, while other functionals considerably underestimate them. The reproducibility of orbital energies is hardly affected by the difference in the short-range part of LC functionals. Fractional occupation calculations are then carried out to clarify the reason for the accurate orbital energies of LC functionals. As a result, only LC functionals are found to keep the orbital energies almost constant for fractional occupied orbitals. The direct orbital energy dependence on the fractional occupation is expressed by the exchange self-interaction (SI) energy through the potential derivative of the exchange functional plus the Coulomb SI energy. On the basis of this, the exchange SI energies through the potential derivatives are compared with the minus Coulomb SI energy. Consequently, these are revealed to be cancelled out only by LC functionals except for H, He, and Ne atoms.     

Pyridyl Pyrrolide Boron Complexes: The Facile Generation of Thermally Activated Delayed Fluorescence and Preparation of Organic Light‐Emitting Diodes

The electron positive boron atom usually does not contribute to the frontier orbitals for several lower‐lying electronic transitions, and thus is ideal to serve as a hub for the spiro linker of light‐emitting molecules, such that the electron donor (HOMO) and acceptor (LUMO) moieties can be spatially separated with orthogonal orientation. On this basis, we prepared a series of novel boron complexes bearing electron deficient pyridyl pyrrolide and electron donating phenylcarbazolyl fragments or triphenylamine. The new boron complexes show strong solvent‐polarity dependent charge‐transfer emission accompanied by a small, non‐negligible normal emission. The slim orbital overlap between HOMO and LUMO and hence the lack of electron correlation lead to a significant reduction of the energy gap between the lowest lying singlet and triplet excited states (ΔE_T‐S) and thereby the generation of thermally activated delay fluorescence (TADF).     

Theoretical investigations on the carbazole‐based conjugated polymers containing electron‐donating divinylaryl

The polycarbazoles have been proved to efficiently suppress the keto defect emission. Three carbazole‐based conjugated polymers, poly[9‐methyl‐3‐(4‐vinylstyryl)‐9H‐carbazole] (PBC), poly[9‐methyl‐3‐(2‐(5‐vinylthiophen‐2‐yl)vinyl)‐9H‐carbazole] (PBT) and poly[9‐methyl‐3‐(2‐(5‐vinylfuran‐2‐yl)vinyl)‐9H‐carbazole] (PBF), were investigated by quantum‐chemical techniques, and gain a detailed understanding of the influence of carbazole units and the introduction of electron‐donating on the electronic and optical properties. The electronic properties of the neutral molecules, HOMO‐LUMO gaps (ΔE), in addition to ionization potential (I_p) and electron affinity (E_a), are studied using B3LYP density functional theory. The lowest excitation energies (E_g) and the absorption wavelength are studied using the time dependent density functional theory (TDDFT). The calculated results show that all three series of polymers have good planarity. And the highest‐occupied molecular orbital (HOMO) energies lift about 0.36–0.61 eV and thus the I_P decrease about 0.01–0.19 eV compared to polycarbazole, suggesting the significant improved hole‐accepting and transporting abilities. By introducing the electron‐donating 1,4‐divinylphenylene or 2,5‐divinylthiophene or 2,5‐divinylfuran units in the backbone, and the lowest‐unoccupied molecular orbital (LUMO) energies decrease 0.20–0.39 eV. In addition, PBC, PBT and PBF have longer maximal absorption wavelengths than polycarbazole. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 706–714, 2009