Structural and electronic properties of polyacetylene and polyyne from hybrid and Coulomb-attenuated density functionals

The bond length alternation (BLA), the highest-occupied-lowest-unoccupied (HO-LU) orbital energy gap, and the corresponding excitation energy are determined for trans-polyacetylene (PA) and polyyne (PY) using density functional theory. Results from the Coulomb-attenuated CAM-B3LYP functional are compared with those from the conventional BHHLYP and B3LYP hybrid functionals. BLA values and HO-LU gaps are determined using both finite oligomer and infinite chain calculations, subject to periodic boundary conditions. TDDFT excitation energies are determined for the oligomers. The oligomer excitation energies and HO-LU gaps are then used, in conjunction with the infinite chain HO-LU gap, to estimate the infinite chain excitation energy. Overall, BHHLYP and CAM-B3LYP give BLA values and excitation energies that are larger and more accurate than those obtained using B3LYP. The results highlight the degree to which excitation energies can be approximated using the HO-LU gaps-at the infinite limit, this approximation works well for B3LYP, but not for the other functionals, where the HO-LU gap is significantly larger. The study provides further evidence for the high-quality theoretical predictions that can be obtained from the CAM-B3LYP functional.     

Twisting of conjugated oligomers and polymers: case study of oligo- and polythiophene

Interring twisting (change in the dihedral angle between conjugated rings) of polythiophene was studied theoretically using periodic boundary conditions (PBC) at the B3LYP/6-31G(d) level. We find that the band gap of polymers is strongly dependent on the interring twist angle; yet twisting requires very little energy. A twist of 30 degrees increases the band gap by 0.75 eV in polythiophene, while requiring only 0.41 kcal mol(-1) per monomer unit. Such a small energetic value is of the order of crystal packing or van der Waals forces. These results are compared with calculations performed on model oligomers. Sexithiophene, its radical cations, and its dication are optimized at 0-180 degrees end-to-end twist angles (which correspond to 0-36 degrees interring dihedral angles) using the B3LYP/6-31G(d) method. The theoretical results suggest that the HOMO-LUMO gap, ionization potential, and charge distribution of oligomers are strongly dependent on twisting, whereas, similar to the case of polythiophene, twisting of neutral oligothiophenes costs very little energy. In the case of the radical cation, the lowest energy transition is shifted to a longer wavelength region on twisting, while the second-lowest energy transition is shifted to a shorter wavelength region. This implies that twisted, doped conducting polymers (modeled here by an oligomer radical cation), in contrast to planar, doped polymers, should be transparent within a certain optical window (in the far-visible region, at approximately 1.5 eV). This observation is explained on the basis of changes in the shape and overlap of the frontier molecular orbitals.     

The role of relativity and dispersion controlled inter-chain interaction on the band gap of thiophene, selenophene, and tellurophene oligomers

Ab initio relativistic density functional theoretical calculations have been carried out on π-conjugated oligomers of increasing length with S, Se, and Te as heteroatoms. The band gap of the corresponding polymers has been obtained by plotting lowest unoccupied molecular orbital (LUMO)-highest occupied molecular orbital (HOMO)gap against the reciprocal of the number of monomer units (1/N) and extrapolating the curve to 1/N = 0. With B3LYP functional, we predict that role of relativistic correction terms is not very significant in the determination of final band gap of thiophene, selenophene, and tellurophene polymer. The origin of this observation is provided through the density of states (DOS) analysis which manifests that DOS contribution across the Fermi level of these polymers is mostly governed by C atoms and as a consequence relativistic correction terms due to heavy heteroatom remain insignificant to the band gap modification. We also inspected the role of inter-chain interaction in determining the net LUMO-HOMO gap of π-stacked double chain oligomers of increasing length. We have found that due to the exciton splitting in the stacked configurations, the LUMO-HOMO gap decreases steadily. Furthermore, we have noticed that dispersion force has important role in the reduction of the LUMO-HOMO gap of the oligomers studied.     

Molecular structure and electronic properties of a series of oligoalkylthiophenes: A theoretical investigation

Molecular geometries and electronic properties of 3-alkylthiophenes (ATs) and their oligomers (OATs) are studied by the density functional theory (DFT). Calculations are performed on the oligomers formed by n repeating units, where n ranges from 1 to 6, using the B3LYP/6-31G** level of theory. The results obtained show that the doped oligomers have more satisfactory structural and electronic characteristics for the conducting polymers. The conjugated system in the doped oligomers has more aromaticity, with expanded and planar chains. The calculated energy gap values between the frontal orbitals and also the ionization potential values for the oligomers indicate that with increase in the oligomer chain length, the conductive band gap decreases. Furthermore, our calculations suggest that an electron-donating alkyl substituent at position 3 of the thiophene ring plays an important role in the structural and electronic properties of the polymers.     

Effect of substitution on the optical properties and HOMO-LUMO gap of oligomeric paraphenylenes

A series of dialkyl amino benzophenone dimers with various alkyl chain lengths is presented. Gaussian B3LYP/6-31G(d) calculations show that the band gap decreases within the dimer series as a function of the donor group efficiency. Theoretical calculations show that the interaction between phenyl-phenyl rings is more important than simple donor-acceptor effects. We report the experimental and electro-optical properties of one of these dimers, N,N-(dibutyl)-4-amino-benzophenone. The experimental and theoretical results enabled us to design a new dimer. Altogether, side chain substituents reported herein tune the theoretical band gap of paraphenylene based dimers by over 8.86 eV.     

聚苯类共轭聚合物的重复单元连接方式对禁带宽度的影响

采用DFT/B3LYP方法对低聚物(p- P)2n、(m- P)2n、(m- P1)n和(m- P2)n(n=1~4)体系进行了全优化, 并用ZINDO, TD- DFT方法计算其吸收光谱性质. 分析了各系列HOMO- LUMO能隙、最大吸收波长随n递增的变化规律. 根据低聚物的上述结果外推得到聚合物的性质, 并由此计算了聚合物的有效共轭长度(ECL). 由于间位连接方式的影响, 削弱了间位聚苯及其衍生物的有效共轭程度, 与对位聚苯比较, 能带带隙变宽, 吸收光谱蓝移约130 nm.     

Assessment of several hybrid DFT functionals for the evaluation of bond length alternation of increasingly long oligomers

We have optimized the ground-state geometry of nine series of increasingly long oligomers, using six hybrid density functionals (O3LYP, B3LYP, B97-1, B98, PBE0, and BHHLYP) combined with three different atomic basis sets. In each case, the obtained bond length alternation (BLA) is compared to the corresponding MP2 values. Three phenomenological categories have been set up. In the first, the BLA exponentially decreases, in which case all the tested functionals give results in very good agreement with MP2. In the second category fall the symmetric oligomers that, due to the Peierls theorem, show large BLA. For these chains, BHHLYP tends to give too large and quickly converging BLA wrt chain length, while O3LYP often leads to the opposite misjudgments, and the remaining hybrids provide valuable results. In the third category, one finds asymmetric compounds presenting significantly unequal bond lengths, for which the divergence between DFT and wave function approaches can be dramatic. Indeed, all hybrids yield too small BLA values, especially for long chain lengths. We also study the effect of chain conformation on the BLA.     

Molecular design of a π‐conjugated single‐chain electronically conductive polymer

This study demonstrates that single‐chain π‐conjugated systems can be made electrically conductive by modifying the molecular structures of both ends of the oligomers making up a polymer. That is, the highest occupied molecular orbital (HOMO)–lowest unoccupied molecular orbital (LUMO) gaps of a fairly long polyyne‐type oligomer with appropriately modified molecular structures at both ends are found to be on the order of thermal energy by calculations using density functional theory (DFT) with B3LYP functionals. This result applies to molecular structures with characteristic bond alternations. The peculiar bond alternations are caused by competition between two effects of the bond alternations of the two mutually perpendicular π‐conjugated systems, which partially cancel each other out. It is probable that we can design one‐dimensional polymers with HOMO–LUMO gaps small enough to be conductive by combining the above‐mentioned oligomers with each other as monomer units in the polymer. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Origin of pressure-induced insulator-to-metal transition in the van der Waals compound FePS3 from first-principles calculations

Pressure-induced insulator-to-metal transition (IMT) has been studied in the van der Waals compound iron thiophosphate (FePS₃) using first-principles calculations within the periodic linear combination of atomic orbitals method with hybrid Hartree–Fock-DFT B3LYP functional. Our calculations reproduce correctly the IMT at ∼15 GPa, which is accompanied by a reduction of the unit cell volume and of the vdW gap. We found from the detailed analysis of the projected density of states that the 3p states of phosphorus atoms contribute significantly at the bottom of the conduction band. As a result, the collapse of the band gap occurs due to changes in the electronic structure of FePS₃ induced by relative displacements of phosphorus or sulfur atoms along the c-axis direction under pressure.     

B3LYP,BLYP and PBE DFT band structures of the nucleotide base stacks

DFT crystal orbital (band structure) calculations have been performed for the nucleotide base stacks of cytosine, thymine, adenine, and guanine arranged in DNA B geometry. The band structures obtained with PBE, BLYP, and B3LYP functionals are presented and compared to other related experimental and theoretical results. The influence of the quality of the basis set on the fundamental gap values was also investigated using Clementi's double ζ, 6‐31G and 6‐31G* basis sets. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Oxidation potential of thiophene oligomers: Theoretical and experimental approach

Intrinsic properties of conducting polymers, such as oxidation potential and band gap, are very important for designing new materials with improved properties. Computational chemistry offers suitable tools capable of predicting these quantities. This work presents electrochemical information about accurate oxidation potentials of oligothiophenes and polymer band gap. These are compared to theoretical predictions based on electronic structure calculations at Density Functional Theory levels, coupled with self‐consistent reaction field. All computational protocols gave a qualitative prediction of the experimental trend. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Quantum chemical studies on polythiophenes containing heterocyclic substituents: effect of structure on the band gap

Color tuning by the tailoring of substituents at the 3-position of thiophene is very encouraging, and comparative experimental and theoretical studies proved to be powerful in the search for a suitable design for the above. Since the novel polythiophene-based materials substituted with five-membered/six-membered ring containing sulphur and nitrogen at different positions are proven to be potential candidates for electron-transporting hole blocking functions, the structure-property relationship of these systems have been focused in the present study. Molecular-orbital calculations are applied to obtain the optimized geometries and band gaps of the thiophene oligomers. An oligomeric approach has been implemented for calculating the band gaps, and the theoretically obtained band gaps for the different model compounds are compared. Density-functional theory B3LYP6-31G* predicted band-gap values are compared with the experimental band gaps obtained from optical-absorption edge. The predicted values show little deviations from experimental band gaps, but the trend in band gap is found to be the same in experimental and theoretical results in most of the cases. Hence, this study illustrates the usefulness of quantum-mechanical calculations in understanding the effects of various structural parameters on optical band gap.     

Theoretical investigation of structures and electronic states of a series of phenyl-capped oligothiophenes

The structures and electronic states of a series of phenyl-capped oligothiophenes (PnTs) and their ionic species were investigated by means of the density functional theory (DFT). The calculations were performed on the oligomers formed by n repeating units, where n ranges from 2 to 6, using the B3LYP/6-31G** level of theory. The results obtained show that the end-substitution plays a fine-tuning effect on the geometries, electronics, and excitation states. It was found that the oligomers in the doped state have more satisfactory structural and electronic characteristics for the conducting polymers. The conjugated system in the doped oligomers has more aromaticity, with expanded and planar chains. The calculated energy gap values between the frontal molecular orbitals for the PnTs indicate that with increasing the oligomer chain length, the conductive band gap decreases. The calculated ?rst excitation energies of the PnTs at the TD-B3LYP/6-31G** level reveal that the doped PnTs have lower excitation energies than the neutral states. The oligomer chains with a phenyl ring as the end-capped group display red shifts in their absorption spectra. The end-caped substituted oligothiophenes display better characteristics than the unsubstituted ones. It could be anticipated that the phenyl-caped substitution would be helpful to charge-carrier hopings between chains, and thereby, enhance the conductivity.     

Ab initio band structure calculations on polymers (C5H3X)n (X=CH,N,P,As)

The ab initio crystal orbital calculations on conjugated aromatic six-membered rings polymers,namely,poly(p-phenylene) (PPP),poly(2,5-pyridinediyl) (PPD),poly(2,5-phosphabenzene) (PPB) and ploy(2,5-arsabenzene) (PAB) are reported.The comparison of the important electronic properties of these polymers,such as band gap,bandwidth,ionization potential and electron affinity,indicates that PPP is the best intrinsic semiconductor,and PPD has the best prospects for forming n-doped conducting materials.     

Density functional theory (DFT) investigation of molecular structure and frontier molecular orbitals (FMOs) of P-N,N-dimethylaminobenzylidenemalononitrile (DBM)

P-N,N-dimethylaminobenzylidenemalononitrile (DBM) dye belongs to a class of organic compounds known as molecular rotors. Its optimized geometry and frontier molecular orbitals (FMOs), before and after ultraviolet (UV) irradiation, were obtained by DFT/B3LYP level with complete relaxation in the potential energy surface using 6-311++G(d,p) basis set. It is found that the length of C-C bonds of the DBM molecule increases after the UV irradiation, which leads to an increase in its dipole moment making it as a promising material for solar cell applications. Also, its HOMO-LUMO gap decreased from 3.46 to 3.34 eV. From the cyclic voltammetry measurements the value of HOMO-LUMO gap is equal to 3.21 eV. This means that B3LYP/6-311++G(d,p) level of theory is the best one for calculations.     

Opto-electronic properties and molecular design of new materials based on pyrrole studied by DFT

In this work, we investigate oligopyrroles and derivatives, which serve as models for corresponding polymers. In order to discuss these materials, we carried out DFT calculations and used DFT methods to calculate ground state electronic structures. We are particularly interested in exploring the potential of several substituent groups as electron donors with numerous ties to electronic materials by exploring and comparing the energies of HOMO, LUMO, Gap energies, and structural properties. Results are discussed in comparison with the properties of the doped oligomers. The theoretical ground-state geometry and electronic structure of the studied molecules were obtained by the DFT method at B3LYP level with 6-31G(d) basis set. The opto-electronic properties of these materials were determined by ZINDO/s and TD//B3LYP/6-31G(d) calculations performed on the B3LYP/6-31(d) optimized geometries. The results of this study demonstrate how electronic properties can be tuned by the backbone ring or side group and suggest these compounds as good candidates for opto-electronic applications.     

Toward a rational design of poly(2,7-carbazole) derivatives for solar cells

On the basis of theoretical models and calculations, several alternating polymeric structures have been investigated to develop optimized poly(2,7-carbazole) derivatives for solar cell applications. Selected low band gap alternating copolymers have been obtained via a Suzuki coupling reaction. A good correlation between DFT theoretical calculations performed on model compounds and the experimental HOMO, LUMO, and band gap energies of the corresponding polymers has been obtained. This study reveals that the alternating copolymer HOMO energy level is mainly fixed by the carbazole moiety, whereas the LUMO energy level is mainly related to the nature of the electron-withdrawing comonomer. However, solar cell performances are not solely driven by the energy levels of the materials. Clearly, the molecular weight and the overall organization of the polymers are other important key parameters to consider when developing new polymers for solar cells. Preliminary measurements have revealed hole mobilities of about 1 x 10(-3) cm2 x V(-1) x s(-1) and a power conversion efficiency (PCE) up to 3.6%. Further improvements are anticipated through a rational design of new symmetric low band gap poly(2,7-carbazole) derivatives.     

Thermochemistry of the higher chlorine oxides ClOx (x=3, 4) and Cl2Ox (x=3–7)†

Heats of formation for ClO₃, ClO₄, Cl₂O₃, Cl₂O₄, Cl₂O₅, Cl₂O₆ and Cl₂O₇ molecules are determined at the B3LYP, B3PW91, mPW1PW91 and B1LYP levels of the density functional theory employing a series of extended basis sets, and using Gaussian-3 model chemistries. Modified Gaussian-3 calculations, which employ accurate B3LYP/6-311+G(3d2f) molecular geometries and vibrational frequencies, were also performed. Heats of formation were calculated from both total atomization energies and isodesmic reaction schemes. The latter method in conjunction with Gaussian-3 models leads to the most reliable results. The best values at 298 K for ClO₃, ClO₄, Cl₂O₃ and Cl₂O₄ as derived from an average of G3//B3LYP and G3//B3LYP/6-311+G(3d2f) calculations are 43.1, 54.8, 31.7 and 37.4 kcal mol⁻¹. From calculations carried out at the G3(MP2)//B3LYP and G3(MP2)//B3LYP/6-311+G(3d2f) levels, heats of formation for Cl₂O₅, Cl₂O₆ and Cl₂O₇ are predicted to be 53.2, 52.2 and 61.5 kcal mol⁻¹. All best values are reproduced within 1 kcal mol⁻¹ by using mPW1PW91/6-311+G(3d2f) isodesmic energies. Enthalpy changes for relevant Cl–O bond fission reactions are reported. Comparisons with previous thermodynamics data are made.     

Electronic and structural properties of the (1010) and (1120) ZnO surfaces

The structural and electronic properties of ZnO (1010) and (1120) surfaces were investigated by means of density functional theory applied to periodic calculations at B3LYP level. The stability and relaxation effects for both surfaces were analyzed. The electronic and energy band properties were discussed on the basis of band structure as well as density of states. There is a significant relaxation in the (1010) as compared to the (1120) terminated surfaces. The calculated direct gap is 3.09, 2.85, and 3.09 eV for bulk, (1010), and (1120) surfaces, respectively. The band structures for both surfaces are very similar.