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.     

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.     

A combined semiempirical-DFT study of oligomers within the finite-chain approximation, evolution from oligomers to polymers

A computationally cheap approach combining time-independent density functional theory (TIDFT) and semiempirical methods with an appropriate extrapolation procedure is proposed to accurately estimate geometrical and electronic properties of conjugated polymers using just a small set of oligomers. The highest occupied molecular orbital-lowest unoccupied molecular orbital gap (HLG) obtained at a TIDFT level (B3PW91) for two polymers, trans-polyacetylene--the simplest conjugated polymer, and a much larger poly(2-methoxy-5-(2,9-ethyl-hexyloxy)-1,4-phenylenevinylene (MEH-PPV) polymer converge to virtually the same asymptotic value than the excitation energy obtained with time-dependent DFT (TDDFT) calculations using the same functional. For TIDFT geometries, the HLG is found to converge to a value within the experimentally accepted range for the band gap of these polymers, when an exponential extrapolation is used; however if semiempirical geometries are used, a linear fit of the HLG versus 1/n is found to produce the best results. Geometrical parameters are observed to reach a saturation value in good agreement with experimental information, within the length of oligomers calculated here and no extrapolation was considered necessary. Finally, the performance of three different semiempirical methods (AM1, PM3, and MNDO) and for the TIDFT calculations, the performance of 7 different full electron basis sets (6-311+G**, 6-31+ +G**, 6-311+ +G**, 6-31+G**, 6-31G**, 6-31+G*, and 6-31G) is compared and it is determined that the choice of semiempirical method or the basis set does not significantly affect the results.     

Nature of the intense near-IR absorption and unusual broad UV-visible-NIR spectra of azulenocyanines: density functional theory studies

The nature of the broad and intense near-IR (NIR) absorptions of azulenocyanine (H(2)Azc) in the range of 720-1300 nm due to the π→π* transitions is clearly revealed on the basis of density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. The electron moving between peripheral conjugated systems and the eighteen electron-π-conjugated core due to different types of electron transitions has also been clarified. Because of the small gap between the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) of all four H(2)Azc isomers, their Q absorption bands in the region of 850-1300 nm are significantly red-shifted relative to its isoelectronic analogue naphthalocyanine H(2)Nc. Observation of the new absorption bands between Q and Soret bands from 720 to 1050 nm for H(2)Azc is considered to be the result of electron transitions from the fused azulene rings to the 18 electron-π-conjugated core. In addition, the introduction of electron-withdrawing or electron-donating substituents onto the periphery of the azulenocyanine ring is revealed to further reduce the LUMO-HOMO gap, leading to a further red-shifted broad and intense NIR absorption band from 900 to 1700 nm for H(2)(F(8)Azc) and H(2)[(NH(2))(8)Azc].     

An oligomer study on small band gap polymers

Small band gap polymers may increase the energy conversion efficiency of polymer solar cells by increased absorption of sunlight. Here we present a combined experimental and theoretical study on the optical and electrochemical properties of a series of well-defined, lengthy, small band gap oligo(5,7-bis(thiophen-2-yl)thieno[3,4-b]pyrazine)s ( E g = 1.50 eV) having alternating donor and acceptor units. The optical absorptions of the ground state, triplet excited state, radical cation, and dication are identified and found to shift to lower energy with increasing chain length. The reduction of the band gap in these alternating small band gap oligomers mainly results from an increase of the highest occupied molecular orbital (HOMO) level. The S 1-T 1 singlet-triplet splitting is reduced from approximately 0.9 eV from the trimeric monomer to -0.5 eV for the pentamer. This significant exchange energy is consistent with the fact that both the HOMO and the lowest unoccupied molecular orbital (LUMO) remain distributed over virtually all units, rather than being localized on the D and A units.     

Group 15 pnictenium cations supported by a conjugated bithiophene backbone

Thiophene based polymers and oligomers have attracted considerable attention because they can be functionalized to alter the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), which enables the design of tunable light emitting materials. One area, which has been less explored, is the incorporation of low coordinate, low oxidation state main group elements into these systems. We have currently developed a novel π-conjugated ligand containing two contiguous thiophene rings in which we have demonstrated its ability to support both pnictogen cations and their metal complexes.     

Charge-doped and heteroatom-substituted polysilane, poly(vinylenedisilanylene), and poly(butadienylenedisilanylene): electronic structures and band gaps

The effects of charge-doping and boron and phosphorus substitution on the electronic structures and band gaps of polysilane, poly(vinylenedisilanylene), and poly(butadienylenedisilanylene) were theoretically investigated by using density functional theory and time-dependent density functional theory. Band gaps of polymers were estimated both by extrapolations from excitation energies of oligomers up to 30 units and by calculations with the periodic boundary condition. It was found that charge-doping in the polysilane decreases the band gap more significantly than B and P substitutions. However, Si-Si bonds are easily broken by charge-doping. In contrast, B and P substitutions exert little influence on the strength of Si-Si bonds. From natural bond orbital analysis, it was concluded that charge-doping and heteroatom substitution bring about a lowering of the band gap in sigma conjugated polysilanes because of strong electron-hole interactions. The introduction of longer pi conjugated moieties was found to reduce band gaps of sigma-pi conjugated chains. In contrast to the sigma conjugated polysilanes, bridged structures and a different distribution of polarons were found in cations of sigma-pi conjugated chains.     

Conformational analysis of diphenylacetylene under the influence of an external electric field

Theoretical investigation of the torsional potentials of a molecular wire, diphenylacetylene, was carried out at the B3LYP/6-311+G** level by considering the influence of the external electric field (EF). It demonstrates that many molecular features are sensitive to the EF applied. In particular, the torsional barrier increases and the LUMO-HOMO gap decreases with the increase of EF. Quantitative correlations between these features and the external EF were revealed. The current-voltage behavior corresponding to different conformers was studied as well by non-equilibrium Green's function method combined with the density functional theory. Further, the evolution of the LUMO-HOMO gap and the spatial distribution of molecular orbital were used to analyze these structure-property relationships.     

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.     

DFT study of conjugational electronic structures of aminoalkyl end-capped oligothiophenes up to octamers

The molecular geometries and electronic properties of a series of bis(aminoalkyl) end-capped oligothiophenes (BRnTs) were investigated by means of the density functional theory (DFT). The calculations were performed on dimers up to octamers in the neutral and ionic species using the B3LYP/6-31G(d,p) level of theory. The results obtained show that the conjugated systems in the p- and n-doped oligomers had more aromaticity, with expanded and planar chains. The calculated energy gap values between the frontier molecular orbitals for the end-capped oligomers were larger than those for the unsubstituted oligomers, in which with increase in the oligomer chain length, the conduction band gap decreased. The calculated first excitation energies of BRnTs at the TD-B3LYP/6-31G(d,p) level indicated that both doped oligomers (p- and n-type) had lower excitation energies than the neutral states, and that they displayed red shifts in their absorption spectra. Moreover, the results obtained for the natural bond orbital (NBO) analysis showed that closing the end-side oligothiophene chains with the aminoalkyl groups eased the hole or electron transfer, owning to better charge delocalization through the backbone structures of BRnTs.     

Tunable third-order NLO properties of acene derivatives with molecular structural modification

The substitution of heteroatoms and the expansion of π-conjugated units have significant effects on the photoelectric properties of polycyclic aromatic hydrocarbons (PAHs). In this study, based on the experimental molecule PBC, 10 acene derivatives containing the pyrrole group were designed by three strategies: (1) changing the connection position of the pyrrole group, (2) exchanging the position of the N atom, and (3) increasing the length of the π-linker. Density functional theory (DFT) was used to optimize the molecular geometric structure. Time-dependent density functional theory (TD-DFT) was used to calculate the relevant parameters of the excited states. The results show that both of the pyrrole group and the N atom in the para-position, and the addition of the π-linker can reduce the energy gap, cause redshift of the linear absorption peak, and increase the two photon absorption (TPA) cross-section. The analyses of the charge density difference (CDD) and the charge-transfer matrix (CTM) proved that the electron transfer is mainly concentrated in the π-linker. Moreover, the participation of the multi-ring skeleton on both sides decreases gradually with the increase of the length of the π-linker. The length of the π-linker changes the dominant transition channel and intramolecular charge-transfer (ICT) characteristics of TPA, thus affecting the transition dipole moments and nonlinear absorption properties. The second hyperpolarizability of the designed molecule PBI5-p5 is also significantly superior to that of similar materials reported. It is expected that the above molecular design strategies and comprehensive analysis of nonlinear optical (NLO) properties could provide theoretical support for the research on acene derivatives.     

Derivative discontinuity, bandgap and lowest unoccupied molecular orbital in density functional theory

The conventional analysis of Perdew and Levy, and Sham and Schlu?ter shows that the functional derivative discontinuity of the exchange-correlation density functional plays a critical role in the correct prediction of bandgaps, or the chemical hardness. In a recent work by the present authors, explicit expressions for bandgap prediction with all common types of exchange-correlation functionals have been derived without invoking the concept of exchange-correlation energy functional derivative discontinuity at all. We here analyze the two approaches and establish their connection and difference. The present analysis further leads to several important results: (1) The lowest unoccupied molecular orbital (LUMO) in DFT has as much meaning in describing electron addition as the highest occupied molecular orbital (HOMO) in describing electron removal. (2) Every term in the total energy functional contributes to the energy gap because of the discontinuity of the derivative of the density (or density matrix) with respect to the number of electrons, ((?ρ(s)(r('),r))/?N)(v(s) ), at integers. (3) Consistent with the Perdew-Levy-Sham-Schlu?ter conclusion that the exact Kohn-Sham energy gap differs from the fundamental bandgap by a finite correction due to the functional derivative discontinuity of the exchange-correlation energy, we show that the exchange-correlation functional cannot be an explicit and differentiable functional of the electron density, either local or nonlocal. The last result is further strengthened when we consider Mott insulators. There, the exact exchange-correlation functional needs to have an explicitly discontinuous (nondifferentiable) dependence on the density or the density matrix. (4) We obtain exact conditions on the derivatives of total energy with respect to the spin-up and spin-down number of electrons.     

Exploring the electro‐optical properties of conjugated polymers based on oligo‐selenophene and oligo(3,4‐ethylenedioxyselenophene)

For seeking high‐efficiency narrow‐band‐gap donor materials to enhance short‐circuit current density for organic solar cells, a series of oligo‐selenophene (OS) and oligo(3,4‐ethylenedioxyselenophene) (OEDOS) with various chain lengths were designed and characterized using density functional theory (DFT) and time‐dependent DFT calculations. Based on the results, it can be seen that with increasing chain length of the oligomers in both syn‐ and anti‐adding manners, the bond length alternation is decreased which indicates that the π‐electron delocalization is increased. Also, when the chain length is increased the electronic energy gap and the optical energy gap are decreased. It can be concluded that the syn‐(OS)_n=10,14,15, anti‐(OS)_n=14 and anti‐(OEDOS)_n=7–12 oligomers can act as low‐band‐gap polymers. Therefore they can absorb more sunlight based on maximum wavelength (higher than 620 nm). Furthermore, a red shift in the simulated absorption spectra of (OS)_n and (OEDOS)_n donors is observed. It is found that (OS)_n=14,15 with syn configuration of the extended oligomers is the most suitable donor for the design of high‐performance organic solar cells possessing a narrow electronic band gap, high exciton lifetime and broad and intense absorption spectra that cover the solar spectrum leading to complete light‐harvesting efficiency.     

Interchain impacts on electronic structures of heterocyclic oligomers and polymers containing group 14, 15, and 16 heteroatoms: quantum chemical calculations in combination with molecular dynamics simulations

The packing structures and packing effects on excitation energies of oligomers of polyfuran (PFu), polypyrrole (PPy), polycyclopentidene (PCp), polythiophene (PTh), polyphosphole (PPh), and polysilole (PSi) are comparatively studied by employing molecular dynamics (MD) simulations and time-dependent density functional theory (TDDFT) calculations. The dependence of packing structures on the main group of heteroatoms in the five-membered heterocyclic oligomers is exhibited from MD simulations. The planarity of backbones and the population of pi-stacked structures increase with the heteroatoms going from group 14 to group 16; i.e., PCp < PPy < PFu; PSi < PPh < PTh. The polymers with the third row elements, PSi and PPh, tend to have larger chain flexibilities in the packing systems than those with the second row elements, PCp and PPy, respectively. On the basis of the second-order M?ller-Plesset perturbation (MP2) and natural bond orbital (NBO) calculations of the pi-stacked pairs, the difference in pi-stack orientations, head-to-tail vs head-to-head, between various packing systems is rationalized by individual interchain bond orbital interactions involved with heteroatoms. The packing systems with higher row elements tend to have narrower band gaps. The band gaps are closely related to the chain torsions driven by interchain interactions. The noticeable chain distortions in the packing systems of PCp, PSi, and PPh lead to the significant increase of band gaps in comparison with those appraised from periodic boundary conditions (PBC) calculations on their planar isolated chains.     

Excited state properties, fluorescence energies, and lifetime of a poly(fluorene-pyridine) copolymer, based on TD-DFT investigation

The structural and electronic properties of the fluorene-pyridine copolymer (FPy)(n), (n = 1-4) were investigated theoretically by means of quantum mechanical calculations based on density functional theory (DFT) and time-dependent DFT (TD-DFT) using the B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest excited state. It was found that (FPy)(n) is nonplanar in its ground state, whereas a more pronounced trend toward planarity is observed in the S(1) state. Absorption and fluorescence energies have been extrapolated to infinite chain length making use of their good linearity with respect to 1/n. An extrapolated value of 2.64 eV is obtained for vertical excitation energy. The S(1)<--S(0) electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is dominating in terms of oscillator strength. Fluorescence energies and radiative lifetime were calculated as well. The obtained results indicate that the fluorescence energy and radiative lifetime of (FPy)(n) are 2.16 eV and 0.38 ns, respectively. The decrease of fluorescence energy and radiative lifetime with the increase in the chain length is discussed.     

二苯乙炔分子导线的电子输运性质

利用第一性原理非平衡态格林函数方法研究了不同构象下二苯乙炔分子导线的电子输运性质. 从分子轨道空间分布和透射谱等方面讨论了外加偏压下分子构象对电子传递特性的影响及内在机理. 结果表明, 随着分子扭转角的增加, 分子的LUMO-HOMO能隙增加, 透射峰显著降低; 外加偏压下, 分子的HOMO分布向低电势端移动, LUMO向高电势端移动. 电流-电压计算表明, 平面构象分子的导电性最好; 随着扭转角的增加, 分子的导电性变差; 垂直构象分子的导电性最差. 最后给出了分子导线电子传递性质与分子构象的定量关系.     

Hückel theory applied to large linear and cyclic conjugated π-systems

By use of rotational symmetry (C_n-symmetry) a lower limit to the frontier orbital (HOMO-LUMO) gap in large molecules with linear and cyclic conjugated π-systems containing simple repetitive units has been calculated within the Hückel approxmation. The frontier orbitals are shown to be the same in series of cyclic oligomers and liner polymers containing the same repetitive units. The orbital gap is calculated from the repetitive units closed on themselves to give a ring of Hückel or, alternatively, Möbius topology depending on the number of conjugated π-electrons in a liner array between the ends of the repetitive unit. For 4n (4n+2) systems the small ring of Hückel (Möbius) topology will give the frontier orbitals.     

Phosphole modified pentathienoacene: synthesis, electronic properties and self-assembly

A series of new ladder π-conjugated materials, phosphole modified pentathienoacene (PO-PTA), are synthesized and characterized. Single-crystal X-ray results demonstrate that methyl-disubstituted PO-PTA forms a face-to-face dimer structure driven by π-π interactions. The investigations of optical properties showed that the oxidized phosphole moiety in this ladder system can effectively narrow the band gap. PO-PTA is a promising building block in π-conjugated polymers and oligomers for optoelectronic applications. The derivative of PO-PTA, obtained by introducing four long alkyl chains, can self-assemble into one-dimensional (1D) fibers based on intermolecular π-π interactions, dipole-dipole interactions and van der Waals interactions. Interestingly, the uniform and well-ordered monolayers were also obtained for PO-PTA derivative on a HOPG (highly oriented pyrolytic graphite) surface.     

杂硼原子簇B6X-(X=N, P, As, Sb, Bi)稳定性和芳香性研究

利用Gaussian 98程序, 采用从头算和密度泛函理论方法, 对B6X-(X=N, P, As, Sb, Bi)杂硼原子簇进行了理论研究, 优化得到了其稳定平衡构型, 讨论了其振动光谱和稳定性等, 通过自然键轨道(NBO)、分子轨道(MO)和核独立化学位移(NICS)分析, 确定这些杂硼原子簇都有离域的π电子和σ电子成键轨道, 满足4n+2电子规则, 具有芳香性, 与纯B6- 或B62- 原子簇呈反芳香性不同.     

基于第一性原理的Mn-AlN和Cr-AlN的半金属性质

基于密度泛函理论(DFT)的第一性原理方法,在广义梯度近似(GGA)下研究了纤锌矿Mn-AlN和Cr-AlN的能带结构、态密度与磁学等性质.结果表明,Mn-AlN和Cr-AlN的半金属能隙都随着杂质浓度的增大而减小.原因可能是随着Mn/Cr掺杂浓度的增大,杂质原子间相互作用增强,Mn/Cr 3d与N 2p杂化减弱,使得自旋交换劈裂变小,从而半金属能隙变窄.在同等掺杂浓度下,Mn-AlN比Cr-AlN的半金属能隙大.这是因为Mn 3d态能级比Cr 3d态能级低,Mn 3d与N 2p杂化更强,导致自旋交换劈裂更大,自旋向下子带的导带底相对远离费米能级,因此Mn-AlN的半金属能隙较大.