Nonspherical model density matrices for Rung 3.5 density functionals

"Rung 3.5" exchange-correlation functionals for Kohn-Sham density functional theory depend linearly on the nonlocal one-particle density matrix of the noninteracting Kohn-Sham reference system. Rung 3.5 functionals also require a semilocal model for the one-particle density matrix. This work presents new model density matrices for Rung 3.5 functionals. The resulting functionals give reasonable predictions for total energies, molecular thermochemistry and kinetics, odd-electron bonds, and conjugated polymer bandgaps. Global-hybrid-like combinations of semilocal and Rung 3.5 exchange, and empirical density matrix models, also show promise.     

Local hybrid functionals: an assessment for thermochemical kinetics

Local hybrid functionals with position-dependent exact-exchange admixture are a new class of exchange-correlation functionals in density functional theory that promise to advance the available accuracy in many areas of application. Local hybrids with different local mixing functions (LMFs) governing the position dependence are validated for the heats of formation of the extended G3/99 set, and for two sets of barriers of hydrogen-transfer and heavy-atom transfer reactions (HTBH38 and NHTBH38 databases). A simple local hybrid Lh-SVWN with only Slater and exact exchange plus local correlation and a one-parameter LMF, g(r)=b(tau(W)(r)tau(r)), performs best and provides overall mean absolute errors for thermochemistry and kinetics that are a significant improvement over standard state-of-the-art global hybrid functionals. In particular, this local hybrid functional does not suffer from the systematic deterioration that standard functionals exhibit for larger molecules. In contrast, local hybrids based on generalized gradient approximation exchange tend to give rise to nonintuitive LMFs, and no improved functionals have been obtained along this route. The LMF is a real-space function and thus can be analyzed in detail. We use, in particular, graphical analyses to rationalize the performance of different local hybrids for thermochemistry and reaction barriers.     

Many-electron self-interaction and spin polarization errors in local hybrid density functionals

Errors for systems with noninteger occupation have been connected to common failures of density functionals. Previously, global hybrids and pure density functionals have been investigated for systems with noninteger charge and noninteger spin state. Local hybrids have not been investigated for either of those systems to the best of our knowledge. This study intends to close this gap. We investigate systems with noninteger charge to assess the many-electron self-interaction error and systems with noninteger spin state to assess the spin polarization error of recently proposed local hybrids and their range-separated variants. We find that long-range correction is very important to correct for many-electron self-interaction error in cations, whereas most full-range local hybrids seem to be sufficient for anions, where long-range-corrected density functionals tend to overcorrect. On the other hand, while all hitherto proposed long-range-corrected density functionals show large spin polarization errors, the Perdew-Staroverov-Tao-Scuseria (PSTS) functional performs best of all local hybrids in this case and shows an outstanding behavior for the dependence of the energy on the spin polarization.     

Electronic Properties of Vinylene-Linked Heterocyclic Conducting Polymers: Predictive Design and Rational Guidance from DFT Calculations

The band structure and electronic properties in a series of vinylene-linked heterocyclic conducting polymers are investigated using density functional theory (DFT). In order to accurately calculate electronic band gaps, we utilize hybrid functionals with fully periodic boundary conditions to understand the effect of chemical functionalization on the electronic structure of these materials. The use of predictive first-principles calculations coupled with simple chemical arguments highlights the critical role that aromaticity plays in obtaining a low band gap polymer. Contrary to some approaches which erroneously attempt to lower the band gap by increasing the aromaticity of the polymer backbone, we show that being aromatic (or quinoidal) in itself does not ensure a low band gap. Rather, an iterative approach which destabilizes the ground state of the parent polymer toward the aromatic ? quinoidal level crossing on the potential energy surface is a more effective way of lowering the band gap in these conjugated systems. Our results highlight the use of predictive calculations guided by rational chemical intuition for designing low band gap polymers in photovoltaic materials.     

On the DFT Ground State of Crystalline Bromine and Iodine

We report on an erroneous ground state within common density functional theory (DFT) methods for the solid elements bromine and iodine. Phonon computations at the GGA level for both molecular crystals yield imaginary vibrational modes, erroneously indicating dynamic instability—that fact alone could easily pass as a computational artefact, but these imaginary modes lead to energetically more favorable and dynamically stable structures, made up of infinite monoatomic chains. In contrast, meta‐GGA and hybrid functionals yield the correct energetic order for bromine, while for iodine, most global hybrids do not improve the GGA result significantly. The qualitatively correct answer, in both cases, is given by the long‐range corrected hybrid LC‐ωPBE, the Minnesota functionals M06L and M06, and by periodic Hartree–Fock and MP2 theory. This poor performance of economic DFT functionals should be kept in mind, for example, during global structure optimizations of systems with significant contributions from halogen bonds.     

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.     

含噻吩窄带隙共轭聚合物类太阳能电池材料的研究进展

含噻吩的窄带隙共轭聚合物类太阳能电池材料因其良好的稳定性和可加工性,已成为新型太阳能电池的研究热点。本论文主要介绍了用于太阳能电池的窄带隙共轭聚合物研究进展,按其结构特征分为烷基/烷氧基取代聚噻吩、含苯基聚噻吩、基于噻吩并吡嗪的共聚物、基于噻吩并噻唑的共聚物、基于噻吩并吩噻嗪的共聚物、基于烷基芴的共聚物以及其它种类的窄带隙的共轭聚合物,并对它们的结构特点、光学带隙、合成方法进行了归纳与总结。本文最后简要介绍了该研究领域目前所面临的一些问题,同时讨论了该类材料在此领域今后的发展趋势。     

Evaluation of range-separated hybrid density functionals for the prediction of vibrational frequencies, infrared intensities, and Raman activities

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-omegaPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.     

An isoindigo-based low band gap polymer for efficient polymer solar cells with high photo-voltage

A new low band gap polymer (E(g) = 1.6 eV) with alternating thiophene and isoindigo units was synthesized and characterized. A PCE of 3.0% and high open-circuit voltage of 0.89 V were realized in polymer solar cells, which demonstrated the promise of isoindigo as an electron deficient unit in the design of donor-acceptor conjugated polymers for polymer solar cells.     

Performance of conventional and range-separated hybrid density functionals in calculations of electronic circular dichroism spectra of transition metal complexes

A number of density functionals, including 'pure' (nonhybrid) functionals, global hybrids, and range-separated hybrids, were used to calculate the electronic circular dichroism (CD) spectra of 10 tris-bidentate transition metal complexes. The results are compared to one another and to experimental CD spectra, in an effort to illustrate the shortcomings of particular approximations in time-dependent density functional theory (TDDFT). The use of an origin invariant formalism to calculate magnetic transition dipole moments with the help of gauge-including atomic orbitals (GIAOs) is also investigated. With valence basis sets of moderate flexibility, good agreement between GIAO results and rotatory strengths calculated from the dipole-velocity representation is obtained for selected test cases. Empirically broadened vertical CD spectra calculated with the global hybrid functionals B3LYP and PBE0 are found to agree overall the best with experimental CD spectra.     

Surface Engineering of Conjugated Polybenzothiadiazoles and Integration with Cobalt Oxides for Photocatalytic Water Oxidation

Conjugated polymers feature promising structure and properties for photocatalytic water splitting. Herein, a hydrolysis strategy was demonstrated to rationally modulate the surface hydrophilicity and band structures of conjugated poly-benzothiadiazoles. High hydrophilicity not only enhances the dispersions of polymeric solids in an aqueous solution but also reduces the absorption energy of water molecules. Besides, both theoretical and experimental results reveal that a more positive valence band potential is generated, which contributes to enhancing the photocatalytic water oxidation performance. Accordingly, the surface-modified conjugated polymers show largely promoted photocatalytic water oxidation activities by deposition of cobalt oxides as cocatalysts.     

Structure and electronic properties of ladder polymers. A new class of conducting polymers

Theoretical calculations have been applied to design novel synthetic polymers which show metallic conductivity without doping. Some selected highly conjugated structures were calculated using a HUCKELMO method extended by introducing elastic sigma bonds. A group of highly conjugated aromatic ladder polymers is promising in this context. Another interesting group consists of laddered heteroaromatic structures in which carbon atoms are replaced by nitrogen. Ionization potentials, electron affinities, band widths, band gaps as well as oxidation and reduction potentials were calculated. Small, band gaps were obtained for polyacene, polyperinaphthalene and polypyridinopyridine. The values are in good aggreement with that obtained on the basis of the VEH method. This paper reports also some efforts to prepare polyacene, polyperinaphthalene and polypyridinopyridine, and to investigate their electronic properties. Concerning their electrochemical properties high specific capacities and good electrochemical stability has been found in aprotic lithium cells.     

Biological–synthetic hybrid block copolymers: Combining the best from two worlds

Although biopolymers and synthetic polymers share many common features, each of these two classes of materials is also characterized by a distinct and very specific set of advantages and disadvantages. Combining biopolymer elements with synthetic polymers into a single macromolecular conjugate is an interesting strategy for synergetically merging the properties of the individual components and overcoming some of their limitations. This article focuses on a special class of biological–synthetic hybrids that are obtained by site‐selective conjugation of a protein or peptide and a synthetic polymer. The first part of the article gives an overview of the different liquid‐phase and solid‐phase techniques that have been developed for the synthesis of well‐defined, that is, site‐selectively conjugated, synthetic polymer–protein hybrids. In the second part, the properties and potential applications of these materials are discussed. The conjugation of biological and synthetic macromolecules allows the modulation of protein binding and recognition properties and is a powerful strategy for mediating the self‐assembly of synthetic polymers. Synthetic polymer–protein hybrids are already used as medicines and show significant promise for bioanalytical applications and bioseparations. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 1–17, 2005     

Assessment of long-range corrected functionals performance for n-->pi* transitions in organic dyes

The first n-->pi* transitions of 18 nitroso and 16 thiocarbonyl dyes have been computed by time-dependent density functional theory (TD-DFT) using pure as well as global and range-separated hybrid functionals. It turns out that the accuracy of all hybrids is relatively similar, i.e., the inclusion of a growing fraction of exact exchange does neither worsen nor improve significantly the raw TD-DFT estimations. However, after a simple linear regression, it appears that the range-separated hybrids provide a better accuracy than global hybrids.     

含联芴烯单元共轭聚合物的合成及表征

以六羰基钨[W(CO)₆]为催化剂, 合成了聚吲哚芴(P1)、 聚梯型四苯(P2)、 聚梯型五苯(P3)和小分子9-联吲哚芴烯(S1).该类聚合物的重复单元含有联芴烯结构, 通过芴9位的双键连接. 光学和电化学等实验结果表明, 聚合物无荧光发射, 是一类窄带隙的共轭聚合物, 其中聚合物P1薄膜的紫外吸收值最大波长为710 nm.     

A thorough benchmark of density functional methods for general main group thermochemistry, kinetics, and noncovalent interactions

A thorough energy benchmark study of various density functionals (DFs) is carried out with the new GMTKN30 database for general main group thermochemistry, kinetics and noncovalent interactions [Goerigk and Grimme, J. Chem. Theor. Comput., 2010, 6, 107; Goerigk and Grimme, J. Chem. Theor. Comput., 2011, 7, 291]. In total, 47 DFs are investigated: two LDAs, 14 GGAs, three meta-GGAs, 23 hybrids and five double-hybrids. Besides the double-hybrids, also other modern approaches, i.e., the M05 and M06 classes of functionals and range-separated hybrids, are tested. For almost all functionals, the new DFT-D3 correction is applied in order to consistently test the performance also for important noncovalent interactions; the parameters are taken from previous works or determined for the present study. Basis set and quadrature grid issues are also considered. The general aim of the study is to work out which functionals are generally well applicable and robust to describe the energies of molecules. In summary, we recommend on the GGA level the B97-D3 and revPBE-D3 functionals. The best meta-GGA is oTPSS-D3 although meta-GGAs represent in general no clear improvement compared to numerically simpler GGAs. Notably, the widely used B3LYP functional performs worse than the average of all tested hybrids and is also very sensitive to the application of dispersion corrections. We discourage its usage as a standard method without closer inspection of the results, as it still seems to be often done nowadays. Surprisingly, long-range corrected exchange functionals do in general not perform better than the corresponding standard hybrids. However, the ωB97X-D functional seems to be a promising method. The most robust hybrid is Zhao and Truhlar's PW6B95 functional in combination with DFT-D3. If higher accuracy is required, double-hybrids should be applied. The corresponding DSD-BLYP-D3 and PWPB95-D3 variants are the most accurate and robust functionals of the entire study. Additional calculations with MP2 and and its spin-scaled variants SCS-MP2, S2-MP2 and SOS-MP2 revealed that double-hybrids in general outperform those. Only SCS-MP2 can be recommended, particularly for reaction energies. We suggest its usage when a large self-interaction error is expected that prohibits usage of double-hybrids. Perdews' metaphoric picture of Jacob's Ladder for the classification of density functionals' performance could unbiasedly be confirmed with GMTKN30. We also show that there is no statistical correlation between a functional's accuracy for atomization energies and the performance for chemically more relevant reaction energies.     

Theoretical prediction of ionization/oxidation potentials in conjugated polymers

Various density functional theory (DFT) functionals and semiempirical techniques were used to predict the ionization potentials of selected conjugated polymers. Ionization potentials at infinite chain lengths were estimated using Meier fit on oligomer data. Calculated gas-phase ionization potentials with BHandH functional showed good correlation with the experimental data. The results from the semiempirical techniques do not compare as favorably as the ones obtained from DFT methods. The data fitting allowed us to estimate the size of “effective ionization length”, which spanned over 20–30 double bonds in the conjugated backbone of the polymer in question.     

Different donor-acceptor structures of dithiafulvalene-fused semiconducting polymers with different band gaps

Two similar dithiafulvalene-fused conjugated polymers, with different donor-acceptor (D-A) structures, were synthesised. The polymers have different band gaps and stacking structures, as proven by the experimental results and computational studies.