Excited state properties,fluorescence energies,and lifetimes of a poly(fluorene‐phenylene), based on TD‐DFT investigation

The structural and electronic properties of fluorene‐phenylene copolymer (FP)_n, n = 1–4 were studied by means of quantum chemical calculations based on density functional theory (DFT) and time dependent density functional theory (TD‐DFT) using B3LYP functional. Geometry optimizations of these oligomers were performed for the ground state and the lowest singlet excited state. It was found that (FP)_n is nonplanar in its ground state while the electronic excitations lead to planarity in its S₁ state. Absorption and fluorescence energies were calculated using TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods. Vertical excitation energies and fluorescence energies were obtained by extrapolating these values to infinite chain length, resulting in extrapolated values for vertical excitation energy of 2.89 and 2.87 eV, respectively. The S₁ ← S₀ electronic excitation is characterized as a highest occupied molecular orbital to lowest unoccupied molecular orbital transition and is distinguishing in terms of oscillator strength. Fluorescence energies of (FP)_n calculated from TD‐B3LYP/SVP and TD‐B3LYP/SVP+ methods are 2.27 and 2.26 eV, respectively. Radiative lifetimes are predicted to be 0.55 and 0.51 ns for TD‐B3LYP/SVP and TD‐B3LYP/SVP+ calculations, respectively. These fundamental information are valuable data in designing and making of promising materials for LED materials. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

QM/MM study of the absorption spectra of DsRed.M1 chromophores

We report geometries and vertical excitation energies for the red and green chromophores of the DsRed.M1 protein in the gas phase and in the solvated protein environment. Geometries are optimized using density functional theory (DFT, B3LYP functional) for the isolated chromophores and combined quantum mechanical/molecular mechanical (QM/MM) methods for the protein (B3LYP/MM). Vertical excitation energies are computed using DFT/MRCI, OM2/MRCI, and TDDFT as QM methods. In the case of the red chromophore, there is a general blue shift in the excitation energies when going from the isolated chromophore to the protein, which is caused both by structural changes and by electrostatic interactions with the environment. For the lowest ππ* transition, these two factors contribute to a similar extent to the overall DFT/MRCI shift of 0.4 eV. An enlargement of the QM region to include active‐site residues does not change the DFT/MRCI excitation energies much. The DFT/MRCI results are closest to experiment for both chromophores. OM2/MRCI and TDDFT overestimate the first vertical excitation energy by 0.3–0.5 and 0.2–0.4 eV, respectively, relative to the experimental or DFT/MRCI values. The experimental gap of 0.35 eV between the lowest ππ* excitation energies of the red (cis‐acylimine) and green (trans‐peptide) forms is well reproduced by DFT/MRCI and TDDFT (0.32 and 0.37 eV, respectively). A histogram spectrum for an equal mixture of the two forms, generated by OM2/MRCI calculations on 450 snapshots along molecular dynamics trajectories, matches the experimental spectrum quite well, with a gap of 0.23 eV and an overall blue shift of about 0.3 eV. DFT/MRCI appears as an attractive choice for calculating excitation energies in fluorescent proteins, without the shortcomings of TDDFT and computationally more affordable than CASSCF‐based approaches. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

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.     

用GGA密度泛函及其长程、色散校正方法计算各类氢键的结合能

应用广义梯度近似(GGA) (PW91和PBE)、含动能密度的广义梯度近似(meta-GGA) (M06-L)、杂化泛函(hyper-GGA)(M06-2X、X3LYP和B3LYP)及其长程校正泛函LC-DFT(CAM-B3LYP、LC-ωPBE和ωB97X)和色散校正密度泛函(DFT-D)(ωB97X-D和B97-D),用多种基函数对15种不同强度的传统氢键和非传统氢键体系的结合能进行了系统的计算与分析.并与高精度的CCSD(T)/aug-cc-pVQZ结果比较发现:在上述各类泛函中,对于氢键结合能的计算M06-2X和ωB97X-D泛函较为精确与可靠,且没有必要使用过大的基函数,6-311++G(2d,2p)或aug-cc-pVDZ水平的基组就已足够,各类泛函所计算结合能的基组重叠误差(BSSE)均较小,除ωB97X和ωB97X-D外,其它9种泛函不经BSSE校正也能得到同样甚至更准确的结果.     

三芴及螺旋三芴等衍生物的吸收和发光性质的理论研究

The structures, ionization potentials （IP）, electron affinities （EA） and HOMO-LUMO gaps （AEH.L） of the terfluorene oligomers were studied by the density functional theory with B3LYP functional. The characters of the front orbitals were analyzed on the basis of the ground structure. The vertical excitation energies Ev and the maximal absorption wavelengths λabs of a series of ter（9,9-diarylfluorene） compounds were studied employing the time dependent density functional theory （TD-DFT） and ZINDO. The calculated maximal absorption wavelengths by both methods are in good agreement with the experimental data. The results show that the differences between terfluorene hh and ter（9,9-diarylfluorene） derivatives are slight in the structures and the electronic states except that there is the spiroconjugation in the latter. The spiroconjugation made these derivatives far from optimization in terms of stability. Excited structure of hh was calculated to be compared with the ground structure, which indicats that it has strong coplanar tendency of aromatic ring with the neighbour in the excited state. Consequently, they are good blue emitting materials with promising thermal stability.     

Host-guest complex of nabumetone: β-cyclodextrin: quantum chemical study and QTAIM analysis

The aim of the present work is the investigation of the inclusion complex of nabumetone (NAB) and β-cyclodextrin (β-CD) using PM3, DFT, DFT-D and ONIOM2 methods. The results indicate that the most energetically favorable structure predicts a preference of the methoxy group to enter the cavity of β-CD from its wide rim. Consequently, the butanone moiety is positioned outside the cavity on the side of the secondary hydroxyls, with a total insertion of naphthalene group. The semi-empirical PM3 results are in good agreement with those obtained by the DFT optimization (with and without dispersion correction). The donor–acceptor interactions between drug and the cavity wall of the host, studied on the basis of natural bonding orbital (NBO) analysis, show the presence of weak intermolecular hydrogen bonds in addition to the most important van der Waals interactions. Furthermore, it is revealed that among the DFT and DFT-D techniques selected to quantify these interactions, WB97X-D functional provides the greatest values of stabilization energies E⁽²⁾. Finally, a detailed topological charge density analysis based on the quantum theory of atoms in molecules (QTAIM), developed by Bader and co-workers, has been accomplished using the WB97X-D and B3LYP methods on the most favorable complexes. A good correlation between the structural parameters and the electronic density is found.     

线性BC2nB (n＝1～12)的结构特征和电子光谱的理论研究

应用密度泛函理论, 在B3LYP/6-31G^*水平上优化得到了线性簇合物BC_2nB (n＝1～12, D_(h)的平衡几何构型, 并计算了它们的谐振动频率. 在优化平衡几何构型下, 通过TD-B3LYP/cc-pvDZ和TD-B3LYP/cc-pvTZ计算, 分别得到了n＝1～12和n＝1～7的电子跃迁的垂直激发能和对应的振子强度. 在B3LYP/6-311＋G^*水平上计算得到了簇合物BC_2nB (n＝1～12, D_(h)的电离能. 基于计算结果, 导出了BC_2nB体系电子跃迁能以及第一电离能与体系大小n的解析表达式.     

Density functional theory study on two D-π-A-type organic dyes containing different anchoring groups for dye-sensitized solar cells

The electronic structure and absorption spectra of two D-π-A-type organic dyes with different anchoring groups have been investigated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). The effect of anchoring groups on the electronic absorption of the free dyes on (TiO₂)₉ has been studied for the two carbazole dyes (MK1 and MK2). Results from DFT calculations indicate that hydroxamic acid anchoring group in MK2 lead to much stronger intermolecular charge transfer and adsorption energies on (TiO₂)₉ cluster. The effect of four different XC functionals (B3LYP, ωB97xD, M06-2X, and CAM-B3LYP) on the transition energies has been tested in order to explore the valid functional for the studied system. The wavelength values from the ωB97xD/6-31+G** level of theory are in excellent agreement with experimental data so this functional was considered to calculate the electronic absorption of the two studied dyes. The highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and the gap energy (H–L) of the studied dyes are slightly influenced by change of anchoring group. Results reveal that the LUMO energy levels of all studied dyes are higher than the conduction band (CB) of TiO₂ (??4.00 eV). Deprotonation process enhances the efficiency of dye-sensitized solar cells during decreasing adsorption energy of dyes with (TiO₂)₉ cluster.

Graphical abstract

     

Ab initio investigation on the structures and spectra of the firefly luciferin

The ground state (S₀) geometry of the firefly luciferin (LH2) was optimized by both DFT B3LYP and CASSCF methods. The vertical excitation energies (T _v) of three low-lying states (S₁, S₂, and S₃) were calculated by TD-DFT B3LYP//CASSCF method. The S₁ geometry was optimized by CASSCF method. Its T _v and the transition energy (T _e) were calculated by MS-CASPT2//CASSCF method. Both the TD-DFT and MS-CASPT2 calculated S₁ state T _v values agree with the experimental one. The IPEA shift greatly affects the MS-CASPT2 calculated T _v values. Some important excited states of LH2 and oxyluciferin (oxyLH2) are charge-transfer states and have more than one dominant configuration, so for deeply researching the firefly bioluminescence, the multireference calculations are desired. Supported by the National Natural Science Foundation of China (Grant No. 20673012) and the Major State Basic Research Development Programs (Grant No. 2004CB719903)     

A theoretical study of the photoelectron spectra of dichloroketene with accurate computation of ionization energies via complete basis set limit extrapolation

We calculated the equilibrium geometries and harmonic vibrational frequencies of the ground state and five cationic states of dichloroketene using (TD-)B3LYP, PBE0, and M06/M06-2X approaches. The photoelectron spectra of dichloroketene were simulated by computing Franck-Condon factors. The ionization energies were computed using the CCSD(T) approach with extrapolation to the complete basis set (CBS) limit. We propose two new CBS energy formulas (E = E_CBS + Aexp(-x) + B/(x−1) ⁿ, n = 2 or 3) and compare the performance of different CBS approaches. A new ionic state of dichloroketene belonging to the C_s point group is reported. This state is identified as the first excited state of Cl₂CCO⁺ having a double-well potential-energy curve along the CCO bending mode with a barrier height of 1.335 eV. The simulated photoelectron spectra are in agreement with the experiment. The vertical ionization energies calculated via spectral simulation are more accurate compared with those obtained at the ground-state structure. Among the CBS formulas used, the proposed ansatz with n = 2 performs best, with a mean absolute error of 0.021 and 0.012 eV for the adiabatic and vertical ionization energies, respectively.     

DFT Study for a Series of Less-Symmetrical Crown Ethers and Their Complexes with Alkali Metal Cations

A series of ring‐contracted (14‐crown‐5, 17‐crown‐6) and ring‐enlarged (16‐crown‐5, 17‐crown‐5, 19‐crown‐6, 20‐crown‐6) crown ethers and their complexes with alkali‐metal cations Na⁺ and K⁺ had been explored using density functional theory (DFT) at B3LYP/6‐31G* level in order to reveal the effects of the methylene‐chain length in a crown ether. The nucleophilicity of all crown ethers had been investigated by the Fukui functions. The quantum chemistry parameters, such as the energy gap (ΔE), the highest occupied molecular orbital energy (E_HOMO) and the lowest unoccupied molecular orbital energy (E_LUMO) for less‐symmetrical crown ethers and symmetrical frameworks (15‐crown‐5, 18‐crown‐6) had been calculated. In addition, the thermodynamic energies of complexation reactions had also been studied. The results of the DFT calculations show that the methylene‐chain length plays an important role in determining the structure characters of the crown ethers and also strongly influences the properties of the ethers. Some of the calculated results are in a good agreement with the experimental values.     

Correlation between Absorption and Substitution of Photochromic 1,2-Bis(thienyl)ethenes (BTEs) Using Modified Spectroscopic Hammett Equations

Series of photochromic 1,2-bis(thienyl)ethenes possessing perfluorocyclopentene backbones, either hydrogen or methyl groups at the β-positions of the thiophenes, and a variety of substituents in their α'-positions were prepared, which cover the range from electron-donating to electron-withdrawing (Me, −CH₂OH, −OTBS, −TMS, −Br, 1,3-dioxan-2-yl, pyridin-4-yl, −CH₂OH, −COOH). As a linear free energy relationship the spectroscopic Hammett equation gives fair to excellent fits to the excitation energy of the absorption maxima of the ring-opened as well as the ring-closed forms of the BTEs, when Hammett substituent constants σ_p were replaced by Brown's modified substituent constants σ_p⁺ and σ_p⁻. Vice versa, hitherto unknown Hammett-Brown substituent constants can be estimated from the UV spectra. Furthermore, we compared the experimentally measured absorption maxima with values which we calculated by three different methods (DFT STEOM-DLPNO-CCSD/def2-TZVPP, TD-DFT ωB97X-D3/6-31G*, TD-DFT ωB97X-D3/6-311++G**).     

Density functional and spin-orbit ab initio study of CF3Br: molecular properties and electronic curve crossing

Quantum chemical calculations of CF(3)Br and the CF(3) radical are performed using density functional theory (DFT) and time-dependent DFT (TDDFT). Molecular structures, vibrational frequencies, dipole moment, bond dissociation energy, and vertical excitation energies of CF(3)Br are calculated and compared with available experimental results. The performance of six hybrid and five hybrid meta functionals in DFT and TDDFT calculations are evaluated. The ωB97X, B3PW91, and M05-2X functionals give very good results for molecular structures, vibrational frequencies, and vertical excitation energies, respectively. The ωB97X functional calculates well the dipole moment of CF(3)Br. B3LYP, one of the most widely used functionals, does not perform well for calculations of the C-Br bond length, bond dissociation energy, and vertical excitation energies. Potential energy curves of the low-lying excited states of CF(3)Br are obtained using the multiconfigurational spin-orbit ab initio method. The crossing point between 2A(1) and 3E states is located near the C-Br bond length of 2.45 ?. Comparison with CH(3)Br shows that fluorination does not alter the location of the crossing point. The relation between the calculated potential energy curves and recent experimental result is briefly discussed.     

Theoretical study of electronic spectra of linear carbon clusters HC2nS (n = 1–5)

In this work we report the structures and stabilities of linear carbon clusters HC_2nS (n = 1–5) in their ground states using the B3LYP density functional. The rotational constants at the optimized geometries give excellent agreement with the experimental and previous theoretical values. The vertical excitation energies of the 2²Π ← X²Π transitions at the CASPT2 level are 3.16, 2.66, 2.05, 1.78, and 1.55 eV, respectively, in good agreement with the corresponding observed values of 3.01, 2.48, 2.10, 1.84, and 1.65 eV. Also, the exponential-decay curves for these vertical excitation energies obtained from experiments and theoretical calculations are illuminated.     

Calculated ionization energies for a series of sesquiterpenes: comparisons with experimental vertical ionization energies and comments on related structure–activity relationships (SARs)

The energies of the highest-occupied molecular orbitals (HOMOs) are known to be excellent predictors of the reactivities of biogenic hydrocarbons, such as terpenes, with reactive atmospheric oxidants including O₃, OH, and NO₃. Structure–Activity Relationships (SARs) have also been effectively employed in such studies and related to HOMO energies and lowest ionization energies (ionization potentials). This study employs density function theory (DFT), at the B3LYP/6-31G** level, to predict vertical ionization energies (IP_v) for a structurally diverse group of sesquiterpenes, each of which has been reported in air samples collected in the lower troposphere. The availability of published UV photoelectron spectra for nine sesquiterpenes permits comparison of experimental and theoretical vertical ionization energy data. The experimental and theoretical data show a good correlation (average discrepancy ± 0.07 eV). This enables predictions of reactivities for sesquiterpenes whose tropospheric lifetimes may last only a few hours before their transformations into secondary organic aerosols (SOA) close to their emission sources.     

Coupled-cluster studies of the lowest excited states of the 11-cis-retinal chromophore

The first few excited states of the 11-cis-retinal (PSB11) chromophore have been studied at the coupled-cluster approximative singles and doubles (CC2) level using triple-zeta quality basis sets augmented with double sets of polarisation functions. The two lowest vertical excitation energies of 2.14 and 3.21 eV are in good agreement with recently reported experimental values of 2.03 and 3.18 eV obtained in molecular beam measurements. Calculations at the time-dependent density functional theory (TDDFT) level using the B3LYP hybrid functional yield vertical excitation energies of 2.34 and 3.10 eV for the two lowest states. Zero-point vibrational energy (ZPVE) corrections of -0.09 and -0.17 eV were deduced from the harmonic vibrational frequencies for the ground and excited states calculated at the density functional theory (DFT) and TDDFT level, respectively, using the B3LYP hybrid functional.     

Electronic structure and absorption spectra of supramolecular complexes of a fullerene crown ether with a π-extended TTF derivative

The present work is a theoretical investigation on supramolecular complexes of a fullerene crown ether (A and B isomers) with a derivative of π-extended tetrathiafulvalene (T). The geometry and the electronic structure of seven different conformers of the complex of dibenzo-18-crown-6 ether of fullero-N-methylpyrrolidine with a N-benzyl-N-(4-{[9,10-bis(1,3-dithiol-2-ylidene)-9,10-dihydroanthracen-2-yl]ethynyl}benzyl)ammonium cation were determined. We calculated the complexation energies and the absorption spectra, i.e., the lowest 50 excited electronic states of the complexes have been determined at the ground state optimum geometry. All calculations were carried out employing the density functional theory (DFT) and the time-dependent DFT, using the B3LYP, CAM-B3LYP, ωB97X-D, and M06-2X functionals in conjunction with the 6-31G(d,p) basis set. Various types of van der Waals interactions are observed in the complexes. Conformer complexation energies (CE) range from 2.54 to 2.14 eV in the gas phase and from 1.75 to 1.34 eV in CHCl(3) solvent at the ωB97X-D/6-31G(d,p)//M06-2X/6-31G(d,p) level of theory. There are three major features at about 390, 330, and 290 nm in the calculated absorption spectra of all the conformers. The major peaks correspond to T→T, T→T/F (electron density in both T and the fullerene F of B) and to T→F transitions, depending on the particular conformer. Other charge transfer T→F transitions are observed close to the T→T transition, indicating the possibility of photoinduced electron transfer in all these complexes.     

An ONIOM and DFT study of water and ammonia adsorption on anatase TiO2 (001) cluster

Density functional theory (DFT) calculations at ONIOM DFT B3LYP/ 6‐31G**‐MD/UFF level are employed to study molecular and dissociative water and ammonia adsorption on anatase TiO₂ (001) surface represented by partially relaxed Ti₂₀O₃₅ ONIOM cluster. DFT calculations indicate that water molecule is dissociated on anatase TiO₂ (001) surface by a nonactivated process with an exothermic relative energy difference of 58.12 kcal/mol. Dissociation of ammonia molecule on the same surface is energetically more favorable than molecular adsorption of ammonia (?37.17 kcal/mol vs. ?23.28 kcal/mol). The vibration frequency values also are computed for the optimized geometries of adsorbed water and ammonia molecules on anatase TiO₂ (001) surface. The computed adsorption energy and vibration frequency values are comparable with the values reported in the literature. Finally, several thermodynamical properties (ΔH°, ΔS°, and ΔG°) are calculated for temperatures corresponding to the experimental studies. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ab initio and density functional theory study of the enthalpies of formation of F2SOx and FClSOx (x=1, 2)

Enthalpies of formation of F₂SO, F₂SO₂, FClSO and FClSO₂ molecules have been determined using ab initio molecular orbital theory and density functional theory (DFT) calculations. Different DFT approaches and levels of the Gaussian-3 and the complete basis set (CBS) ab initio model chemistries have been employed to calculate enthalpies of formation from both total atomization energies and isodesmic reaction schemes. The best values at 298 K for F₂SO, F₂SO₂, FClSO and FClSO₂ as derived from an average of G3, G3B3, CBS-Q and CBS-QB3 isodesmic energies are −140.6, −181.1, −92.6 and −132.3 kcal mol⁻¹, respectively. The results obtained suggest that the accumulated small component errors found in the DFT-based methods are significantly reduced at the ab initio levels employed. Structural properties, harmonic vibrational frequencies, mode assignations and infrared intensities derived from B3LYP and mPW1PW91 functional with the 6-311+G(3df) basis set are presented.