Relationship between orbital energy gaps and excitation energies for long‐chain systems

The difference between the excitation energies and corresponding orbital energy gaps, the exciton binding energy, is investigated based on time‐dependent (TD) density functional theory (DFT) for long‐chain systems: all‐trans polyacetylenes and linear oligoacenes. The optimized geometries of these systems indicate that bond length alternations significantly depend on long‐range exchange interactions. In TDDFT formalism, the exciton binding energy comes from the two‐electron interactions between occupied and unoccupied orbitals through the Coulomb‐exchange‐correlation integral kernels. TDDFT calculations show that the exciton binding energy is significant when long‐range exchange interactions are involved. Spin‐flip (SF) TDDFT calculations are then carried out to clarify double‐excitation effects in these excitation energies. The calculated SF‐TDDFT results indicate that double‐excitation effects significantly contribute to the excitations of long‐chain systems. The discrepancies between the vertical ionization potential minus electron affinity (IP–EA) values and the HOMO–LUMO excitation energies are also evaluated for the infinitely long polyacetylene and oligoacene using the least‐square fits to estimate the exciton binding energy of infinitely long systems. It is found that long‐range exchange interactions are required to give the exciton binding energy of the infinitely long systems. Consequently, it is concluded that long‐range exchange interactions neglected in many DFT calculations play a crucial role in the exciton binding energies of long‐chain systems, while double‐excitation correlation effects are also significant to hold the energy balance of the excitations. © 2016 Wiley Periodicals, Inc.     

A Theoretical Study on Hydrogen‐Bonded Complex of Proflavine Cation and Water: The Site‐dependent Feature of Hydrogen Bond Strengthening and Weakening

The intermolecular hydrogen‐bonds between proflavine cation (PC) and water molecules are investigated by density functional theory (DFT) and time‐dependent density functional theory (TDDFT) methods. The ground‐state geometry optimizations, electronic excitation energies and corresponding oscillation strengths of the low‐lying electronically excited states for the isolated proflavine cation, the hydrogen‐bonded PC–H2O dimer and PC–(H2O)2 trimer are calculated. Intermolecular hydrogen bonds at the central site of proflavine molecule are found to be stronger than the peripheral site. The hydrogen bond N–H???O for the hydrogen‐bonded dimer are indicated to be weakened in the excited states, since the excitation energy is increased slightly comparing to the monomer. Hydrogen bonds of PC–(H2O)2 trimer with the same type as the dimer are strengthened in the excited state, which is demonstrated by the decrease of the excited energies. Thus, hydrogen bond strengthening and weakening are observed to reveal site dependent feature in proflavine molecule. Furthermore, the hydrogen bond at central site induces the blue‐shift of the absorption spectrum, while the ones at peripheral site induce red‐shift. Hydrogen bonds with the same type at peripheral and central sites of proflavine molecule provide different effects on the photochemical and photophysical properties of proflavine.     

Theoretical investigations on geometrical and electronic structures of silver clusters

Geometrical structures and ground and excited states of silver clusters are theoretically investigated using long-range corrected (LC) density functional theory (DFT) calculations. The discrepancy between HOMO-LUMO gaps and the vertical ionization potential minus vertical electron affinity values, which should be the same values, is explored to reveal the significance of long-range exchange effects on the electronic states of metal clusters. The difference between HOMO-LUMO gaps and HOMO-LUMO excitation energies, which is called “exciton binding energy,” is also tested. As a result, it is found that the long-range exchange effects are requisite in DFT calculations to quantitatively investigate the ground and excited states of metal clusters. © 2018 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     

Theoretical investigations of the perylene electronic structure: Monomer,dimers, and excimers

The structural and electronic properties of perylene molecule, dimers, and excimers have been computationally studied. The present work represents the first systematic study of perylene molecule and dimer forms by means of long‐range corrected time‐dependent density functional theory (TDDFT) approaches. Initially, the study explores the photophysical properties of the molecular species. Vertical transitions to many excited singlet states have been computed and rationalized with different exchange‐correlation functionals. Differences between excitation energies are discussed and compared to the absorption spectrum of perylene in gas phase and diluted solution. De‐excitation energy from the relaxed geometry of the lowest excited singlet is in good agreement with the experimental fluorescence emission. Optimization of several coplanar forms of the perylene pair prove that, contrary to generalized gradient approximation (GGA) and hybrid exchange‐correlation functionals, corrected TDDFT is able to bind the perylene dimer in the ground state. Excitation energies from different dimer conformers point to dimer formation prior to photoexcitation. The fully relaxed excimer geometry belongs to the perfectly eclipsed conformation with D_2h symmetry. The excimer equilibrium intermolecular distance is shorter than the separation found for the ground state, which is an indication of stronger interchromophore interaction in the excimer state. Excimer de‐excitation energy is in rather good agreement with the excimer band of perylene in concentrated solution. The study also scans the energy profiles of the ground and lowest excited states along several geometrical distortions. The nature of the interactions responsible for the excimer stabilization is explored in terms of excitonic and charge resonance contributions. © 2015 Wiley Periodicals, Inc.     

Excited States of Xanthene Analogues: Photofragmentation and Calculations by CC2 and Time‐Dependent Density Functional Theory

Action spectroscopy has emerged as an analytical tool to probe excited states in the gas phase. Although comparison of gas‐phase absorption properties with quantum‐chemical calculations is, in principle, straightforward, popular methods often fail to describe many molecules of interest—such as xanthene analogues. We, therefore, face their nano‐ and picosecond laser‐induced photofragmentation with excited‐state computations by using the CC2 method and time‐dependent density functional theory (TDDFT). Whereas the extracted absorption maxima agree with CC2 predictions, the TDDFT excitation energies are blueshifted. Lowering the amount of Hartree–Fock exchange in the DFT functional can reduce this shift but at the cost of changing the nature of the excited state. Additional bandwidth observed in the photofragmentation spectra is rationalized in terms of multiphoton processes. Observed fragmentation from higher‐lying excited states conforms to intense excited‐to‐excited state transitions calculated with CC2. The CC2 method is thus suitable for the comparison with photofragmentation in xanthene analogues.     

A long-range-corrected time-dependent density functional theory

We apply the long-range correction (LC) scheme for exchange functionals of density functional theory to time-dependent density functional theory (TDDFT) and examine its efficiency in dealing with the serious problems of TDDFT, i.e., the underestimations of Rydberg excitation energies, oscillator strengths, and charge-transfer excitation energies. By calculating vertical excitation energies of typical molecules, it was found that LC-TDDFT gives accurate excitation energies, within an error of 0.5 eV, and reasonable oscillator strengths, while TDDFT employing a pure functional provides 1.5 eV lower excitation energies and two orders of magnitude lower oscillator strengths for the Rydberg excitations. It was also found that LC-TDDFT clearly reproduces the correct asymptotic behavior of the charge-transfer excitation energy of ethylene-tetrafluoroethylene dimer for the long intramolecular distance, unlike a conventional far-nucleus asymptotic correction scheme. It is, therefore, presumed that poor TDDFT results for pure functionals may be due to their lack of a long-range orbital-orbital interaction.     

Star-shaped Organic Molecules That Comprise a 1,3,5-Trisubs-tituted Benzene Core and Three Oligoaryleneethynylene Arms as Light-emitting Materials

Star‐shaped rigid molecules that comprise a 1,3,5‐trisubstitued benzene core and three oligoaryleneethynylene arms have great potential application in organic light‐emitting devices (OLEDs). Their optical and electronic properties are tuned by the star‐shaped molecular size. To reveal the relationship between the properties and structures, we perform a systemic investigation for these organic molecules. The ground and excited state molecules are studied using density functional theory (DFT), the ab initio HF, and the single excitation configuration interaction (CIS), respectively. And the electronic absorption and emission spectra are investigated with time‐dependent density functional theory (TDDFT) and Zerner's intermediate neglect of differential overlap (ZINDO) methods. The results show that the HOMOs, LUMOs, energy gaps, ionization potentials (IP), electron affinities (EA), absorption and emission spectra are controlled by the star‐shaped molecular size, which favor the hole and electron injection into OLEDs. With increasing the molecular conjugated length, the absorption and emission spectra exhibit red shifts to some extent and are in good agreement with the experimental ones. Also, the calculated emission spectra range from 330 to 440 nm. All the calculated show that the star‐shaped molecules are promising as blue light emitting materials     

Time-dependent density functional theoretical study of low lying excited states of F2

The utility of time-dependent density functional theory (TDDFT) in predicting excitation energies is tested for the low lying excited states of F₂, a system that has posed severe challenges to ab initio quantum theory. It is shown that TDDFT using B3LYP functional predicts the excitation energies in good agreement with experiment. In some cases, the agreement is better than that for the post-Hartree–Fock methods like CASSCF and MRCI.     

Analysis of self‐interaction correction for describing core excited states

Core‐excitation energies are calculated by the self‐interaction‐corrected time‐dependent density functional theory (SIC‐TDDFT) and SIC‐delta‐self‐consistent field (SIC‐ΔSCF) methods. For carbon monoxide, SIC‐TDDFT severely overestimates core‐excitation energies, while the SIC‐ΔSCF method using Kohn–Sham density functional theory (KS‐DFT) slightly overestimates. These behaviors are attributed to the fact that the self‐interaction errors in the total and orbital energies considerably differ. We evaluate the difference of the self‐interaction errors for the Slater exchange functional. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

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.     

Theoretical Study on the Optical Properties for 2,7- and 3,6-Linked Carbazole Trimers by Time-dependent Density Functional Theory

Electronic properties, such as HOMO and LUMO energies, band gaps, ionization potential (IP) and electron affinity (EA) of 2,7- and 3,6-linked carbazole trimers, two conjugated oligomers with different linkages of carbazole, were studied by the density functional theory with Becke-Lee-Young-Parr composite exchange correlation functional (B3LYP). The absorption spectra of these compounds were also investigated by time-dependent density functional theory (TD-DFT) with 6-31G* basis set. The calculated results indicated that the HOMO and LUMO of the 2,7- and 3,6-linked carbazole trimers are both slightly destabilized on going from methyl substitution to sec-butyl substitution. Both IP and EA exhibit their good hole-transporting but poor electron- accepting ability. The presence of alkyl groups on the nitrogen atoms does not affect the intra-chain electronic delocalization along the molecular frame. Thus no significant effect on the band gap and absorption spectra of compounds has been found.     

芴与苯并硒化二唑共聚物的电子结构和光谱性质的理论研究

用密度泛函B3LYP方法对低聚体(DEF-BSeD)n(n=1~4)[其中9,9二乙基芴(DEF)单元与苯并硒化二唑(BSeD)单元的摩尔比分别为1∶1和2∶1]进行全优化, 计算电离能(PI)、电子亲和势(EA)和能隙(ΔH-L), 在基态结构的基础上用TD-DFT和ZINDO方法计算激发能和电子吸收光谱, 并利用外推法得到高聚物的相应性质. 从外推结果看出, 随着聚合物中BSeD比例的增大, 聚合物的最低单激发能呈减小的趋势, 最大电子吸收光谱红移. 用CIS方法优化得到单体的S1激发态结构, 计算结果表明, 激发态的结构更趋近于平面构型.     

Prediction of excited‐state properties of oligoacene crystals using polarizable continuum model‐tuned range‐separated hybrid functional approach

A methodology combining the polarizable continuum model and optimally‐tuned range‐separated (RS) hybrid functional was proposed for the quantitative characterization of the excited‐state properties in oligoacene (from anthracene to hexacene) crystals. We show that it provides lowest vertical singlet and triplet excitation energies, singlet‐triplet gap, and exciton binding energies in very good agreement with the available experimental data. We further find that it significantly outperforms its non‐tuned RS counterpart and the widely used B3LYP functional, and even many‐body perturbation theory within the GW approximation (based on a PBE starting point). Hence, this approach provides an easily applicable and computationally efficient tool to study the excited‐state properties of organic solids of complexity. © 2017 Wiley Periodicals, Inc.     

Description of core excitations by time-dependent density functional theory with local density approximation, generalized gradient approximation, meta-generalized gradient approximation, and hybrid functionals

Time-dependent density functional theory (TDDFT) is employed to investigate exchange-correlation-functional dependence of the vertical core-excitation energies of several molecules including H, C, N, O, and F atoms. For the local density approximation (LDA), generalized gradient approximation (GGA), and meta-GGA, the calculated X1s-->pi* excitation energies (X = C, N, O, and F) are severely underestimated by more than 13 eV. On the other hand, time-dependent Hartree-Fock (TDHF) overestimates the excitation energies by more than 6 eV. The hybrid functionals perform better than pure TDDFT because HF exchange remedies the underestimation of pure TDDFT. Among these hybrid functionals, the Becke-Half-and-Half-Lee-Yang-Parr (BHHLYP) functional including 50% HF exchange provides the smallest error for core excitations. We have also discovered the systematic trend that the deviations of TDHF and TDDFT with the LDA, GGA, and meta-GGA functionals show a strong atom-dependence. Namely, their deviations become larger for heavier atoms, while the hybrid functionals are significantly less atom-dependent.     

Excited state geometry optimizations by analytical energy gradient of long-range corrected time-dependent density functional theory

An analytical excitation energy gradient of long-range corrected time-dependent density functional theory (LC-TDDFT) is presented. This is based on a previous analytical TDDFT gradient formalism, which avoids solving the coupled-perturbed Kohn-Sham equation for each nuclear degree of freedom. In LC-TDDFT, exchange interactions are evaluated by combining the short-range part of a DFT exchange functional with the long-range part of the Hartree-Fock exchange integral. This LC-TDDFT gradient was first examined by calculating the excited state geometries and adiabatic excitation energies of small typical molecules and a small protonated Schiff base. As a result, we found that long-range interactions play a significant role even in valence excited states of small systems. This analytical LC-TDDFT gradient was also applied to the investigations of small twisted intramolecular charge transfer (TICT) systems. By comparing with calculated ab initio multireference perturbation theory and experimental results, we found that LC-TDDFT gave much more accurate absorption and fluorescence energies of these systems than those of conventional TDDFTs using pure and hybrid functionals. For optimized excited state geometries, LC-TDDFT provided fairly different twisting and wagging angles of these small TICT systems in comparison with conventional TDDFT results.     

Long‐range corrected functionals satisfy Koopmans' theorem: Calculation of correlation and relaxation energies

In this article, we show that the long‐range‐corrected (LC) density functionals LC‐BOP and LCgau‐BOP reproduce frontier orbital energies and highest‐occupied molecular orbital (HOMO)—lowest‐unoccupied molecular orbital (LUMO) gaps better than other density functionals. The negative of HOMO and LUMO energies are compared with the vertical ionization potentials (IPs) and electron affinities, respectively, using CCSD(T)/6‐311++G(3df,3pd) for 113 molecules, and we found LC functionals to satisfy Koopmans' theorem. We also report that the frontier orbital energies and the HOMO‐LUMO gaps of LC‐BOP and LCgau‐BOP are better than those of recently proposed ωM05‐D (Lin et al., J. Chem. Phys. 2012, 136 , 154109). We express the exact IP in terms of orbital relaxation, and correlation energies and hence calculate the relaxation and correlation energies for the same set of molecules. It is found that the LC functionals, in general, includes more relaxation effect than Hartree–Fock and more correlation effect than the other density functionals without LC scheme. Finally, we scan μ parameter in LC scheme from 0.1 to 0.6 bohr^?1 for the above test set molecules with LC‐BOP functional and found our parameter value, 0.47 bohr^?1, is usefully applicable to our tested systems. © 2013 Wiley Periodicals, Inc.