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.     

Functional dependence of core-excitation energies

We examine in depth the functional dependence of computed core-electron binding and excitation energies based on a total-energy difference approach within Kohn-Sham density functional theory. Twenty-seven functional combinations were studied using a database of reliable experimental data on 18 molecules. The computed core-electron binding energies are largely dependent on the choice of exchange functional. The term value of the first resonant excited state and energy differences between the lowest core-excited states are, however, quite insensitive to the choice of functionals since the errors due to the core-region cancel out. Using these results we define a different exchange functional, which mixes two functionals designed by Perdew and Wang (PD86 and PD91), with the best results for both excitation and binding energies obtained for a mixing ratio 60:40 between these. We also reexamine the relativistic corrections for inner-shell excitations.     

Optical absorption and luminescence energies of F centers in CaO from ab initio embedded cluster calculations

We calculated the optical absorption and luminescence energies of electrons trapped at oxygen vacancies in CaO using a consistent embedded cluster method which accounts for the long-range polarization effects and partial covalence of CaO. Optical absorption and luminescence energies of neutral (F center) and positively charged (F+ center) vacancies are calculated by means of time dependent density functional theory using the B3LYP exchange-correlation density functional. Our results demonstrate that using large basis sets to describe a diffuse nature of excited states, and properly accounting for long-range polarization induced by charged and excited defect states, is crucial for accurate predictions of optical excitation and luminescence energies of these defects.     

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.     

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     

Electronic excitations of glycine, alanine, and cysteine conformers from first-principles calculations

The electronic and optical properties are studied for three conformers of amino acid molecules using gradient-corrected (spin-) density functional theory within a projector-augmented wave scheme and the supercell method. We investigate single-particle excitations such as ionization energies and electron affinities as well as pair excitations. By comparing eigenvalues resulting from several local and nonlocal energy functionals, the influence of treatment of exchange and correlation is demonstrated. The excitations are described within the Delta-self-consistent field method with an occupation number constraint to obtain excitation energies and Stokes shifts. The results are used to also discuss the optical absorption properties. In contrast to the lowest single- and two-particle excitation energies, remarkable changes are found in absorption spectra in dependence on the conformation of the molecule geometry.     

Bonding nature and electron delocalization of An(COT)2, An = Th, Pa, U

A systematic study of a series of An(COT)(2) compounds, where An = Th, Pa, U, and COT represents cyclooctatetraene, has been performed using relativistic density functional theory. The ZORA Hamiltonian was applied for the inclusion of relativistic effects, taking into account all of the electrons for the optimization and explicitly including spin-orbit coupling effects. Time-dependent density functional theory (TDDFT) was used to calculate the excitation energies with the GGA SAOP functional, and the electronic transitions were analyzed using double group irreducible representations. The calculated excitation energies are in perfect correlation with the increment of the ring delocalization as it increases along the actinide series. These results are sufficient to ensure that, for these complexes, the increment in delocalization, as indicated by ELF bifurcation and NICS analysis, leads to a shift in the maximum wavelength of absorption in the visible region. Also, delocalization in the COT ring increases along the actinide series, so the systems become more aromatic because of a modulation induced by the actinides.     

Excited-State Electronic Structure with Configuration Interaction Singles and Tamm-Dancoff Time-Dependent Density Functional Theory on Graphical Processing Units

Excited-state calculations are implemented in a development version of the GPU-based TeraChem software package using the configuration interaction singles (CIS) and adiabatic linear response Tamm-Dancoff time-dependent density functional theory (TDA-TDDFT) methods. The speedup of the CIS and TDDFT methods using GPU-based electron repulsion integrals and density functional quadrature integration allows full ab initio excited-state calculations on molecules of unprecedented size. CIS/6-31G and TD-BLYP/6-31G benchmark timings are presented for a range of systems, including four generations of oligothiophene dendrimers, photoactive yellow protein (PYP), and the PYP chromophore solvated with 900 quantum mechanical water molecules. The effects of double and single precision integration are discussed, and mixed precision GPU integration is shown to give extremely good numerical accuracy for both CIS and TDDFT excitation energies (excitation energies within 0.0005 eV of extended double precision CPU results).     

On low‐lying excited states of extended nanographenes

Low‐lying excited states of planarly extended nanographenes are investigated using the long‐range corrected (LC) density functional theory (DFT) and the spin‐flip (SF) time‐dependent density functional theory (TDDFT) by exploring the long‐range exchange and double‐excitation correlation effects on the excitation energies, band gaps, and exciton binding energies. Optimizing the geometries of the nanographenes indicates that the long‐range exchange interaction significantly improves the C C bond lengths and amplify their bond length alternations with overall shortening the bond lengths. The calculated TDDFT excitation energies show that long‐range exchange interaction is crucial to provide accurate excitation energies of small nanographenes and dominate the exciton binding energies in the excited states of nanographenes. It is, however, also found that the present long‐range correction may cause the overestimation of the excitation energy for the infinitely wide graphene due to the discrepancy between the calculated band gaps and vertical ionization potential (IP) minus electron affinity (EA) values. Contrasting to the long‐range exchange effects, the SF‐TDDFT calculations show that the double‐excitation correlation effects are negligible in the low‐lying excitations of nanographenes, although this effect is large in the lowest excitation of benzene molecule. It is, therefore, concluded that long‐range exchange interactions should be incorporated in TDDFT calculations to quantitatively investigate the excited states of graphenes, although TDDFT using a present LC functional may provide a considerable excitation energy for the infinitely wide graphene mainly due to the discrepancy between the calculated band gaps and IP–EA values. © 2017 Wiley Periodicals, Inc.     

线性簇合物SC2nS2－(n =1～12)电子吸收光谱

应用密度泛函理论,在B3LYP/6-31G*水平上优化了线性簇合物SC2nS2－(n =1～12)的基态平衡几何结构,并计算了它们的谐振动频率.在基态平衡构型下,通过TD-B3LYP/cc-pvTZ和TD-B3LYP/cc-pvDZ计算,确定了簇合物SC2nS2－(n =1～10) 电子跃迁的垂直激发能和对应的振子强度.基于计算结果,导出了电子跃迁吸收波长与体系大小n的解析关系式,以及SC2nS2－体系第一电离能与体系大小n的解析表达式,并讨论了不同端位原子对碳链体系激发态性质的影响.     

Quantum chemical studies of three-photon absorption of some stilbenoid chromophores

Three-photon absorption of a series of donor-acceptor trans-stilbene derivatives is studied by means of density functional theory applied to the third-order response function and its residues. The results obtained by using different functionals are compared with experimental data for similar systems obtained from the literature. With a Coulomb attenuated, asymptotically corrected functional, the excitation energy to the first resonance state is much improved. Comparison with experiment indicates that this is the case for the three-photon cross section as well. In particular, the overestimation of the cross sections and underestimation of excitation energies offered by the density functional theory using common density functionals is corrected for. It is argued that a reliable theory for three-photon absorption in charge transfer and other chromophore systems thereby has been obtained. Further elaboration of the theory and its experimental comparison call for explicit inclusion of solvent polarization and pulse propagation effects.     

Calculation of near-edge X-ray absorption fine structure with the CIS(D) method

We report an investigation into the calculation of near-edge X-ray absorption fine structure with the CIS(D) method. Core excitation energies computed with time-dependent density functional theory using standard exchange-correlation functionals are systematically underestimated. CIS(D) predicts core excitation energies that are closer to experiment. However, excitation energies for Rydberg states are too low with respect to valence states, and for some systems spectra that are qualitatively incorrect are obtained. A scaled opposite spin only approach is proposed that reduces the error in the computed core excitation energies, and results in spectra that are in good agreement with experiment.     

Bonding and excitation in COCu(001) from a cluster model and density functional treatments

The bonding properties and charge distributions of the COCu(001) system have been studied within density functional theory (DFT) with several density functionals. A Cu18(9,4,5)CO three layer cluster was found to give bond distances and energies in agreement with previous experimental and theoretical results for low coverage systems, provided the atomic basis set includes diffuse orbitals and d-orbitals at the Cu atoms. Charge distributions give insight on the nature of the localized adsorbate bonding. Time-dependent DFT results on excitation energies and on transition and average electric dipoles, relevant to photodesorption, are also presented.     

Influence of geometry relaxation on the energies of the S1 and S2 states of violaxanthin, zeaxanthin, and lutein

Precise knowledge of the excitation energies of the lowest excited states S(1) and S(2) of the carotenoids violaxanthin, lutein, and zeaxanthin is a prerequisite for a fundamental understanding of their role in light harvesting and photoprotection during photosynthesis. By means of density functional theory (DFT) and time-dependent DFT (TDDFT), the electronic and structural properties of the ground and first and second excited states are studied in detail. According to our calculations, all-s-cis-zeaxanthin and s-cis-lutein conformers possess lower total ground-state energies than the corresponding s-trans conformers. Thus, only s-cis isomers are probably physiologically relevant. Furthermore, the influence of geometric relaxation on the energies of the ground state and S(1) and S(2) states has been studied in detail. It is demonstrated that the energies of these states change significantly if the carotenoid adopts the equilibrium geometry of the S(1) state. Considering these energetic effects in the interpretation of S(1) excitation energies obtained from fluorescence and transient absorption spectroscopy shifts the S(1) excitation energies about 0.2 eV to higher energy above the excitation energy of the chlorophyll a.     

Average excitation energies from time-dependent density functional response theory

The authors present an occupation number averaging scheme for time-dependent density functional response theory (TD-DFRT) in frequency domain. The known problem that TD-DFRT within the local (spin) density approximation (LDA/LSDA) inaccurately predicts Rydberg and charge-transfer excitation energies has been reexamined from the methodology of linear response, without explicit correction of the exchange-correlation potential. The working equations of TD-DFRT are adapted to treat arbitrary difference of orbital occupation numbers, using the nonsymmetric matrix form of Casida's formulation of TD-DFRT [M. E. Casida, in Recent Advances in Density Functional Methods, edited by D. P. Chong (World Scientific, Singapore, 1995), Pt. I, p. 155]. The authors' scheme is applied to typical closed-shell and open-shell molecular systems by examining the dependence of excitation energies on the fraction of excited electron. Good performance of this modified linear response scheme is shown, and is consistent with the authors' previous examination by the real-time propagation approach, suggesting that the calculation of average excitation energies might be one of the ways to better decode excitation energies from LDA/LSDA. Different techniques for treating singlet, triplet, and doublet states are discussed.     

Ab initio calculation of the vibrational and electronic spectra of trans- and cis-azobenzene

We report accurate geometries and harmonic force fields for trans- and cis-azobenzene determined by second-order M?ller-Plesset perturbation theory. For the trans isomer, the planar structure with C(2h) symmetry, found in a recent gas electron diffraction experiment, is verified. The calculated vibrational spectra are compared with experimental data and density functional calculations. Important vibrational frequencies are localized and discussed. For both isomers, we report UV spectra calculated using the second-order approximate coupled-cluster singles-and-doubles model CC2 with accurate basis sets. Vertical excitation energies and oscillator strengths have been determined for the lowest singlet n(pi)* and (pi)(pi)* transitions. The results are compared with the available experimental data and second-order polarization propagator (SOPPA) and density functional (DFT) calculations. For both isomers, the CC2 results for the excitation energies into the S(1) and S(2) states agree within 0.1 eV with experimental gas-phase measurements.     

Tuning of electronic structures of poly(p-phenylenevinylene) analogues of phenyl, thienyl, furyl, and pyrrolyl by double-bond linkages of group 14 and 15 elements

We investigated electronic structures of four sets of monomers and polymers comprising of phenyl rings and five-membered hetero(aromatic) moieties connected with double-bond -X=X- linkages (X = CH, SiH, GeH, N, P, As) by density functional theory, time-dependent density functional theory, and periodic boundary condition calculations with B3LYP functional. Electronic structures of poly(p-phenylenevinylene) (PPV) analogues are primarily dominated by central double-bond moieties. The introduction of ethylene homologues with group 14 and 15 elements was demonstrated to be a promising approach to modify electronic structures of conjugated oligomers and polymers. Excitation energies of monomers with double-bond linkages were reduced by around 13-50% with respect to corresponding dimers of phenyl, thienyl, furyl, and pyrrolyl rings. Similarly, band gaps of poly(p-phenylene) and polythiophene were decreased by 0.3-0.9 eV upon the insertion of double-bond linkages. Furthermore, excitation energies of monomers presented decreasing trends when descending through groups 14 and 15. For group 14 ethylene homologues, the decreasing trend in the lowest excitation energies was rationalized by a progressively favoring of pi-sigma* interactions as descending X = CH, SiH, and GeH. Increasing p contents of central bonds along X = N, P, and As accounted for geometry features and the lowest excitation energies of group 15 species. A decrease in the extent of electronic communications between aromatic rings and -X=X- linkages within higher congeners was also revealed.     

Ab initio calculation of the electronic absorption of functionalized octahedral silsesquioxanes via time-dependent density functional theory with range-separated hybrid functionals

Recent advances in the ability to functionalize octahedral silsesquioxanes with different photoactive ligands, and thereby tune their optical properties, suggest that these molecules may serve as potential building blocks of light-harvesting, photovoltaic, and photonic devices. In this paper we report extensive ab initio calculations of the excitation energies underlying the absorption spectra of these systems. The calculations are based on density functional theory for the ground electronic state and time-dependent density functional theory for the excited electronic states. The ability of the commonly used B3LYP functional to reproduce the experimentally observed absorption excitation energies is compared to that of recently developed range-separated hybrid functionals. The importance of pairing the range-separated hybrid functionals with basis sets that include diffuse and polarization basis functions is demonstrated in the case of vinyl-functionalized silsesquioxanes. Absorptive excitation energies are then calculated and compared with experiment for octahedral silsesquioxanes functionalized with larger ligands. The tunability of optical properties is demonstrated by considering the effect on the excitation energies of functionalizing the ligands with electron-donating or -withdrawing groups.