Excitations, optical absorption spectra, and optical excitonic gaps of heterofullerenes. I. C60, C59N+, and C48N12: theory and experiment

Low-energy excitations and optical absorption spectrum of C(60) are computed by using time-dependent (TD) Hartree-Fock, TD-density functional theory (TD-DFT), TD DFT-based tight-binding (TD-DFT-TB), and a semiempirical Zerner intermediate neglect of diatomic differential overlap method. A detailed comparison of experiment and theory for the excitation energies, optical gap, and absorption spectrum of C(60) is presented. It is found that electron correlations and correlation of excitations play important roles in accurately assigning the spectral features of C(60), and that the TD-DFT method with nonhybrid functionals or a local spin density approximation leads to more accurate excitation energies than with hybrid functionals. The level of agreement between theory and experiment for C(60) justifies similar calculations of the excitations and optical absorption spectrum of a monomeric azafullerene cation C(59)N(+), to serve as a spectroscopy reference for the characterization of carborane anion salts. Although it is an isoelectronic analogue to C(60), C(59)N(+) exhibits distinguishing spectral features different from C(60): (1) the first singlet is dipole-allowed and the optical gap is redshifted by 1.44 eV; (2) several weaker absorption maxima occur in the visible region; (3) the transient triplet-triplet absorption at 1.60 eV (775 nm) is much broader and the decay of the triplet state is much faster. The calculated spectra of C(59)N(+) characterize and explain well the measured ultraviolet-visible (UV-vis) and transient absorption spectra of the carborane anion salt [C(59)N][Ag(CB(11)H(6)Cl(6))(2)] [Kim et al., J. Am. Chem. Soc. 125, 4024 (2003)]. For the most stable isomer of C(48)N(12), we predict that the first singlet is dipole-allowed, the optical gap is redshifted by 1.22 eV relative to that of C(60), and optical absorption maxima occur at 585, 528, 443, 363, 340, 314, and 303 nm. We point out that the characterization of the UV-vis and transient absorption spectra of C(48)N(12) isomers is helpful in distinguishing the isomer structures required for applications in molecular electronics. For C(59)N(+) and C(48)N(12) as well as C(60), TD-DFT-TB yields reasonable agreement with TD-DFT calculations at a highly reduced cost. Our study suggests that C(60), C(59)N(+), and C(48)N(12), which differ in their optical gaps, have potential applications in polymer science, biology, and medicine as single-molecule fluorescent probes, in photovoltaics as the n-type emitter and/or p-type base of a p-n junction solar cell, and in nanoelectronics as fluorescence-based sensors and switches.     

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.     

Spectroscopic Characteristics of Hyperbranched Conjugated Polymers Studied by One- and Two-Photon Excitations

Spectroscopic properties of new hyperbranched conjugated polymers functionalized in periphery with N,N-dimethylaniline and tert-butyl-benzene as terminal groups are investigated by one- and two-photon excitations. The absorption, °uorescence excitation and emission spectra are examined in chloroform and N,N-dimethylformamide. The two-photon excitation measurements show that the new hyperbranched conjugated polymer possesses large two-photon excitation cross section which makes it a very attractive candidate for the potential application as nonlinear optical materials. As an example, the two-photon induced three-dimensional data storage is also demonstrated.     

Electronic Structure and Optical Properties of the Surface F-Centers in MgO: A Theoretical Analysis by DFT Approach

Electronic structure of Mg9O9 and Mg9O8 clusters modeling nano-crystalline powders of magnesium oxide has been analyzed within the frames of the density functional theory (DFT). In the framework of time-dependent DFT method (TD-DFT), the relationship between the surface and bulk properties of nano-crystals is analyzed based on variations in the density of electronic states (DOS) and changes of electronic spectra. The spectroscopy of spatial defects like low-coordinated oxygen ions and of surface point defects like F⁺- and F-centers is investigated. Optical properties of the nano-sized crystalline magnesium oxide are characterized by a spectrum of absorption bands in the range of 1-5 eV. Point defects such as F-centers absorb light in the range of 1.2-1.5 eV. Spatial defects O_LC in nano-crystals generate absorption bands in the range of 2.5-5.0 eV. According to calculations, there is no direct relation between coordination numbers of surface ions and excitation energies. Theoretical excitation energies are compared with experimental optical properties of the F⁺- and F-centers.     

Copper doping of small gold cluster cations: influence on geometric and electronic structure

The effect of Cu doping on the properties of small gold cluster cations is investigated in a joint experimental and theoretical study. Temperature-dependent Ar tagging of the clusters serves as a structural probe and indicates no significant alteration of the geometry of Au(n) (+) (n = 1-16) upon Cu doping. Experimental cluster-argon bond dissociation energies are derived as a function of cluster size from equilibrium mass spectra and are in the 0.10-0.25 eV range. Near-UV and visible light photodissociation spectroscopy is employed in conjunction with time-dependent density functional theory calculations to study the electronic absorption spectra of Au(4-m)Cu(m) (+) (m = 0, 1, 2) and their Ar complexes in the 2.00-3.30 eV range and to assign their fragmentation pathways. The tetramers Au(4) (+), Au(4) (+)[middle dot]Ar, Au(3)Cu(+), and Au(3)Cu(+)[middle dot]Ar exhibit distinct optical absorption features revealing a pronounced shift of electronic excitations to larger photon energies upon substitution of Au by Cu atoms. The calculated electronic excitation spectra and an analysis of the character of the optical transitions provide detailed insight into the composition-dependent evolution of the electronic structure of the clusters.     

Effects of donor/acceptor strengths on the multiphoton absorption: an EOM-CCSD correction vector study

We have developed a correction method (CV) to calculate the single- and multiphoton absorption (MPA) spectra of organic pi-conjugated systems within the equation of motion coupled-cluster method with single and double excitations (EOM-CCSD). The effects of donor/acceptor strengths on the multiphoton absorption in a series of symmetrically substituted stilbene derivatives have been reinvestigated at both the ab initio and the semiempirical intermediate neglect of differential overlap (INDO) Hamiltonian levels. Both ab initio and INDO calculations show that the electron-donating or electron-withdrawing substituents lead to enhancements of two- and three-photon absorption cross sections, more pronounced for two-photon absorption than for three-photon absorption. The ab initio calculations usually produce larger excitation energies than the semiempirical, which lead to lower MPA cross sections.     

Theoretical study of the electronic spectroscopy of CO adsorbed on Pt(111)

The excited states of CO adsorbed on the Pt(111) surface are studied using a time-dependent density functional theory formalism. To reduce the computational cost, electronic excitations are computed within a reduced single excitation space. Using cluster models of the surface, excitation energies are computed for CO in the on-top, threefold, and bridge binding sites. On adsorption, there is a lowering of the 5sigma orbital energy. This leads to a large blueshift in the 5sigma- -> pi(CO*) excitation energy for all adsorption sites. The 1pi and 4sigma orbital energies are lowered to a lesser extent, and smaller shifts in the corresponding excitation energies are predicted. For the larger clusters, pi* excitations at lower energies are observed. These transitions correspond to excitations to virtual orbitals of pi* character which lie below the pi* orbitals of gas phase CO. These orbitals are associated predominantly with the metal atoms of the cluster. The excitation energies are also found to be sensitive to changes in the adsorption geometry. The electronic spectrum of CO on Pt(111) is simulated and the assignment of the bands observed in experimental electron energy loss spectroscopy discussed.     

Extended Hückel tight-binding approach to electronic excitations

In this work, we propose the application of a self-consistent extended Huckel tight-binding (EHTB) method in the computation of the absorption optical spectrum of molecules within the linear response time dependent density functional formalism. The EHTB approach is presented as an approximation to the Kohn-Sham energy functional. The method is applied to the computation of excitation energies and oscillator strengths of benzene, pyridine, naphthalene, diazines, and the fullerenes: C(60)(I(h)), C(70)(D(5h)), and C(80)(D(2)). The very good agreement with experimental data is very encouraging and suggests the possibility of using the EHTB as a computational efficient and reliable tool to study optical properties of a wide variety of molecular systems.     

Crystal structure, electronic structure, and optical and photoluminescence properties of Eu(III) ion-doped Lu6Mo(W)O12

Lu(6)WO(12) and Lu(6)MoO(12) doped with Eu(3+) ions have been prepared by using a citrate complexation route, followed by calcination at different temperatures. The morphology, structure, and optical and photoluminescence properties of the compounds were studied as a function of calcination temperature. Both compositions undergo transitions from a cubic to a hexagonal phase when the calcination temperature increases. All the compositions have strong absorption of near-UV light and show intense red luminescence under a near-UV excitation, which is related to the transfer of energy from the host lattices to dopant Eu(3+) ions. Density functional theory calculations have also been performed. The calculation reveals that hexagonal Lu(6)WO(12) and Lu(6)MoO(12) are indirect bandgap materials, and the near-UV excitations are due to the electronic transitions from the O-2p orbitals to W-5d and Mo-4d orbitals, respectively. The lattice parameters and bandgap energies of hexagonal Lu(6)WO(12) and Lu(6)MoO(12) were determined.     

Investigation of the electronic spectra and excited-state geometries of poly(para-phenylene vinylene) (PPV) and poly(para-phenylene) (PP) by the symmetry-adapted cluster configuration interaction (SAC-CI) method

The symmetry-adapted cluster-configuration interaction (SAC-CI) method has been used to investigate the optical and geometric properties of the oligomers of poly(para-phenylene vinylene) (PPV) and poly(para-phenylene) (PP). Vertical singlet and triplet absorption spectra and emission spectra have been calculated accurately; the mean average deviation from available experimental results lies within 0.2 eV. The chain length dependence of the transition energies has been improved in comparison to earlier TDDFT and MRSDCI calculations. The present analysis suggests that conventional TDDFT with the B3LYP functional should be used carefully, as it can provide inaccurate estimates of the chain length dependence of the excitation energies of these molecules with long pi conjugation. The T1 state was predicted to be at a lower energy, by 1.0-1.5 eV for PPV and by 0.9-1.7 eV for PP, than the S1 state, which indicates a localized T1 state with large exchange energy. By calculating the SAC-CI electron density difference between the ground and excited states, the geometry relaxations due to excitations can be analyzed in detail using electrostatic force theory. For trans-stilbene, the doubly excited 21Ag state was studied, and the calculated transition energy of 4.99 eV agrees very well with the experimental value of 4.84 eV. In contrast to previous ab initio calculations, we predict this doubly excited 21Ag state to lie above the 11Bu state.     

Quantum chemical modeling of electrochromism of tungsten oxide films

A cluster model is proposed to describe the excitations in solid tungsten oxide. The density-functional theory approach is used to calculate the ground-state electronic structure of the model cluster and its optimum geometry; subsequently, time-dependent density-functional theory calculations are performed to obtain the oscillator strengths and energies of the excited states. The results are reported both for the electrically neutral cluster and for the cluster with an extra electron (mimicking the effect of electron injection from the cathode). They correctly locate the electrochemically active transition. The corresponding wave functions are delocalized, suggesting that electron localization at one tungsten center is rather unlikely, thereby shedding doubt as to the validity of the polaron model. Local lattice distortions presumably created at the stage of sample preparation are found to affect the excitation energies to a considerable extent, which explains the experimentally observable large width of optical absorption responsible for electrochromism.     

Impact of the computational method on the geometric and electronic properties of oligo(phenylene vinylene) radical cations

We report on a quantum-chemical study of the electronic and optical properties of unsubstituted oligo(phenylene vinylene) (OPV) radical cations. Our goal is to distinguish the impact of the choice of molecular geometry from the impact of the choice of quantum-chemical method, on the calculated optical transition energies. The geometry modifications upon ionization of the OPV chains are found to depend critically on the theoretical formalism: Hartree-Fock (HF) geometry optimizations lead to self-localization of the charged defects while pure density functional theory (DFT) results in a complete delocalization of the geometric modifications over the whole conjugated backbone. The electronic structure and vertical transition energy associated with the lowest excited state of the radical cations have been calculated at the post-Hartree-Fock level within a configuration interaction (HF-CI) scheme and using the time-dependent DFT (TD-DFT) formalism for different radical cation geometries. Interestingly, the changes in the calculated optical properties obtained when using different geometric structures are less important within a given method than the differences between methods for a given structure. The optical excitation is localized with HF-CI and delocalized with TD-DFT, almost irrespective of the molecular geometry; as a result, HF-CI excitation energies tend to saturate as the chain length increases, in contrast to the results from TD-DFT.     

Electronic excitation energies of Zn(i)O(i) clusters

Time-dependent density-functional theory (TDDFT) is used to study the excitation energies of the global minima of small Zn(i)O(i) clusters, i = 1-15. The relativistic compact effective core potentials and shared-exponent basis set of Stevens, Krauss, Basch, and Jasien (SKBJ), systematically enlarged with extra functions, were used throughout this work. In general, the calculated excitations occur from the nonbonding p orbitals of oxygen. These orbitals are perpendicular to the molecular plane in the case of the rings and normal to the spheroid surface for 3D clusters. The calculated excitation energies are larger for ringlike clusters as compared to 3D clusters, with the excitation energies of the latter structures lying close to the visible spectrum. The difference between Kohn-Sham eigenvalues of the orbitals involved in the electronic excitations studied have also been compared to the TDDFT results of the corresponding excitations for two approximate density functionals, that is, MPW1PW91 and B3LYP, the latter being more accurate. Moreover, they approach the TDDFT value as the cluster size increases. Therefore, this might be a practical method for estimating excitation energies of large Zn(i)O(i) clusters.     

The merits of the frozen-density embedding scheme to model solvatochromic shifts

We investigate the usefulness of a frozen-density embedding scheme within density-functional theory [J. Phys. Chem. 97, 8050 (1993)] for the calculation of solvatochromic shifts. The frozen-density calculations, particularly of excitation energies have two clear advantages over the standard supermolecule calculations: (i) calculations for much larger systems are feasible, since the time-consuming time-dependent density functional theory (TDDFT) part is carried out in a limited molecular orbital space, while the effect of the surroundings is still included at a quantum mechanical level. This allows a large number of solvent molecules to be included and thus affords both specific and nonspecific solvent effects to be modeled. (ii) Only excitations of the system of interest, i.e., the selected embedded system, are calculated. This allows an easy analysis and interpretation of the results. In TDDFT calculations, it avoids unphysical results introduced by spurious mixings with the artificially too low charge-transfer excitations which are an artifact of the adiabatic local-density approximation or generalized gradient approximation exchange-correlation kernels currently used. The performance of the frozen-density embedding method is tested for the well-studied solvatochromic properties of the n-->pi(*) excitation of acetone. Further enhancement of the efficiency is studied by constructing approximate solvent densities, e.g., from a superposition of densities of individual solvent molecules. This is demonstrated for systems with up to 802 atoms. To obtain a realistic modeling of the absorption spectra of solvated molecules, including the effect of the solvent motions, we combine the embedding scheme with classical molecular dynamics (MD) and Car-Parrinello MD simulations to obtain snapshots of the solute and its solvent environment, for which then excitation energies are calculated. The frozen-density embedding yields estimated solvent shifts in the range of 0.20-0.26 eV, in good agreement with experimental values of between 0.19 and 0.21 eV.     

Singly and doubly excited states of butadiene, acrolein, and glyoxal: Geometries and electronic spectra

Excited-state geometries and electronic spectra of butadiene, acrolein, and glyoxal have been investigated by the symmetry adapted cluster configuration interaction (SAC-CI) method in their s-trans conformation. Valence and Rydberg states below the ionization threshold have been precisely calculated with sufficiently flexible basis sets. Vertical and adiabatic excitation energies were well reproduced and the detailed assignments were given taking account of the second moments. The deviations of the vertical excitation energies from the experiment were less than 0.3 eV for all cases. The SAC-CI geometry optimization has been applied to some valence and Rydberg excited states of these molecules in the planar structure. The optimized ground- and excited-state geometries agree well with the available experimental values; deviations lie within 0.03 A and 0.7 degrees for the bond lengths and angles, respectively. The force acting on the nuclei caused by the excitations has been discussed in detail by calculating the SAC-CI electron density difference between the ground and excited states; the geometry relaxation was well interpreted with the electrostatic force theory. In Rydberg excitations, geometry changes were also noticed. Doubly excited states (so-called 2 (1)A(g) states) were investigated by the SAC-CI general-R method considering up to quadruple excitations. The characteristic geometrical changes and large energetic relaxations were predicted for these states.     

First-principles calculation of electronic spectra of light-harvesting complex II

We report on a fully quantum chemical investigation of important structural and environmental effects on the site energies of chlorophyll pigments in green-plant light-harvesting complex II (LHC II). Among the tested factors are technical and structural aspects as well as effects of neighboring residues and exciton couplings in the chlorophyll network. By employing a subsystem time-dependent density functional theory (TDDFT) approach based on the frozen density embedding (FDE) method we are able to determine site energies and electronic couplings separately in a systematic way. This approach allows us to treat much larger systems in a quantum chemical way than would be feasible with a conventional density functional theory. Based on this method, we have simulated a series of mutagenesis experiments to investigate the effect of a lack of one pigment in the chlorophyll network on the excitation properties of the other pigments. From these calculations, we can conclude that conformational changes within the chlorophyll molecules, direct interactions with neighboring residues, and interactions with other chlorophyll pigments can lead to non-negligible changes in excitation energies. All of these factors are important when site energies shall be calculated with high accuracy. Moreover, the redistribution of the oscillator strengths due to exciton coupling has a large impact on the calculated absorption spectra. This indicates that modeling mutagenesis experiments requires us to consider the entire set of chlorophyll molecules in the wild type and in the mutant, rather than just considering the missing chlorophyll pigment. An analysis of the mixing of particular excitations and the coupling elements in the FDEc calculation indicates that some pigments in the chlorophyll network act as bridges which mediate the interaction between other pigments. These bridges are also supported by the calculations on the "mutants" lacking the bridging pigment.     

Excitation spectra of dibenzoborole containing pi-electron systems: controlling the electronic spectra by changing the p(pi)-pi* conjugation

We report time-dependent density functional theory calculations of the vertical excitation energies for the singlet states of three-coordinate 5H-dibenzoborole (DBB) derivatives and four-coordinate 5-fluoro-5H-dibenzoborole ion (FDBB) derivatives. These molecules show remarkable hypsochromic (blue) shifts in their fluorescence spectra and bathochromic (red) shifts in their absorption spectra when the bridging boron atoms change their coordination number from three to four. We constructed a series of derivatives of DBB and FDBB and studied how the energies of the electronic excitations change. The states with prominent oscillator strength in all of the DBB and FDBB derivatives show similar shifts of their excitation energies upon coordination. The three-coordinate DBB derivative 5-(2,4,6-triisopropylphenyl)-2,8-dimethoxy-3,7-bis[p-(N,N-diphenylamino)phenyl]-5H-dibenzo[d,b]borole has an intense absorption at 3.25 eV, which shifts in the four-coordinate FDBB derivative 5-fluro-5-(2,4,6-triisopropylphenyl)-2,8-dimethoxy-3,7-bis[p-(N,N-dip henylamino)phenyl]-5H-dibenzo[d,b]borole ion to 3.17 eV. The experimental absorption peaks are 3.43 and 3.31 eV, respectively. In addition, we investigated and analyzed the nature of these electronic excitations using attachment/detachment density plots, with which we characterized the changes in electron density that arose from the excitations.     

Performance of the M11 and M11-L density functionals for calculations of electronic excitation energies by adiabatic time-dependent density functional theory

Adiabatic time-dependent density functional theory is a powerful method for calculating electronic excitation energies of complex systems, but the quality of the results depends on the choice of approximate density functional. In this article we test two promising new density functionals, M11 and M11-L, against databases of 214 diverse electronic excitation energies, and we compare the results to those for 16 other density functionals of various kinds and to time-dependent Hartree-Fock. Charge transfer excitations are well known to be the hardest challenge for TDDFT. M11 is a long-range-corrected hybrid meta-GGA, and it shows better performance for charge transfer excitations than any of the other functionals except M06-HF, which is a specialized functional that does not do well for valence excitations. Several other long-range-corrected hybrid functionals also do well, and we especially recommend M11, ωB97X, and M06-2X for general spectroscopic applications because they do exceptionally well on ground-state properties as well as excitation energies. Local functionals are preferred for many applications to extended systems because of their significant cost advantage for large systems. M11-L is a dual-range local functional and-unlike all previous local functionals-it has good performance for Rydberg states as well as for valence states. Thus it is highly recommended for excitation energy calculations on extended systems.