Charge-transfer excitations in uranyl tetrachloride ([UO2Cl4]2-): how reliable are electronic spectra from relativistic time-dependent density functional theory?

Four-component relativistic time-dependent density functional theory (TD-DFT) is used to study charge-transfer (CT) excitation energies of the uranyl molecule as well as the uranyl tetrachloride complex. Adiabatic excitation energies and vibrational frequencies of the excited states are calculated for the lower energy range of the spectrum. The results for TD-DFT with the CAM-B3LYP exchange-correlation functional for the [UO(2)Cl(4)](2-) system are in good agreement with the experimentally observed spectrum of this species and agree also rather well with other theoretical data. Use of the global hybrid B3LYP gives qualitatively correct results, while use of the BLYP functional yields results that are qualitatively wrong due to the too low CT states calculated with this functional. The applicability of the overlap diagnostic of Peach et al. (J. Chem. Phys.2008, 128, 044118) to identify such CT excitations is investigated for a wide range of vertical transitions using results obtained with three different approximate exchange-correlation functionals: BLYP, B3LYP, and CAM-B3LYP.     

Can TD‐DFT calculations accurately describe the excited states behavior of stacked nucleobases? The cytosine dimer as a test case

By using calculations rooted in the time dependent density functional theory (TD-DFT) we have investigated how the lowest energy excited states of a face-to-face pi-stacked cytosine dimer vary with the intermonomer distance (R). The perfomances of different density functionals have been compared, focussing mainly on the lowest energy single excited state of the dimer (S(1))(2). TD-PBE0, TD-LC-omegaPBE, and TD-M05-2X provide a picture very similar to that obtained at the CASPT2 level by Merchan et al. (J Chem Phys 2006, 125, 231102), predicting that (S(1))(2) has a minimum for R approximately 3 A, with a binding energy of approximately 0.5 eV, whereas TD-B3LYP, TD-CAM-B3LYP, and TD-PBE understimate the binding energy. However, independently of the functional employed, no low-energy spurious charge transfer transitions are predicted by TD-DFT calculations, also when a nonsymmetric dimer is investigated, providing encouraging indications for the use of TD-DFT for studying the excited state of pi-stacked nucleobases.     

Theoretical investigation of the energies and geometries of photoexcited uranyl(VI) ion: a comparison between wave-function theory and density functional theory

In order to assess the accuracy of wave-function and density functional theory (DFT) based methods for excited states of the uranyl(VI) UO2(2+) molecule excitation energies and geometries of states originating from excitation from the sigma(u), sigma(g), pi(u), and pi(g) orbitals to the nonbonding 5f(delta) and 5f(phi) have been calculated with different methods. The investigation included linear-response CCSD (LR-CCSD), multiconfigurational perturbation theory (CASSCFCASPT2), size-extensivity corrected multireference configuration interaction (MRCI) and AQCC, and the DFT based methods time-dependent density functional theory (TD-DFT) with different functionals and the hybrid DFTMRCI method. Excellent agreement between all nonperturbative wave-function based methods was obtained. CASPT2 does not give energies in agreement with the nonperturbative wave-function based methods, and neither does TD-DFT, in particular, for the higher excitations. The CAM-B3LYP functional, which has a corrected asymptotic behavior, improves the accuracy especially in the higher region of the electronic spectrum. The hybrid DFTMRCI method performs better than TD-DFT, again compared to the nonperturbative wave-function based results. However, TD-DFT, with common functionals such as B3LYP, yields acceptable geometries and relaxation energies for all excited states compared to LR-CCSD. The structure of excited states corresponding to excitation out of the highest occupied sigma(u) orbital are symmetric while that arising from excitations out of the pi(u) orbitals have asymmetric structures. The distant oxygen atom acquires a radical character and likely becomes a strong proton acceptor. These electronic states may play an important role in photoinduced proton exchange with a water molecule of the aqueous environment.     

Charge-transfer excited states in a pi-stacked adenine dimer, as predicted using long-range-corrected time-dependent density functional theory

The lowest few electronic excitations of a pi-stacked adenine dimer in its B-DNA geometry are investigated, in the gas phase and in a water cluster, using a long-range-corrected version of time-dependent density functional theory (TD-DFT) that asymptotically incorporates Hartree-Fock exchange. Long-range correction is shown to eliminate the catastrophic underestimation of charge-transfer (CT) excitation energies that plagues conventional TD-DFT, at the expense of introducing one adjustable parameter, mu, that determines the length scale on which Hartree-Fock exchange is turned on. This parameter allows us to interpolate smoothly between hybrid density functionals and time-dependent Hartree-Fock theory. Excitation energies for CT states (in which an electron is transferred from one adenine molecule to the other) are found to increase dramatically as a function of mu. Uncorrected hybrid functionals underestimate the CT excitation energies, placing them well below the valence excitations, while time-dependent Hartree-Fock calculations place these states well above the valence states. Values for mu determined from certain benchmark calculations place the CT states well above the valence pipi* and npi* states at the Franck-Condon point.     

Comparison of DFT methods for molecular orbital eigenvalue calculations

We report how closely the Kohn-Sham highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) eigenvalues of 11 density functional theory (DFT) functionals, respectively, correspond to the negative ionization potentials (-IPs) and electron affinities (EAs) of a test set of molecules. We also report how accurately the HOMO-LUMO gaps of these methods predict the lowest excitation energies using both time-independent and time-dependent DFT (TD-DFT). The 11 DFT functionals include the local spin density approximation (LSDA), five generalized gradient approximation (GGA) functionals, three hybrid GGA functionals, one hybrid functional, and one hybrid meta GGA functional. We find that the HOMO eigenvalues predicted by KMLYP, BH&HLYP, B3LYP, PW91, PBE, and BLYP predict the -IPs with average absolute errors of 0.73, 1.48, 3.10, 4.27, 4.33, and 4.41 eV, respectively. The LUMOs of all functionals fail to accurately predict the EAs. Although the GGA functionals inaccurately predict both the HOMO and LUMO eigenvalues, they predict the HOMO-LUMO gap relatively accurately (approximately 0.73 eV). On the other hand, the LUMO eigenvalues of the hybrid functionals fail to predict the EA to the extent that they include HF exchange, although increasing HF exchange improves the correspondence between the HOMO eigenvalue and -IP so that the HOMO-LUMO gaps are inaccurately predicted by hybrid DFT functionals. We find that TD-DFT with all functionals accurately predicts the HOMO-LUMO gaps. A linear correlation between the calculated HOMO eigenvalue and the experimental -IP and calculated HOMO-LUMO gap and experimental lowest excitation energy enables us to derive a simple correction formula.     

Performance of time-dependent density functional and Green functions methods for calculations of excitation energies in radicals and for Rydberg electronic states

Time-dependent density functional (TD-DFT) and perturbation theory-based outer valence Green functions (OVGF) methods have been tested for calculations of excitation energies for a set of radicals, molecules, and model clusters simulating points defects in silica. The results show that the TD-DFT approach may give unreliable results not only for diffuse Rydberg states, but also for electronic states involving transitions between MOs localized in two remote from each other spatial regions, for example, for charge-transfer excitations. For the. O-SiX(3) clusters, where X is a single-valence group, TD-DFT predicts reasonable excitation energies but incorrect sequence of electronic transitions. For a number of cases where TD-DFT is shown to be unreliable, the OVGF approach can provide better estimates of excitation energies, but this method also is not expected to perform universally well. The OVGF performance is demonstrated to be satisfactory for excitations with predominantly single-determinant wave functions where the deviations of the calculated energies from experiment should not exceed 0.1-0.3 eV. However, for more complicated transitions involving multiple bonds or for excited states with multireference wave functions the OVGF approach is less reliable and error in the computed energies can reach 0.5-1 eV.     

Probing the electronic and optical properties of silica-coated quantum dots with first-principles calculations

The electronic and optical natures of silica-coated semiconductor nanocrystals (Cd(2)Te(2)@(SiO(2))(24)) have been investigated by density functional theory (DFT) and time-dependent DFT calculations. The calculated results of Cd(2)Te(2)@(SiO(2))(24) have revealed that the structural synergy effect between the Cd(2)Te(2) quantum dots (QDs) and the silica coating shell plays a dominant role in the photoelectric properties. The binding of embedded Cd(2)Te(2) to the outer silica coating shell leads to the distortion of the silica nanocage, indicating strong coupling between the QDs and silica shell. The optical features of Cd(2)Te(2) clusters and Cd(2)Te(2)@(SiO(2))(24) complexes were evaluated using the time-dependent DFT method. It is determined that the maximal absorption peak of isolated Cd(2)Te(2) in a UV-Vis absorption spectrum appears at 584 nm, which shifts to 534 nm when the Cd(2)Te(2) QDs were encapsulated by silica, in close agreement with the experimental evidence. The excited process has a direct electronic transition character from the occupied Cd(2)Te(2) states to the outer silica nanocage excited states (core → shell electronic transitions). A deep insight into silica-coated QD systems is beneficial for understanding their optical nature and the development of core/shell QDs.     

Magic number silicon dioxide-based clusters: laser ablation-mass spectrometric and density functional theory studies

The magic number silica clusters [(SiO(2))(n)O(2)H(3)](-) with n = 4 and 8 have been observed in the XeCl excimer laser (308 nm) ablation of various porous siliceous materials. The structural origin of the magic number clusters has been studied by the density functional theoretical calculation at the B3LYP/6-31G** level, with a genetic algorithm as a supplementary tool for global structure searching. The DFT results of the first magic number cluster are parallel to the corresponding Hartree-Fock results previously reported with only small differences in the structural parameters. Theoretical calculation predicts that the first magic number cluster (SiO(2))(4)O(2)H(4) and its anion [(SiO(2))(4)O(2)H(3)](-) will most probably take pseudotetrahedral cage-like structures. To study the structural properties of the second magic number cluster, geometries of the bare cluster (SiO(2))(8), the neutral complex cluster (SiO(2))(8)O(2)H(4), and the anionic cluster [(SiO(2))(8)O(2)H(3)](-) are fully optimized at the B3LYP/6-31G** level, and the corresponding vibrational frequencies are calculated. The DFT calculations predict that the ground state of the bare silica octamer (SiO(2))(8) has a linear chain structure, whereas the second magic number complex cluster (SiO(2))(8)O(2)H(4) and its anion [(SiO(2))(8)O(2)H(3)](-) are most probably a mixture of cubic cage-like structural isomers with an O atom inside the cage and several quasi-bicage isomers with high intercage interactions. The stabilization of these structures can also be attributed to the active participation of the group of atoms 2O and 4H (3H for the anion) in chemical bonding during cluster formation. Our theoretical calculation gives preliminary structural interpretation of the presence of the first and second magic number clusters and the absence of higher magic numbers.     

Why are time-dependent density functional theory excitations in solids equal to band structure energy gaps for semilocal functionals, and how does nonlocal Hartree-Fock-type exchange introduce excitonic effects?

We examine the time-dependent density functional theory (TD-DFT) equations for calculating excitation energies in solids with Gaussian orbitals and analytically show that for semilocal functionals, their lowest eigenvalue collapses to the minimum band orbital energy difference. With the introduction of nonlocal Hartree-Fock-type exchange (as in hybrid functionals), this result is no longer valid, and the lowest TD-DFT eigenvalue reflects the appearance of excitonic effects. Previously reported "charge-transfer" problems with semilocal TD-DFT excitations in molecules can be deduced from our analysis by taking the limit to infinite lattice constant.     

The charge-transfer states in a stacked nucleobase dimer complex: a benchmark study

Electronic singlet excitations of stacked adenine-thymine (AT) and guanine-cytosine (GC) complexes have been investigated with respect to local excitation and charge-transfer (CT) characters. Potential energy curves for rigid displacement of the nucleobases have been computed to establish the distance dependence of the CT states. The second-order algebraic diagrammatic construction [ADC(2)] method served as reference approach for comparison to a selected set of density functionals used within the time-dependent density functional theory (TD-DFT). Particular attention was dedicated to the performance of the recently developed family of M06 functionals. The calculations for the stacked complexes show that at the ADC(2) level, the lowest CT state is S(6) for the AT and as S(4) for the GC pair. At the reference geometry, the actual charge transferred is found to be 0.73 e for AT. In case of GC, this amount is much smaller (0.17 e). With increasing separation of the two nucleobases, the CT state is strongly destabilized. The M06-2X version provides a relatively good reproduction of the ADC(2) results. It avoids the serious overstabilization and overcrowding of the spectrum found with the B3LYP functional. On the other hand, M06-HF destabilizes the CT state too strongly. TD-DFT/M06-2X calculations in solution (heptane, isoquinoline, and water) using the polarizable continuum model show a stabilization of the CT state and an increase in CT character with increasing polarity of the solvent.     

TD-CI simulation of the electronic optical response of molecules in intense fields II: comparison of DFT functionals and EOM-CCSD

Time-dependent configuration interaction (TD-CI) simulations can be used to simulate molecules in intense laser fields. TD-CI calculations use the excitation energies and transition dipoles calculated in the absence of a field. The EOM-CCSD method provides a good estimate of the field-free excited states but is rather expensive. Linear-response time-dependent density functional theory (TD-DFT) is an inexpensive alternative for computing the field-free excitation energies and transition dipoles needed for TD-CI simulations. Linear-response TD-DFT calculations were carried out with standard functionals (B3LYP, BH&HLYP, HSE2PBE (HSE03), BLYP, PBE, PW91, and TPSS) and long-range corrected functionals (LC-ωPBE, ωB97XD, CAM-B3LYP, LC-BLYP, LC-PBE, LC-PW91, and LC-TPSS). These calculations used the 6-31G(d,p) basis set augmented with three sets of diffuse sp functions on each heavy atom. Butadiene was employed as a test case, and 500 excited states were calculated with each functional. Standard functionals yield average excitation energies that are significantly lower than the EOM-CC, while long-range corrected functionals tend to produce average excitation energies slightly higher. Long-range corrected functionals also yield transition dipoles that are somewhat larger than EOM-CC on average. The TD-CI simulations were carried out with a three-cycle Gaussian pulse (ω = 0.06 au, 760 nm) with intensities up to 1.26 × 10(14) W cm(-2) directed along the vector connecting the end carbons. The nonlinear response as indicated by the residual populations of the excited states after the pulse is far too large with standard functionals, primarily because the excitation energies are too low. The LC-ωPBE, LC-PBE, LC-PW91, and LC-TPSS long-range corrected functionals produce responses comparable to EOM-CC.     

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.     

Density functional analysis of geometries and electronic structures of gold-phosphine clusters. The case of Au4(PR3)42+ and A(u4μ2-I)2(PR3)4

Geometries, ligand binding energies, electronic structure, and excitation spectra are determined for Au(4)(PR(3))(4)(2+) and Au(4)(μ(2)-I)(2)(PR(3))(4) clusters (R = PH(3), PMe(3), and PPh(3)). Density functionals including SVWN5, Xα, OPBE, LC-ωPBE, TPSS, PBE0, CAM-B3LYP, and SAOP are employed with basis sets ranging from LANL2DZ to SDD to TZVP. Metal--metal and metal--ligand bond distances are calculated and compared with experiment. The effect of changing the phosphine ligands is assessed for geometries and excitation spectra. Standard DFT and hybrid ONIOM calculations are employed for geometry optimizations with PPh(3) groups. The electronic structure of the gold--phosphine clusters examined in this work is analyzed in terms of cluster ("superatom") orbitals and d-band orbitals. Transitions out of the d band are significant in the excitation spectra. The use of different basis sets and DFT functionals leads to noticeable variations in the relative intensities of strong transitions, although the overall spectral profile remains qualitatively unchanged. The replacement of PMe(3) with PPh(3) changes the nature of the electronic transitions in the cluster due to low-lying π*-orbitals. To reproduce the experimental geometries of clusters with PPh(3) ligands, computationally less expensive PH(3) or PMe(3) ligands are sufficient for geometry optimizations. However, to predict cluster excitation spectra, the full PPh(3) ligand must be considered.     

Time-dependent density functional theory as a tool for isomer assignments of hydrogen-bonded solute.solvent clusters

Can isomer structures of hydrogen-bonded solute x solvent clusters be assigned by correlating gas-phase experimental S0 <--> S1 transitions with vertical or adiabatic excitation energies calculated by time-dependent density functional theory (TD-DFT)? We study this question for 7-hydroxyquinoline (7HQ), for which an experimental database of 19 complexes and clusters is available. The main advantage of the adiabatic TD-B3LYP S0 <--> S1 excitations is the small absolute error compared to experiment, while for the calculated vertical excitations, the average offset is +1810 cm(-1). However, the empirically adjusted vertical excitations correlate more closely with the experimental transition energies, with a standard deviation of sigma = 72 cm(-1). For the analogous correlation with calculated adiabatic TD-DFT excitations, the standard deviation is sigma = 157 cm(-1). The vertical and adiabatic TD-DFT correlation methods are applied for the identification of isomers of the 7-hydroxyquinoline.(MeOH) n , n = 1-3 clusters [Matsumoto, Y.; Ebata, T.; Mikami, N. J. Phys. Chem. B 2002, 106, 5591]. These confirm that the vertical TD-DFT/experimental correlation yields more effective isomer assignments.     

Ab initio description of photoabsorption and electron transfer in a doubly-linked porphyrin-fullerene dyad

Structure, photoabsorption and excited states of two representative conformations obtained from molecular dynamics (MD) simulations of a doubly-linked porphyrin-fullerene dyad DHD6ee are studied by using both DFT and wavefunction based methods. Charge transfer from the donor (porphyrin) to the acceptor (fullerene) and the relaxation of the excited state are of special interest. The results obtained with LDA, GGA, and hybrid functionals (SVWN, PBE, and B3LYP, respectively) are analyzed with emphasis on the performance of used functionals as well as from the point of view of their comparison with wavefunction based methods (CCS, CIS(D), and CC2). Characteristics of the MD structures are retained in DFT optimization. The relative orientation of porphyrin and fullerene is significantly influencing the MO energies, the charge transfer (CT) in the ground state of the dyad and the excitation of ground state CT complex (g-CTC). At the same time, the excitation to the locally excited state of porphyrin is only little influenced by the orientation or cc distance. TD-DFT underestimates the excitation energy of the CT state, however for some cases (with relatively short donor-acceptor separations), the use of a hybrid functional like B3LYP alleviates the problem. Wavefunction based methods and CC2 in particular appear to overestimate the CT excitation energies but the inclusion of proper solvation models can significantly improve the results.     

The structural and electronic properties of Ag-adsorbed (SiO2)n (n=1-7) clusters

Equilibrium geometries, charge distributions, stabilities, and electronic properties of the Ag-adsorbed (SiO(2))(n) (n=1-7) clusters have been investigated using density functional theory with generalized gradient approximation for exchange-correlation functional. The results show that the Ag atom preferably binds to silicon atom with dangling bond in nearly a fixed direction, and the incoming Ag atoms tend to cluster on the existing Ag cluster leading to the formation of Ag islands. The adsorbed Ag atom only causes charge redistributions of the atoms near itself. The effect of the adsorbed Ag atom on the bonding natures and structural features of the silica clusters is minor, attributing to the tendency of stability order of Ag(SiO(2))(n) (n=1-7) clusters in consistent with silica clusters. In addition, the energy gaps between the highest occupied and lowest unoccupied molecular orbitals remarkably decrease compared with the pure (SiO(2))(n) (n=1-7) clusters, eventually approaching the near infrared radiation region. This suggests that these small clusters may be an alternative material which has a similar functionality in treating cancer to the large gold-coated silica nanoshells and the small Au(3)(SiO(2))(3) cluster.     

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 (Tv) 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 Tv and the transition energy (Te) were calculated by MS-CASPT2//CASSCF method. Both the TD-DFT and MS-CASPT2 calculated S1 state Tv values agree with the experimental one. The IPEA shift greatly affects the MS-CASPT2 calculated Tv 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.