PBE0 Hybrid Research Articles

A TDDFT and PCM-TDDFT studies on absorption spectra of N-substituted 1,8-naphthalimides dyes

The electronic absorption spectra of 39 N-substituted 1,8-naphthalimides dyes have been investigated in the framework of time-dependent density functional theory (TDDFT) and polariable continuum TDDFT (PCM-TDDFT). The B3LYP and PBE0 hybrid functionals together with 6-31+G(d) basis set were selected to calculate the excitation energies of 3–30 lowest-lying singlet excited states. Comparing the experimental spectra with calculated excitation energy, the mean absolute error (MAE) of TD-B3LYP/6-31+G(d) is 0.21 eV. Including solvent effect, the PCM-TD-B3LYP/6-31+G(d) provides a very high accuracy for compounds 1–5 (in cyclohexane) and 20–26 (in chloroform), but a larger error with 0.37–0.47 eV for compounds 6–19 and 27–39 (in DMF). The PBE0 hybrid functional provides a slight higher accuracy than B3LYP. The MAE is 0.28 eV for PCM-TD-B3LYP/6-31+G(d), and 0.21 eV for PCM-TD-PBE0/6-31+G(d), respectively. All calculation reveals that the maximum absorption band mainly results from the π → π ∗ transition from HOMO to LUMO.

Structure, bonding and physical properties of tetragonal and orthorhombic SiS 2 from (hybrid) DFT calculations

The energetics, structure and physical properties of tetragonal and orthorhombic SiS 2 were calculated by periodic density functional theory (DFT) calculations, using both localized orbital and projected augmented wave basis-sets. All methods applied agree upon the relative energies of the different polymorphs but show differences in the predicted geometries, which are minimized upon improving the basis-set quality. The hybrid PBE0 functional was found to give the best match between experimental and calculated structures. When comparing SiS 2 with its much better studied oxide analog silica, we observe that upon substituting sulphur for oxygen, the energy landscape changes dramatically. Other effects of changing S for O are found to be smaller Si–X–Si angles, a broader distribution of X–Si–X angles, a more flexible framework and a significantly reduced band gap. The latter is in line with the experimental observation of photoluminescence in related GaGeS 2 compounds and suggests that SiS 2 might find application in UV light emitting diodes. Finally, a comparison of the maximally localized Wannier functions demonstrates that the Si–S bonds in SiS 2 have a considerably more covalent character than the Si–O bonds in silica.

Assessment of the Accuracy of TD-DFT Absorption Spectra: Substituted Benzenes

Using the parameter-free PBE0 hybrid functional in conjunction with the conducting PCM model, we compute the UV/VIS spectra of a series of solvated phenol and nitrobenzene chromogens. For the first series, the average deviation with respect to experiment is large (about 0.5 eV) but the auxochromic shifts are very accurately and consistently predicted. Therefore, after a statistical treatment, the TD-DFT values are within 0.02 eV of the experimental data. For nitrobenzenes, the average discrepancy is smaller than for phenols, though the impact of individual substitution is much less consistent with experimental trends. We also confirm that push-pull compounds with donor and acceptor groups in meta positions are especially problematic for TD-DFT calculations relying on conventional hybrids, and we unravel the origin of this specific difficulty.

On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters: Benchmarks approaching the complete basis set limit

The ability of several density-functional theory (DFT) exchange-correlation functionals to describe hydrogen bonds in small water clusters (dimer to pentamer) in their global minimum energy structures is evaluated with reference to second order Moller-Plesset perturbation theory (MP2). Errors from basis set incompleteness have been minimized in both the MP2 reference data and the DFT calculations, thus enabling a consistent systematic evaluation of the true performance of the tested functionals. Among all the functionals considered, the hybrid X3LYP and PBE0 functionals offer the best performance and among the nonhybrid generalized gradient approximation functionals, mPWLYP and PBE1W perform best. The popular BLYP and B3LYP functionals consistently underbind and PBE and PW91 display rather variable performance with cluster size.

Interplay of Intrinsic, Environmental, and Dynamic Effects in Tuning the EPR Parameters of Nitroxides: Further Insights from an Integrated Computational Approach

The role of stereoelectronic, environmental, and short-time dynamic effects in tuning the hyperfine and gyromagnetic tensors of a prototypical nitroxide spin probe has been investigated by an integrated computational approach based on extended Lagrangian molecular dynamics and discrete-continuum solvent models. Trajectories were generated in two protic solvents as well as in the gas phase for reference; structural analysis of the dynamics, and comparison with optimized solute-solvent clusters, allowed for the identification of the prevailing solute-solvent hydrogen-bonding patterns and helped to define the strategy for the computation of magnetic parameters. This was performed in a separate step, on a large number of frames, by a high-level DFT approach coupling the PBE0 hybrid functional with a tailored basis set and with proper account of specific and bulk solvent effects. Remarkable changes in solvation networks are found on going from aqueous to methanol solution, thus providing a rationalization of indirect experimentally available evidence. The computed magnetic parameters are in satisfactory agreement with the available measured values and allow for an unbiased evaluation of the role of different effects in tuning the overall EPR observables. Apart from their intrinsic interest, our results pave the route toward the development of tunable detection protocols based on specific spectroscopic signatures.

Lagrangian approach to molecular vibrational Raman intensities using time-dependent hybrid density functional theory

The authors propose a new route to vibrational Raman intensities based on analytical derivatives of a fully variational polarizability Lagrangian. The Lagrangian is constructed to recover the negative frequency-dependent polarizability of time-dependent Hartree-Fock or adiabatic (hybrid) density functional theory at its stationary point. By virtue of the variational principle, first-order polarizability derivatives can be computed without using derivative molecular orbital coefficients. As a result, the intensities of all Raman-active modes within the double harmonic approximation are obtained at approximately the same cost as the frequency-dependent polarizability itself. This corresponds to a reduction of the scaling of computational expense by one power of the system size compared to a force constant calculation and to previous implementations. Since the Raman intensity calculation is independent of the harmonic force constant calculation more, computationally demanding density functionals or basis sets may be used to compute the polarizability gradient without much affecting the total time required to compute a Raman spectrum. As illustrated for fullerene C60, the present approach considerably extends the domain of molecular vibrational Raman calculations at the (hybrid) density functional level. The accuracy of absolute and relative Raman intensities of benzene obtained using the PBE0 hybrid functional is assessed by comparison with experiment.

Density functional theory analysis of the structural and electronic properties of TiO2 rutile and anatase polytypes: Performances of different exchange-correlation functionals

The two polymorphs of TiO2, rutile and anatase, have been investigated at the ab initio level using different Hamiltonians with all-electron Gaussian and projector augmented plane wave basis sets. Their equilibrium lattice parameters, relative stabilities, binding energies, and band structures have been evaluated. The calculations have been performed at the Hartree-Fock, density functional theory (DFT), and hybrid (B3LYP and PBE0) levels. As regards DFT, the local density and generalized gradient (PBE) approximations have been used. Our results show an excellent agreement with the experimental band structures and binding energies for the B3LYP and PBE0 functionals, while the best structural descriptions are obtained at the PBE0 level. However, no matter which Hamiltonian and method are used, anatase is found more stable than rutile, in contrast with recent experimental reports, although the relative stabilities of the two phases are very close to each other. Nevertheless, based on the overall results, the hybrid PBE0 functional appears as a good compromise to obtain an accurate description of both structural and electronic properties of solids.

Structural, electronic and magnetic properties of methylviologen in its reduced forms

Structural, electronic and magnetic properties of methylviologen have been studied by model rooted in the density functional theory, both in the gas phase and in aqueous solution. In particular, vertical excitation energies were computed by PBE0 hybrid functional in the framework of a time dependent DFT (TDDFT) approach, whereas the polarizable continuum model (PCM) was used to take solvent effect into account. From a quantitative point of view, the PBE0 hybrid functional provides accurate description of structural, vibrational, magnetic properties, as well as of redox potential in the solvent. Some insights on the differences observed for methylviologen in changing the redox state and the medium are given.

Electron, hole and exciton self-trapping in germanium doped silica glass from DFT calculations with self-interaction correction

Density functional theory (DFT) calculations were employed to understand the refractive index change in germanium doped silica glasses for the trapped states of electronic excitations induced by UV irradiation. Local structure relaxation and excess electron density distribution were calculated upon self-trapping of an excess electron, hole, and exciton in germanium doped silica glass. The results show that both the trapped exciton and excess electron are highly localized on germanium ion and, to some extent, on its oxygen neighbors. Exciton self-trapping is found to lead to the formation of a Ge E′ center and a non-bridging hole center. Electron trapping changes the GeO 4 tetrahedron structure into trigonal bi-pyramid with the majority of the excess electron density located along the equatorial line. The self-trapped hole is localized on bridging oxygen ions that are not coordinated to germanium atoms that lead to elongation of the Si–O bonds and change of the Si–O–Si bond angles. We carried out a comparative study of standard DFT versus DFT with a hybrid PBE0 exchange and correlation functional. The results show that the two methods give qualitatively similar relaxed structure and charge distribution for electron and exciton trapping in germanium doped silica glass; however, only the PBE0 functional produces the self-trapped hole.

Relative energy of the high-(T2g5) and low-(A1g1) spin states of [Fe(H2O)6]2+, [Fe(NH3)6]2+, and [Fe(bpy)3]2+: CASPT2 versus density functional theory

High-level ab initio calculations using the CASPT2 method and extensive basis sets were performed on the energy differences of the high-[(5)T(2g):t(2g) (4)e(g) (2)] and low-[(1)A(1g):t(2g) (6)] spin states of the pseudo-octahedral Fe(II) complexes [Fe(H(2)O)(6)](2+), [Fe(NH(3))(6)](2+), and [Fe(bpy)(3)](2+). The results are compared to the results obtained from density functional theory calculations with the generalized gradient approximation functional BP86 and two hybrid functionals B3LYP and PBE0, and serve as a calibration for the latter methods. We find that large basis set CASPT2 calculations may provide results for the high-spin/low-spin splitting DeltaE(HL) that are accurate to within 1000 cm(-1), provided they are based on an adequately large CAS[10,12] reference wave function. The latter condition was found to be much more stringent for [Fe(bpy)(3)](2+) than for the other two complexes. Our "best" results for DeltaE(HL) (including a zero-point energy correction) are -17 690 cm(-1) for [Fe(H(2)O)(6)](2+), -8389 cm(-1) for [Fe(NH(3))(6)](2+), and 3820 cm(-1) for [Fe(bpy)(3)](2+).

The absorption wavelengths of sulfur chromophors of ultramarines calculated by time-dependent density functional theory

The neutral tetrasulfur and the trisulfur and tetrasulfur anion radicals were studied by density functional theory (DFT) employing the hybrid functionals B3LYP, PBE0 and PB95 and large basis sets. The spectral data were obtained by time-dependent density functional theory (TD-DFT). The calculated absorption wavelengths for the calculated vertical electronic transitions in the visible region were compared with the wavelengths of the absorption maxima of ultramarines and of synthetic sulfur compounds measured in matrices or in solution. The chromophore of ultramarine blue was considered as a test case and the chromophore of ultramarine red studied in several model calculations. The calculated transition energies and intensities favour the cis tetrasulfur chromophore of red ultramarine. The excellent agreement between the theoretical and experimental absorption wavelengths of the color bands supports earlier assignments. The electronic structure of cis and trans tetrasulfur is discussed in terms of ylidic and biradical resonance structures by natural resonance theory. The singlet ground states display RKS/UKS instability. The broken-symmetry UKS structure is of lower energy than the RKS structure, which does, however, not influence the molecular and electronic structure significantly.

Structures and Electronic Absorption Spectra of a Recently Synthesised Class of Photodynamic Therapy Agents

A theoretical study was performed on a novel class of boron-containing molecules (various substituted tetraarylazadipyrromethenes), which show in vitro activity for application in photodynamic therapy. Geometric optimisation of the structures for the singlet and triplet electronic states was carried out on compounds in vacuo at the density functional level of theory, by employing the PBE0 hybrid functional and the split-valence plus polarisation basis set. The absorbance properties in the UV-visible region were examined by means of time-dependent density functional response theory, using the same functional as mentioned above. To evaluate the influence of the solvent on the excitation energies, the continuum polarisable model was applied. Calculated electronic excitations, such as those regarding the Q-like band, were found to be in good agreement (within 0.01-0.1 eV) with experimental values and experimental trends on changing both the substituents and solvent.

Time-dependent density functional theory determination of the absorption spectra of naphthoquinones

The electronic excited states of solvated 1,4-naphthoquinone dyes have been determined using time-dependent density functional theory (TD-DFT) combined with the polarizable continuum model (PCM). It turns out that the 6-311+G(2d,p) and 6-311G(d,p) basis sets provide, respectively, almost perfectly converged excitation spectra, and geometries. Using the PBE0 hybrid functional, we obtain a valuable correlation between PCM-TD-DFT and experimental transitions in both the ultraviolet and the visible parts of the absorption spectra. Indeed, for the 69 1,4-naphthoquinone studied transitions, the mean signed/absolute deviation are limited to +3.6nm (−0.048eV)/9.5nm (0.100eV). Qualitative correlations between the geometrical, vibrational and electronic characteristics has been established. In addition, the spectra of several 1,2-naphthoquinones have been considered.

Accurate predictions of the EPR parameters in planar cobalt(II) complexes by hybrid density functional theory

The hybrid density functional theory is applied to calculate the electron paramagnetic resonance parameters, i.e, the g- and A-tensors of some planar Cobalt(II) complexes with a C 2 v symmetry. Calculations were done for four systems: Co( acacen), Co( tacacen), Co( seacacen) and Co( sacsac) 2. The following hybrid functionals were employed: B3LYP, B3PW91, mPW1PW91 and PBE0. The expected large deviation of the g- and A-tensors is well reproduced, and is in very good agreement with the experimental observations. Comparative study shows that the PBE0 hybrid model yields the best agreement with experimental data.

Excitation spectra of nitro-diphenylaniline: Accurate time-dependent density functional theory predictions for charge-transfer dyes

Using time-dependent density functional theory (TD-DFT) and the polarizable continuum model (PCM), we have computed the absorption spectra of nitro-diphenylamine dyes. It turns out that the 6-311+G(2d,p) and 6-311G(d,p) basis sets provide, respectively, almost perfectly converged excitation spectra and geometries. Using the PBE0 hybrid functional, we obtain a valuable correlation between PCM-TD-DFT and experimental lambdamax with mean signed/absolute deviations of -4 nm (0.03 eV)8 nm (0.06 eV) and relatively small extreme discrepancies, although the excitations responsible for the color of this class of dyes present a charge-transfer character. The changes in the electron density upon absorption are analyzed through an orbital picture. In addition, a relationship between the light fastness and a well-identified vibrational frequency is proposed.

Absorption and emission spectra in gas-phase and solution using TD-DFT: Formaldehyde and benzene as case studies

The first vertical and relaxed singlet excited states of formaldehyde and benzene have been computed using time-dependent density functional theory in conjunction with the hybrid PBE0 functional. Absorption, adiabatic and fluorescence transition energies have been determined. In addition to a basis set study, we have assessed the bulk solvent effects using the polarizable continuum model. It turns out that 6-311+G(d,p) provides converged results for all investigated spectroscopic characteristics, although 6-31G(d,p) could be sufficient for determining the ground and excited structures of benzene. The solvent effects are quite small (0.1 eV variations) and, in first approximation, can be neglected during the excited-state optimization.

Toward a Theoretical Quantitative Estimation of the λmax of Anthraquinones-Based Dyes.

We have computed the absorption spectra of a large series of anthraquinone dyes by using the time-dependent density functional theory (TD-DFT) for the excited-state calculations and the polarizable continuum model (PCM) for evaluating bulk solvent effects. On one hand, we compare the results obtained with the B3LYP and the PBE0 hybrid functionals, combined with different atomic basis sets. On the other hand, using multiple linear regression, we take advantage of the λmax predicted by these two functionals in order to reach the best agreement between theoretical estimates and experimental measurements. It turns out that 1. PBE0 provides more accurate results than B3LYP; in addition the average errors provided by the former are less basis set dependent. 2. Multiple linear regression provides excited state spectra in better agreement with experiment than any simple linear fit that could be performed. 3. Using our best fitting procedure, we obtained a mean absolute error of 6 nm for a set of 66 anthraquinones, with no deviations exceeding 25 nm. The related standard deviation, useful for predictions, is only 8 nm, i.e.,[Formula: see text] =[Formula: see text] ± 8 nm (or ±0.05 eV) for unknown anthraquinone compounds.

Static and dynamic approaches for the calculation of NMR parameters: Permanganate ion as a case study

Magnetic shielding constants of the permanganate ion ( MnO 4 - ) were computed by the means of density functional theory both from static and dynamic simulations. The hybrid PBE0 exchange correlation functional was used for the determination of structural and magnetic properties. Ab-initio molecular dynamic simulations were performed at the same level of theory using the atom-centred density matrix propagation (ADMP) method. With the aim of understanding the role of coupling of different vibrations, the results obtained at static level and as average along large amplitude motions representing each of the normal modes of the ion were compared to those resulting from dynamic approaches.

Spectroscopic Properties of Porphyrin-Like Photosensitizers: Insights from Theory

Electronic absorption spectra of six porphyrin-like photosensitizers, porphyrin, chlorin, bacteriochlorin, pheophytin a, porphyrazin, and texaphyrin, have been calculated within the time-dependent DFT framework (TDDFT) in conjunction with the PBE0 hybrid functional. Energetic and orbital aspects are discussed by comparing systems together so as to assess the best molecules for photodynamic therapy applications. Excitation energies and oscillator strengths are found to be in good agreement with both experimental data and previous theoretical works. In particular, whereas significant discrepancies (0.3 eV) appear for Qx bands, results become more reliable as wavelengths decrease. To elucidate the effect of the local environment, we have taken into account solvation either with explicit water molecules interacting via hydrogen bonds with the system or with a continuum model (C-PCM). The supramolecular approach does not affect spectra, while using C-PCM improves Qx and B band values and strengthens intensities significantly. In both gaseous and aqueous phases, texaphyrin, pheophytin a, and bacteriochlorin Qx bands are found in the 600-800 nm range as expected by experimental works. These data are particularly interesting in the perspective of systematic studies of other photosensitizers and should make experimentalists' works easier.

Assessment of PBE0 for evaluating the absorption spectra of carbonyl molecules

AbstractUsing the parameter‐free PBE0 hybrid functional, we compute the UV/Vis spectra of a series of solvated compounds presenting a carbonyl chromophoric unit linked to a carbon–carbon double bond. It turns out that PBE0 is extremely efficient for accurately reproducing experimental values, with a mean unsigned error of 7 nm for an extended set of compounds, although no fitting or statistical treatments are performed. PBE0 has a predictive efficiency comparable to the well‐known Woodward–Fieser empirical formula, and can therefore be used to extend these rules without requiring additional experimental results. Consequently, the UV/Vis spectra of several compounds that have not yet been synthesized are predicted. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006