Hybrid Functional PBE0 Research Articles

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.

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.

A multi-step procedure for evaluating the EPR parameters of indolinonic aromatic aminoxyls: A combined DFT and spectroscopic study

A DFT study on indolinonic aromatic aminoxyls has been carried out at different levels of theory. The comparison with previous experimental data from ENDOR, X-rays and PND (polarized neutron diffraction) techniques confirms that such a computational approach represents an important aid for understanding the properties of this class of aminoxyls such as hyperfine coupling constants (hfcc), isotropic g-factors, spin density distributions and geometries. At first, a model compound was studied with different model chemistries; B1LYP, B3LYP and PBE0 hybrid functionals were employed in conjunction with various medium to large size basis sets. The study outlines that none of the model chemistries considered is able to correctly describe the EPR features of these radicals by itself. For this reason, by taking into account a compromise between accuracy and computational cost, a multi-step procedure was checked over a homogeneous series of indolinonic aminoxyls and then proposed.

Density functional theory study of MnO by a hybrid functional approach

The ground state properties of MnO are investigated using the plane wave based projector augmented wave technique and the so-called ''parameter-free'' hybrid functional approach PBE0 for the approximation of the exchange-correlation energy and potential. The insulating, antiferromagnetically ordered and rhombohedrally distorted B1 structure is found to be the most stable phase of MnO, consistent with experiment. The band gap of 4.02 eV, spin magnetic moment of $4.52\phantom{\rule{0.3em}{0ex}}{\ensuremath{\mu}}_{B}$, optimized lattice parameter $a=4.40\phantom{\rule{0.3em}{0ex}}\mathrm{\AA{}}$, rhombohedral distortion angle $\ensuremath{\alpha}={0.88}^{0}$, density of states, and magnetic properties are all in good agreement with experiment. Results obtained from standard methods such as generalized gradient approximation (GGA), $\mathrm{GGA}+\mathrm{U}$ and periodic Hartee-Fock are also reported for comparative purposes. In line with previous studies, our results suggest that the applied hybrid functional method PBE0, which combines 25% of the exact exchange with a generalized-gradient approximation, corrects the deficiency of semilocal density functionals and provides an accurate quantitative description of the structural, electronic, and magnetic properties of MnO without any adjustable parameter.

Accurate Calculation of the Heats of Formation for Large Main Group Compounds with Spin-Component Scaled MP2 Methods

Three MP2-type electron correlation treatments and standard density functional theory (DFT) approaches are used to predict the heats of formation for a wide variety of different molecules. The SCF and MP2 calculations are performed efficiently using the resolution-of-the-identity (RI) approximation such that large basis set (i.e., polarized valence quadruple-zeta quality) treatments become routinely possible for systems with 50-100 atoms. An atom equivalent scheme that corrects the calculated atomic energies is applied to extract the "real" accuracy of the methods for chemically relevant problems. It is found that the spin-component-scaled MP2 method (SCS-MP2, J. Chem. Phys, 2003, 118, 9095) performs best and provides chemical accuracy (MAD of 1.18 kcal/mol) for a G2/97 test set of molecules. The computationally more economical SOS-MP2 variant, which retains only the opposite-spin part of the correlation energy, is slightly less accurate (MAD of 1.36 kcal/mol) than SCS-MP2. Both spin-component-scaled MP2 treatments perform significantly better than standard MP2 (MAD of 1.77 kcal/mol) and DFT-B3LYP (MAD of 2.12 kcal/mol). These conclusions are supported by results obtained for a second test set of complex systems containing 70 molecules, including charged, strained, polyhalogenated, hypervalent, and large unsaturated species (e.g. C60). For this set, DFT-B3LYP performs badly (MAD of 8.6 kcal/mol) with many errors >10-20 kcal/mol while the spin-component-scaled MP2 methods are still very accurate (MAD of 2.8 and 3.7 kcal/mol, respectively). DFT-B3LYP shows an obvious tendency to underestimate molecular stability as the system size increases. Out of six density functionals tested, the hybrid functional PBE0 performs best. All in all, the SCS-MP2 method, together with large AO basis sets, clearly outperforms current DFT approaches and seems to be the most accurate quantum chemical model that routinely can predict the thermodynamic properties of large main group compounds.

Comparison of density functionals for energy and structural differences between the high- [5T2g:(t2g)4(eg)2] and low- [1A1g:(t2g)6(eg)] spin states of iron(II) coordination compounds. II. More functionals and the hexaminoferrous cation, [Fe(NH3)6]2+

The ability of different density functionals to describe the structural and energy differences between the high- [(5)T(2g):(t(2g))(4)(e(g))(2)] and low- [(1)A(1g):(t(2g))(6)(e(g))(0)] spin states of small octahedral ferrous compounds is studied. This work is an extension of our previous study of the hexaquoferrous cation, [Fe(H(2)O)(6)](2+), [J. Chem. Phys. 120, 9473 (2004)] to include a second compound-namely, the hexaminoferrous cation, [Fe(NH(3))(6)](2+)-and several additional functionals. In particular, the present study includes the highly parametrized generalized gradient approximations (GGAs) known as HCTH and the meta-GGA VSXC [which together we refer to as highly parametrized density functionals (HPDFs)], now readily available in the GAUSSIAN03 program, as well as the hybrid functional PBE0. Since there are very few experimental results for these molecules with which to compare, comparison is made with best estimates obtained from second-order perturbation theory-corrected complete active space self-consistent field (CASPT2) calculations, with spectroscopy oriented configuration interaction (SORCI) calculations, and with ligand field theory (LFT) estimations. While CASPT2 and SORCI are among the most reliable ab initio methods available for this type of problem, LFT embodies many decades of empirical experience. These three methods are found to give coherent results and provide best estimates of the adiabatic low-spin-high-spin energy difference, DeltaE(LH) (adia), of 12 000-13 000 cm(-1) for [Fe(H(2)O)(6)](2+) and 9 000-11 000 cm(-1) for [Fe(NH(3))(6)](2+). All functionals beyond the purely local approximation produce reasonably good geometries, so long as adequate basis sets are used. In contrast, the energy splitting, DeltaE(LH) (adia), is much more sensitive to the choice of functional. The local density approximation severely over stabilizes the low-spin state with respect to the high-spin state. This "density functional theory (DFT) spin pairing-energy problem" persists, but is reduced, for traditional GGAs. In contrast the hybrid functional B3LYP underestimates DeltaE(LH) (adia) by a few thousands of wave numbers. The RPBE GGA of Hammer, Hansen, and Norskov gives good results for DeltaE(LH) (adia) as do the HPDFs, especially the VSXC functional. Surprisingly the HCTH functionals actually over correct the DFT spin pairing-energy problem, destabilizing the low-spin state relative to the high-spin state. Best agreement is found for the hybrid functional PBE0.

CHIH-DFT determination of the electrical, optical, and magnetic properties and NICS aromaticity of megazol

The infectious diseases are one the most important causes of mortality in the world. Two of these are the American trypanosomiasis or Chagas disease and the African trypanosomiasis or sleeping sickness. At this moment there exist some medicines to fight them, but they are not effective in the chronic stage. Thus, there are a number of drugs being developed, among them megazol and its derivatives. In this work, some electrical, optical and magnetic properties have been determined for megazol, by using Density Functional Theory and a model chemistry called CHIH-DFT, which uses a modification of the hybrid functional PBE0 named PBEg, where G is a structure factor. Also, a NICS study of aromaticity is included.

Assessment of density functional theory for the prediction of the nature of the oxirene stationary point

The nature of the stationary point of oxirene, cyclic C 2H 2O, has been examined using selected GGA and hybrid functionals in combination with a number of basis sets. All GGA functionals (BLYP, BP91, PBE, HCTH, HCTH147, and HCTH407) predict the stationary point to be a transition state and show very little basis set dependence. The hybrid functionals (B3LYP, B3P91, PBE0, B97, B97-1, and B3P86), on the other hand, show more basis set dependence and predict oxirene to be a minimum in a number of cases. However, these parameterized hybrid functionals are not consistent in their characterization of oxirene. The theoretically derived hybrid functional PBE0 predicts oxirene to be a minimum with 11 of the 12 basis sets used and results with the largest basis set are in good agreement with earlier predictions with the high level correlated method, CCSD(T).

Electron momentum spectroscopy and linear combination of atomic orbitals calculation of bulk Na2O

This paper presents an experimental measurement of the electronic structure of Na2Oin the solid phase using electron momentum spectroscopy and comparesthe results with ab initio calculations performed within the linearcombination of atomic orbitals (LCAO) approximation. While Hartree–Fock(HF) can reproduce elastic properties we find it overestimates splittingof the oxygen valence bands by around 30% and the width of the O2p band by a factor of 2. Our experimental values are 15.85 ± 0.2 and 0.6 ± 0.2 eVfor these two quantities, respectively. Density functional methods are significantlybetter, with the hybrid functional PBE0 predicting the oxygen bandgap towithin the experimental error. PBE0 also gives the best estimate of theNa core level energies. In contrast, HF performs best for the splittingbetween the oxygen and sodium bands. Our experimental values of 32.85 ± 0.2 and 27.45 ± 0.2 eVfor the Na 2p–Na 2s and O 2p–Na 2p splittings agree well with previousmeasurements. Distribution of electron density both within the bands andbetween the bands is not reproduced by any of the computational methodsemployed.