PBE0 Hybrid Research Articles

Theoretical investigation of the magnetic exchange interactions in copper(II) oxides under chemical and physical pressures.

It remains a challenge to understand the unconventional mechanisms that cause high-TC superconductivity in cuprate superconductors, high-TC multiferroicity in CuO, or low-dimensional magnetism in the spin-Peierls transition compounds such as CuGeO3. A common feature of all these copper oxide compounds (containing Cu2+ ions) is the presence of large magnetic superexchange interactions J. It is a general strategy to apply chemical and/or physical pressure in order to tune these exotic properties. Here we show theoretically, for the first time, the impact of physical pressure on J on CuO, for which we predict a strong enhancement of the low-dimensionality of the magnetic interactions and the spin-frustration at high-pressures. Such modifications are expected to strongly influence the multiferroic properties of CuO. We finally demonstrate that PBE0 hybrid DFT calculations provide reliable J values for a wide range of copper(II) oxides compounds, i.e. CuGeO3, BaCu2Si2O7, BaCu2Ge2O7, and La2CuO4.

Density-Functional Theory forf-Electron Systems: Theα−γPhase Transition in Cerium

The isostructural α-γ phase transition in cerium is analyzed using density-functional theory with different exchange-correlation functionals, in particular the PBE0 hybrid functional and the exact-exchange plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach. We show that the Hartree-Fock exchange part of the hybrid functional gives rise to two distinct solutions at zero temperature that can be associated with the α and γ phases of cerium. However, despite the relatively good structural and magnetic properties, PBE0 predicts the γ phase to be the stable phase at ambient pressure and zero temperature, in contradiction with low temperature experiments. EX+cRPA reverses the energetic ordering, which emphasizes the importance of correlation for rare-earth systems.

A DFT-D study of structural and energetic properties of TiO2 modifications

The structures and relative energies of the three naturally occurring modifications of titanium dioxide (rutile, brookite and anatase) were investigated. For an accurate description, atom-pairwise dispersion-corrected density functional theory (DFT-D) was applied. The DFT-D3 scheme was extended non-empirically to improve the description of Ti atoms in bulk systems. New dispersion coefficients were derived from TDDFT calculations for electrostatically embedded TiO2 clusters. The dispersion coefficient is reduced by a factor of 18 compared to the free atom. The three TiO2 modifications were optimized in periodic plane-wave calculations with dispersion-corrected GGA (PBE, revPBE) and hybrid density functionals (PBE0, revPBE0). The calculated lattice parameters are in good agreement with experimental data, in particular the dispersion-corrected PBE0 and revPBE0 hybrid functionals. Although the observed relative stabilities could not be reproduced in all cases, dispersion corrections improve the results. For an accurate description of bulk metal oxides, London dispersion is a prominent force that should not be neglected when energies and structures are computed with DFT. Additionally, the influence of dispersion interactions on the relaxation of the TiO2(110) surface is investigated.

High-pressure ionic and molecular phases of ammonia within density functional theory

We have studied ammonia under pressure using density functional theory (DFT) methods. We have used four density functionals; the local density approximation (LDA) and Perdew-Burke-Ernzerhof (PBE) semilocal functionals, the $\mathrm{PBE}+\mathrm{G}06$ semilocal functional which includes an empirical dispersion correction, and the PBE0 hybrid functional, finding results in reasonable agreement with the available experimental data in each case. Using a combination of DFT and a random-structure-searching technique, we have found a molecular phase of ammonia of space group symmetry $Pa\overline{3}$ which has not been reported in experimental studies. This phase is calculated to have a region of thermodynamic stability at low pressures with each of the four density functionals. Results with both the PBE and PBE0 functionals indicate that ammonium amide (NH${{}_{4}}^{+}$NH${{}_{2}}^{\ensuremath{-}}$) proton transfer ionic solids are stable at pressures above about 100 GPa.

Density-Functional Theory for f-Electron Systems: The alpha-gamma Phase Transition in Cerium

The isostructural {\alpha}-{\gamma} phase transition in cerium is analyzed using density-functional theory with different exchange-correlation functionals, in particular the PBE0 hybrid functional and the exact- exchange plus correlation in the random-phase approximation [(EX+cRPA)@PBE0] approach. We show that the Hartree-Fock exchange part of the hybrid functional actuates two distinct solutions at zero temperature that can be associated with the {\alpha} and {\gamma} phases of cerium. However, despite the relatively good structural and magnetic properties, PBE0 predicts the {\gamma} phase to be the stable phase at ambient pressure and zero temperature, in contradiction with low temperature experiments. EX+cRPA reverses the energetic ordering, which emphasizes the importance of correlation for rare- earth systems.

Passivation of CuI Quantum Dots

Using the first-principles band structure method, the electronic properties and optical properties of cupric iodide (CuI) quantum dots (QDs) are studied for the first time. A model is proposed to passivate the surface atoms of CuI QDs. In this model, pseudohydrogen atoms are used to passivate the dangling surface bonds, which remove the localized in-gap surface states. The size dependence of the QD gaps is obtained and is found to evolve as ΔEg = 1.60/d0.84 as the effective diameter d decreases. The energy of the calculated absorption peak is shifted higher with the decreasing d and the full width at half-maximum of the peak becomes larger as d increases, which are in good agreement with previous experiments. It is confirmed, although the local density approximation (LDA) calculations underestimate the band gap, that they give the trend of band gap shift as much as that obtained by the hybrid PBE0 for CuI QDs. These results provide understanding of the effects of the dimensionality of CuI nanocrystals, an...

DFT calculation of geometrical structure and electronic absorption spectra for neutral, mono-, and diprotonated forms of Risperidone (Risperdal)

Vertical electronic transitions to singlet valence states of an antipsychotic drug, Risperidone (Risperdal), in its neutral, mono-, and diprotonated forms have been calculated within the time-dependent density functional theory using the PBE0 hybrid functional with the 6–31+G* basis set. The results of the computations show that the lowest-energy allowed π–π* electronic excitation is affected by protonation effects, the spectral shifts of this transition being potentially useful to individuate the different forms of risperidone

High pressure ionic and molecular crystals of ammonia monohydrate within density functional theory

A combination of first-principles density functional theory calculations and a search over structures is used to predict the stability of a proton-transfer modification of ammonia monohydrate with space group P4∕nmm. The phase diagram is calculated with the Perdew-Burke-Ernzerhof (PBE) density functional, and the effects of a semi-empirical dispersion correction, zero point motion, and finite temperature are investigated. Comparison with MP2 and coupled cluster calculations shows that the PBE functional over-stabilizes proton transfer phases because too much electronic charge moves with the proton. This over-binding is partially corrected by using the PBE0 hybrid exchange-correlation functional, which increases the enthalpy of P4∕nmm by about 0.6 eV per formula unit relative to phase I of ammonia monohydrate and shifts the transition to the proton transfer phase from the PBE pressure of 2.8 GPa to about 10 GPa. This is consistent with experiment as proton transfer phases have not been observed at pressures up to ∼9 GPa, while higher pressures have not yet been explored experimentally.

Combined inelastic neutron scattering and solid-state DFT study of dynamics of hydrogen atoms in trioctahedral 1M phlogopite

Inelastic neutron scattering (INS) was used to study the vibrational dynamics of the hydrogen atoms in natural trioctahedral phlogopite, K0.93Na0.03(Mg2.47Fe0.22Al0.16Fe0.04Tl0.06)[Si2.84Al1.16]O10OH1.71F0.28Cl0.01, within the 50–1,000 cm−1 energy range. The INS spectra collected using direct geometry spectrometer SEQUOIA (ORNL) were interpreted by means of the solid-state DFT calculations covering both normal mode analysis and molecular dynamics. To optimize the structure and to calculate the vibrational modes under harmonic approximation, both a hybrid PBE0 and the AM05 functional were used, while the molecular dynamics calculations (60 ps/1 fs) were performed only with the computationally less-demanding AM05 functional. The main contributions to the dominant band within ~750–550 cm−1 are symmetric and antisymmetric Mg–O–H bending modes, overlapping with the skeletal stretching and bending modes causing weaker secondary movements of H atoms of inner hydroxyl groups. Signatures of the Mg–O–H bending modes appear down to ~400 cm−1, where a region of octahedra deformation modes starts. These deformations cause just shallow movements of the hydrogen atoms and are mirrored by the modes with close vibrational energies. The region from ~330 cm−1 down to the low-energy end of the spectrum portrays induced vibrations of the H atoms caused by deformation of individual polyhedra, translational vibrations of the parts of the 2:1 layer relative one to another, and librational and translational vibrations of the layer. The main difference between the INS spectrum of dioctahedral Al-muscovite and trioctahedral Mg-phlogopite is that the Mg–O–H modes are all assigned to in-plane vibrations of the respective hydrogen atoms.

Two-Dimensional Boron Monolayer Sheets

Boron, a nearest-neighbor of carbon, is possibly the second element that can possess free-standing flat monolayer structures, evidenced by recent successful synthesis of single-walled and multiwalled boron nanotubes (MWBNTs). From an extensive structural search using the first-principles particle-swarm optimization (PSO) global algorithm, two boron monolayers (α(1)- and β(1)-sheet) are predicted to be the most stable α- and β-types of boron sheets, respectively. Both boron sheets possess greater cohesive energies than the state-of-the-art two-dimensional boron structures (by more than 60 meV/atom based on density functional theory calculation using PBE0 hybrid functional), that is, the α-sheet previously predicted by Tang and Ismail-Beigi and the g(1/8)- and g(2/15)-sheets (both belonging to the β-type) recently reported by Yakobson and co-workers. Moreover, the PBE0 calculation predicts that the α-sheet is a semiconductor, while the α(1)-, β(1)-, g(1/8)-, and g(2/15)-sheets are all metals. When two α(1) monolayers are stacked on top each other, the bilayer α(1)-sheet remains flat with an optimal interlayer distance of ~3.62 Å, which is close to the measured interlayer distance (~3.2 Å) in MWBNTs.

First‐principles calculations on thermodynamic properties of BaTiO3rhombohedral phase

The calculations based on the linear combination of atomic orbitals have been performed for the low-temperature phase of BaTiO(3) crystal. Structural and electronic properties, as well as phonon frequencies were obtained using hybrid PBE0 exchange-correlation functional. The calculated frequencies and total energies at different volumes have been used to determine the equation of state and thermal contribution to the Helmholtz free energy within the quasiharmonic approximation. For the first time, the bulk modulus, volume thermal expansion coefficient, heat capacity, and Grüneisen parameters in BaTiO(3) rhombohedral phase have been estimated at zero pressure and temperatures form 0 to 200 K, based on the results of first-principles calculations. Empirical equation has been proposed to reproduce the temperature dependence of the calculated quantities. The agreement between the theoretical and experimental thermodynamic properties was found to be satisfactory.

First principles study of the oxygen vacancy formation and the induced defect states in hafnium silicates

Using first-principles density functional theory calculations, we have investigated the O vacancy formation and the relevant induced defect states in hafnium silicates over a wide range of compositions. The PBE0 hybrid density functional was employed for the analysis of the electronic properties and the charge transition levels of the O vacancy in crystalline HfSiO4 and in amorphous Hf-silicates, respectively. Based on the generated structure models, eight typical kinds of O coordination structures were identified in amorphous Hf-silicates. Our calculated results show that the positions of the induced defect energy levels in the band gap and the formation energies of O vacancy are largely determined by the local structures of the vacancy sites, which appear to be nearly independent of the composition of amorphous Hf-silicates. Our calculations also show that O vacancy can possess the negative-U behavior in crystalline HfSiO4 but not in amorphous Hf-silicates, where most of the O vacancies can simply exhibit the negative-U behavior as in the positive charge states. Given the measured band offset of 3.40 eV between Si and amorphous Hf-silicates, a considerable number of O vacancies were found to prefer to stay in the charge neutral state as the Fermi level lies within the band gap region of Si. Furthermore, due to its relatively higher formation energy, the concentration of O vacancy in Hf-silicates can be much lower than that in m-HfO2 when the Fermi level lies below the midgap region of Si. Accordingly, a significantly reduced flat band voltage shift and less transient threshold voltage instability can be found in Hf-silicates as compared with m-HfO2, which are in good agreement with the recent experimental findings.

Non-empirical improvement of PBE and its hybrid PBE0 for general description of molecular properties

Imposition of the constraint that, for the hydrogen atom, the exchange energy cancels the Coulomb repulsion energy yields a non-empirical re-parameterization of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) exchange-correlation energy functional, and of the related PBE hybrid (PBE0). The re-parameterization, which leads to an increase of the gradient contribution to the exchange energy with respect to the original PBE functional, is tested through the calculation of heats of formation, ionization potentials, electron affinities, proton affinities, binding energies of weakly interacting systems, barrier heights for hydrogen and non-hydrogen transfer reactions, bond distances, and harmonic frequencies, for some well known test sets designed to validate energy functionals. The results for the re-parameterized PBE GGA, called PBEmol, give substantial improvement over the original PBE in the prediction of the heats of formation, while retaining the quality of the original PBE functional for description of all the other properties considered. The results for the hybrids indicate that, although the PBE0 functional provides a rather good description of these properties, the predictions of the re-parameterized functional, called PBEmolβ0, are, except in the case of the ionization potentials, modestly better. Also, the results for PBEmolβ0 are comparable to those of B3LYP. In particular, the mean absolute error for the bond distance test set is 17% lower than the corresponding error for B3LYP. The re-parameterization for the pure GGA (PBEmol) differs from that for the hybrid (PBEmolβ0), illustrating that improvement at the GGA level of complexity does not necessarily provide the best GGA for use in a hybrid.

A TDDFT investigation of bay substituted perylenediimides: Absorption and intersystem crossing

The conformational structure and electronic spectra properties of a series of bay substituted perylenediimides (PDI) derivatives have been investigated by means of density functional theory (DFT) and time-dependent DFT. The B3LYP and PBE0 hybrid exchange-correlation functionals were applied in conjunction with the double-ζ quality SVP basis set. These compounds are interesting for organic materials science and as photosensitizers in cancer phototherapy (PDT), because of their intense absorption in the visible region. Results show that the substitution at the bay position of the PDI parent molecule with N-alkyl groups shifts the absorption maxima towards the red part of the visible spectrum (around 650-700 nm) as required for the applications in PDT. The main PDT action mechanisms have been investigated by computing of electron affinities, ionization potentials, triplet energies and spin-orbit matrix elements between singlet and triplet excited states.

First‐principles calculations on the four phases of BaTiO3

The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO(3) crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange-correlation density functional theory (DFT) functionals for four stable phases of BaTiO(3). A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO(3). The comparative phonon symmetry analysis in BaTiO(3) four phases has been made basing on the site symmetry and irreducible representation indexes for the first time.

Simulated Photoemission Spectra of Hydroxylated MgO(100) at Elevated Temperatures

Density functional theory has been used to investigate photoemission O1s core-level shifts (CLS) of hydroxylated MgO(100). Rapid proton exchange at elevated temperatures (300 K) yields broad features in the simulated photoemission signal, in good agreement with experimental observations. The results provide further evidence that the stable structure of hydroxylated MgO(100) consists of a partly dissociated water monolayer. Analysis of the CLS for adsorbed hydroxyl groups at different coverage reveals a pronounced effect on hydrogen bonding to neighboring H2O molecules. The inclusion of exact exchange by use of the hybrid PBE0 functional leads to quantitatively similar results as the gradient corrected PBE functional.

Difficulties in applying pure Kohn–Sham density functional theory electronic structure methods to protein molecules

Self-consistency-based Kohn–Sham density functional theory (KS-DFT) electronic structure calculations with Gaussian basis sets are reported for a set of 17 protein-like molecules with geometries obtained from the Protein Data Bank. It is found that in many cases such calculations do not converge due to vanishing HOMO–LUMO gaps. A sequence of polyproline I helix molecules is also studied and it is found that self-consistency calculations using pure functionals fail to converge for helices longer than six proline units. Since the computed gap is strongly correlated to the fraction of Hartree–Fock exchange, test calculations using both pure and hybrid density functionals are reported. The tested methods include the pure functionals BLYP, PBE and LDA, as well as Hartree–Fock and the hybrid functionals BHandHLYP, B3LYP and PBE0. The effect of including solvent molecules in the calculations is studied, and it is found that the inclusion of explicit solvent molecules around the protein fragment in many cases gives a larger gap, but that convergence problems due to vanishing gaps still occur in calculations with pure functionals. In order to achieve converged results, some modeling of the charge distribution of solvent water molecules outside the electronic structure calculation is needed. Representing solvent water molecules by a simple point charge distribution is found to give non-vanishing HOMO–LUMO gaps for the tested protein-like systems also for pure functionals.

The infrared spectrum of ortho-enstatite from reflectance experiments and first-principle simulations

Infrared (IR) spectra provide a rich amount of information concerning chemical composition, lattice structure, size and shape of circumstellar dust. Accurate reference data are then required for the analysis of the various detected components. This study provides the IR characterization of one of the most frequently observed compounds, MgSiO3 ortho-enstatite, and shows that IR experiments and ab initio techniques can be used synergically to obtain high-quality data concerning crystalline materials. The IR reflectance spectrum of synthetic ortho-enstatite was collected and compared to ab initio results (Gaussian-type basis set, PBE0 hybrid density functional theory (DFT) functional). An excellent agreement is observed both for vibrational frequencies (ν) and intensities, the latter estimated through the oscillator strength. The mean absolute difference between experimental and calculated ν is of the order of 7–8 cm−1 (43 out of 65 peaks differ by less than 10 cm−1, only four peaks differ by 15–19 cm−1). The static dielectric tensor and its components (electronic and ionic contributions) were measured and compared to calculated data: differences are in the 2–5 per cent range.

Performance of Conventional and Range-Separated Hybrid Density Functionals in Calculations of Electronic Circular Dichroism Spectra of Transition Metal Complexes

A number of density functionals, including 'pure' (nonhybrid) functionals, global hybrids, and range-separated hybrids, were used to calculate the electronic circular dichroism (CD) spectra of 10 tris-bidentate transition metal complexes. The results are compared to one another and to experimental CD spectra, in an effort to illustrate the shortcomings of particular approximations in time-dependent density functional theory (TDDFT). The use of an origin invariant formalism to calculate magnetic transition dipole moments with the help of gauge-including atomic orbitals (GIAOs) is also investigated. With valence basis sets of moderate flexibility, good agreement between GIAO results and rotatory strengths calculated from the dipole-velocity representation is obtained for selected test cases. Empirically broadened vertical CD spectra calculated with the global hybrid functionals B3LYP and PBE0 are found to agree overall the best with experimental CD spectra.

RASPT2/RASSCF vs Range-Separated/Hybrid DFT Methods: Assessing the Excited States of a Ru(II)bipyridyl Complex.

The excited states of the trans(Cl)-Ru(bpy)Cl2(CO)2 (bpy = bypyridyl) transition-metal (TM) complex are assessed using the newly developed second-order perturbation theory restricted active space (RASPT2/RASSCF) method. The delicate problem of partitioning the RAS subspaces (RAS1, RAS2, and RAS3) is addressed, being the choice of the RAS2 the bottleneck to obtain a balanced description of the excited states of different nature when TMs are present. We find that the RAS2 should be composed by the correlation orbitals involved in covalent metal-ligand bonds. The level of excitations within the RAS1 and RAS3 subspaces is also examined. The performance of different flavors of time-dependent density functional theory including pure, hybrid, meta-hybrid, and range-separated functionals in the presence of solvent effects is also evaluated. It is found that none of the functionals can optimally describe all the excited states simultaneously. However, the hybrid M06, B3LYP, and PBE0 functionals seem to be the best compromise to obtain a balanced description of the excited states of trans(Cl)-Ru(bpy)Cl2(CO)2, when comparing with the experimental spectrum. The conclusions obtained in this molecule should pave the road to properly treat excited states of larger Ru-polypyridyl complexes, which are of particular interest in supramolecular chemistry.