Gradient-corrected Density Functionals Research Articles

Band gap engineering of anatase TiO2 by ambipolar doping: A first principles study

Pure Anatase TiO2 is limited to photocatalytic activity only in the UV region of solar energy, (i.e Eg = 3.2 eV and λ = < 388 nm), which utilizes only 5% of the solar spectrum. Adding external impurities to Anatase TiO2 facilitates absorption of the visible spectrum by reducing the band gap of TiO2. Hence, we investigated the effect of Sc and V mono-doping and co-doping on the pure anatase TiO2 by Density Functional Theory (DFT). To elucidate the effect of doping on the electronic structure, the accurate band structure and density of states are derived using the hybrid functional methodology (HSE06). The defect formation energy of the dopants in their different charge states is calculated using the gradient-corrected density functionals using the PBE method. The bonding characteristics were analyzed using the charge density and electron-localization function (ELF) plots, which indicate that the impurities cause a local lattice distortion, which further influences the band features of TiO2. It is observed that the formation of additional energy states by the external impurities below the conduction band minimum, reduces the band gap of the material significantly. The optical absorption analysis shows that Sc and V co-doping not only improves the absorption in the UV region, but also reaches redshift absorption. Hence the ambipolar co-doping by Sc and V to the pure anatase TiO2 makes it a better for visible light active photocatalyst.

Structure, Dynamics, and Spectral Diffusion of Water from First-Principles Molecular Dynamics

We have carried out first-principles Born–Oppenheimer molecular dynamics (BOMD) simulations of heavy water using density functional theory in conjunction with either empirical van der Waals (vdW) corrections or semilocal (van der Waals) exchange and correlation functionals. Specifically, gradient-corrected density functionals (BLYP), semiempirical vdW methods (BLYP-D2, BLYP-D3, PBE-D3, revPBE-D3), and vdW density functionals (DRSLL-PBE, DRSLL-optB88) are applied to evaluate their accuracy in describing the hydrogen-bonded network of heavy water. Ab initio trajectories are used to calculate structural and dynamical properties, with special emphasis on vibrational spectral diffusion and hydrogen bond dynamics. Our results show that inclusion of vdW interactions in DFT-GGA significantly affects the structure of liquid water and results in a faster diffusion. The combination of BLYP and revPBE functionals with the semiempirical vdW method of Grimme et al. [J. Chem. Phys. 2010, 132, 154104] and modified B88 fu...

Hydration structure of Na+ and K+ from ab initio molecular dynamics based on modern density functional theory

Molecular dynamics (Born–Oppenheimer) simulations based on density functional theory have been carried out to investigate the solvation structure of monovalent Na+ and K+ cations in water under ambient conditions. Four recently proposed van der Waals (vdW) density functionals (LMKLL, DRSLL, DRSLL-PBE, DRSLL-optB88), the semiempirical vdW method of Grimme (BLYP-D3) and conventional gradient-corrected (GGA-BLYP) density functionals are applied in order to evaluate their accuracy in describing the hydration structure of alkali metal ions. Theoretical results are compared to available experimental data. Our results indicate that addition of corrections accounting for dispersion forces significantly improves the agreement between predicted and measured coordination numbers for both Na+ and K+ cations. Analysis of radial distribution functions brings further support to the notion that the choice of the generalised gradient approximation density functional impacts crucially on the computed structural properties. DRSLL-optB88 and BLYP-D3 provide the best agreement with experiment.

Infrared spectra of inorganic aerosols: ab initio study of (NH4)2SO4, NH4NO3, and NaNO3

The structures and vibrational spectra of inorganic aerosols, including ammonium sulfate (NH4)2SO4, ammonium nitrate NH4NO3, and sodium nitrate NaNO3 are investigated at the periodic ab initio quantum mechanical level with the CRYSTAL code, which is based on Gaussian basis sets. Local density (LDA), gradient-corrected (PW91), and hybrid (B3LYP) density functionals have been used and the results are compared with experiment. All three functionals reproduce the equilibrium geometry of these aerosols to a high level of accuracy. The calculations of the frequencies gave a mean absolute deviation from experiment of 3% for B3LYP, clearly showing that this functional performs extremely well in this case. The mean absolute deviation is about 7% and 6% for PW91 and LDA, respectively.

Communication: Electronic structure of the solvated chloride anion from first principles molecular dynamics

We present first principles molecular dynamics simulations of the chloride anion in liquid water performed using gradient-corrected and hybrid density functionals. We show that it is necessary to use hybrid functionals both for the generation of molecular dynamics trajectories and for the calculation of electronic states in order to obtain a qualitatively correct description of the electronic properties of the solution. In particular, it is only with hybrid functionals that the highest occupied molecular orbital of the anion is found above the valence band maximum of water, consistent with photoelectron detachment measurements. Similar results were obtained using many body perturbation theory within the G0W0 approximation.

Comparing van der Waals Density Functionals for CO2 Adsorption in Metal Organic Frameworks

The accuracy of five recently proposed van der Waals (vdW) density functionals (optB86b, optB88, optPBE, revPBE, and rPW86), the semiempirical vdW method of Grimme (DFT-D2), and conventional local (LDA) and gradient-corrected (GGA-PBE) density functionals are assessed with respect to experimental enthalpies (ΔH) for CO2 adsorption in four prototypical metal organic frameworks (MOFs) containing coordinatively unsaturated metal sites: M/DOBDC (M = Mg, Ni, and Co) and Cu-HKUST-1. Although the LDA and GGA functionals partially capture trends, they significantly overbind (LDA) and underbind (GGA) CO2 with respect to the experimental enthalpies. The addition of a semiempirical r–6 dispersion term to the GGA exchange-correlation energy using “off the shelf” DFT-D2 parameters results in a substantial improvement both in trends and in the magnitude of the adsorption enthalpies. However, on average this approach still underbinds CO2 as compared to the experimental data by ∼7 kJ/mol (18%). Better accuracy is obtained with some of the nonempirical vdW density functionals, with the revPBE-based functional of Dion et al. [Phys. Rev. Lett.2004, 92, 246401] yielding an average error of only ∼2 kJ/mol (4%) relative to experiment. This improvement in energetics is accompanied by a slight decrease in the accuracy of predicted structures, as the revPBE functional overestimates the metal–CO2 bond length by about 10%. The identification of an efficient vdW density functional capable of predicting the thermodynamics of CO2 adsorption will facilitate rapid computational screening for optimal CO2 adsorbents.

On the influence of basis sets and quantum chemical methods on the prediction accuracy of COSMO-RS

This paper examines how the accuracy of activity coefficients at infinite dilution calculated from the conductor-like screening model for real solvents (COSMO-RS) depends on the basis set and the quantum chemical method used. Activity coefficients at various temperatures serve as experimental parameters for optimising the COSMO-RS parameters. A modification of the electrostatic misfit term of the energy function of COSMO-RS is presented that leads to a slightly higher accuracy. COSMO-RS parameter sets for nine different systematically varied basis sets using the density functional theory with the BP86 functional show that at least a valence double-zeta basis set is necessary for good accuracy. Larger basis sets show no advantages. Investigations of eight different quantum chemical calculation methods using a valence triple-zeta basis set are documented. Hartree-Fock and local density approximations give relatively poor results. The gradient-corrected density functionals investigated and the B3LYP hybrid functional show practically identical accuracy. The most accurate parameterisation was obtained with MP2.

First Principles Simulations of the Structural and Dynamical Properties of Hydrated Metal Ions Me2+and Solvated Metal Carbonates (Me = Ca, Mg, and Sr)

The structural and dynamical properties of the alkaline earth metal ions Mg2+, Ca2+, and Sr2+ and their carbonate and bicarbonate complexes in aqueous solution are examined through first principles molecular dynamics simulations based on the density functional theory. Calculations were conducted in explicit heavy water molecules and at the average temperature of 400 K, conditions which are necessary to obtain a liquid-like water structure and diffusion time-scales when using gradient corrected density functionals. According to these simulations, the magnesium ion undergoes a significant contraction of its coordination sphere in the Mg(H)CO3(+) aqueous complex, whereas calcium and strontium increase their average first shell coordination number when coordinated to HCO3− or CO32−. The analysis of the water exchange processes in the hydration shells of the metals suggests the following order for metal reactivity in solution: Mg2+ < Ca2+ < Sr2+. Moreover, our simulations suggest that the structures of the mos...

Calculation of the first static hyperpolarizability tensor of three-dimensional periodic compounds with a local basis set: A comparison of LDA, PBE, PBE0, B3LYP, and HF results

The computational scheme for the evaluation of the second-order electric susceptibility tensor in periodic systems, recently implemented in the CRYSTAL code within the coupled perturbed Hartree-Fock (HF) scheme, has been extended to local-density, gradient-corrected, and hybrid density functionals (coupled-perturbed Kohn-Sham) and applied to a set of cubic and hexagonal semiconductors. The method is based on the use of local basis sets and analytical calculation of derivatives. The high-frequency dielectric tensor (epsilon(infinity)) and second-harmonic generation susceptibility (d) have been calculated with hybrid functionals (PBE0 and B3LYP) and the HF approximation. Results are compared with the values of epsilon(infinity) and d obtained from previous plane-wave local density approximation or generalized gradient approximation calculations and from experiment. The agreement is in general good, although comparison with experiment is affected by a certain degree of uncertainty implicit in the experimental techniques.

Synthesis and Structural and Computational Studies of a Conformationally Locked (η1-Perfluoroalkylidene)(η2-alkene) Transition Metal Complex: Ir(Cp*)(CFCF3)(C2H4)

Reaction of Cp*Ir(CO)(C2F5)I with N-methylmorpholine-N-oxide (NMO) afforded the iodide-bridged dimer complex [Cp*Ir(C2F5)I]2. The dimer reacted reversibly with ethylene to give Cp*Ir(CH2═CH2)(C2F5)I, which dissociated ethylene under reduced pressure. Treatment of Cp*Ir(CH2═CH2)(C2F5)I with AgOTf gave isolable Cp*Ir(CH2═CH2)(C2F5)(OTf). Reduction of this compound with potassium graphite gave the first example of an (ethylene)(perfluoroethylidene) complex, Cp*Ir(CH2═CH2)(CFCF3), which has been characterized crystallographically, spectroscopically, and computationally. Comparisons of a variety of hybrid and gradient-corrected density functionals in predicting geometric parameters, energies, barriers to ligand rotation, and possible alkene metathesis in Cp*Ir(CH2═CH2)(CFCF3) are presented.

The 1,4-phenylenediisocyanide dimer: gas-phase properties and insights into organic self-assembled monolayers

The 1,4-phenylenediisocyanide (PDI) dimer serves as an intriguing case of the substituted benzene dimer, as well as a prototype system for self-assembled monolayers of organic isocyanide complexes. Structures and binding energies are explored using recently developed dual-basis second-order Møller-Plesset perturbation theory energies and gradients. The structures are dictated by a combination of dispersion and electrostatics, a combination not properly treated with local or gradient-corrected density functionals. The PDI dimer binds more than twice as strongly as unsubstituted benzene dimers in several configurations, and greater directional specificity between parallel-displaced and T-shaped structures is observed. A rotated-parallel structure is the predicted lowest-energy, gas-phase configuration, in which the isocyanide ligands are staggered on the monomers. Relevant potential energy curves of the dimer are also presented, and insights into PDI monolayer formation on metal surfaces are explored via simple two-body models. Based on the adsorbate interaction alone, a high-coverage configuration and non-vertical tilt are predicted to be favorable, although the total binding for PDI in these configurations is still insufficient to form ordered monolayers, a result consistent with previous experimental findings. Additional phenyl rings (biphenyldiisocyanide, triphenyldiisocyanide) significantly stabilize the interaction and provide the additional dispersion necessary for an ordered monolayer.

Application of Hybrid Functionals to the Modeling of NO Adsorption on Cu−SAPO-34 and Co−SAPO-34: A Periodic DFT Study

The structural and chemical properties of Cu- and Co-exchanged silicoaluminophosphates with a chabazite-type structure (SAPO-34) and the adsorption of NO molecules on the extraframework cations have been studied using periodic density functional (DFT) calculations using both convential gradient-corrected exchange-correlation functionals and hybrid functionals mixing exact (i.e., Hartree−Fock) and DFT exchange. To assess the importance of the cation-support interaction, comparative studies of NO adsorption on isolated metal atoms and ions have been performed. We find that whereas the geometrical properties for stoichiometric aluminophosphate (ALPO-34) and protonated silicoaluminophosphate (H−SAPO-34) calculated using both types of functionals are essentially on par, the hybrid functionals predict much wider energy gaps in better agreement with experiment. Significant differences arise for the coordination of extraframework cations in the metal-exchanged silicoaluminophosphates (Cu−SAPO-34 and Co−SAPO-34) and, in particular, for the electronic eigenstates of the cations. The different metal−framework coordination and the differences in the electronic properties lead to markedly different predictions of the chemical reactivities: hybrid functionals predict a weaker binding of molecular adsorbates such as NO. The reduction of the adsorption energy is more pronounced for the magnetic Cu(II) and Co(II) cations than for the nonmagnetic Cu(I) cation. This is a consequence of a much larger exchange splitting of the d states of the cation and also of an enhanced ligand-field splitting due to the binding to the framework. The occupied d states of the transition-metal cations are shifted to larger binding energies, and the empty d states are located in the upper part of the energy gap. Hybrid functionals tend to overestimate the N−O stretching frequency even for the isolated molecule and for gas-phase nitrosyls, whereas conventional functionals predict eigenvalues that are too low. This tendency is also reflected in the vibrational spectra of the Cu(Co)−NO adsorption complexes, whereas the adsorption-induced frequency shifts predicted by both types of functionals are in reasonable agreement with experiment. Significant differences are found in the prediction of the spin states of the adsorption complexes. Altogether, we conclude that conventional gradient-corrected DFT functionals describe these complex materials with good accuracy, whereas the inclusion of exact exchange in the hybrid functionals does not lead to improved performance for the metal-exchanged systems.

Adiabatic Corrections to Density Functional Theory Energies and Wave Functions

The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT.

Self-consistentGWcalculations for semiconductors and insulators

We present $GW$ calculations for small and large gap systems comprising typical semiconductors (Si, SiC, GaAs, GaN, ZnO, ZnS, CdS, and AlP), small gap semiconductors (PbS, PbSe, and PbTe), insulators (C, BN, MgO, and LiF), and noble gas solids (Ar and Ne). It is shown that the ${G}_{0}{W}_{0}$ approximation always yields too small band gaps. To improve agreement with experiment, the eigenvalues in the Green's function $G$ $(G{W}_{0})$ and in the Green's function and the dielectric matrix $(GW)$ are updated until self-consistency is reached. The first approximation leads to excellent agreement with experiment, whereas an update of the eigenvalues in $G$ and $W$ gives too large band gaps for virtually all materials. From a pragmatic point of view, the $G{W}_{0}$ approximation thus seems to be an accurate and still reasonably fast method for predicting quasiparticle energies in simple $sp$-bonded systems. We furthermore observe that the band gaps in materials with shallow $d$ states (GaAs, GaN, and ZnO) are systematically underestimated. We propose that an inaccurate description of the static dielectric properties of these materials is responsible for the underestimation of the band gaps in $G{W}_{0}$, which is itself a result of the incomplete cancellation of the Hartree self-energy within the $d$ shell by local or gradient corrected density functionals.

On the performance of gradient-corrected approximation functionals and polarizable continuum model in the study of 1,2,3-triazine in water

Time dependent density functional theory (TD-DFT) using different gradient-corrected density functionals, Becke's three-parameter hybrid method using the Lee–Yang–Parr correlation functional (B3LYP), Becke's exchange functional and Lee–Yang–Parr correlation functional (BLYP) and an hybrid DFT/HF approach based on the Perdew–Burke–Erzenrhof exchange-correlation functional (PBE1PBE), are applied to calculate vertical transitions from ground to the low-lying singlet electronic excited states of 1,2,3-triazine, in vacuum and in aqueous solution. Our results are in excellent agreement with a recent high resolution UV/VUV experimental work in the gas phase and with previous high level computational methods in vacuum and in solution. The results clearly show the potentialities of the combined TD-DFT/CPCM approach, within the gradient-corrected approximation (GGA), on aquo-complexes for the study of structural and spectroscopic properties in liquid phase.

On the accuracy of density functional theory in transition metal chemistry

Density Functional Theory has become very widely used to study the electronic structure and related properties of transition metal complexes. Despite the many successes obtained using modern functionals, care is still needed as quite large errors can occur. These can be best understood by taking into consideration how density functional theory works, and how well it performs for the simpler case of main-group compounds. This serves to highlight the critical role of the exchange functional, which describes such varied effects as electron self-interaction, static (or non-dynamic) correlation, and dynamic correlation. A poor balance between these effects can lead to significant errors even for main-group compounds. This is even truer for transition metal compounds. Benchmark data published in the last year suggest that all existing functionals can lead to severe errors for some transition metal compounds. There is a slight trend for systems involving more static correlation to be treated better using second- or third-generation gradient-corrected or kinetic energy density functionals, rather than hybrid functionals. This trend is however quite variable from one type of compound to another. Computed spin-state splittings are highly variable from one functional to another, and this is also diagnostic of differences in the extent of static correlation. The increasing awareness of transition metal compounds by the developers of new exchange–correlation functionals should lead in the medium term to more accurate and hence (even) more useful functionals.

Calculation of 19F NMR chemical shifts in uranium complexes using density functional theory and pseudopotentials

Abstract The 19 F NMR nuclear shieldings of fluoride ligands in uranium complexes UF n Cl 6 − n ( n = 1–6) have been studied quantum chemically, using different exchange-correlation functionals and a relativistic small-core pseudopotential on uranium. In contrast to a recent study [G. Schreckenbach, S.W. Wolff, T. Ziegler, J. Phys. Chem. A 104 (2000) 8244] we find that pseudopotential methods are well suited for calculations of ligand chemical shifts in actinide compounds, provided that a sufficiently small core-size definition is used. With modern relativistic small-core pseudopotentials and gradient-corrected density functionals we obtain results of the same accuracy as were found with all-electron density functional ZORA or Pauli calculations. The unusually large dependence of the shifts on the exchange-correlation functional is discussed in the context of the description of σ- and π-bonding, and also with respect to the accuracy of the optimized structures.

Infrared Spectra of Hydrogen‐Bonded Ionic Crystals: Ab initio Study of Mg(OH)2 and β‐Be(OH)2.

AbstractFor Abstract see ChemInform Abstract in Full Text.

The performance of nonhybrid density functionals for calculating the structures and spin states of Fe(II) and Fe(III) complexes.

The local density approximation and a range of nonhybrid gradient corrected density functionals (PW91, BLYP, PBE, revPBE, RPBE) have been assessed with respect to the prediction of geometries and spin-state energy preferences for a range of homoleptic Fe(II)L6 and Fe(III)L6 complexes, where L = Cl-, CN-, NH3, pyridine, imidazole, H2O, O=CH2 and tetrahydrofuran. While the qualitative spin-state energies from in vacuo structure optimizations are reasonable the geometries are relatively poorly treated, especially for [FeCl6]3-/4-. Structural results for all the complexes are significantly improved by including environmental effects. The best compromise between structural and spin-state predictive accuracy was obtained for the RPBE functional in combination with the COSMO solvation approach. This approach systematically overestimates the energetic preference for a low spin state, which is partly due to the well-known effect of the lack of exact exchange in nonhybrid functionals and partly due to the larger solvation stabilization of low-spin complexes that have shorter bond lengths and thus smaller molecular volumes than their high-spin partners. Calculations on low spin [Fe(bipy)3]2+ and [Fe(phen)3]2+ and their ortho methyl substituted analogs, which are high spin at room temperature but cross over to low spin at low temperature, suggest the RPBE/COSMO combination generates low spin states which are too stable by approximately 13 kcal mol(-1).

Infrared Spectra of Hydrogen-Bonded Ionic Crystals: Ab Initio Study of Mg(OH)2 and β-Be(OH)2

Ab initio periodic calculations have been performed with the CRYSTAL code, which is based on Gaussian basis sets, to investigate the structure and OH vibrational features (both harmonic and anharmonic) of Mg(OH)2 and β-Be(OH)2 crystals, which represent two extreme situations in which the OH group can be involved. In the latter, it participates in H-bonds of intermediate strength, whereas, in the former, it is essentially free. Hartree−Fock (HF), local density (LDA), gradient-corrected (PW91), and hybrid (B3LYP) density functionals have been used and the results compared with experiment. For Mg(OH)2, the B3LYP OH frequencies are in very good agreement with experiment, whereas, for β-Be(OH)2, they are ∼100 cm-1 too low. LDA grossly underestimates the OH frequency (330 and 800 cm-1 for Mg(OH)2 and β-Be(OH)2, respectively), and PW91 moderately does (170 and 400 cm-1, respectively).