The shortcomings of semi-local and hybrid functionals: what we can learn from surface science studies

A study of the adsorption of CO on late 4d and $5d$ transition metal (111) surfaces (Ru, Rh, Pd, Ag, Os, Ir, and Pt) considering atop and hollow site adsorption is presented. The applied functionals include the gradient corrected PBE and BLYP functional, and the corresponding hybrid Hartree-Fock density functionals HSE and B3LYP. We find that PBE based hybrid functionals (specifically HSE) yield, with the exception of Pt, the correct site order on all considered metals, but they also considerably overestimate the adsorption energies compared to experiment. On the other hand, the semi-local BLYP functional and the corresponding hybrid functional B3LYP yield very satisfactory adsorption energies and the correct adsorption site for all surfaces. We are thus faced with a Procrustean problem: the B3LYP and BLYP functionals seem to be the overall best choice for describing adsorption on metal surfaces, but they simultaneously fail to account well for the properties of the metal, vastly overestimating the equilibrium volume and underestimating the atomization energies. Setting out from these observations, general conclusions are drawn on the relative merits and drawbacks of various semi-local and hybrid functionals. The discussion includes a revised version of the PBE functional specifically optimized for bulk properties and surface energies (PBEsol), a revised version of the PBE functional specifically optimized to predict accurate adsorption energies (rPBE), as well as the aforementioned BLYP functional. We conclude that no semi-local functional is capable to describe all aspects properly, and including non-local exchange also only improves some, but worsens other properties.Comment: 12 pages, 6 figures; to be published in New Journal of Physic

Reactive Force Field for Proton Diffusion in BaZrO3 using an empirical valence bond approach

A new reactive force field to describe proton diffusion within the solid-oxide fuel cell material BaZrO3 has been derived. Using a quantum mechanical potential energy surface, the parameters of an interatomic potential model to describe hydroxyl groups within both pure and yttrium-doped BaZrO3 have been determined. Reactivity is then incorporated through the use of the empirical valence bond model. Molecular dynamics simulations (EVB-MD) have been performed to explore the diffusion of hydrogen using a stochastic thermostat and barostat whose equations are extended to the isostress-isothermal ensemble. In the low concentration limit, the presence of yttrium is found not to significantly influence the diffusivity of hydrogen, despite the proton having a longer residence time at oxygen adjacent to the dopant. This lack of influence is due to the fact that trapping occurs infrequently, even when the proton diffuses through octahedra adjacent to the dopant. The activation energy for diffusion is found to be 0.42 eV, in good agreement with experimental values, though the prefactor is slightly underestimated.Comment: Corrected titl

Structural studies of titanyl and zirconyl sulphate hydrates

The aim of this thesis was to use a combination of computer simulations and experimental methods to gain insight into the unknown structure of the material titanyl sulphate dihydrate, TiOSO4*2H2O.Samples of TiOSO4*2H2O, along with TiOSO4*H2O, were produced and analysed using X-ray and neutron diffraction at both laboratory and synchrotron facilities. Both ex-situ and in-situ experiments were performed in order to analyse both the structure and growth of the crystals. The diffraction data resulting from these experiments was then used in various structure determination programs. A unit cell was able to be determined from the synchrotron X-ray diffraction patterns, and the first neutron diffraction pattern of a TiOSO4*2D2O sample was produced. In-situ synchrotron X-ray diffraction studies showed that the formation of the crystals followed a single step process, and indicated the possibility of meta-stable phases being present in the sample.In parallel with the experimental studies, computer modelling was used to develop and create candidate TiOSO4*2H2O structures. Initially both forcefield and first principles techniques were validated against a series of test cases. These included the first such calculations for the TiOSO4 and TiOSO4*H2O structures. The candidate structures of TiOSO4*2H2O thus produced were then used as input into the structural determination step.Structure determination was attempted with multiple approaches, using the determined unit cell and a variety of space group settings. Despite a thorough treatment and validation of the method using the diffraction data and known structure of TiOSO4*H2O, the structure was unable to be solved. However, structural motifs consistent with a layered, needle-like morphology, as observed in experimental studies, were commonly found to be present in solutions offered by these approaches. Future use of techniques such as the substitution of isotopic titanium in neutron diffraction may provide enough information to more accurately determine atomic positions

Exactitud del DFT en la Descripció de Propietats de Bulk de Metalls de Transició

Treballs Finals de Grau de Química, Facultat de Química, Universitat de Barcelona, Any: 2021, Tutor: Francesc Viñes SolanaDensity Functional Theory would be exact in estimating a polyelectronic chemical system energy, when the exchange-correlation (xc) functional would be known. Unfortunately, it is not, and has to be approximated, with dozens of xc functionals developed in the last decades, belonging to different rungs of Jacob’s ladder of xc improvement. In the case of Transition Metals (TMs), mostly describing few late TMs and their structural properties. Recent studies expanded the analysis covering different bulk properties and surface features. Here we carry out such performance evaluation on so far ignored xc functionals, either within the most basic local density approximations, including the, Hendin-Lundqvist (HL) and Perdew-Zunger (PZ) xc functionals, or within the Generalized Gradient Approximation (GGA), exploring the revised Perdew-Burke-Ernzerhof (revPBE) and the Armiento-Mattson (AM05) xc functionals. Aside from these, the recent meta-GGA Strongly Constrained Appropriately Normed (SCAN) functional is analysed, characterized by fulfilling all 17 mathematical conditions an xc must comply, plus the Bayesian Error Estimation Functional (BEEF) is explored, a functional where artificial intelligence, in the form of a machine learning algorithm, was used to adjust the mathematical expression to a large and diverse set of experimental results. The present results, acquired for 27 TM bulks in their crystallographic structures —body-centred cubic, face-centred cubic, and hexagonal close-packed—, reveal that none of the explored functionals is best in describing TM bulks, were Viñes-Vega (VV) excels, and highlighting that, while SCAN performance is acceptable, BEEF is not. When accounting for TM surface properties, acquired on 81 low-index Miller surfaces, the same situation applies, not improving the VV xc adapted for solids (VVsol)

Big Data meets Quantum Chemistry Approximations: The Δ\Delta-Machine Learning Approach

Chemically accurate and comprehensive studies of the virtual space of all possible molecules are severely limited by the computational cost of quantum chemistry. We introduce a composite strategy that adds machine learning corrections to computationally inexpensive approximate legacy quantum methods. After training, highly accurate predictions of enthalpies, free energies, entropies, and electron correlation energies are possible, for significantly larger molecular sets than used for training. For thermochemical properties of up to 16k constitutional isomers of C$_7$H$_{10}$O$_2$ we present numerical evidence that chemical accuracy can be reached. We also predict electron correlation energy in post Hartree-Fock methods, at the computational cost of Hartree-Fock, and we establish a qualitative relationship between molecular entropy and electron correlation. The transferability of our approach is demonstrated, using semi-empirical quantum chemistry and machine learning models trained on 1 and 10\% of 134k organic molecules, to reproduce enthalpies of all remaining molecules at density functional theory level of accuracy

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012

Consistent Atomic Geometries and Electronic Structure of Five Phases of Potassium Niobate from Density-Functional Theory

We perform a comprehensive theoretical study of the structural and electronic properties of potassium niobate (KNbO3) in the cubic, tetragonal, orthorhombic, monoclinic, and rhombohedral phase, based on density-functional theory. The influence of different parametrizations of the exchange-correlation functional on the investigated properties is analyzed in detail, and the results are compared to available experimental data. We argue that the PBEsol and AM05 generalized gradient approximations as well as the RTPSS meta-generalized gradient approximation yield consistently accurate structural data for both the external and internal degrees of freedom and are overall superior to the local-density approximation or other conventional generalized gradient approximations for the structural characterization of KNbO3. Band-structure calculations using a HSE-type hybrid functional further indicate significant near degeneracies of band-edge states in all phases which are expected to be relevant for the optical response of the material

DFT plus U study of the structures and properties of the actinide dioxides

The actinide oxides play a vital role in the nuclear fuel cycle. For systems where current experimental measurements are difficult, computational techniques provide a means of predicting their behaviour. However, to date no systematic methodology exists in the literature to calculate the properties of the series, due to the lack of experimental data and the computational complexity of the systems. Here, we present a systematic study where, within the DFT+U formulism, we have parametrized the most suitable Coulombic (U) and exchange (J) parameters for different functionals (LDA, PBE, PBE-Sol and AM05) to reproduce the experimental band-gap and lattice parameters for ThO2, UO2, NpO2, PuO2, AmO2 and CmO2. After successfully identifying the most suitable parameters for these actinide dioxides, we have used our model to describe the electronic structures of the different systems and determine the band structures, optical band-gaps and the Bulk moduli. In general, PBE-Sol provides the most accurate reproduction of the experimental properties, where available. We have employed diamagnetic order for ThO2, PuO2 and CmO2, transverse 3k antiferromagnetic order for UO2 and AmO2, and longitudinal 3k antiferromagnetic order for NpO2. The Fm m cubic symmetry is preserved for diamagnetic ThO2, PuO2 and CmO2 and longitudinal 3k NpO2. For UO2 and AmO2, the transverse 3k antiferromagnetic state results in Pa symmetry, in agreement with recent experimental findings. Although the electronic structure of ThO2 cannot be reproduced by DFT or DFT+U, for UO2, PuO2, NpO2, AmO2 and CmO2, the experimental properties are very well represented when U = 3.35 eV, 6.35 eV, 5.00 eV, 7.00 eV and 6.00 eV, respectively, with J = 0.00 eV, 0.00 eV, 0.75 eV, 0.50 eV and 0.00 eV, respectively

DFT+U study of the structures and properties of the actinide dioxides

The actinide oxides play a vital role in the nuclear fuel cycle. For systems where current experimental measurements are difficult, computational techniques provide a means of predicting their behaviour. However, to date no systematic methodology exists in the literature to calculate the properties of the series, due to the lack of experimental data and the computational complexity of the systems. Here, we present a systematic study where, within the DFT+U formulism, we have parametrized the most suitable Coulombic (U) and exchange (J) parameters for different functionals (LDA, PBE, PBE-Sol and AM05) to reproduce the experimental band-gap and lattice parameters for ThO2, UO2, NpO2, PuO2, AmO2 and CmO2. After successfully identifying the most suitable parameters for these actinide dioxides, we have used our model to describe the electronic structures of the different systems and determine the band structures, optical band-gaps and the Bulk moduli. In general, PBE-Sol provides the most accurate reproduction of the experimental properties, where available. We have employed diamagnetic order for ThO2, PuO2 and CmO2, transverse 3k antiferromagnetic order for UO2 and AmO2, and longitudinal 3k antiferromagnetic order for NpO2. The Fm m cubic symmetry is preserved for diamagnetic ThO2, PuO2 and CmO2 and longitudinal 3k NpO2. For UO2 and AmO2, the transverse 3k antiferromagnetic state results in Pa symmetry, in agreement with recent experimental findings. Although the electronic structure of ThO2 cannot be reproduced by DFT or DFT+U, for UO2, PuO2, NpO2, AmO2 and CmO2, the experimental properties are very well represented when U = 3.35 eV, 6.35 eV, 5.00 eV, 7.00 eV and 6.00 eV, respectively, with J = 0.00 eV, 0.00 eV, 0.75 eV, 0.50 eV and 0.00 eV, respectively