Self-consistent Density Functional Theory Research Articles

A DFT-D investigation of the energetic and structural aspects of dehydrogenation of methanol on a bimetallic surface PtGe(110) exploring the germanium effect on the anti-poisoning of pt(110) catalytic activity

Platinum is the most active pure metal for dehydrogenating methanol to create hydrogen, which is crucial for fuel cells. However, one significant disadvantage that reduces the effectiveness and long-term performance of platinum catalysts is their susceptibility to CO poisoning. In the current study, we examine and elucidate the promotional impact of Ge on Pt catalysts with increased resistance to deactivation by CO poisoning. We do this by combining partial density of states calculations with electronic configuration and Mulliken atomic charges. The self-consistent periodic density functional theory with dispersion correction (DFT-D) was used to investigate the methanol adsorption and dehydrogenation mechanisms on the surface of PtGe (110). On the surface, several adsorption mechanisms of pertinent intermediates were found. Furthermore, a thorough analysis of a reaction network comprising four reaction paths revealed that, in terms of activation barriers, the first O—H bond scission of CH3OH appears to be more advantageous than C—H bond cleavage on the PtGe(110) surface. Additionally, it has been demonstrated that the main route on the PtGe(110) surface is CH3OH→CH3O→CH2O→CHO→CO evolution. The remarkable differences in the predominant reaction pathway on the Pt(110) surface, and PtGe(110) surface indicate that the Ge-doped Pt Nano catalyst is more selective and resistant to deactivation.

GPAW: An open Python package for electronic structure calculations.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for the implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE), providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation, variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support for graphics processing unit (GPU) acceleration has been achieved with minor modifications to the GPAW code thanks to the CuPy library. We end the review with an outlook, describing some future plans for GPAW.

Density-Corrected Density Functional Theory for Open Shells: How to Deal with Spin Contamination.

Density functional theory (DFT) is usually used self-consistently to predict chemical properties, but the use of the Hartree-Fock (HF) density improves energetics in certain, well-characterized cases. Density-corrected (DC) DFT provides the theory behind this, but unrestricted Hartree-Fock (UHF) densities yield poor energetics in cases of strong spin contamination. Here we compare with restricted open-shell HF (ROHF) across 13 different functionals and two DC-DFT methods. For significant spin contamination, ROHF densities outperform UHF densities by as much as a factor of 3, depending on the energy functional, and ROHF-DFT improves over self-consistent DFT for most of the tested functionals. We refine the DC(HF)-DFT algorithm to use ROHF densities in cases of severe spin contamination.

Solution Self-Assembly of Amphiphilic Tadpole-like Giant Molecules Constructed by Monotethering Diblock Copolymer Chain onto a Nanoparticle.

The self-assembly behavior of a tadpole-like giant molecule (TGM) constructed from a hydrophobic nanoparticle (NP) monotethered by a single amphiphilic AB diblock copolymer chain was investigated by combining self-consistent field theory and density functional theory in solution. The effects of the hydrophobicities of the B blocks and NPs (i.e., solvent properties) on the self-assembly behavior of the TGMs were investigated in the cases of weak and strong intramolecular interactions (i.e., incompatibilities) between the components of giant molecules, respectively. Besides conventional ordered aggregates (such as spheres, rings, and vesicles) with hydrophobic B-cores covered by NP shells, several aggregates with novel hierarchical structures, including vesicles with NP-inserted hydrophobic walls, bead-string-like micelles, and long cylindrical micelles with NP bumps, were obtained by tuning the solvent properties under different intramolecular interactions. Noteworthy that the simulation results show that the arrangement of the NP bumps on the long cylindrical micelles may have a certain degree of helicity, which means that these micelles may have some unique electromagnetic features such as circular dichroism. Phase diagrams as a function of the hydrophobicities of the B blocks and NPs were constructed to show the formation conditions of these novel structures. These findings can not only offer new insights into understanding of the self-assembly behavior of the TGM in solution but also provide useful guidance for simple and efficient regulation of the morphology, as well as the NP distribution and arrangement of the ordered aggregates in experiments.

Density-Corrected Density Functional Theory for Molecular Properties.

Density-corrected (DC) density functional theory (DFT) has been proposed to overcome difficulties related to the self-interaction error. The procedure uses the Hartree-Fock electron density (matrix) non-self-consistently in conjunction with an approximate functional. DC-DFT has so far mainly been tested for total energy differences, whereas other types of molecular properties have not been evaluated systematically. This work focuses on the performance of DC-DFT for molecular properties, namely, dipole moments, static polarizabilities, and electric field gradients (EFGs) at atomic nuclei. Accurate reference data were generated from coupled-cluster theory to assess the performance of DC and self-consistent DFT calculations for twelve molecules, including diatomics with transition metals. DC-DFT does no harm in dipole moment calculations, but it negatively impacts the polarizability in at least one case. DC-DFT performs well for EFGs, even for the difficult case of CuCl.

Theory of magnetic 3d transition metal dopants in gallium nitride

Using first-principles density functional theory (DFT) methods and size-converged supercell models, we analyze the electronic and atomic structure of magnetic $3d$ transition metal dopants in cubic gallium nitride (c-GaN). All stable defect charge states for Fermi levels across the full experimental gap are computed using a method that correctly resolves the boundary condition problem (without a jellium approximation) and eliminates finite-size errors. The resulting computed defect levels are not impacted by the DFT band-gap problem, they span a width consistent with the experimental gap rather than being limited to the single-particle DFT gap. All defects with electronically degenerate (half-metal) ${T}_{d}$ ground states are found to have significant distortions, relaxing to ${D}_{2d}$ structures driven by the Jahn-Teller instability. This leads to insulating ground states for all substitutional $3d$ dopants, refuting claims in the literature that $+U$ or hybrid functional methods are required to avoid artificial half-metal results. Interpreting the ${d}^{n}$ atomic occupations within a crystal-field model and exchange splittings, we identify a systematic trend across the $3d$ transition metal series. Approaches to estimate excited-state energies as observed in photoluminescence from defect centers are assessed, ranging from a Koopmans-type single-particle energy interpretation to relaxed total energy differences in fully self-consistent DFT. The single-particle interpretations are found to be qualitatively predictive and the calculations are consistent with the limited available experimental data across the $3d$ dopant series. These results provide a baseline understanding to guide future studies and a conceptual framework within which to interpret new results.

Role of orbital selectivity on crystal structures and electronic states in BiMnO3 and LaMnO3 perovskites

Correlated oxides, such as ${\mathrm{BiMnO}}_{3}$ and ${\mathrm{LaMnO}}_{3}$, show a complex interplay of electronic correlations and crystal structure exhibiting multiple first-order phase transitions, some without a clear order parameter. The quantitative theoretical description of this temperature-dependent electronic-structural interplay in the vicinity of a Mott transition is still a challenge. Here we address this issue by simultaneously considering both structural and electronic degrees of freedom, within a self-consistent density functional theory with embedded dynamical mean field theory. Our results show the existence of novel electronic states characterized by the coexistence of insulating, semimetallic, and metallic orbitals. This state is in agreement with resonant x-ray scattering. We also show that electronic entropy plays a decisive role in both electronic and structural phase transitions. By self-consistent determination of both the electronic state and the corresponding crystal structure, we show that the temperature evolution of these phases can be quantitatively explained from first principles, thus demonstrating the predictive power of the theoretical method for both the structural and the electronic properties.

Robustness in half-metallicity, thermophysical and structural properties of Co2YAl (Y = Pd, Ag) Heuslers: a first-principles perspective

Heusler materials validates an extensive range of properties characteristically for the prospective high-tech interests. The extensive tunability of these materials through chemical substitutions as well as structural designs sorts the family explicitly fascinating. Self-consistent density functional theory, based on the full-potential linearized augmented plane wave is employed within the WIEN2k simulation code to investigate the structural, magneto-electronic and thermophysical properties of Co2PdAl and Co2AgAl Heusler compounds. The steadiness in P–V plot designates the absence of any structural phase transition from a cubic symmetry structure towards other structural phase. The GGA allows calculating the exchange-correlation energy. The proposed compounds are found stable in a Cu2MnAl prototype phase state. The cohesive and formation energy calculations approve the thermodynamic stability of compounds. The optimized lattice parameters in the stable Fm-3m phase are 5.90 Å for Co2PdAl and 5.97 Å for Co2AgAl respectively. At Fermi level, these alloys exhibit 100% spin polarization and display half-metallicity. The charge shearing among the constituents’ atoms is presented through the two-dimensional (2D) electron density plot with unique color contrast. The low anharmonicity possessed by the material is favored by the thermal parameters and compounds is predicted stable at a wider range of pressure and temperatures.

Constrained Density Functional Theory: A Potential-Based Self-Consistency Approach.

Chemical reactions, charge transfer reactions, and magnetic materials are notoriously difficult to describe within Kohn–Sham density functional theory, which is strictly a ground-state technique. However, over the last few decades, an approximate method known as constrained density functional theory (cDFT) has been developed to model low-lying excitations linked to charge transfer or spin fluctuations. Nevertheless, despite becoming very popular due to its versatility, low computational cost, and availability in numerous software applications, none of the previous cDFT implementations is strictly similar to the corresponding ground-state self-consistent density functional theory: the target value of constraints (e.g., local magnetization) is not treated equivalently with atomic positions or lattice parameters. In the present work, by considering a potential-based formulation of the self-consistency problem, the cDFT is recast in the same framework as Kohn–Sham DFT: a new functional of the potential that includes the constraints is proposed, where the constraints, the atomic positions, or the lattice parameters are treated all alike, while all other ingredients of the usual potential-based DFT algorithms are unchanged, thanks to the formulation of the adequate residual. Tests of this approach for the case of spin constraints (collinear and noncollinear) and charge constraints are performed. Expressions for the derivatives with respect to constraints (e.g., the spin torque) for the atomic forces and the stress tensor in cDFT are provided. The latter allows one to study striction effects as a function of the angle between spins. We apply this formalism to body-centered cubic iron and first reproduce the well-known magnetization amplitude as a function of the angle between local magnetizations. We also study stress as a function of such an angle. Then, the local collinear magnetization and the local atomic charge are varied together. Since the atomic spin magnetizations, local atomic charges, atomic positions, and lattice parameters are treated on an equal footing, this formalism is an ideal starting point for the generation of model Hamiltonians and machine-learning potentials, computation of second or third derivatives of the energy as delivered from density-functional perturbation theory, or for second-principles approaches.

A molecular analysis on nitrile-based collectors and their application to chalcopyrite flotation

In this research, one of the newest nitrile-based collectors so-called Tecflote-S10, was re-structured to increase its application in the flotation of copper-bearing sulfide minerals. For this purpose, a systematic theoretical study was conducted using a self-consistent periodic density functional theory (DFT) calculation to identify the adsorption properties of several new-designed nitrile-based collectors on the chalcopyrite (100) surface. In the new collector design, the long hydrocarbon chain of the Tecflote-S10 was replaced with a phenyl ring having several functional groups in different positions to address the electron-donating effect on the strength of the adsorption. The electronic properties and reactivity of new-designed collectors were evaluated, and a proper synthesis route was proposed. Collector-surface interaction and adsorption efficiency of new collectors on chalcopyrite surface were investigated using adsorption energy, the Fukui function (FF), and partial density of state (PDOS) analyses. It was found that replacing phenyl ring in the collector structure instead of a long hydrocarbon chain lead to an improvement in the collector adsorption efficiency. Accordingly, all new-designed collectors showed higher adsorption ability on chalcopyrite than the Tecflote-S10. However, collectors with the acronyms Tf(Ph)-3-R5, Tf(Ph)-N-2R1, and Tf(Ph)-N-2R2 with higher adsorption energies compared to others could be potentially used as a proper alternative in chalcopyrite flotation. To verify the results experimentally, futuristic adsorption, wettability, and floatability tests will be examined for this study.

Engineering of A-π-D-π-A system based non-fullerene acceptors to enhance the photovoltaic properties of organic solar cells; A DFT approach

In photovoltaic mechanization, central core alteration is an efficient tool to regulate photo-electronic features of the organic photovoltaic cells. Four fullerene free π-conjugated acceptor moieties (D1-D4) in the acceptor–donor-acceptor (A-D-A) geometries were constructed, by using quantum mechanical reproduction, from the reported acceptor molecule R with 10.27% and 13.97% solar efficiency for single and tandem organic photovoltaic cells. For the exhaustive investigation of reference molecule R and all other modified compounds through time dependent self-consistent field (TD-SCF) and density functional theory (DFT) method, MPW1PW91 functional with 6-31G (d,p) basis set was elected. Fundamental details about charge delocalization between the reference and constructed structures were obtained. Amongst all, D4 molecule elucidates the most shrunk band-gap of 2.24 eV, maximum absorption at 697 nm in chlorobenzene solvent, and a smaller binding energy of 0.47 eV that helps to effectively transmit the electron densities from bonding orbitals/HOMO to anti-bonding orbitals/LUMO. Electron and hole mobilities revealed by all constructed molecules were found to be lower when contrasted to the reference molecule R. Upon testing all modified molecules with polymer donor PTB7-Th, D3 moiety gave a higher open-circuit photo-voltage (Voc) value (1.23 eV) as compared to all other molecules, which shows that it has higher electronic charge transfer than other molecules. This current work indicates that by replacing the central part of R with some prominent donor cores, we can efficiently tune the binding energy, open-circuit photo-voltage, frontier molecular orbitals, absorption spectra, band-gap, and reorganization energy in the thus constructed structures. Thus in the future, tailored compounds ought to be suggested for the manufacture of OSCs with high solar efficiency.

Self-assembly of magnetic Co atoms on stanene

We have investigated magnetic Co atoms self-assembled on ultraflat stanene on Cu(111) substrate by utilizing scanning tunneling microscopy/spectroscopy (STM/STS) in conjunction with density functional theory (DFT). By means of depositing Co onto the stanene/Cu(111) held at 80 K, Co atoms have developed into monomer, dimer, and trimer structures containing one, two, and three Co atoms, respectively. As per atomically resolved topographic images and bias-dependent apparent heights, the atomic structure models based on Sn atoms substituted by Co atoms have been deduced, which are in agreement with both self-consistent DFT calculations and STM simulations. Apart from that, the projected density of states has revealed a maximum at around $\ensuremath{-}0.5$ eV from the Co-3${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ minority band, which contributes predominately to the peak feature at about $\ensuremath{-}0.3$ eV in tunneling conductance $(dI/dU)$ spectra taken at the Co atomic sites. As a result of the exchange splitting between the $\mathrm{Co}\text{\ensuremath{-}}3d$ majority and minority bands, there are nonzero magnetic moments, including about $0.60{\ensuremath{\mu}}_{B}$ in monomer, $0.56{\ensuremath{\mu}}_{B}$ in dimer, and $0.29{\ensuremath{\mu}}_{B}$ in trimer of the Co-atom assembly on the stanene. Such a magnetic Co-atom assembly, therefore, could provide the vital building blocks to stabilize the local magnetism on two-dimensional stanene with nontrivial topological properties.

Hubbard U parameters for transition metals from first principles

Using the linear response-based constrained local density approximation (cLDA) approach we systematically computed the Hubbard $U$ parameters for series of $3d, 4d,$ and $5d$ transition metals. We compare the results with estimations by the constrained random phase approximation (cRPA) method and discuss the performance of the self-consistent density functional theory + $U$ ($\mathrm{DFT}+U$) method for prediction of lattice parameters, work functions, $d$-bandwidths and $d$-band centers. Interestingly, we found that blindly applied the standard, fully localized limit (FLL) version of the $\mathrm{DFT}+U$ approach heavily overestimates the positions of $d$-band centers with respect to the Fermi level, but much better agreement with experiment is obtained when applying a more realistic, Wannier-type representation of $d$ orbitals for projection of $d$ states occupancies. We present another, independent estimate of the Hubbard $U$ parameter based on the comparison of Hartree-Fock and DFT eigenvalues, and positions of $d$-band centers. The so-derived estimates are surprisingly well consistent with the ones derived from the above-mentioned first principles approaches, and allow for validation of cRPA or cLDA results for the disputed cases, including Cu, Ag, and Au for which large $U$ parameters are obtained from the cLDA method.

Dynamical correlations in single-layer CrI3

Chromium triiodide is an intrinsically magnetic van der Waals material down to the single-layer limit. Here, we provide a first-principles description of finite-temperature magnetic and spectral properties of monolayer (ML) ${\mathrm{CrI}}_{3}$ based on fully charge self-consistent density functional theory (DFT) combined with dynamical mean-field theory, revealing a formation of local moments on Cr from strong local Coulomb interactions. We show that the presence of local dynamical correlations leads to a modification of the electronic structure of ferromagnetically ordered ${\mathrm{CrI}}_{3}$. In contrast to conventional $\mathrm{DFT}+U$ calculations, we find that the top of the valence band in ML ${\mathrm{CrI}}_{3}$ demonstrates essentially different orbital character for minority and majority spin states, which is closer to the standard DFT results. This leads to a strong spin polarization of the optical conductivity upon hole doping, which could be verified experimentally.

Effect of cation configuration and solvation on the band positions of zinc ferrite (100)

Zinc ferrite ZnFe_{2}O_{4} belongs to the spinel-type ferrites that have been proposed as photocatalysts for water splitting. The electronic band gap and the band edge positions are of utmost importance for the efficiency of the photocatalytic processes. We, therefore, calculated the absolute band energies of the most stable surface of ZnFe_{2}O_{4}, the Zn-terminated (100) surface at self-consistent hybrid density functional theory level. The effect of Fe- and Zn-rich environments, cation exchange as antisite defects and implicit solvation on the band positions is investigated. Calculated flat band potentials of the pristine surface model ranges from -0.9 to -0.8 V against SHE in vacuum. For Zn-rich (Fe-rich) models this changes 0.3–0.9 (0.0–0.7) V against SHE. Fe-rich models are closest to the experimental range of reported flat band potentials. Solvent effects lower the calculated flat band potentials by up to 1.8 eV. The calculated band gaps range from 1.5 to 2.9 eV in agreement with previous theoretical work and experiment. Overall, our calculations confirm the experimentally observed low activity of ZnFe_{2}O_{4} and its dependence on preparation conditions.Graphical abstract

Calculating dynamical mean-field theory forces in ab initio ultrasoft pseudopotential formalism

In this paper, we show how to calculate analytical atomic forces within self-consistent density functional theory + dynamical mean-field theory (DFT+DMFT) approach in the case when ultra-soft or norm-conserving pseudopotentials are used. We show how to treat the non-local projection terms arising within the pseudopotential formalism and circumvent the problem of non-orthogonality of the Kohn-Sham eigenvectors. Our approach is, in principle, independent of the DMFT solver employed, and here was tested with the Hubbard I solver. We benchmark our formalism by comparing against the forces calculated in Ce$_{2}$O$_{3}$ and PrO$_2$ by numerical differentiation of the total free energy, as well as by comparing the energy profiles against the numerically integrated analytical forces.

Coverage-dependent adsorption of nitrous oxide (N2O) on perfect and defective Cu(0 0 1) surfaces: A DFT investigation with and without van der Walls forces

The adsorption of the harmful nitrous oxide (N2O) on the perfect and defective Cu(001) surfaces was studied using self-consistent periodic density functional theory (DFT) with the GGA-PBE functional and vdW-DF dispersion correction. We have considered Cu adatom on Cu(001) surface as a model of defective Cu(001) surface. On the perfect Cu(001) surface, our GGA-PBE results show that the N2O molecule adsorbs very weakly onto the Cu(001) surface for 0.25 and 0.50 ML coverages, but a desorption is observed at 0.75 and 1.0 ML coverages. The inclusion of the vdW-DF correction increases the adsorption energies relative to values obtained from pure GGA-PBE functional, however, both types of processes, i.e., adsorption and desorption are retained with respect to the coverages. The dissociative adsorption of N2O on the bare Cu(001) surface is energetically preferred to the molecular adsorption, using the GGA-PBE functional. Regarding the defective surface, we note that the presence of a Cu adatom stabilize the adsorption of N2O better than a flat surface using the GGA-PBE functional, while the opposite effect is observed with vdW-DF correction. The electronic structure was analyzed in terms of the projected density of states (PDOS).

Self-energy self-consistent density functional theory plus dynamical mean field theory

We propose a hybrid approach which employs the dynamical mean-field theory (DMFT) self-energy for the correlated, typically rather localized orbitals and a conventional density functional theory (DFT) exchange-correlation potential for the less correlated, less localized orbitals. We implement this self-energy (plus charge density) self-consistent DFT+DMFT scheme in a basis of maximally localized Wannier orbitals using Wien2K, wien2wannier, and the DMFT impurity solver w2dynamics. As a testbed material we apply the method to SrVO$_3$ and report a significant improvement as compared to previous $d$+$p$ calculations. In particular the position of the oxygen $p$ bands is reproduced correctly, which has been a persistent hassle with unwelcome consequences for the $d$-$p$ hybridization and correlation strength. Taking the (linearized) DMFT self-energy also in the Kohn-Sham equation renders the so-called "double-counting" problem obsolete.

A self-consistent perturbative density functional theory for hard-core fluids: phase diagrams, structural and interfacial properties

The classical Density functional theory (DFT) has become a powerful tool to describe the microscopic structure of fluids as the radial distribution function. One of its particular capabilities is to express the thermodynamic properties of those fluids even under the influence of external potentials, such as fluid-solid interaction. However, good models for the Helmholtz free-energy functionals are necessary to improve the results. In this work, we present a self-consistent thermodynamic perturbation theory for the excess Helmholtz free-energy from the DFT applied to hard-core fluids. The new perturbation theory is solved self-consistently without any closure relation to solving the Ornstein-Zernike equation explicitly. We compare the performance of our self-consistent perturbation theory with the results obtained with the well-known second-order Barker-Henderson perturbation theory for the hard-core Yukawa and square-well fluids. Moreover, we propose two versions of the DFT to describe the perturbative contribution: one based on the weighted density approximation theory and another from a modified mean-field theory. The present results confirm the modified mean-field theory as a better option to calculate the thermodynamic and structural properties of hard-core fluids.

Identification of the Mott Insulating Charge Density Wave State in 1T-TaS_{2}.

We investigate the low-temperature charge density wave (CDW) state of bulk TaS_{2} with a fully self-consistent density-functional theory with the Hubbard U potential, over which the controversy has remained unresolved regarding the out-of-plane metallic band. By examining the innate structure of the Hubbard U potential, we reveal that the conventional use of atomic-orbital basis could seriously misevaluate the electron correlation in the CDW state. By adopting a generalized basis, covering the whole David star, we successfully reproduce the Mott insulating nature with the layer-by-layer antiferromagnetic order. Similar consideration should be applied for description of the electron correlation in molecular solid.