Density Functional Theory Description Research Articles

Minimal Experimental Bias on the Hydrogen Bond Greatly Improves Ab Initio Molecular Dynamics Simulations of Water.

Experiment directed simulation (EDS) is a method within a class of techniques seeking to improve molecular simulations by minimally biasing the system Hamiltonian to reproduce certain experimental observables. In a previous application of EDS to ab initio molecular dynamics (AIMD) simulation based on electronic density functional theory (DFT), the AIMD simulations of water were biased to reproduce its experimentally derived solvation structure. In particular, by solely biasing the O-O pair correlation function, other structural and dynamical properties that were not biased were improved. In this work, the hypothesis is tested that directly biasing the O-H pair correlation (and hence the H-O···H hydrogen bonding) will provide an even better improvement of DFT-based water properties in AIMD simulations. The logic behind this hypothesis is that for most electronic DFT descriptions of water the hydrogen bonding is known to be deficient due to anomalous charge transfer and over polarization in the DFT. Using recent advances to the EDS learning algorithm, we thus train a minimal bias on AIMD water that reproduces the O-H radial distribution function derived from the highly accurate MB-pol model of water. It is then confirmed that biasing the O-H pair correlation alone can lead to improved AIMD water properties, with structural and dynamical properties even closer to experiment than the previous EDS-AIMD model.

SAPT codes for calculations of intermolecular interaction energies.

Symmetry-adapted perturbation theory (SAPT) is a method for calculations of intermolecular (noncovalent) interaction energies. The set of SAPT codes that is described here, the current version named SAPT2020, includes virtually all variants of SAPT developed so far, among them two-body SAPT based on perturbative, coupled cluster, and density functional theory descriptions of monomers, three-body SAPT, and two-body SAPT for some classes of open-shell monomers. The properties of systems governed by noncovalent interactions can be predicted only if potential energy surfaces (force fields) are available. SAPT is the preferred approach for generating such surfaces since it is seamlessly connected to the asymptotic expansion of interaction energy. SAPT2020 includes codes for automatic development of such surfaces, enabling generation of complete dimer surfaces with a rigid monomer approximation for dimers containing about one hundred atoms. These codes can also be used to obtain surfaces including internal degrees of freedom of monomers.

Shallow impurity band in ZrNiSn

ZrNiSn and related half Heusler compounds are candidate materials for efficient thermoelectric energy conversion with a reported thermoelectric figure-of-merit of n-type ZrNiSn exceeding unity. Progress on p-type materials has been more limited, which has been attributed to the presence of an impurity band, possibly related to Ni interstitials in a nominally vacant 4d position. The specific energetic position of this band, however, has not been resolved. Here, we report the results of a concerted theory-experiment investigation for a nominally undoped ZrNiSn, based on the electrical resistivity, the Hall coefficient, the Seebeck coefficient, and the Nernst coefficient, measured in a temperature range from 80 to 420 K. The results are analyzed with a semianalytical model combining a density functional theory (DFT) description for ideal ZrNiSn, with a simple analytical correction for the impurity band. The model provides a good quantitative agreement with experiment, describing all salient features in the full temperature span for the Hall, conductivity, and Seebeck measurements, while also reproducing key trends in the Nernst results. This comparison pinpoints the impurity band edge to 40 meV below the conduction band edge, which agrees well with a separate DFT study of a supercell containing Ni interstitials. Moreover, we corroborate our result with a separate study of the ZrNiSn0.9Pb0.1 sample showing similar agreement with an impurity band edge shifted to 32 meV below the conduction band.

Ab Initio Extended Hartree-Fock plus Dispersion Method Applied to Dimers with Hundreds of Atoms.

The Hartree-Fock plus dispersion plus first-order correlation (HFDc(1)) method consists in augmenting the HF interaction energy by the correlation part of the first-order interaction energy and the second-order dispersion and exchange-dispersion energies. All of the augmentation terms are computed using the symmetry-adapted perturbation theory based on density functional theory description of monomers [SAPT(DFT)]; thus, HFDc(1) is a fully ab initio method. A partly empirical version of this method, HFDasc(1), uses a damped asymptotic expansion for the dispersion plus exchange-dispersion term fitted to SAPT(DFT) ab initio values. The HFDc(1) interaction energies for dimers in the S22, S66, S66x8, NCCE31, IonHB, and UD-ARL benchmark data sets are more accurate than those given by most ab initio methods with comparable costs. HFDc(1) can be used routinely for dimers with nearly 200 atoms, such as included in the S12L benchmark set, giving results comparable to those obtained by the most expensive methods applicable.

Accurate Ground State Electronic and Related Properties of Hexagonal Boron Nitride (h-BN)

We present an ab initio, self consistent density functional theory (DFT) description of ground state electronic and related properties of hexagonal boron nitride (hex-BN). We used a local density approximation (LDA) potential and the linear combination of atomic orbitals (LCAO) formalism. We rigorously implemented the Bagayoko, Zhao, and Williams (BZW) method, as enhanced by Ekuma and Franklin (BZW-EF). The method ensures a generalized minimization of the energy that is far beyond what can be obtained with self-consistency iterations using a single basis set. The method leads to the ground state of the material, in a verifiable manner, without employing over-complete basis sets. Consequently, our results possess the full, physical content of DFT, as per the second DFT theorem. We report the ground state band structure, band gap, total and partial densities of states, and electron and hole effective masses. Our calculated, indirect band gap of 4.37 eV,obtained with room temperature experimental lattice constant, is in agreement with the measured value of 4.3 eV. The valence band maximum is slightly to the left of the K point, while the conduction band minimum is at the M point. Our calculated total width of the valence and total and partial densities of states are in agreement with corresponding, experimental findings.

Impact of Approximate DFT Density Delocalization Error on Potential Energy Surfaces in Transition Metal Chemistry.

For approximate density functional theory (DFT) to be useful in catalytic applications of transition metal complexes, modeling strategies must simultaneously address electronic, geometric, and energetic properties of the relevant species. We show that for representative transition metal triatomics (MO2, where M = Cr, Mn, Fe, Co, or Ni) and related diatomics the incorporation of Hartree-Fock (HF) exchange in most cases improves the properties of the Born-Oppenheimer potential energy surface (PES) with respect to accurate experimental or CCSD(T) references. We rationalize this observation by noting reduced delocalization obtained with hybrid functionals (20-40% HF exchange), as evidenced by reduced hybridization of non-bonding orbitals and increases in metal partial charges. Although we show that the optimal exchange fraction is both property and system specific, incorporating HF exchange synergistically improves properties of density, structure, and energetics within a single PES characterized by moderately covalent bonding. The same improvement is not observed in the ordering of MO2 spin states, as good agreement of semi-local DFT spin state ordering is worsened by over-stabilization of higher spin states when HF exchange is added. More work is needed to understand minimal functional forms capable of improving multiple properties with respect to semi-local DFT descriptions of transition metal chemistry.

Polarizable Embedding with a Transferable H2O Potential Function I: Formulation and Tests on Dimer.

The incorporation of mutual polarization in multiscale simulations where different regions of the system are treated at different level of theory is important in studies of, for example, electronic excitations and charge transfer processes. We present here an energy functional for describing a quantum mechanics/molecular mechanics (QM/MM) scheme that includes reciprocal polarization between the two subsystems. The inclusion of polarization alleviates shortcomings inherent in electrostatic embedding QM/MM models based on point-charge force fields. A density functional theory (DFT) description of the QM subsystem is coupled to a single center multipole expansion (SCME) description of H2O molecules in the MM subsystem that includes anisotropic dipole and quadrupole polarizability as well as static multipoles up to and including the hexadecapole. The energy functional and the coupling scheme is general and can be extended to arbitrary order in terms of both the static and induced moments. Tests of the energy surface for the H2O dimer show that the QM/MM results lie in between the pure DFT and pure SCME values. The consistency of the many-body contributions to the energy and analytical forces is demonstrated for an H2O pentamer.

Hybrid density functional theory description of non-metal doping in perovskite BaTiO3 for visible-light photocatalysis

Non-metal doping is one of the major strategies to reduce the large band gap of semiconductors into the visible light region. In this work, first-principles calculations based on density functional theory have been performed to investigate the effect of non-metal dopants X (X=C, Si, N, P, S, Se, F, Cl, Br and I) with X@O and X@Ti on the geometric and electronic structures, stability, and photocatalytic property of perovskite BaTiO3 with wide band gap. Our calculations provide reasonable explanations on experimental observations of the narrow band gap for N-doped BaTiO3. It is found that the preferred site of dopant X depends on the ionic size of dopant with respect to that of O2− or Ti4+. The complexity of doping depends on the distortion of local structure and electronegativity of dopants. C- and I-doped BaTiO3 with X@O induce the extension of absorption edge to visible light range with improved abilities of photocatalytic water splitting. The replacement of lattice O/Ti with S or Se not only leads to the band gap narrowing but also enhances the photo-oxidation and photo-reduction capabilities of semiconductor. Further experimental studies are highly demanded to explore the promising application of these four systems for the photocatalytic field.

New strategies for colloidal-quantum-dot-based intermediate-band solar cells.

The intermediate-band solar cell (IBSC) concept promises to increase the efficiency limit in a single-junction solar cell through the absorption of below-bandgap-energy photons. Despite their operating principle having been proposed over 20 years ago, IBSCs have not delivered on this promise yet, and the devices fabricated so far, mainly based on embedded epitaxial quantum dots, have instead operated with lower efficiency than conventional solar cells. A new paradigm, based on the exploitation as the intermediate band of the intragap states naturally occurring in the density functional theory description of colloidal (i.e., chemically synthesized) quantum dots, was suggested recently. Here, we revisit this intriguing concept unveiling its shortcomings and propose two alternative schemes: in the first, the localized electron surface trap states, ubiquitously found in commonly synthesized colloidal quantum dots, are used as intermediate bands in strongly coupled films made of small InAs nanocrystals and, in the second scheme, the intermediate band is provided by the conduction-band-minimum-derived miniband in films of larger InAs nanocrystals. Both schemes yield estimated limiting IBSC efficiencies exceeding Shockley-Queisser's limit for a single absorber.

Coverage-dependent anisotropy of the NTCDA/Ag(111) interface state dispersion

We employ density functional theory (DFT) to analyze the dispersion of the electronic state that exists at the commensurate interface between a monolayer of 1,4,5,8-naphthalene-tetracarboxylic acid dianhydride (NTCDA) and the Ag(111) surface. First, we present and verify a hydrogen-termination approach which allows a meaningful DFT description of the interface state with relatively thin silver slabs. Complemented with a projection technique which maps the interface electronic structure onto the original Ag(111) Shockley state, the DFT calculations enable us to analyze the evolution of the dispersion of the NTCDA/Ag(111) interface state when changing of the molecular coverage. Our calculations yield a difference between the interface state energy and the Shockley state energy that scales linearly with coverage. Furthermore, they predict a pronounced anisotropy of the dispersion of the interface state at long wavelengths which also depends linearly on the molecular coverage. The dispersion anisotropy is fully confirmed by our Fourier transform (FT) scanning tunneling spectroscopy (STS) experiments performed on a relaxed phase NTCDA/Ag(111) monolayer. Using feature detection STS (FD-STS), we moreover measure a band gap in the interface state band structure at the Brillouin zone boundary which indicates Bragg scattering of the interface state electrons in the periodic potential of the molecular layer. We thus observe an influence of the molecular layer on the interface state both at long (DFT, STS) and short wavelengths (STS).

How To Extract Quantitative Information on Electronic Transitions from the Density Functional Theory "Black Box".

Electronic couplings and vertical excitation energies are crucial determinants of charge and excitation energy transfer rates in a broad variety of processes ranging from biological charge transfer to charge transport through inorganic materials, from molecular sensing to intracellular signaling. Density Functional Theory (DFT) is generally used to calculate these critical parameters, but the quality of the results is unpredictable because of the semiempirical nature of the available DFT approaches. This study identifies a small set of fundamental rules that enables accurate DFT computation of electronic couplings and vertical excitation energies in molecular complexes and materials. These rules are applied to predict efficient DFT approaches to coupling calculations. The result is an easy-to-use guide for reliable DFT descriptions of electronic transitions.

Direct orbital selection for projection-based embedding.

Projection-based embedding (PbE) has become increasingly popular in recent years due to its simplicity and robustness. It is a very promising method for highly accurate calculations of reaction barriers and reaction energies via embedding of a correlated wavefunction or sophisticated density functional theory (DFT) method for the reaction center into a more cost effective DFT description of the environment. PbE enables an arbitrary partitioning of the supersystem orbitals into subsystems. In most applications so far, the selection of orbitals for the active system was directly linked to the selection of "active atoms." We propose an inexpensive approach that automatically selects orbitals as active that change during the reaction and that assigns all remaining orbitals to the environment. This approach is directly coupled to the reaction under investigation and does not rely on any specification of active atoms. We compare different variants of this approach for the selection of orbitals along the reaction path for embedding of Adamo and Barone's hybrid functional (known as PBE0) into Perdew, Burke, and Ernzerhof's exchange-correlation functional (PBE), a method dubbed as PBE0-in-PBE embedding, based on orbitalwise partial charges and the kinetic energy. The most successful comparison scheme is based on shellwise intrinsic atomic orbital charges. We show for a set of six reactions of different types that the corresponding errors in reaction energies and barriers converge quickly to zero with the extension of the active-orbital space.

NMR chemical shifts of urea loaded copper benzoate. A joint solid-state NMR and DFT study

We report solid-state 13C NMR spectra of urea-loaded copper benzoate, Cu2(C6H5CO2)4·2(urea), a simplified model for copper paddlewheel-based metal-organic frameworks (MOFs), along with first-principles density functional theory (DFT) computation of the paramagnetic NMR (pNMR) chemical shifts. Assuming a Boltzmann distribution between a diamagnetic open-shell singlet ground state (in a broken-symmetry Kohn-Sham DFT description) and an excited triplet state, the observed δ(13C) values are reproduced reasonably well at the PBE0-⅓/IGLO-II//PBE0-D3/AE1 level. Using the proposed assignments of the signals, the mean absolute deviation between computed and observed 13C chemical shifts is below 30 ppm over a range of more than 1100 ppm.

A complete DFT description on structural, electronic, elastic, mechanical and thermodynamic properties of some intermetallic AuX2 (X = Al, Ga, In) compounds

The electronic structure, elastic, mechanical and thermodynamic properties of some cubic intermetallic compounds AuX2(X = Al, Ga, In) have been studied within the density functional theory (DFT) using the full potential linearized augmented plane-wave technique (FP-LAPW). The designed values of structural parameters including lattice constant, bulks modulus and ground-states energies are found in good agreement with the available data. The spin included electronic examination presents the metallic nature for all the three compounds with symmetry in spin-up and spin-down states. The elastic properties have been calculated under ambient conditions and have been used to envisage some vital mechanical factors like bulk modulus (B), Young’s modulus (Y), shear modulus (G), Poisson ratio ( $ \nu$ ) and anisotropic factor (A). The calculated results reveal that AuX2(X = Al, Ga, In) compounds establish low elastic anisotropy, low hardness and high ductility. Quasi-harmonic Debye approximation has been used to investigate pressure and temperature dependence of bulk modulus (B), heat capacity (Cv), thermal expansion ( $ \alpha$ , and Debye temperature ( $ \theta_{\rm D}$ . Furthermore, Cv was found to strictly follow the Debye T3-law and Dulong-Petit limit for all the three compounds.

A Coupled Density Functional Theory–Microkinetic Modeling for the Hydrodeoxygenation of Glycerol to Propylene on MoO3

The production of propylene from renewable resources might be relevant to provide this compound in a scenario of scarcity due to the use of shale gas as a raw material. In the present, work we provide a full density functional theory description of the reaction network that drives the hydrodeoxygenation of glycerol on molybdenum oxide. From these results, a microkinetic model is built that allows the analysis of the most common routes and the potential bottlenecks compromising the activity and selectivity of the process. With this integrated scheme, we have found that the reaction proceeds mainly through the formation of hydroxypropanal, propanal, and 1-propanol, and the reaction order for hydrogen is close to 1. Our work paves the way toward the evaluation of complex reaction networks for the study of biomass compounds.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δs GM+,wat◦ of the Li+ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χwat◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li+ are also compared to those for Na+ and K+ from a previous study in terms of relative hydration free energies ΔΔs GM+,wat◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔs GM+,wat• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li+ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

Coupled Cluster and Time-Dependent Density Functional Theory Description of Inner Shell Photoabsorption Cross Sections of Molecules.

Near K-edge photoabsorption cross section spectra of a number of molecules, namely, water, ammonia, acetone, acetaldehyde, furan, and pyrrole, were obtained at the nitrogen, oxygen, and carbon K-edges with the Coupled Cluster ansatz (CC) and with the Time-Dependent Density Functional Theory (TDDFT) by treating the inner shell excitations as individual channels, separated from the valence part of the spectrum. The discretized electronic pseudospectrum, obtained with quadratically integrable basis sets ( a.k.a. L2) at the CC or TDDFT level, is used to reconstruct the complex dipole polarizability function, from which the photoabsorption cross section near the K-edge is obtained by a continued fraction based analytic continuation procedure. The CC2 and CCSD results are in good agreement with experimental data, while the TDDFT results yield reliable cross sections. Overall, the results obtained in this work indicate that our method can be used for the treatment of the NEXAFS spectra, with the advantage that the electronic excitations in the K-edges can be easily obtained at low computational cost using TDDFT.

Multiscale energy density algorithm and application to surface structure of Ni matrix of superalloy

Multiscale materials modeling as a new technique could offer more accurate predictive capabilities. The most active area of research for multiscale modeling focuses on the concurrent coupling by considering models on disparate scales simultaneously. In this paper, we present a new concurrent multiscale approach, the energy density method (EDM), which couples the quantum mechanical (QM) and the molecular dynamics (MD) simulations simultaneously. The coupling crossing different scales is achieved by introducing a transition region between the QM and MD domains. In order to construct the energy formalism of the entire system, concept of site energy and weight parameters of disparate scales are introduced. The EDM is applied to the study of the multilayer relaxation of the Ni (001) surface structure and is validated against the periodic density functional theory (DFT) calculations. The results show that the concurrent EDM could combine the accuracy of the DFT description with the low computational cost of the MD simulation and is suitable to the study of the local defects subjected to the influence of the long-range environment.

Iron(II) and Iron(III) Spin Crossover: Toward an Optimal Density Functional.

Spin crossover (SCO) plays a major role in biochemistry, catalysis, materials, and emerging technologies such as molecular electronics and sensors, and thus accurate prediction and design of SCO systems is of high priority. However, the main tool for this purpose, density functional theory (DFT), is very sensitive to applied methodology. The most abundant SCO systems are Fe(II) and Fe(III) systems. Even with average good agreement, a functional may be significantly more accurate for Fe(II) or Fe(III) systems, preventing balanced study of SCO candidates of both types. The present work investigates DFT's performance for well-known Fe(II) and Fe(III) SCO complexes, using various design types and customized versions of GGA, hybrid, meta-GGA, meta-hybrid, double-hybrid, and long-range-corrected hybrid functionals. We explore the limits of DFT performance and identify proficient Fe(II)-Fe(III)-balanced functionals. We identify and quantify remarkable differences in the DFT description of Fe(II) and Fe(III) systems. Most functionals become more accurate once Hartree-Fock exchange is adjusted to 10-17%, regardless of the type of functionals involved. However, this typically introduces a clear Fe(II)-Fe(III) bias. The most accurate functionals measured by mean absolute errors <10 kJ/mol are CAMB3LYP-17, B3LYP*, and B97-15 with 15-17% Hartree-Fock exchange, closely followed by CAMB3LYP and CAMB3LYP-15, OPBE, rPBE-10, and B3P86-15. While GGA functionals display a small Fe(II)-Fe(III) bias, they are generally inaccurate, except the O exchange functional. Hybrid functionals (including B2PLYP double hybrids and meta hybrids) tend to favor HS too much in Fe(II) vs Fe(III), which is important in many studies where the oxidation state of iron can vary, e.g. rational SCO design and studies of catalytic processes involving iron. The only functional with a combined bias <5 kJ/mol and a decent MAE (15 kJ/mol) is our customized PBE0-12 functional. Alternatively one has to sacrifice Fe(II)-Fe(III) balance to use the best functionals for each group separately. We also investigated the precision (measured as the standard deviation of errors) and show that the target accuracy for iron SCO is 10 kJ/mol for accuracy and 5 kJ/mol for precision, and DFT is probably not going to break this limit in the near future. Importantly, all four types of functional behavior (accurate/precise, accurate/imprecise, inaccurate/precise, inaccurate/imprecise) are observed. More generally, our work illustrates the importance not only of overall accuracy but also of balanced accuracy for systems likely to occur in context.

The role of dopant charge state on defect chemistry and grain growth of doped UO2

Additives are widely used to control the microstructure of materials via their effect on defect chemistry during sintering. As the primary nuclear fuel, the properties of UO2 are crucial for safe and efficient reactor operation. UO2 has been manipulated by fuel vendors through doping to enhance grain size to provide improved fission gas retention and plasticity. In this work the common phenomenon that governs the effect of Mg, Ti, V, Cr, Mn, and Fe doping of UO2 for enhanced grain growth is revealed, elucidating experimental observations. A combined density functional theory and empirical potential description of defect free energy is used to calculate the doped UO2 defect concentrations as a function of temperature. At high (sintering) temperatures all dopants studied transition to a positively charged interstitial defect. Furthermore, a number of dopants (Ti, V, Cr, and Mn) do so in sufficiently high concentrations to greatly increase the negatively charged uranium vacancy concentration. High uranium vacancy concentrations can enhance grain growth and fission gas diffusion. Mg and Fe also enhance uranium vacancy concentrations but to a lesser extent, while Al has no impact. The enhanced uranium vacancy concentrations, associated with solution of dopants interstitially, is proposed as the mechanism responsible for the enlarged grains seen experimentally in (Ti/V/Cr/Mg)-doped systems. Mn- and V-doped UO2 have been predicted to have higher uranium vacancy concentrations than the more widely used Cr-doped UO2, leading to higher grain growth and fission gas diffusivity.