Hybrid Density Functional Theory Level Research Articles

Efficient periodic resolution-of-the-identity Hartree-Fock exchange method with k-point sampling and Gaussian basis sets.

Simulations of condensed matter systems at the hybrid density functional theory level pose significant computational challenges. The elevated costs arise from the non-local nature of the Hartree-Fock exchange (HFX) in conjunction with the necessity to approach the thermodynamic limit. In this work, we address these issues with the development of a new efficient method for the calculation of HFX in periodic systems, employing k-point sampling. We rely on a local atom-specific resolution-of-the-identity scheme, the use of atom-centered Gaussian type orbitals, and the truncation of the Coulomb interaction to limit computational complexity. Our real-space approach exhibits a scaling that is, at worst, linear with the number of k-points. Issues related to basis set diffuseness are effectively addressed through the auxiliary density matrix method. We report the implementation in the CP2K software package, as well as accuracy and performance benchmarks. This method demonstrates excellent agreement with equivalent Γ-point supercell calculations in terms of relative energies and nuclear gradients. Good strong and weak scaling performances, as well as graphics processing unit (GPU) acceleration, make this implementation a promising candidate for high-performance computing.

Deposition products predicted from conceptual DFT: The hydrolysis reactions of MoF6, WF6, and UF6.

Metal hexafluorides hydrolyze at ambient temperature to deposit compounds having fluorine-to-oxygen ratios that depend upon the identity of the metal. Uranium-hexafluoride hydrolysis, for example, deposits uranyl fluoride (UO2F2), whereas molybdenum hexafluoride (MoF6) and tungsten hexafluoride deposit trioxides. Here, we pursue general strategies enabling the prediction of depositing compounds resulting from multi-step gas-phase reactions. To compare among the three metal-hexafluoride hydrolyses, we first investigate the mechanism of MoF6 hydrolysis using hybrid density functional theory (DFT). Intermediates are then validated by performing anharmonic vibrational simulations and comparing with infrared spectra [McNamara et al., Phys. Chem. Chem. Phys. 25, 2990 (2023)]. Conceptual DFT, which is leveraged here to quantitatively evaluate site-specific electrophilicity and nucleophilicity metrics, is found to reliably predict qualitative deposition propensities for each intermediate. In addition to the nucleophilic potential of the oxygen ligands, several other contributing characteristics are discussed, including amphoterism, polyvalency, fluxionality, steric hindrance, dipolar strength, and solubility. To investigate the structure and composition of pre-nucleation clusters, an automated workflow is presented for the simulation of particle growth. The workflow entails a conformer search at the density functional tight-binding level, structural refinement at the hybrid DFT level, and computation of a composite free-energy profile. Such profiles can be used to estimate particle nucleation kinetics. Droplet formation is also considered, which helps to rationalize the different UO2F2 particle morphologies observed under varying levels of humidity. Development of predictive methods for simulating physical and chemical deposition processes is important for the advancement of material manufacturing involving coatings and thin films.

Developing machine-learned potentials to simultaneously capture the dynamics of excess protons and hydroxide ions in classical and path integral simulations.

The transport of excess protons and hydroxide ions in water underlies numerous important chemical and biological processes. Accurately simulating the associated transport mechanisms ideally requires utilizing abinitio molecular dynamics simulations to model the bond breaking and formation involved in proton transfer and path-integral simulations to model the nuclear quantum effects relevant to light hydrogen atoms. These requirements result in a prohibitive computational cost, especially at the time and length scales needed to converge proton transport properties. Here, we present machine-learned potentials (MLPs) that can model both excess protons and hydroxide ions at the generalized gradient approximation and hybrid density functional theory levels of accuracy and use them to perform multiple nanoseconds of both classical and path-integral proton defect simulations at a fraction of the cost of the corresponding abinitio simulations. We show that the MLPs are able to reproduce abinitio trends and converge properties such as the diffusion coefficients of both excess protons and hydroxide ions. We use our multi-nanosecond simulations, which allow us to monitor large numbers of proton transfer events, to analyze the role of hypercoordination in the transport mechanism of the hydroxide ion and provide further evidence for the asymmetry in diffusion between excess protons and hydroxide ions.

High-Throughput Condensed-Phase Hybrid Density Functional Theory for Large-Scale Finite-Gap Systems: The SeA Approach.

High-throughput electronic structure calculations (often performed using density functional theory (DFT)) play a central role in screening existing and novel materials, sampling potential energy surfaces, and generating data for machine learning applications. By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal DFT and furnish a more accurate description of the underlying electronic structure, albeit at a computational cost that often prohibits such high-throughput applications. To address this challenge, we have constructed a robust, accurate, and computationally efficient framework for high-throughput condensed-phase hybrid DFT and implemented this approach in the PWSCF module of Quantum ESPRESSO (QE). The resulting SeA approach (SeA = SCDM + exx + ACE) combines and seamlessly integrates: (i) the selected columns of the density matrix method (SCDM, a robust noniterative orbital localization scheme that sidesteps system-dependent optimization protocols), (ii) a recently extended version of exx (a black-box linear-scaling EXX algorithm that exploits sparsity between localized orbitals in real space when evaluating the action of the standard/full-rank operator), and (iii) adaptively compressed exchange (ACE, a low-rank approximation). In doing so, SeA harnesses three levels of computational savings: pair selection and domain truncation from SCDM + exx (which only considers spatially overlapping orbitals on orbital-pair-specific and system-size-independent domains) and low-rank approximation from ACE (which reduces the number of calls to SCDM + exx during the self-consistent field (SCF) procedure). Across a diverse set of 200 nonequilibrium (H2O)64 configurations (with densities spanning 0.4-1.7 g/cm3), SeA provides a 1-2 order-of-magnitude speedup in the overall time-to-solution, i.e., ≈8-26× compared to the convolution-based PWSCF(ACE) implementation in QE and ≈78-247× compared to the conventional PWSCF(Full) approach, and yields energies, ionic forces, and other properties with high fidelity. As a proof-of-principle high-throughput application, we trained a deep neural network (DNN) potential for ambient liquid water at the hybrid DFT level using SeA via an actively learned data set with ≈8,700 (H2O)64 configurations. Using an out-of-sample set of (H2O)512 configurations (at nonambient conditions), we confirmed the accuracy of this SeA-trained potential and showcased the capabilities of SeA by computing the ground-truth ionic forces in this challenging system containing >1,500 atoms.

Defect Formation Thermodynamics of (A,A′)(B,B′)O3 (A = Mg,Ca,Sr and B = Ti,Mn,Cr,Fe,Mo) Perovskites

In a previous theoretical study [B. Grimm and T. Bredow, Oxygen Defect Formation Thermodynamics of CaMnO3: A Closer Look. Phys. Status Solidi B 2022, https://doi.org/10.1002/pssb.202200427], the structural, thermodynamic, and electronic properties of have been studied. The present study increases the range of compounds to ternary perovskites in a search for suitable anode materials for high‐temperature water electrolysis. compounds containing the abundant elements A = Mg,Ca,Sr and B = Ti,Mn,Cr,Fe,Mo are studied theoretically on hybrid density functional theory level. Criteria for a suitable electrode material are low‐oxygen defect formation energy and high reaction energy for decomposition into other phases. Based on these criteria, the most suitable perovskites are chosen as starting points to create stable mixed compounds. The compound δ is found to be the optimal choice as electrode material, with an oxygen defect concentration of at least δ present at 520 K and highly endothermic decomposition reactions.

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

The effect of composition on phonon softening in ABO3-type perovskites: DFT modelling.

The evolution of ferroelectric instability in ABO3 perovskites is systematically investigated for tantalates, niobates and titanates at the hybrid density-functional theory level. The influence of the A cation is analysed in terms of the frequency of the lowest F1u IR-active phonon mode at different volumes for (Cs, Rb, K, Na)TaO3, (Ba, Pb, Sn, Ge)TiO3 and (Rb, K, Na, Li)NbO3 and correlated with the ionic radius as well as the degree of hybridization in the bonds. The atomic displacement corresponding to each mode is described as a function of volume, and the static permittivity is calculated for the stable Pm3̄m phases. It is shown that the amplitude of the atomic displacements associated with the soft mode linked to the ferroelectric instability increases at a given volume when the ionic radius of the cation A decreases and when the hybridization of the B-O bond increases. This provides criteria for optimizing the dielectric properties of materials and for suggesting effective solid solutions. Tantalum perovskites presenting para-ferroelectric phase transitions, some of which are close to ambient conditions, are interesting materials for high-permittivity dielectrics in view of lead-free compounds with a high static dielectric response.

Radicals and molecular products from the gas-phase pyrolysis of lignin model compounds: Coniferyl alcohol, theory and experiment

Coniferyl alcohol (CFA) is one of lignin’s main building blocks and a relevant model compound. Two aspects of CFA pyrolysis are studied in the current work to gain insight into the molecular mechanism of lignin thermolysis: (i) the nature of intermediate radicals generated from vacuum pyrolysis of CFA, and (ii) the product distribution from pyrolysis of CFA dispersed into the gas phase. Low temperature matrix isolation electron paramagnetic resonance (LTMI-EPR) spectroscopy is employed to investigate the intermediate radicals associated with gas phase low-pressure pyrolysis of CFA. An anisotropic EPR spectrum of radicals trapped at liquid nitrogen temperature was registered throughout the studied temperature range (400–700 °C) characterized by high g-value (≤ 2.0100), and broad EPR line-width (~13.5–13.0 G) prescribed to a mixture of O-centered radicals produced from cleavage of O−CH3 and O−H terminal bonds. Thermal annealing of frozen radicals suggested a major contribution of methylperoxyl (CH3O2) radicals produced by the liberated CH3 and trace amounts of oxygen. The pyrolysis of CFA, for the first time, was conducted in a dispersed, gas-phase conditions to minimize the heterogeneous secondary reactions mediated by particle surfaces typical for condensed-phase pyrolysis in conventional reactors. Several unique products including polyhydroxylated derivatives of mandelic acid and some carboxylic compounds were identified in addition to those normally produced during the conventional pyrolysis - coniferyl aldehyde, vanillin (and its oxidized form homovanilic acid), eugenol and its isomers. A comprehensive analysis of product formation mechanisms, particularly the pathways for generating abundant hydroxylated compounds is performed and the role of trace oxygen is studied at the wB97XD and M06-2X hybrid density functional theory levels.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based Ab Initio Molecular Dynamics. 1. Theory, Algorithm, and Performance.

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car-Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson's equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical (NVT) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500-1000 atoms (e.g., (H2O)256) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.

BiVO3 : A Bi-based material with promising uv-visible light absorption properties

Spin polarized density functional theory calculations on a predicted ${\mathrm{BiVO}}_{3}$ crystal structure is presented. An orthorhombic phase with space group $Pnma$ is observed to be highly stable compared to the aristotype cubic structure. An optical band gap of 1.92 eV and a strong optical absorption at 2.25 eV---which lie in the visible region of the solar spectra---are estimated at the coupled-perturbed hybrid density-functional theory level. In addition, the band-structure analysis somewhat shows dispersion at the valence and conduction bands, and the binding energy of the excitons is calculated to be quite low, which can be possibly dissociated at room temperature. ${\mathrm{BiVO}}_{3}$ is, therefore, expected to be a promising candidate worth being investigated for visible light driven photocatalytic applications. Simulated infrared and Raman spectra are reported, which could represent a guideline for future experiments, along with a full characterization of structural, electronic, and dynamic properties.

A molecular mechanics and ab initio prediction of the 1 H chemical shifts of pinanes.

Molecular mechanics calculations plus the application of a refined Karplus equation gave the conformations of 19 pinanes. These range from a Y-shaped geometry in the apopinene and α-pinene series to a pseudo chair conformation in β-pinene, nopinone and verbanone, a flattened chair in pinocarvone and the pinocarveols and a distorted Y shape for iso-verbanone. These structures were then used as input to predict the 1 H chemical shifts of these compounds by semi-empirical (1 H-NMR spectra (HSPEC)) and ab initio gauge-invariant atomic orbital (GIAO) calculations, the latter at the B3LYP hybrid density functional theory level using 6-31++G** basis set. The two methods gave generally good agreement with the 184 observed shifts with root mean square (RMS) errors 0.07ppm (HSPEC) and 0.10ppm (GIAO), but the GIAO calculations gave several significant (>0.25ppm) errors. One was for the H3 proton in apopinenone and other α,β unsaturated ketones; the others occurred for protons in close proximity to hydroxyl groups. To provide more information, smaller analogues of known geometry and chemical shifts were subject to the same analysis. In cyclopentenone, the Gaussian geometry gave good agreement with the observed shifts, but the MMFF94, MMX and MM3 geometries all gave errors for different protons. These results show clearly that the molecular geometries of the α,β unsaturated ketones are responsible for the errors. The errors for the alcohols were examined using ethanol as model and were shown to be due to the different possible conformations of the OH group. Similar GIAO calculations on substituted methanes gave good agreement for the methyl compounds but poor agreement for di and tri halosubstituted methanes. The aforementioned method of molecular mechanics plus GIAO calculations is shown to be a very useful tool for the investigation of molecular geometries and conformations. However, multihalogen compounds may require different basis sets for accurate calculations. Copyright © 2017 John Wiley & Sons, Ltd.

A Robust and Accurate Tight-Binding Quantum Chemical Method for Structures, Vibrational Frequencies, and Noncovalent Interactions of Large Molecular Systems Parametrized for All spd-Block Elements (Z = 1-86).

We propose a novel, special purpose semiempirical tight binding (TB) method for the calculation of structures, vibrational frequencies, and noncovalent interactions of large molecular systems with 1000 or more atoms. The functional form of the method is related to the self-consistent density functional TB scheme and mostly avoids element-pair-specific parameters. The parametrization covers all spd-block elements and the lanthanides up to Z = 86 using reference data at the hybrid density functional theory level. Key features of the Hamiltonian are the use of partially polarized Gaussian-type orbitals, a double-ζ orbital basis for hydrogen, atomic-shell charges, diagonal third-order charge fluctuations, coordination number-dependent energy levels, a noncovalent halogen-bond potential, and the well-established D3 dispersion correction. The accuracy of the method, called Geometry, Frequency, Noncovalent, eXtended TB (GFN-xTB), is extensively benchmarked for various systems in comparison with existing semiempirical approaches, and the method is applied to a few representative structural problems in chemistry.

Quantum Dynamics and Spectroscopy of Ab Initio Liquid Water: TheInterplay of Nuclear and Electronic Quantum Effects.

Understanding the reactivity and spectroscopy of aqueous solutions at the atomistic level is crucial for the elucidation and design of chemical processes. However, the simulation of these systems requires addressing the formidable challenges of treating the quantum nature of both the electrons and nuclei. Exploiting our recently developed methods that provide acceleration by up to 2 orders of magnitude, we combine path integral simulations with on-the-fly evaluation of the electronic structure at the hybrid density functional theory level to capture the interplay between nuclear quantum effects and the electronic surface. Here we show that this combination provides accurate structure and dynamics, including the full infrared and Raman spectra of liquid water. This allows us to demonstrate and explain the failings of lower-level density functionals for dynamics and vibrational spectroscopy when the nuclei are treated quantum mechanically. These insights thus provide a foundation for the reliable investigation of spectroscopy and reactivity in aqueous environments.

First-Principles Free-Energy Barriers for Photoelectrochemical Surface Reactions: Proton Abstraction at TiO_{2}(110).

We explicitly calculate the free-energy barrier for the initial proton abstraction in the water splitting reaction at rutile TiO_{2}(110) through abinitio molecular dynamics. Combining solid-state embedding, an energy based reaction coordinate and state-of-the-art free-energy reconstruction techniques renders the calculation tractable at the hybrid density-functional theory level. The obtained free-energy barrier of approximately 0.2eV, depending slightly on the orientation of the first acceptor water molecule, suggests a hindered reaction on the pristine rutile surface.

Structural and electronic properties of UnOm (n=1-3,m=1-3n) clusters: A theoretical study using screened hybrid density functional theory.

The structural and electronic properties of small uranium oxide clusters UnOm (n=1-3, m=1-3n) are systematically studied within the screened hybrid density functional theory. It is found that the formation of U-O-U bondings and isolated U-O bonds are energetically more stable than U-U bondings. As a result, no uranium cores are observed. Through fragmentation studies, we find that the UnOm clusters with the m/n ratio between 2 and 2.5 are very stable, hinting that UO2+x hyperoxides are energetically stable. Electronically, we find that the O-2p states always distribute in the deep energy range, and the U-5f states always distribute at the two sides of the Fermi level. The U-6d states mainly hybridize with the U-5f states in U-rich clusters, while hybridizing with O-2p states in O-rich clusters. Our work is the first one on the screened hybrid density functional theory level studying the atomic and electronic properties of the actinide oxide clusters.

Structure and IR vibrational spectra of Na8[AlSiO4]6(BH4)2: comparison of theory and experiment.

The structure and IR vibrational spectra of tetrahydroborate sodalite (Na8[AlSiO4]6(BH4)2) were calculated using density functional theory (DFT) methods. The calculations, performed at the GGA hybrid DFT level yield a close agreement with XRD refinements of the structure and allow interpretation of observed bands of the enclosed BH4(–) and the framework and, in particular, a verification of hydrogen positions (Buhl, J.-C., Gesing, T. M., and Rüscher, C. H. Microporous Mesoporous Mater. 2005, 80, 57−63). In a first step, different basis sets and functionals were tested on NaBH4 and Na8[AlSiO4]6Cl2. We show that accurate treatment of B–H stretching modes requires anharmonic corrections, while lattice vibrations are well described within the harmonic approximation.

Structure and properties of cerium oxides in bulk and nanoparticulate forms

Abstract The experimental and computational studies on the cerium oxide nanoparticles, as well as stoichiometric phases of bulk ceria are reviewed. Based on structural similarities of these phases in hexagonal aspect, electroneutral and non-polar pentalayers are identified as building blocks of type A sesquioxide structure. The idealized core/shell structure of the ceria nanoparticles is described as dioxide core covered by a single pentalayer of sesquioxide, which explains the exceptional stability of subsurface vacancies in nanoceria. The density functional theory (DFT) predictions of the lattice parameters and elastic moduli for the Ce(IV) and Ce(III) oxides at the hybrid DFT level are also presented. The calculated values for both compounds agree with available experimental data and allow predicting changes in the lattice parameter with decreasing size of the nanoparticles. The lattice parameter is calculated as equilibrium between contraction of sesquioxide structure in the core, and expansion of dioxide structure in the shell of the nanoparticle. This is consistent with available XRD data on ceria NPs obtained in mild aqueous conditions. The core/shell model, however, breaks down when applied to the size dependence of lattice parameter in NPs obtained by the laser ablation techniques.

The Loewenstein rule: the increase in electron kinetic energy as the reason for instability of Al–O–Al linkage in aluminosilicate zeolites

Problem of Al–O–Al linkage in aluminosilicate materials or Al-avoidance is discussed for two zeolite structures (phillipsite and brewsterite) exchanged with Mg2+ cations. All models are fully optimized at periodic Hartree–Fock and hybrid density functional theory levels (the CRYSTAL code). Their properties are then calculated at the periodic level with the same basis sets. The reasons for the instability of the zeolite structures including the Al–O–Al moieties are interpreted on the basis of cell energy decomposition. This destabilization comes from an increase in kinetic energy if the Al–O(Mg)–Al moieties are present in zeolites. This effect is discussed in parallel with already known variational evidences in favor of dominating role of kinetic energy for stability of molecular systems.

Protonation Effect on One- and Two-photon Absorption Property of a Newly Synthesized Octupolar Chromophore

The protonation effects on one- and two-photon absorption properties of an octupolar molecule TA with 1,3,5-triazine core and pyrrole electron-donating end-groups have been studied at hybrid density functional theory level. A computational scheme is developed to simulate a proton attached to an atom. The numerical results show that large changes in both one- and two-photon absorption properties are observed when the compound is transformed from neutral to threefold protonated states. When the compound is protonated, more charge transfer states appear and the absorption band has a red-shift. Furthermore, the two-photon absorption cross-section is largely enhanced. The theoretical calculations demonstrate the protonation effect on promoting the intramolecular charge transfer strength. The results present qualitative agreement with the experimental observations. A two-photon absorption switch with the compound TA based on the protonation effect is proposed.

Seminumerical calculation of the Hartree–Fock exchange matrix: Application to two‐component procedures and efficient evaluation of local hybrid density functionals

A two-component extension of the seminumerical procedure for the calculation of the Hartree-Fock (HF) exchange matrix recently presented by Neese et al. (Chem Phys 2009, 356, 98) was implemented into the program system TURBOMOLE. It is demonstrated that this allows for efficient self-consistent treatment of spin-orbit coupling at HF and hybrid density functional theory level. One-component HF calculations were performed to study the accuracy of integration grids and the exploitation of the molecular point group symmetry. The efficiency was tested, and for one-component calculations compared to the implementation realized by Neese. It was further demonstrated that local hybrid density functionals can be evaluated with this technique. The "prototype" of this class of functionals, Lh-BLYP, was applied to an organic molecule with more than 150 atoms.