Ground-state Density Functional Theory Research Articles

Excitonic and Environmental Screening Effects in Two-Dimensional Janus MSO (M = Ga, In).

In this work, we investigate Janus monolayer MSO (M = Ga, In) systems using the state-of-the-art GW method within the framework of the many-body perturbation theory. Ground-state density functional theory calculations reveal that both the substitution of S atoms with O atoms and the chemisorption of the O atoms on a single side of the MS layer narrow the band gaps and reduce the carrier mobilities. Notably, one-shot GW calculations demonstrate that the GaSO-2 and InSO-1 systems exhibit optimal band gaps for visible light absorption. Based on the Bethe-Salpeter equation, the exciton binding energies of isolated Janus monolayer GaSO-2 and InSO-1 systems are lower than those of their prototype GaS and InS by 0.37 and 0.17 eV, respectively. Further calculations show that the exciton binding energies of the Janus GaSO-2 and InSO-1 systems can be precisely tuned by adjusting their thicknesses and the thicknesses of their substrates. A deep understanding of the mechanisms for tuning the exciton binding energies in Janus GaSO-2 and InSO-1 systems is crucial for the future design of advanced photovoltaic devices.

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

Abstract Ensemble Density Functional Theory (EDFT) is a generalization of ground-state Density Functional Theory (GS DFT), which is based on an exact formal theory of finite collections of a system's ground and excited states. EDFT in various forms has been shown to improve the accuracy of calculated energy level differences in isolated model systems, atoms, and molecules, but it is not yet clear how EDFT could be used to calculate band gaps for periodic systems. We extend the application of EDFT toward periodic systems by estimating the thermodynamic limit with increasingly large finite one-dimensional "particle in a box" systems, which approach the uniform electron gas (UEG). Using ensemble-generalized Hartree and Local Spin Density Approximation (LSDA) exchange-correlation functionals, we find that corrections go to zero in the infinite limit, as expected for a metallic system. However, there is a correction to the effective mass, with results comparable to other calculations on 1D, 2D, and 3D UEGs, which indicates promise for non-trivial results from EDFT on periodic systems.

Sparse-Stochastic Fragmented Exchange for Large-Scale Hybrid Time-Dependent Density Functional Theory Calculations.

We extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.

Inverse Hypercorroles.

Ground-state and time-dependent density functional theory (TDDFT) calculations with the long-range-corrected, Coulomb-attenuating CAMY-B3LYP exchange-correlation functional and large, all-electron STO-TZ2P basis sets have been used to examine the potential "inverse hypercorrole" character of meso-p-nitrophenyl-appended dicyanidocobalt(III) corrole dianions. The effect is most dramatic for 5,15-bis(p-nitrophenyl) derivatives, where it manifests itself in intense NIR absorptions. The 10-aryl groups in these complexes play a modulatory role, as evinced by experimental UV-visible spectroscopic and electrochemical data for a series of 5,15-bis(p-nitrophenyl) dicyanidocobalt(III) corroles. TDDFT (CAMY-B3LYP) calculations ascribe these features clearly to a transition from the corrole's a2u-like HOMO (retaining the D4h irrep used for metalloporphyrins) to a nitrophenyl-based LUMO. The outward nature of this transition contrasts with the usual phenyl-to-macrocycle direction of charge transfer transitions in many hyperporphyrins and hypercorroles; thus, the complexes studied are aptly described as inverse hypercorroles.

Accurate Excitation Energies of Point Defects from Fast Particle-Particle Random Phase Approximation Calculations.

We present an efficient particle-particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV-) and silicon-vacancy (SiV0) centers in diamond and the divacancy center (VV0) in 4H silicon carbide, with errors of ±0.2 eV compared with experimental values. Starting from the (N + 2)-electron ground state calculated with density functional theory (DFT), the ppRPA excitation energies of the N-electron system are calculated as the differences between the two-electron removal energies of the (N + 2)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials.

Exchange energies with forces in density-functional theory.

We propose exchanging the energy functionals in ground-state density-functional theory with physically equivalent exact force expressions as a new promising route toward approximations to the exchange-correlation potential and energy. In analogy to the usual energy-based procedure, we split the force difference between the interacting and auxiliary Kohn-Sham system into a Hartree, an exchange, and a correlation force. The corresponding scalar potential is obtained by solving a Poisson equation, while an additional transverse part of the force yields a vector potential. These vector potentials obey an exact constraint between the exchange and correlation contribution and can further be related to the atomic shell structure. Numerically, the force-based local-exchange potential and the corresponding exchange energy compare well with the numerically more involved optimized effective potential method. Overall, the force-based method has several benefits when compared to the usual energy-based approach and opens a route toward numerically inexpensive nonlocal and (in the time-dependent case) nonadiabatic approximations.

My life in science: Lessons for yours?

Because of an acquired obsession to understand as much as possible in a limited but important area of science and because of optimism, luck, and help from others, my life in science turned out to be much better than I or others could have expected or planned. This is the story of how that happened, and also the story of the groundstate density functional theory of electronic structure, told from a personal perspective.

Prediction of Strong Solvatochromism in a Molecular Photocatalyst.

Based on quantum chemical calculations, we predict strong solvatochromism in a light-driven molecular photocatalyst for hydrogen generation, that is we show that the electronic and optical properties of the photocatalyst strongly depend on the solvent it is dissolved in. Our calculations in particular indicate a solvent-dependent relocation of the highest occupied molecular orbital (HOMO). Ground-state density functional theory and linear response time-dependent density functional theory calculations were applied in order to investigate the influence of implicit solvents on the structural, electronic and optical properties of a molecular photocatalyst. Only at high dielectric constants of the solvent, is the HOMO located at the metal center of the photosensitizer, whereas at low dielectric constants the HOMO is centered at the metal atom of the catalytically active complex. We elucidate the electronic origins of this strong solvatochromic effect and sketch the consequences of these insights for the use of photocatalysts in different environments.

Disclosing Early Excited State Relaxation Events in Prototypical Linear Carbon Chains.

One-dimensional (1D) linear nanostructures comprising sp-hybridized carbon atoms, as derivatives of the prototypical allotrope known as carbyne, are predicted to possess outstanding mechanical, thermal, and electronic properties. Despite recent advances in their synthesis, their chemical and physical properties are still poorly understood. Here, we investigate the photophysics of a prototypical polyyne (i.e., 1D chain with alternating single and triple carbon bonds) as the simplest model of finite carbon wire and as a prototype of sp-carbon-based chains. We perform transient absorption experiments with high temporal resolution (<30 fs) on monodispersed hydrogen-capped hexayne H─(C≡C)6─H synthesized by laser ablation in liquid. With the support of computational studies based on ground state density functional theory (DFT) and excited state time-dependent (TD)-DFT calculations, we provide a comprehensive description of the excited state relaxation processes at early times following photoexcitation. We show that the internal conversion from a bright high-energy singlet excited state to a low-lying singlet dark state is ultrafast and takes place with a 200 fs time constant, followed by thermalization on the picosecond time scale and decay of the low-energy singlet state with hundreds of picoseconds time constant. We also show that the time scale of these processes does not depend on the end groups capping the sp-carbon chain. The understanding of the primary photoinduced events in polyynes is of key importance both for fundamental knowledge and for potential optoelectronic and light-harvesting applications of low-dimensional nanostructured carbon-based materials.

Chemical Bonding in Large Systems Using Projected Population Analysis from Real-Space Density Functional Theory Calculations.

We present an efficient and scalable computational approach for conducting projected population analysis from real-space finite-element (FE)-based Kohn-Sham density functional theory calculations (DFT-FE). This work provides an important direction toward extracting chemical bonding information from large-scale DFT calculations on materials systems involving thousands of atoms while accommodating periodic, semiperiodic, or fully nonperiodic boundary conditions. Toward this, we derive the relevant mathematical expressions and develop efficient numerical implementation procedures that are scalable on multinode CPU architectures to compute the projected overlap and Hamilton populations. The population analysis is accomplished by projecting either the self-consistently converged FE discretized Kohn-Sham orbitals or the FE discretized Hamiltonian onto a subspace spanned by a localized atom-centered basis set. The proposed methods are implemented in a unified framework within the DFT-FE code where the ground-state DFT calculations and the population analysis are performed on the same FE grid. We further benchmark the accuracy and performance of this approach on representative material systems involving periodic and nonperiodic DFT calculations with LOBSTER, a widely used projected population analysis code. Finally, we discuss a case study demonstrating the advantages of our scalable approach to extract the quantitative chemical bonding information of hydrogen chemisorbed in large silicon nanoparticles alloyed with carbon, a candidate material for hydrogen storage.

Fractional-Electron and Transition-Potential Methods for Core-to-Valence Excitation Energies Using Density Functional Theory.

Methods for computing X-ray absorption spectra based on a constrained core hole (possibly containing a fractional electron) are examined. These methods are based on Slater's transition concept and its generalizations, wherein core-to-valence excitation energies are determined using Kohn-Sham orbital energies. Methods examined here avoid promoting electrons beyond the lowest unoccupied molecular orbital, facilitating robust convergence. Variants of these ideas are systematically tested, revealing a best-case accuracy of 0.3-0.4 eV (with respect to experiment) for K-edge transition energies. Absolute errors are much larger for higher-lying near-edge transitions but can be reduced below 1 eV by introducing an empirical shift based on a charge-neutral transition-potential method, in conjunction with functionals such as SCAN, SCAN0, or B3LYP. This procedure affords an entire excitation spectrum from a single fractional-electron calculation, at the cost of ground-state density functional theory and without the need for state-by-state calculations. This shifted transition-potential approach may be especially useful for simulating transient spectroscopies or in complex systems where excited-state Kohn-Sham calculations are challenging.

Rational design of one inorganic-organic hybrid Z-scheme heterojunction for high-performance photocatalytic water splitting

Searching high-performance Z-scheme heterojunction is of great significance for the solution of energy shortage and environmental pollution. Combining density functional theory (DFT) calculation and time-dependent ab-initio diabatic molecular dynamics (NAMD) simulation, we theoretically found one new inorganic–organic hybrid Z-scheme heterojunction CdS/C6N7, involving the stacking of CdS monolayer with C6N7 monolayer. The unique electronic properties (e.g. staggered band alignment, charge transfer) of Z-scheme heterojunction was strictly verified via the ground-state DFT calculations, and time-dependent NAMD simulations demonstrated the dynamic processes of photogenerated carriers separation and recombination. The strong built-in electric field from CdS to C6N7 layer promotes the non-adiabatic coupling of pristine carriers, resulting in the strong redox ability of CdS/C6N7. Catalytic property shown that CdS/C6N7 features outstanding performance for overall water splitting (OWS), where the synergy of strong redox ability and effective spatial separation of electron-holes plays an important role.

Efficient All-Electron Time-Dependent Density Functional Theory Calculations Using an Enriched Finite Element Basis.

We present an efficient and systematically convergent approach to all-electron real-time time-dependent density functional theory (TDDFT) calculations using a mixed basis, termed as enriched finite element (EFE) basis. The EFE basis augments the classical finite element basis (CFE) with a compactly supported numerical atom-centered basis, obtained from atomic ground-state DFT calculations. Particularly, we orthogonalize the enrichment functions with respect to the classical finite element basis to ensure good conditioning of the resultant basis. We employ the second-order Magnus propagator in conjunction with an adaptive Krylov subspace method for efficient time evolution of the Kohn-Sham orbitals. We rely on a priori error estimates to guide our choice of an adaptive finite element mesh as well as the time step to be used in the TDDFT calculations. We observe close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretizations. Notably, we attain a 50-100 times speedup for the EFE basis over the CFE basis. We also demonstrate the efficacy of the EFE basis for both linear and nonlinear responses by studying the absorption spectra in sodium clusters, the linear to nonlinear response transition in the green fluorescence protein chromophore, and the higher harmonic generation in the magnesium dimer. Lastly, we attain good parallel scalability of our numerical implementation of the EFE basis for up to ∼1000 processors, using a benchmark system of a 50-atom sodium nanocluster.

Ab initio study of electron mobility in V[formula omitted]O[formula omitted] via polaron hopping

We investigate the polaron transport in V2O5 using Density Functional Theory (DFT)+U. The Bond Distortion Method (BDM) is utilized to help stabilize an excess electron as a self-trapped polaron. The polaron hopping on a linearly interpolated pathway between two trapping sites is evaluated by Landau–Zener equations with parameters extracted using a model Hamiltonian and DFT ground state energies. The polaronic contribution of the electronic mobility is obtained from the Einstein relation and compared to experimental data. The influence of the Hubbard U correction used in DFT+U on both the polaron static and dynamic properties has also been studied.

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.

TTDFT: A GPU accelerated Tucker tensor DFT code for large-scale Kohn-Sham DFT calculations

We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximation to the Kohn-Sham Hamiltonian. The discrete Kohn-Sham problem is solved using Chebyshev filtered subspace iteration method that relies on matrix-matrix multiplications of a sparse symmetric Hamiltonian matrix and a dense wavefunction matrix, expressed in the localized Tucker tensor basis. These matrix-matrix multiplication operations, which constitute the most computationally intensive step of the solution procedure, are GPU accelerated providing ∼8-fold GPU-CPU speedup for these operations on the largest systems studied. The computational performance of the TTDFT code is presented using benchmark studies on aluminum nano-particles and silicon quantum dots with system sizes ranging up to ∼7,000 atoms. Program summaryProgram Title: TTDFT: Tucker tensor density functional theory codeCPC Library link to program files:https://doi.org/10.17632/8dgmcs8ys2.1Licensing provisions: LGPLProgramming language: C/C++External routines/libraries: TuckerMPI (https://gitlab.com/tensors/TuckerMPI), cuBLAS (https://docs.nvidia.com/cuda/cublas/index.html), cuSparse (https://docs.nvidia.com/cuda/cusparse/index.html), ALGLIB (http://www.alglib.net/), Boost (https://www.boost.org/), BLAS (http://www.netlib.org/blas/), LAPACK (http://www.netlib.org/lapack/), PETSc (https://www.mcs.anl.gov/petsc), SLEPc (http://slepc.upv.es)Nature of problem: Real-space Kohn-Sham density functional theory calculations using localized Tucker tensor basis.Solution method: We present a real-space Kohn-Sham density functional theory code based on tensor-structured techniques with GPU acceleration. Tensor-structured techniques are adopted for computing a Tucker tensor basis, representing the eigenfunctions of an additive separable approximation to the Kohn-Sham Hamiltonian. The Tucker tensor basis is further localized using L1 regularization to improve the sparsity of the Kohn-Sham Hamiltonian matrix, and improve the computational efficiency and parallel scalability of the proposed algorithm. The solution to the Kohn-Sham problem in the localized Tucker tensor basis is computed using the Chebyshev filtered subspace iteration (ChFSI) method.Additional comments including restrictions and unusual features: The code works with Troullier-Martin (TM) pseudopotentials in Kleinman-Bylander form. The current release supports only non-periodic DFT calculations with the local density approximation (LDA) for exchange-correlation functional.This TTDFT project uses GitHub via Git, a free distributed version control software. The archived version at the time of submission of this work can be found on the CPC program library through program files DOI provided above. The GitHub repository of this project can be found on https://github.com/ttdftdev/ttdft_public.

Design, synthesis, spectroscopic characterizations, in vitro pancreatic lipase as well as tyrosinase inhibition evaluations and in silico analysis of novel aryl sulfonate-naphthalene hybrids

One of the primary purposes of this study is to synthesize new aryl sulfonate-naphthalene hybrid structures possessing divergent electron-withdrawing and electron-releasing functional groups. Following the improved reaction conditions, we successfully gathered ten distinct sulfonate derivatives (3a-j) with good yields. The synthesized naphthalene-based sulfonate derivatives were then characterized using appropriate analytical methods (FT-IR, 1H-NMR, 13C-NMR, HRMS, and elemental analysis). Additionally, in vitro and in silico enzyme inhibitory properties of the prepared aryl sulfonate-naphthalene hybrid structures were evaluated against pancreatic lipase and tyrosinase enzymes. Corresponding in vitro enzyme activity investigations revealed that the produced compounds inhibit pancreatic lipase and tyrosinase enzymes significantly. According to the lowest IC50 values, 3h (95.3 ± 4.0 µM) demonstrated the most effective inhibition against pancreatic lipase, whereas 3a (40.8 ± 3.3 µM) was found as the most effective inhibition against the tyrosinase. According to in silico studies, 3a exhibited the highest affinity value (−9.9 kcal/mol) against pancreatic lipase, whereas 3f demonstrated the best affinity value (−8.7 kcal/mol) against tyrosinase. Furthermore, we investigated various structural and physicochemical properties of the target molecules, namely frontier orbital’ (HOMO, LUMO, and bandgap) energies (including their corresponding contour plots), global reactivity descriptors (ionization energy and electron affinity), and electronegativity values gathered from ground-state (GS) density functional theory (DFT) calculations. These investigations demonstrated that the observed electrostatic interactions effectively contributed to the studied molecules’ experimentally demonstrated enzyme inhibition potential. Also, ADMET studies were evaluated to enlighten the molecular interactions of the compounds with the enzymes. Communicated by Ramaswamy H. Sarma

Bond-Valence Parameterization for the Accurate Description of DFT Energetics.

We report a bond-valence method (BVM) parameterization framework that captures density functional theory (DFT)-computed relative stabilities using the BVM global instability index (GII). We benchmarked our framework against a dataset of 188 experimentally observed ABO3 perovskite oxides, each of which was generated in 11 unique Glazer octahedral tilt systems and optimized using DFT. Our constrained minimization procedure minimizes the GIIs of the 188 perovskite ground state structures predicted by DFT while enforcing a linear correlation between the GIIs and DFT energies of all 2068 competing structures. GIIs based on BVM parameters determined using our framework correctly identified the DFT ground state perovskite structure in 135 of 188 compositions or one of the two lowest energy structures in 152 of 188 compositions. Using the most common approach to parameterize BVM, which minimizes the root-mean-square deviation of the BVM site discrepancy factors, GIIs correctly identified the DFT ground state perovskite structure in only 41 of 188 compositions. Our new parameterization framework is therefore a marked improvement over the existing procedure and an important first step toward BVM-based structure generation protocols that reproduce DFT.

Relativistic Orbital-Optimized Density Functional Theory for Accurate Core-Level Spectroscopy.

Core-level spectra of 1s electrons of elements heavier than Ne show significant relativistic effects. We combine advances in orbital-optimized density functional theory (OO-DFT) with the spin-free exact two-component (X2C) model for scalar relativistic effects to study K-edge spectra of third period elements. OO-DFT/X2C is found to be quite accurate at predicting energies, yielding a ∼0.5 eV root-mean-square error versus experiment with the modern SCAN (and related) functionals. This marks a significant improvement over the >50 eV deviations that are typical for the popular time-dependent DFT (TDDFT) approach. Consequently, experimental spectra are quite well reproduced by OO-DFT/X2C, sans empirical shifts for alignment. OO-DFT/X2C combines high accuracy with ground state DFT cost and is thus a promising route for computing core-level spectra of third period elements. We also explored K and L edges of 3d transition metals to identify limitations of the OO-DFT/X2C approach in modeling the spectra of heavier atoms.

Stochastic Vector Techniques in Ground-State Electronic Structure.

We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.