Kohn-Sham Density Functional Theory Research Articles

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations.

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

High-Throughput Aqueous Electrolyte Structure Prediction Using IonSolvR and Equivariant Graph Neural Network Potentials.

Neural network potentials have recently emerged as an efficient and accurate tool for accelerating ab initio molecular dynamics (AIMD) in order to simulate complex condensed phases such as electrolyte solutions. Their principal limitation, however, is their requirement for sufficiently large and accurate training sets, which are often composed of Kohn-Sham density functional theory (DFT) calculations. Here we examine the feasibility of using existing density functional tight-binding (DFTB) molecular dynamics trajectory data available in the IonSolvR database in order to accelerate the training of E(3)-equivariant graph neural network potentials. We show that the solvation structure of Na+ and Cl- in aqueous NaCl solutions can be accurately reproduced with remarkably small amounts of data (i.e., 100 MD frames). We further show that these predictions can be systematically improved further via an embarrassingly parallel resampling approach.

Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes.

During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

Doubly Tuned Exchange-Correlation Functionals for Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory.

It is demonstrated that significant accuracy improvements in MRSF-TDDFT can be achieved by introducing two different exchange-correlation (XC) functionals for the reference Kohn-Sham DFT and the response part of the calculations, respectively. Accordingly, two new XC functionals of doubly tuned Coulomb attenuated method-vertical excitation energy (DTCAM-VEE) and DTCAM-AEE were developed on the basis of the "adaptive exact exchange (AEE)" concept in the framework of the Coulomb-attenuating XC functionals. The values by DTCAM-VEE are in excellent agreement with those of Thiel's set [mean absolute errors (MAEs) and the interquartile range (IQR) values of 0.218 and 0.327 eV, respectively]. On the other hand, DTCAM-AEE faithfully reproduced the qualitative aspects of conical intersections (CIs) of trans-butadiene and thymine and the nonadiabatic molecular dynamics (NAMD) simulations on thymine. The latter functional also remarkably exhibited the exact 1/R asymptotic behavior of the charge-transfer state of an ethylene-tetrafluoroethylene dimer and the accurate potential energy surfaces (PESs) along the two torsional angles of retinal protonated Schiff base model with six double bonds (rPSB6). Overall, DTCAM-AEE generally performs well, as its MAE (0.237) and IQR (0.41 eV) are much improved as compared to BH&HLYP. The current idea can also be applied to other XC functionals as well as other variants of linear response theories, opening a new way of developing XC functionals.

KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory.

Orbital-free density functional theory (OF-DFT) holds promise to compute ground state molecular properties at minimal cost. However, it has been held back by our inability to compute the kinetic energy as a functional of electron density alone. Here, we set out to learn the kinetic energy functional from ground truth provided by the more expensive Kohn-Sham density functional theory. Such learning is confronted with two key challenges: Giving the model sufficient expressivity and spatial context while limiting the memory footprint to afford computations on a GPU and creating a sufficiently broad distribution of training data to enable iterative density optimization even when starting from a poor initial guess. In response, we introduce KineticNet, an equivariant deep neural network architecture based on point convolutions adapted to the prediction of quantities on molecular quadrature grids. Important contributions include convolution filters with sufficient spatial resolution in the vicinity of nuclear cusp, an atom-centric sparse but expressive architecture that relays information across multiple bond lengths, and a new strategy to generate varied training data by finding ground state densities in the face of perturbations by a random external potential. KineticNet achieves, for the first time, chemical accuracy of the learned functionals across input densities and geometries of tiny molecules. For two-electron systems, we additionally demonstrate OF-DFT density optimization with chemical accuracy.

Spectral-partitioned Kohn-Sham density functional theory

Spectral-partitioned Kohn-Sham density functional theory

Machine Learning Density Functionals from the Random-Phase Approximation.

Kohn-Sham density functional theory (DFT) is the standard method for first-principles calculations in computational chemistry and materials science. More accurate theories such as the random-phase approximation (RPA) are limited in application due to their large computational cost. Here, we use machine learning to map the RPA to a pure Kohn-Sham density functional. The machine learned RPA model (ML-RPA) is a nonlocal extension of the standard gradient approximation. The density descriptors used as ingredients for the enhancement factor are nonlocal counterparts of the local density and its gradient. Rather than fitting only RPA exchange-correlation energies, we also include derivative information in the form of RPA optimized effective potentials. We train a single ML-RPA functional for diamond, its surfaces, and liquid water. The accuracy of ML-RPA for the formation energies of 28 diamond surfaces reaches that of state-of-the-art van der Waals functionals. For liquid water, however, ML-RPA cannot yet improve upon the standard gradient approximation. Overall, our work demonstrates how machine learning can extend the applicability of the RPA to larger system sizes, time scales, and chemical spaces.

Leveling the Mountain Range of Excited-State Benchmarking through Multistate Density Functional Theory.

The performance of multistate density functional theory (MSDFT) with nonorthogonal state interaction (NOSI) is assessed for 100 vertical excitation energies against the theoretical best estimates extracted to the full configuration interaction accuracy on the database developed by Loos et al. in 2018 (Loos2018). Two optimization techniques, namely, block-localized excitation and target state optimization, are examined along with two ways of estimating the transition density functional (TDF) for the correlation energy of the Hamiltonian matrix density functional. The results from the two optimization methods are similar. It was found that MSDFT-NOSI using the spin-multiplet degeneracy constraint for the TDF of spin-coupling interaction, along with the M06-2X functional, yields a root-mean-square error (RMSE) of 0.22 eV, which performs noticeably better than time-dependent density functional theory (DFT) at an RMSE of 0.43 eV using the same functional and basis set on the Loos2018 database. In comparison with wave function theory, NOSI has smaller errors than CIS(D∞), LR-CC2, and ADC(3) all of which have an RMSE of 0.28 eV, but somewhat greater than STEOM-CCSD (RMSE of 0.14 eV) and LR-CCSD (RMSE of 0.11 eV) wave function methods. In comparison with Kohn-Sham (KS) DFT calculations, the multistate DFT approach has little double counting of correlation. Importantly, there is no noticeable difference in the performance of MSDFT-NOSI on the valence, Rydberg, singlet, triplet, and double-excitation states. Although the use of another hybrid functional PBE0 leads to a greater RMSE of 0.36 eV, the deviation is systematic with a linear regression slope of 0.994 against the results with M06-2X. The present benchmark reveals that density functional approximations developed for KS-DFT for the ground state with a noninteracting reference may be adopted in MSDFT calculations in which the state interaction is key.

The significance of fluctuating charges for molecular polarizability and dispersion coefficients.

The influence of fluctuating charges or charge flow on the dynamic linear response properties of isolated molecules from the TS42 database is evaluated, with particular emphasis on dipole polarizability and C6 dispersion coefficients. Two new descriptors are defined to quantify the charge-flow contribution to response properties, making use of the recoupled dipole polarizability to separate isotropic and anisotropic components. Molecular polarizabilities are calculated using the "frequency-dependent atom-condensed Kohn-Sham density functional theory approximated to second order," i.e., the ACKS2ω model. With ACKS2ω, the charge-flow contribution can be constructed in two conceptually distinct ways that appear to yield compatible results. The charge-flow contribution is significantly affected by molecular geometry and the presence of polarizable bonds, in line with previous studies. We show that the charge-flow contribution qualitatively reproduces the polarizability anisotropy. The contribution to the anisotropic C6 coefficients is less pronounced but cannot be neglected. The effect of fluctuating charges is only negligible for small molecules with at most one non-hydrogen atom. They become important and sometimes dominant for larger molecules or when highly polarizable bonds are present, such as conjugated, double, or triple bonds. Charge flow contributions cannot be explained in terms of individual atomic properties because they are affected by non-local features such as chemical bonding and geometry. Therefore, polarizable force fields and dispersion models can benefit from the explicit modeling of charge flow.

The application of the SCAN density functional to color centers in diamond.

Detailed characterization of deep-level color centers requires understanding their electronic and atomic structure, which is most commonly investigated utilizing the Kohn-Sham density functional theory. Standard semilocal functionals based on the generalized gradient approximation (GGA) are inclined toward an imprecise quantitative description of defects' electronic structure. Hybrid functionals provide an improved prediction of electronic properties, albeit at a much higher computational cost. In this work, we test the newly developed Strongly Constrained and Appropriately Normed (SCAN) family of meta-GGA density functionals for selected color centers in diamond. In particular, we study nitrogen-, silicon-, germanium-, and tin-vacancy centers that have been recently investigated for their use in quantum technological applications. We show that SCAN and its derivatives, the rSCAN and r2SCAN functionals, significantly improve the calculated energies of optical transitions within the delta-self-consistent-field approach, almost reaching the accuracy of the hybrid Heyd-Scuseria-Ernzerhof (HSE) functional. In the case of the NV- center, we also show that the SCAN family of functionals improves the description of the adiabatic potential energy surfaces compared to both GGA and hybrid functionals, improving calculated luminescence lineshapes. As a result of these findings, we recommend using the SCAN family of functionals as a promising alternative for studying color centers in solids.

Quantum Chemical Studies on Possible Molecular Devices Based on Electric Field-Induced Intramolecular Charge Transfer.

We report quantum chemical studies on possible molecular devices working based on electric field-induced intramolecular charge transfer (EFIMCT). In the case of donor-acceptor (DA)-type molecular systems, intramolecular charge transfer (IMCT) can be induced by applying the external electric field to molecular systems along the charge transport direction, providing a possible switching mechanism which does not depend upon the electron-phonon coupling effect and is different from the negative differential resistance mechanism observed in the well-known NO2-substituted phenylene ethynylene oligomers. When the EFIMCT proceeds, the molecular systems have strong static electron correlation effects, where the standard nonequilibrium Green's function-density functional theory (DFT) approach cannot be applied to the molecular junction. As a first step toward practical switching devices, we do quantum chemical studies on the EFIMCT in such molecular systems as an isolated molecule, instead of using the electrode-junction-electrode open quantum system model. A prototype molecule P1 is designed as a tentative candidate molecule where the EFIMCT can proceed. The complete active space self-consistent field (CASSCF) molecular orbital calculations on P1 indicate that the EFIMCT can proceed at the external electric field intensity of 0.003 au, corresponding to about 2.25 V bias voltage. This calculated result strongly suggests that the development of this type of switching devices working at practically low bias voltage is feasible if the molecular system is properly designed. Broken symmetry unrestricted Hartree-Fock and spin-polarized Kohn-Sham DFT calculations also qualitatively reproduce the CASSCF results on P1, to some extent, indicating that these approaches can be employed for rough estimations on the EFIMCT such as the first screening of a large quantity of candidate molecules for this type of molecular devices. The possibility of molecular memory devices based on the EFIMCT is also discussed by analyzing the ground and excited potential energy surface model. Remaining challenges to develop practical molecular devices are discussed.

Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals.

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Computational quantum chemistry of metal–organic frameworks

Metal–organic frameworks (MOFs) have premium exceptional properties for a variety of functions, such as gas separation and storage and catalysis. The large variety of possible inorganometallic nodes and organic linkers provide an almost unlimited number of combinations for assembling MOFs, which makes the experimental characterization and examination of all potentially useful combinations practically impossible. Furthermore, experimental studies of MOFs typically fall short in uncovering crucial details regarding their mechanisms of action or the molecular details responsible for their functional properties, such as the nature of adsorbate binding or the structures of transition states. Computational modeling has, therefore, become an efficient and important tool for strategizing the functionalization of MOFs and explicating the mechanisms of their functions. Here, we review the computational methodologies used for computational studies of MOFs, especially Kohn–Sham density functional theory and combined quantum mechanical and molecular mechanical methods for calculating their structural, electronic, and magnetic properties, as well as for understanding the mechanisms of MOFs' applications to magetic devices, thermal conduction, gas adsorption, separation, storage, and sensing, thermal catalysis, photocatalysis, and electrocatalysis.

Quantum capacitance of quasi-2D-crystals

Results of research in the quantum capacitance [Formula: see text] of quasi-2D-crystals are presented. The detected extraordinary behavior of [Formula: see text] manifests itself in the existence of such energy ranges in which it is practically equal to zero. The causes for the existence of such ranges are: (a) dimensional quantization as a result of the nanoscale of the van der Waals gap, (b) a certain value of the width of the allowed zone in the plane of the layers, which is determined by the value of the effective mass. Intercalation and external electric field are effective factors capable of changing the position of ranges. Thus, in a system connected in a series of electrostatic and quantum capacitances, the resulting capacitance will significantly depend on the [Formula: see text] behavior. Comparative analyses of structures, chemical bonds, majority of coinciding characteristics of physical quantities in graphite, transition metal dichalcogenides (TMD), and layered crystals A3B6 allow us to assert that the obtained qualitative conclusions can be applied for each of them. Calculations of density of states (DOS) of quasi-2D crystals performed by authors within the framework of the improved Kohn–Sham density functional theory (DFT), namely the DFT taking into account the van der Waals forces in it, show a step-like form of DOS qualitatively similar to ours.

Subspace recursive Fermi-operator expansion strategies for large-scale DFT eigenvalue problems on HPC architectures.

Quantum mechanical calculations for material modeling using Kohn-Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for N smallest eigenvector-eigenvalue pairs, with N proportional to the number of electrons in the material system. These calculations are computationally demanding and have asymptotic cubic scaling complexity with the number of electrons. Large-scale matrix eigenvalue problems arising from the discretization of the Kohn-Sham DFT equations employing a systematically convergent basis traditionally rely on iterative orthogonal projection methods, which are shown to be computationally efficient and scalable on massively parallel computing architectures. However, as the size of the material system increases, these methods are known to incur dominant computational costs through the Rayleigh-Ritz projection step of the discretized Kohn-Sham Hamiltonian matrix and the subsequent subspace diagonalization of the projected matrix. This work explores the potential of polynomial expansion approaches based on recursive Fermi-operator expansion as an alternative to the subspace diagonalization of the projected Hamiltonian matrix to reduce the computational cost. Subsequently, we perform a detailed comparison of various recursive polynomial expansion approaches to the traditional approach of explicit diagonalization on both multi-node central processing unit and graphics processing unit architectures and assess their relative performance in terms of accuracy, computational efficiency, scaling behavior, and energy efficiency.

Mechanistic study on the synergy of cold plasma and sulfate radical in the degradation of azo and triarylmethane dyes using density functional theory

The activation of persulfate using cold plasma and the synergy of plasma-generated reactive species and SO4•− in mineralization of organic dyes were assessed. In this regard, solutions of crystal violet (CV) as a triarylmethane dye and methyl orange (MO) as an azo dye, were treated with cold plasma, UV-C-activated sulfate radicals, and their combination. The achieved results showed 95% TOC removal, a synergy factor of 1.3 and an energy yield of 1.68 (g kWh−1) for the combined system. The contribution of oxidant species in CV (SO4•− > O2•- > •OH) and MO (SO4•−> O2•- >1O2) degradation was explored. Moreover, analysis of degradation products and density functional theory (DFT) calculations were adopted to find the degradation mechanism based on the minimum energy pathway. Experimental and DFT results revealed that while radical and nucleophilic pathways were the drivers of CV degradation, the electrophilic attack of oxidants was a more plausible mechanism for MO degradation. Additionally, a comparison of the results of different DFT methods with experimental values showed that the Kohn–Sham DFT yielded more accurate results compared to recommended double hybrid methods. Analysis of a treated real wastewater revealed that the background constituents had negligible effects on MO and CV degradation. The high TOC removal efficiency of the combined system suggests its feasibility for treating wastewater from fertilizer and pharmaceutical production facilities.

Multiscale Methods Framework with the 3D-RISM-KH Molecular Solvation Theory for Supramolecular Structures, Nanomaterials, and Biomolecules: Where Are We Going?

3D-RISM-KH molecular solvation theory based on statistical mechanics has been an engine of the multiscale methods framework, which also includes molecular simulation techniques. Its applications range from the solvation energy of small molecules to the phase behavior of polymers and biomolecules. Molecular solvation theory predicts and explains the molecular mechanisms and functioning of a variety of chemical and biomolecular systems. This includes the self-assembly and conformational stability of synthetic organic rosette nanotubes (RNTs), the aggregation of peptides and proteins related to neurodegeneration, the binding of ligands to proteins, and the solvation properties of biomolecules related to their functions. The replica RISM-KH-VM molecular solvation theory predicts and explains the structure, thermodynamics, and electrochemistry of electrolyte solutions sorbed in nanoporous carbon supercapacitor electrodes, and is part of recent research and development efforts. A new quasidynamics protocol couples multiple time step molecular dynamics (MTS-MD) stabilized with an optimized isokinetic Nosé–Hoover (OIN) thermostat driven by 3D-RISM-KH mean solvation forces at gigantic outer time steps of picoseconds, which are extrapolated forward at short inner time steps of femtoseconds with generalized solvation force extrapolation (GSFE). The OIN/3D-RISM-KH/GSFE quasidynamics is implemented in the Amber Molecular Dynamics package. It is validated on miniprotein 1L2Y and protein G in ambient aqueous solution, and shows the rate of sampling 150 times faster than in standard MD simulations on these biomolecules in explicit water. The self-consistent field version of Kohn–Sham DFT in 3D-RISM-KH mean solvation forces is implemented in the Amsterdam Density Functional (ADF) package. Its applications range from solvation thermochemistry, conformational equilibria, and photochemistry to activation barriers of different nanosystems in solutions and ionic liquids.

Real-space solution to the electronic structure problem for nearly a million electrons.

We report a Kohn-Sham density functional theory calculation of a system with more than 200 000 atoms and 800 000 electrons using a real-space high-order finite-difference method to investigate the electronic structure of large spherical silicon nanoclusters. Our system of choice was a 20nm large spherical nanocluster with 202 617 silicon atoms and 13 836 hydrogen atoms used to passivate the dangling surface bonds. To speed up the convergence of the eigenspace, we utilized Chebyshev-filtered subspace iteration, and for sparse matrix-vector multiplications, we used blockwise Hilbert space-filling curves, implemented in the PARSEC code. For this calculation, we also replaced our orthonormalization + Rayleigh-Ritz step with a generalized eigenvalue problem step. We utilized all of the 8192 nodes (458 752 processors) on the Frontera machine at the Texas Advanced Computing Center. We achieved two Chebyshev-filtered subspace iterations, yielding a good approximation of the electronic density of states. Our work pushes the limits on the capabilities of the current electronic structure solvers to nearly 106 electrons and demonstrates the potential of the real-space approach to efficiently parallelize large calculations on modern high-performance computing platforms.

Solving the electronic structure problem for over 100 000 atoms in real space

Using a real-space high-order finite-difference approach, we investigate the electronic structure of large spherical silicon nanoclusters. Within Kohn-Sham density functional theory and using pseudopotentials, we report the self-consistent field convergence of a system with over 100 000 atoms: a ${\mathrm{Si}}_{107,641}{\mathrm{H}}_{9,084}$ nanocluster with a diameter of 16 nm. Our approach uses Chebyshev-filtered subspace iteration to speed up the convergence of the eigenspace, and blockwise Hilbert space-filling curves to speed up sparse matrix-vector multiplications, all of which are implemented in the parsec code. For the largest system, we utilized 2048 nodes (114 688 cores) on the Frontera machine in the Texas Advanced Computing Center. Our quantitative analysis of the electronic structure shows how it gradually approaches its bulk counterpart as a function of nanocluster size. The band gap is enlarged due to quantum confinement in nanoclusters, but decreases as the system size increases, as expected. Our work serves as a proof of concept for the capacity of the real-space approach in efficiently parallelizing very large calculations using high-performance computer platforms, which can straightforwardly be replicated in other systems with more than ${10}^{5}$ atoms.

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.