Efficient Electronic Structure Research Articles

Ternary ordered L10-Pt-Co-Fe intermetallics for efficient ORR catalysis through dissociation pathway

Developing efficient and durable Pt-based electrocatalysts for oxygen reduction reaction (ORR) is critical for the practical application of fuel cells but still remains challenge at present. Here we successfully synthesized a series of ternary L10-PtCoxFe1-x (x=0.33, 0.50 and 0.67) intermetallic nanoparticles (NPs) supported on reduced graphene oxide for ORR catalysis. L10-PtCo0.50Fe0.50 exhibits the highest mass activity (MA) of 0.93 A mg−1Pt at 0.9 V (1.82 times the corresponding binary L10-PtCo intermetallics) and minimal activity loss (24.73 % loss in MA) after 30,000 potential cycles. By Density Functional Theory calculations, the excellent performance of ternary L10-PtCo0.50Fe0.50 can be ascribed to: (1) more efficient electronic structure regulation caused by dual-element driven electron transfer, which leads to more electron accumulation on Pt and weakens the over-binding of oxygen-containing species, (2) the unique two-center bridge pattern of O2 adsorption over Pt-Fe site leads to ORR proceeding via. the dissociative mechanism, avoiding the formation of OOH*.

Electrosynthesis of formate coupled green hydrogen production on the interface of CuMoO4 nanostructures: A novel electrocatalyst for hybrid water electrolysis system

Developing affordable/efficient catalysts for electrolytic co-production of green hydrogen and value-added products is a prime interest. However, efficient electronic structure engineering of transition metal-based catalysts remains challenging. Herein, we develop high-valent capsule-like copper molybdate (c-CMO) via ultrasonication-assisted strategy. XPS, XANES, KPFM, and DFT studies suggest strong Mo-Cu interaction in c-CMO alters its electronic structure, reduces work function, and lowers ∆GH*. In HER, c-CMO/PNF electrode achieved 130 mV@10 mA/cm² with higher MA and TOF than CO/PNF and MO/PNF electrodes and superior methanol-tolerance than Pt/C. MOR investigations suggest c-CMO/PNF requires 1.39 V@10 mA/cm², 0.239 V lower than OER. Qualitative/quantitative 1H NMR confirms impressive HCOO− selectivity with ∼96 % Faradaic efficiency. The assembled hybrid AEM water-electrolyzer (HER+MOR) demonstrates 1 A/cm²@2 V (at 60 °C), outperforming HER+OER (2.25 V). The stability test of HAEMWE modeled/predicted using Time-Series-Analysis reveals statistically significant lags, indicating zero autocorrelation. This study emphasizes the development of efficient TMO based catalyst for HAEMWE.

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Modulating single-atom sulfur-vacancy defect in MoS2-x catalysts to boost cathode redox kinetics for vanadium flow batteries

Vanadium flow batteries (VFBs) have great potential for application in energy storage systems. However, the sluggish cathode redox kinetics still greatly restricts their operation at high current densities. Herein, we boost cathode redox chemistry by modulating single-atom sulfur-vacancy (S-vacancy) defect of MoS2-x in-situ grown on carbon felts via a facile chemical etching method. Firstly, the optimized S-vacancy concentration is figured out via high throughput calculations based on d-band center theory. By precisely controlling etching duration, we achieve a tailored S-vacancy concentration, leading to highly dispersed S-vacancies, increased specific surface area, and improved hydrophilicity. Electrochemical characterizations demonstrate that optimized S-vacancy state can significantly facilitate the VO2+/VO2+ kinetics. Moreover, analysis of electron density difference and integrated crystal orbital Hamiltonian group further reveals that dispersed S-vacancy distribution also contribute to efficient surface electronic structure and enhanced adsorption process. Benefiting from enhanced VO2+/VO2+ kinetics, VFB single cell achieves a superior EE of 78.73 % at 300 mA cm−2 and is able to last for 500 cycles without decay. This work demonstrates the promising potential of single-atom S-vacancies catalysts in the fabrication of flow battery electrodes and more importantly sheds light on the fundamental modulation essence of d-band center in MoS2-x towards enhanced cathode redox kinetics.

Machine learning for accuracy in density functional approximations.

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Combining low-cost electronic structure theory and low-cost parallel computing architecture.

The computational efficiency of low-cost electronic structure methods can be further improved by leveraging heterogenous computing architectures. The software package TeraChem has been developed since 2008 to make use of graphical processing units (GPUs), particularly their strong single-precision performance, for the acceleration of quantum chemical calculations. Here, we present the implementation of three low-cost methods, namely HF-3c, PBEh-3c, and the recently introduced ωB97X-3c. We show that these can benefit in terms of performance when combined with "consumer grade" GPUs by leveraging the mixed precision integral handling in TeraChem. The current limitation of the latter's GPU integral library is that Gaussian integrals only for functions with angular momentum l < 3 can be computed, which generally restricts the achievable accuracy in terms of the one-particle basis set. Particularly, the implementation of the ωB97X-3c method now enables higher accuracy with this setting which, in turn, provides the most efficient implementation accessible with consumer-grade hardware. We furthermore show that the implemented 3c methods can be combined with the hh-TDA formalism. This gives new and efficient low-cost multi-configurational excited states methods, which are benchmarked for the description of lowest vertical excitation energies in this work. All in all, the combination of these efficient electronic structure theory methods with affordable highly parallelized computing hardware provides an optimal computational and monetary cost to accuracy ratio.

A machine learning-based high-precision density functional method for drug-like molecules

In computer-aided drug discovery, accurately determining the structure and properties of drug-like molecules is of utmost importance. This necessitates the use of precise and efficient electronic structure methods. Here, we developed two deep learning-based density functional methods, namely DeePHF and DeePKS, specifically tailored for drug-like molecules. Notably, DeePKS incorporates self-consistency into its framework. With a limited dataset labelled at the CCSD(T)/def2-TZVP level, both models have been able to achieve chemical accuracy in calculating molecular energies and have demonstrated excellent transferability. We anticipate that further advancements in this field will lead to the development of high-quality density functional methods designed specifically for drug discovery purposes. This research showcases the capabilities of deep learning approaches in simplifying the construction complexity associated with traditional DFT methods.

Real-Time Extension of TAO-DFT.

Thermally assisted occupation density functional theory (TAO-DFT) has been an efficient electronic structure method for studying the ground-state properties of large electronic systems with multi-reference character over the past few years. To explore the time-dependent (TD) properties of electronic systems (e.g., subject to an intense laser pulse), in this work, we propose a real-time (RT) extension of TAO-DFT, denoted as RT-TAO-DFT. Moreover, we employ RT-TAO-DFT to study the high-order harmonic generation (HHG) spectra and related TD properties of molecular hydrogen H2 at the equilibrium and stretched geometries, aligned along the polarization of an intense linearly polarized laser pulse. The TD properties obtained with RT-TAO-DFT are compared with those obtained with the widely used time-dependent Kohn-Sham (TDKS) method. In addition, issues related to the possible spin-symmetry breaking effects in the TD properties are discussed.

General framework for E(3)-equivariant neural network representation of density functional theory Hamiltonian

The combination of deep learning and ab initio calculation has shown great promise in revolutionizing future scientific research, but how to design neural network models incorporating a priori knowledge and symmetry requirements is a key challenging subject. Here we propose an E(3)-equivariant deep-learning framework to represent density functional theory (DFT) Hamiltonian as a function of material structure, which can naturally preserve the Euclidean symmetry even in the presence of spin–orbit coupling. Our DeepH-E3 method enables efficient electronic structure calculation at ab initio accuracy by learning from DFT data of small-sized structures, making the routine study of large-scale supercells (>104 atoms) feasible. The method can reach sub-meV prediction accuracy at high training efficiency, showing state-of-the-art performance in our experiments. The work is not only of general significance to deep-learning method development but also creates opportunities for materials research, such as building a Moiré-twisted material database.

Learning Conductance: Gaussian Process Regression for Molecular Electronics.

Experimental studies of charge transport through single molecules often rely on break junction setups, where molecular junctions are repeatedly formed and broken while measuring the conductance, leading to a statistical distribution of conductance values. Modeling this experimental situation and the resulting conductance histograms is challenging for theoretical methods, as computations need to capture structural changes in experiments, including the statistics of junction formation and rupture. This type of extensive structural sampling implies that even when evaluating conductance from computationally efficient electronic structure methods, which typically are of reduced accuracy, the evaluation of conductance histograms is too expensive to be a routine task. Highly accurate quantum transport computations are only computationally feasible for a few selected conformations and thus necessarily ignore the rich conformational space probed in experiments. To overcome these limitations, we investigate the potential of machine learning for modeling conductance histograms, in particular by Gaussian process regression. We show that by selecting specific structural parameters as features, Gaussian process regression can be used to efficiently predict the zero-bias conductance from molecular structures, reducing the computational cost of simulating conductance histograms by an order of magnitude. This enables the efficient calculation of conductance histograms even on the basis of computationally expensive first-principles approaches by effectively reducing the number of necessary charge transport calculations, paving the way toward their routine evaluation.

Extending multi-layer energy-based fragment method for excited-state calculations of large covalently bonded fragment systems.

Recently, we developed a low-scaling Multi-Layer Energy-Based Fragment (MLEBF) method for accurate excited-state calculations and nonadiabatic dynamics simulations of nonbonded fragment systems. In this work, we extend the MLEBF method to treat covalently bonded fragment ones. The main idea is cutting a target system into many fragments according to chemical properties. Fragments with dangling bonds are first saturated by chemical groups; then, saturated fragments, together with the original fragments without dangling bonds, are grouped into different layers. The accurate total energy expression is formulated with the many-body energy expansion theory, in combination with the inclusion-exclusion principle that is used to delete the contribution of chemical groups introduced to saturate dangling bonds. Specifically, in a two-layer MLEBF model, the photochemically active and inert layers are calculated with high-level and efficient electronic structure methods, respectively. Intralayer and interlayer energies can be truncated at the two- or three-body interaction level. Subsequently, through several systems, including neutral and charged covalently bonded fragment systems, we demonstrate that MLEBF can provide accurate ground- and excited-state energies and gradients. Finally, we realize the structure, conical intersection, and path optimizations by combining our MLEBF program with commercial and free packages, e.g., ASE and SciPy. These developments make MLEBF a practical and reliable tool for studying complex photochemical and photophysical processes of large nonbonded and bonded fragment systems.

Lightweight mechatronic system for humanoid robot

Abstract This paper presents the technical specifications of a lightweight humanoid robot platform named Robinion Sr. including its mechanical and electrical design. We describe a versatile and robust mechatronic system, efficient walking gait, and software architecture of the humanoid robot. The humanoid robot platform is targeted for use in a range of applications, including research and development, competitions, and the service industry. A reduced platform cost was an essential consideration in our design. We introduce a specialized and inexpensive mechanical design, which includes a parallel-kinematics leg design, external gears, and low-cost controllers and sensors. The humanoid robot is equipped with an efficient electronic structure and a tablet computer for task scheduling, control, and perception, as well as an embedded controller for solving forward &amp; inverse kinematics and low-level actuator control. The perception system recognizes objects at real-time inference with Deep Learning-based detection algorithms without a dedicated GPU. We present and evaluate the capabilities of our newly developed advanced humanoid robot and believe it is a suitable platform for the academic and industrial robotics community.

Photochemistry of Thymine in Solution and DNA Revealed by an Electrostatic Embedding QM/MM Combined with Mixed-Reference Spin-Flip TDDFT

The photochemistry of nucleobases, important for their role as building blocks of DNA, is largely affected by the electrostatic environment in which they are soaked. For example, despite the numerous studies of thymine in solution and DNA, there is still a debate on the photochemical deactivation pathways after UV absorption. Many theoretical models are oversimplified due to the lack of computationally accurate and efficient electronic structure methodologies that capture excited state electron correlation effects when nucleobases are embedded in large electrostatic media. Here, we combine mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) with electrostatic embedding QM/MM using electrostatic potential fittingfitted (ESPF) atomic charges, as a strategy to accurately and efficiently describe the electronic structure of chromophores polarized by an electrostatic medium. In particular, we develop analytic expressions for the energy and gradient of MRSF/MM based on the ESPF coupling using atom-centered grids and total charge conservation. We apply this methodology to the study of solvation effects on thymine photochemistry in water and thymine dimers in DNA. In the former, the combination of trajectory surface hopping (TSH) nonadiabatic molecular dynamics (NAMD) with MRSF/MM remarkably revealed accelerated deactivation decay pathways, which is consistent with the experimental decay time of ∼400 fs. The enhanced hopping rate can be explained by the preferential stabilization of corresponding conical interactions due to their increased dipole moments. Structurally, it is a consequence of characteristic methyl puckered geometries near the conical intersection region. For the thymine dimer in B-DNA, we found new photochemical pathways through conical intersections that could explain the formation of cyclobutadiene dimers and 6-4 photoproducts.

Accelerating Hybrid Density Functional Theory Molecular Dynamics Simulations by Seminumerical Integration, Resolution-of-the-Identity Approximation, and Graphics Processing Units.

The computationally very demanding evaluation of the 4-center-2-electron (4c2e) integrals and their respective integral derivatives typically represents the major bottleneck within hybrid Kohn-Sham density functional theory molecular dynamics simulations. Building upon our previous works on seminumerical exact-exchange (sn-LinK) [Laqua, H., Thompsons, T. H., Kussmann, J., Ochsenfeld, C., J. Chem. Theory Comput. 2020, 16, 1465] and resolution-of-the-identity Coulomb (RI-J) [Kussmann, J., Laqua, H., Ochsenfeld, C., J. Chem. Theory Comput. 2021, 17, 1512], the expensive 4c2e integral evaluation can be avoided entirely, resulting in a highly efficient electronic structure theory method, allowing for fast ab initio molecular dynamics (AIMD) simulations even with large basis sets. Moreover, we propose to combine the final self-consistent field (SCF) step with the subsequent nuclear forces evaluation, providing the forces at virtually no additional cost after a converged SCF calculation, reducing the total runtime of an AIMD simulation by about another 25%. In addition, multiple independent MD trajectories can be computed concurrently on a single node, leading to a greatly increased utilization of the available hardware─especially when combined with graphics processing unit acceleration─improving the overall throughput by up to another 5 times in this way. With all of those optimizations combined, our proposed method provides nearly 3 orders of magnitude faster execution times than traditional 4c2e integral-based methods. To demonstrate the practical utility of the approach, quantum-mechanical/molecular-mechanical dynamics simulations on double-stranded DNA were performed, investigating the relative hydrogen bond strength between adenine-thymine and guanine-cytosine base pairs. In addition, this illustrative application also contains a general accuracy assessment of the introduced approximations (integration grids, resolution-of-the-identity) within AIMD simulations, serving as a protocol on how to apply these new methods to practical problems.

Graph-|Q⟩⟨C|, a Graph-Based Quantum/Classical Algorithm for Efficient Electronic Structure on Hybrid Quantum/Classical Hardware Systems: Improved Quantum Circuit Depth Performance.

We present a procedure to reduce the depth of quantum circuits and improve the accuracy of results in computing post-Hartree-Fock electronic structure energies in large molecular systems. The method is based on molecular fragmentation where a molecular system is divided into overlapping fragments through a graph-theoretic procedure. This allows us to create a set of projection operators that decompose the unitary evolution of the full system into separate sets of processes, some of which can be treated on quantum hardware and others on classical hardware. Thus, we develop a procedure for an electronic structure that can be asynchronously spawned onto a potentially large ensemble of classical and quantum hardware systems. We demonstrate this method by computing Unitary Coupled Cluster Singles and Doubles (UCCSD) energies for a set of [H2]n clusters, with n ranging from 4 to 128. We implement our methodology using quantum circuits, and when these quantum circuits are processed on a quantum simulator, we obtain energies in agreement with the UCCSD energies in the milli-hartree energy range. We also show that our circuit decomposition approach yields up to 9 orders of magnitude reduction in the number of CNOT gates and quantum circuit depth for the large-sized clusters when compared to a standard quantum circuit implementation available on IBM's Quantum Information Science kit, known as Qiskit.

The ΔSCF method for non-adiabatic dynamics of systems in the liquid phase.

Computational studies of ultrafast photoinduced processes give valuable insights into the photochemical mechanisms of a broad range of compounds. In order to accurately reproduce, interpret, and predict experimental results, which are typically obtained in a condensed phase, it is indispensable to include the condensed phase environment in the computational model. However, most studies are still performed in vacuum due to the high computational cost of state-of-the-art non-adiabatic molecular dynamics (NAMD) simulations. The quantum mechanical/molecular mechanical (QM/MM) solvation method has been a popular model to perform photodynamics in the liquid phase. Nevertheless, the currently used QM/MM embedding techniques cannot sufficiently capture all solute-solvent interactions. In this Perspective, we will discuss the efficient ΔSCF electronic structure method and its applications with respect to the NAMD of solvated compounds, with a particular focus on explicit quantum mechanical solvation. As more research is required for this method to reach its full potential, some challenges and possible directions for future research are presented as well.

Efficient Electronic Modulation of g-C 3 N 4 Photocatalyst by Implanting Atomically Dispersed Ag 1 -N 3 for Extremely High Hydrogen Evolution Rates

Efficient Electronic Modulation of g-C ₃ N ₄ Photocatalyst by Implanting Atomically Dispersed Ag ₁ -N ₃ for Extremely High Hydrogen Evolution Rates

Strategies for solving the excited-state self-consistent-field problem for highly excited and multiply ionized states

The dynamics of molecules exposed to intense x-ray radiation involve a large number of multiply ionized and highly excited electronic configurations. To model these dynamics a reliable and efficient electronic structure model is imperative. Employing the Hartree-Fock-Slater electronic structure model in combination with the maximum overlap method, we quantify the associated convergence failures when calculating electronic states of carbon monoxide with multiple vacancies in the core and valence levels. We characterize these cases and describe strategies to overcome the convergence problems. The described techniques not only eliminate all convergence issues for CO but also result in a significant reduction of convergence failures for simulations of the x-ray-induced multiple ionization dynamics of the phenol molecule.

EQMO: Equation of motion method for efficient electronic structure calculations

Equation of motion method has proven efficient for electronic structure calculations of very large systems, i.e. containing several million atoms. In this work, we redesign its previously published implementation and hereby release a revised software tool, EQMO, now capable of solving a crystalline TiO2 test sample of nearly a quarter of a billion atoms on NEC SX-Aurora TSUBASA vector computer. The legacy code has been rewritten in modern free-form Fortran, and the main developments include MPI support and optimisations for parallel execution. New Version Program SummaryProgram Title: EQMOCPC Library link to program files:https://doi.org/10.17632/5m7jp4nb4y.1Developer's repository link:https://git.icm.edu.pl/herman/eqmoLicensing provisions: GPLv3Programming language: FortranJournal reference of previous version: Marek T. Michalewicz, Herbert B. Shore, N. Tit, J.W. Halley, Equation of motion method for the electronic structure of disordered transition metal oxides, Comput. Phys. Commun. 71 (1992) 222–234.Does the new version supersede the previous version?: YesReasons for the new version: Major revisionSummary of revisions: The legacy Fortran code has been rewritten in modern free-form Fortran. The OpenMP support has been replaced with OpenMPI suitable for NEC SX-Aurora TSUBASA architecture. The sequential and MPI versions can be built independently to produce two separate binary files for both x86_64 CPU and NEC vector computer. The program has been developed and tested with GNU Fortran and NEC Fortran compilers.Nature of problem: Electronic structure calculation of a large system, i.e. containing several million atoms, is a computationally demanding task. The problem is to determine electronic properties of solid state systems in an efficient manner. The program, at its current development stage, is capable of calculating electronic properties (density of electronic states) of rutile TiO2 structure distorted by point defects, and is intended to be further developed towards treating a wide range of crystalline systems.Solution method: EQMO software tool is an equation of motion implementation designed to determine electronic structure (density of electronic states) of large-scale crystalline systems. The solution method is based on solving the Schrödinger equation with a tight-binding Hamiltonian, and its physical and mathematical foundations remain unchanged with respect to the previous release. For an explicit formalism with elaborate description, the reader is referred to the literature referenced below [1,2,3,4,5,6,7,8,9,10], and in particular – to the journal reference of the previous implementation along with the supplemented dataset [5]. The program is able to perform a benchmark on a TiO2 sample of nearly a quarter of a billion atoms on NEC SX-Aurora TSUBASA vector computer, and its functionality can be further expanded.

Analytical derivatives of the individual state energies in ensemble density functional theory. II. Implementation on graphical processing units (GPUs).

Conical intersections control excited state reactivity, and thus, elucidating and predicting their geometric and energetic characteristics are crucial for understanding photochemistry. Locating these intersections requires accurate and efficient electronic structure methods. Unfortunately, the most accurate methods (e.g., multireference perturbation theories such as XMS-CASPT2) are computationally challenging for large molecules. The state-interaction state-averaged restricted ensemble referenced Kohn-Sham (SI-SA-REKS) method is a computationally efficient alternative. The application of SI-SA-REKS to photochemistry was previously hampered by a lack of analytical nuclear gradients and nonadiabatic coupling matrix elements. We have recently derived analytical energy derivatives for the SI-SA-REKS method and implemented the method effectively on graphical processing units. We demonstrate that our implementation gives the correct conical intersection topography and energetics for several examples. Furthermore, our implementation of SI-SA-REKS is computationally efficient, with observed sub-quadratic scaling as a function of molecular size. This demonstrates the promise of SI-SA-REKS for excited state dynamics of large molecular systems.