DFTpy : An efficient and object-oriented platform for orbital-free DFT simulations
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Abstract Within density functional theory (DFT), adding a Hubbard U correction can mitigate some of the deficiencies of local and semi-local exchange-correlation functionals, while maintaining computational efficiency. However, the accuracy of DFT+U largely depends on the chosen Hubbard U values. We propose an approach to determining the optimal U parameters for a given material by machine learning. The Bayesian optimization (BO) algorithm is used with an objective function formulated to reproduce the band structures produced by more accurate hybrid functionals. This approach is demonstrated for transition metal oxides, europium chalcogenides, and narrow-gap semiconductors. The band structures obtained using the BO U values are in agreement with hybrid functional results. Additionally, comparison to the linear response (LR) approach to determining U demonstrates that the BO method is superior.
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. In conclusion, 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.
Accounting for parametric uncertainty in models is essential for quantifying the models’ predictive ability. Recently, approaches have been introduced to estimate parametric uncertainty in kinetic models while accounting for correlations among energy parameters. However, correlations have been estimated indirectly and correlations in entropies have not been accounted for. For surface-catalyzed microkinetic models of >C2 (more than two carbon-containing) molecules, which consist of thousands of reaction steps and intermediate surface species, first-principles density functional theory (DFT) is costly, and thus, estimation of thermochemistry and reaction barriers requires surrogate methods of DFT, such as group additivity and Brønsted–Evans–Polanyi relationships, respectively. For such parametrization, model uncertainty is unclear. This work develops a framework to overcome these gaps using group additivity and a single DFT functional. We estimate correlations in parameters of kinetic models and quantify uncertainty for thermochemistry, reaction barriers, reaction paths, and ultimately reaction rates, accounting also for the contribution of entropic uncertainty. Furthermore, the approach is illustrated on propane combustion and ethane oxidative dehydrogenation reactions.
Thermocatalytic decomposition (TCD) of methane can produce hydrogen and valuable nanocarbon co-products with low to near-zero CO2 emission. In this study, a series of Pd promoted Ni catalysts, prepared with various Ni/Pd ratios on a CNT support, were evaluated for methane TCD performance. Characterization and calculations using density functional theory (DFT) were carried out to elucidate the activity–structure relationship and growth mechanism of carbon nanomaterials. It was found that the methane conversion and stability of the catalysts were highly dependent on the Ni/Pd ratio and reaction temperature. DFT calculations revealed that the diffusion of carbon in the metal sublayer required for CNT growth was more favorable in the Ni–Pd alloy lattice suggesting that the buildup of carbon in the metal alloy sublayer facilitated the formation of CNTs and CNFs. A cyclic reaction–regeneration process for self-sustained TCD was experimentally demonstrated. In each cycle, a portion of the separated CNT product was used to re-synthesize the Ni–Pd/CNT catalyst for use in the next reaction cycle. After five cycles of operation, the CH4 conversion, morphology and crystallinity of the carbon product remained unchanged.
Adsorptive desulfurization with Cu and Ce ion-exchanged Y zeolite (CuCeY) has proven to be an effective method for the removal of sulfur compounds from hydrocarbon fuels. In this study, Cu and Ce exchanged Y materials including CuY, CeY, and CuCeY were prepared and examined to investigate the mechanism behind the superior sulfur adsorption and selectivity of CuCeY. In situ conditions were used to study the materials as prepared for optimal desulfurization. X-ray diffraction (XRD) confirmed the absence of large well-ordered crystalline phases from metallic or oxide Cu and Ce after the reduction of the samples. The oxidation states and local environments of Cu and Ce were determined using X-ray adsorption fine structure (XAFS) analysis and correlated to theoretical findings obtained from density functional theory (DFT) calculations. XAFS data indicate the successful reduction of Cu species to Cu + and Cu o , and Ce to Ce 3+ . Analysis of XAFS spectra located Cu and Ce within the Y zeolite framework with Cu cations in the six-member ring sites and as small metallic Cu clusters. Ce cations were found to occupy both six-member ring and hexagonal prism sites. Furthermore, these results reveal the structure of CuCeY as prepared for desulfurization and provide insight into its superior sulfur adsorption performance.
Cu/SSZ-13 selective catalytic reduction catalysts display activity loss after mild hydrothermal aging without support degradation or loss of isolated Cu ion content. By applying electron paramagnetic resonance spectroscopy to compare hydrated, dehydrated and NH3-saturated catalysts before and after hydrothermal aging, as well as density functional theory calculations, it is found that hydrothermal aging induces Cu relocation, leading to stronger Cu-support interactions. This is particularly evidenced by ZCuOH conversion to Z2Cu, which leads to the generation of a unique structure with two Cu(II) ions positioned in a double 6-membered ring prism. The Cu(II) ions that do not undergo such dramatic changes also appear to stay closer to framework windows as evidenced by the overall increased anisotropy during EPR measurements. In situ EPR measurements under SCR conditions demonstrate that, in comparison to the fresh catalyst, higher percentages of Cu species stay as Cu(II) in the aged catalyst. This suggests that the reduction half-cycle of the SCR redox, i.e., Cu(II) ? Cu(I), becomes slower for the hydrothermally aged catalyst.
Using a newly designed and developed parallelized photoreactor and colorimetric detection method, a large sampling of bimetallic co-catalysts (Pd/Sn, Pd/Mo, Pd/Ru, Pd/Pb, Pd/Ni, Ni/Sn, Mo/Sn and Pt/Sn) for photocatalytic water reduction have been tested in this work. Of these co-catalysts, the combination of palladium and tin showed the highest synergistic behavior and peak hydrogen gas production at a low relative fraction of palladium. The resulting Pd/Sn bimetallic co-catalysts were characterized using high-angle annular dark-field (HAADF) and scanning transmission electron microscopy energy dispersive X-ray spectroscopy (STEM-EDS), and specifically, investigation of the palladium/tin mixture indicated that palladium and tin elements reside within the same particle. The experimental catalytic activity for the palladium/tin mixture was compared to density functional theory-derived energy values associated with the adsorption of hydrogen onto a surface. This comparison demonstrated that the typical peak found in electrochemical Sabatier volcano plots at ΔG H* = ~0 eV was replicated in the experimental photocatalytic system with a peak activity observed at ΔG H* = -0.036 eV. Computational confirmation of the results expressed here demonstrates the efficacy of colorimetric detection of hydrogen in parallel and presents a model for increasingly rapid catalyst screening.
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The interesting properties of f -electron systems comes from a simultaneous existence of free and discrete level electrons. The challenge we have is to describe free electrons and discrete level electrons equally well in a unified picture. The ELF index can be used to find regions in real space where discrete level physics needs to be taken into account. We have identified the HO gas as a model system that can be used to gain insight about this kind of physics. We will use the HO gas model system for creating a functional suitable for these systems via the subsystem functional scheme. With a predictive capability for the rare earths and lanthindes, we can identify new materials with new/improved properties. This is crucial for, e.g., developing material and technology substitutes for addressing the challenges associated with the use of rare earth elements and other critical materials.
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Predicting the compositional phase stability of strongly correlated electron materials is an outstanding challenge in condensed matter physics, requiring precise computations of total energies. In this work, we employ the density functional theory plus dynamical mean-field theory (DFT+DMFT) formalism to address local correlations due to transition metal $\textit{d}$ electrons on compositional phase stability in the prototype rechargeable battery cathode material Li x CoO 2 , and detailed comparisons are made with the simpler DFT+$\textit{U}$ approach (i.e., the Hartree-Fock solution of the DMFT impurity problem). Local interactions are found to strongly impact the energetics of the band insulator LiCoO 2 , most significantly via the $E_g$ orbitals, which are partially occupied via hybridization with $\textit{O p}$ states. We find CoO 2 and Li 1/2 CoO 2 to be moderately correlated Fermi liquids with quasiparticle weights of 0.6–0.8 for the $T_{2g}$ states, which are most impacted by the interactions. Further, as compared to DFT+$\textit{U}$, DFT+DMFT considerably dampens the increase in total energy as $\textit{U}$ is increased, which indicates that dynamical correlations are important to describe this class of materials despite the relatively modest quasiparticle weights. Unlike DFT+$\textit{U}$, which can incorrectly drive Li x CoO 2 toward spurious phase separating or charge-ordered states, DFT+DMFT correctly captures the system's phase stability and does not exhibit a strong charge-ordering tendency. Most importantly, the error within DFT+$\textit{U}$ varies strongly as the composition changes, challenging the common practice of artificially tuning $\textit{U}$ within DFT+$\textit{U}$ to compensate the errors of Hartree-Fock. DFT+DMFT predicts the average intercalation voltage decreases relative to DFT, opposite to the result of DFT+$\textit{U}$, which would yield favorable agreement with experiment in conjunction with the overprediction of the voltage by the strongly constrained and appropriately normed DFT functional.
The hydrated electron, an excess electron in liquid water, plays a crucial role in a plethora of chemical processes, motivating extensive research efforts to characterize its structure, dynamics, and reactivity in solution. Recent theoretical approaches to understanding this intriguing object have involved ab initio simulations based on density functional theory (DFT). Although DFT allows for the study of hydrated electron reactivity and quantum mechanical behavior, it is well-known that anionic systems can suffer from significant density-driven errors (DDEs). Density-corrected DFT (DC-DFT) provides a framework to mitigate such errors; the method reduces DDEs by replacing the self-consistent (SC) density associated with a given density functional with the Hartree–Fock (HF) density. Since HF densities tend to be more localized than DFT SC densities, the DC-DFT scheme significantly improves errors in calculations where the SC density is spuriously delocalized. Here, we investigate how the use of density correction affects the calculated properties of the DFT-simulated (PBEh) hydrated electron, a particularly challenging diffuse anionic system to simulate. First, we analyze charge delocalization in a system consisting of a model octahedral hydrated electron water cluster (the so-called Kevan structure) along with a spatially separated sulfur atom. We show that the use of density correction indeed reduces DDEs in comparison to a standard DFT global hybrid functional. We then propagate molecular dynamics trajectories of the hydrated electron using DC-DFT, where we find that DC further localizes electron density in the cavity region, a signature of reduced charge delocalization. Unfortunately, the decreased radius of gyration of the spin density and corresponding tightening of the local solvation structure from density correction causes predicted observables to deviate further from experimental measurements than when density correction is not employed. Here, we argue that DC’s worse agreement with experiment results from the removal of a fortuitous cancellation of errors that is intrinsic to the PBEh functional. This indicates that the difficulties with DFT to simulate hydrated electrons are primarily due to the inherent approximations in DFT rather than to density-driven errors.
An accurate prediction of NMR chemical shifts at affordable computational cost is very important for different types of structural assignments in experimental studies. Density functional theory (DFT) and gauge-including atomic orbital (GIAO) are two of the most popular computational methods for NMR calculation, yet they often fail to resolve ambiguities in structural assignments. In this work, we present a new method that uses machine learning (ML) techniques (DFT + ML) that significantly increases the accuracy of 13 C/ 1 H NMR chemical shift prediction for a variety of organic molecules. The input of the generalizable DFT + ML model contains two critical parts: one is a vector providing insights into chemical environments, which can be evaluated without knowing the exact geometry of the molecule; the other one is the DFT-calculated isotropic shielding constant. The DFT + ML model was trained with a data set containing 476 13 C and 270 1 H experimental chemical shifts. For the DFT methods used here, the root mean square deviations (RMSDs) for the errors between predicted and experimental 13 C/ 1 H chemical shifts can be as small as 2.10/0.18 ppm, which is much lower than those from simple DFT (5.54/0.25 ppm), or DFT + linear regression (LR) (4.77/0.23 ppm) approaches. It also has a smaller maximum absolute error than two previously proposed NMR-predicting ML models. The robustness of the DFT + ML model is tested on two classes of organic molecules (TIC10 and hyacinthacines), where the correct isomers were unambiguously assigned to the experimental ones. Overall, the DFT + ML model shows promise for structural assignments in a variety of systems, including stereoisomers, that are often challenging to determine experimentally.
Redox-driven conductance changes are critical processes in molecular- and coordination-complex-based memristive thin films and devices that are envisioned for neuromorphic technologies, but fundamental mechanisms of conductance switching are not fully understood. Here, we explore charge disproportionation (CD) processes in [Ru II L 2 ](PF 6 ) 2 molecular systems that intrinsically involve interfragment charge transfer (IFCT). Using a combination of ab initio molecular dynamics simulation (AIMD), time-dependent density functional theory (TD-DFT), and density functional theory (DFT) calculations, we investigate the electron transfer mechanisms and the roles of temperature and cell volumetric expansion in facilitating the counterion movements and electronic transitions required for low-cost IFCT and charge redistribution. A detailed analysis of the density of states and TD-DFT calculations highlights that unpaired electrons play a crucial role in low-energy transitions, with the azo (N=N) groups of the ligand serving as the primary sites for electronic transport between molecular fragments, further stabilizing the asymmetric state. Localization of added electrons on azo ligands occurs with negligible change at the Ru centers, supported by atomic volume expansions up to +4.74 bohr 3 , and goes along with a progressive reduction of the HOMO−LUMO gap across redox states, suggesting enhanced conductivity. The TD-DFT analysis reveals a dominant IFCT excitation at 2082.76 nm in the doubly reduced (22) state, while a stabilization energy of 1.20 eV of the asymmetric (13) state relative to the symmetric (22) state is predicted by constrained DFT. Periodic DFT and AIMD simulations emulating a molecular film show that the stabilization of the asymmetric state, relative to a symmetric one, translates in net charge separation values (order of ∼0.33 e) that are strongly linked to increased counterion mobility (average counterion displacements exceeding 0.7 Å per atom during CD events) and the involvement of azo groups in electron redistribution. These findings, which align with previously reported experimental and computational data, provide key insights into the IFCT mechanisms and electronic transport facilitated by azo groups, with important implications for redox-driven memristive and neuromorphic technologies.