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1. Quantum chemical accuracy from density functional approximations via machine learning

   https://doi.org/10.1038/s41467-020-19093-1  

   Bogojeski, Mihail; Vogt-Maranto, Leslie; Tuckerman, Mark E.; Müller, Klaus-Robert; Burke, Kieron (October 2020, Nature Communications)

   Abstract Kohn-Sham density functional theory (DFT) is a standard tool in most branches of chemistry, but accuracies for many molecules are limited to 2-3 kcal ⋅ mol⁻¹with presently-available functionals. Ab initio methods, such as coupled-cluster, routinely produce much higher accuracy, but computational costs limit their application to small molecules. In this paper, we leverage machine learning to calculate coupled-cluster energies from DFT densities, reaching quantum chemical accuracy (errors below 1 kcal ⋅ mol⁻¹) on test data. Moreover, density-basedΔ-learning (learning only the correction to a standard DFT calculation, termedΔ-DFT ) significantly reduces the amount of training data required, particularly when molecular symmetries are included. The robustness ofΔ-DFT  is highlighted by correcting “on the fly” DFT-based molecular dynamics (MD) simulations of resorcinol (C₆H₄(OH)₂) to obtain MD trajectories with coupled-cluster accuracy. We conclude, therefore, thatΔ-DFT  facilitates running gas-phase MD simulations with quantum chemical accuracy, even for strained geometries and conformer changes where standard DFT fails. 

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2. Describing proton transfer modes in shared proton systems with constrained nuclear–electronic orbital methods

   https://doi.org/10.1063/5.0151544  

   Zhang, Yuzhe; Xu, Xi; Yang, Nan; Chen, Zehua; Yang, Yang (June 2023, The Journal of Chemical Physics)

   Proton transfer is crucial in various chemical and biological processes. Because of significant nuclear quantum effects, accurate and efficient description of proton transfer remains a great challenge. In this Communication, we apply constrained nuclear–electronic orbital density functional theory (CNEO-DFT) and constrained nuclear–electronic orbital molecular dynamics (CNEO-MD) to three prototypical shared proton systems and investigate their proton transfer modes. We find that with a good description of nuclear quantum effects, CNEO-DFT and CNEO-MD can well describe the geometries and vibrational spectra of the shared proton systems. Such a good performance is in significant contrast to DFT and DFT-based ab initio molecular dynamics, which often fail for shared proton systems. As an efficient method based on classical simulations, CNEO-MD is promising for future investigations of larger and more complex proton transfer systems. 

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3. Noise reduction of stochastic density functional theory for metals

   https://doi.org/10.1063/5.0207244  

   Vu, Jake P; Chen, Ming (June 2024, The Journal of Chemical Physics)

   Density Functional Theory (DFT) has become a cornerstone in the modeling of metals. However, accurately simulating metals, particularly under extreme conditions, presents two significant challenges. First, simulating complex metallic systems at low electron temperatures is difficult due to their highly delocalized density matrix. Second, modeling metallic warm-dense materials at very high electron temperatures is challenging because it requires the computation of a large number of partially occupied orbitals. This study demonstrates that both challenges can be effectively addressed using the latest advances in linear-scaling stochastic DFT methodologies. Despite the inherent introduction of noise into all computed properties by stochastic DFT, this research evaluates the efficacy of various noise reduction techniques under different thermal conditions. Our observations indicate that the effectiveness of noise reduction strategies varies significantly with the electron temperature. Furthermore, we provide evidence that the computational cost of stochastic DFT methods scales linearly with system size for metal systems, regardless of the electron temperature regime. 

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4. Efficiently searching extreme mechanical properties via boundless objective-free exploration and minimal first-principles calculations

   https://doi.org/10.1038/s41524-022-00836-1  

   Ojih, Joshua; Al-Fahdi, Mohammed; Rodriguez, Alejandro David; Choudhary, Kamal; Hu, Ming (July 2022, npj Computational Materials)

   Abstract Despite the machine learning (ML) methods have been largely used recently, the predicted materials properties usually cannot exceed the range of original training data. We deployed a boundless objective-free exploration approach to combine traditional ML and density functional theory (DFT) in searching extreme material properties. This combination not only improves the efficiency for screening large-scale materials with minimal DFT inquiry, but also yields properties beyond original training range. We use Stein novelty to recommend outliers and then verify using DFT. Validated data are then added into the training dataset for next round iteration. We test the loop of training-recommendation-validation in mechanical property space. By screening 85,707 crystal structures, we identify 21 ultrahigh hardness structures and 11 negative Poisson’s ratio structures. The algorithm is very promising for future materials discovery that can push materials properties to the limit with minimal DFT calculations on only ~1% of the structures in the screening pool. 

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5. Extensive Benchmarking of DFT+U Calculations for Predicting Band Gaps

   https://doi.org/10.3390/app11052395  

   Kirchner-Hall, Nicole E.; Zhao, Wayne; Xiong, Yihuang; Timrov, Iurii; Dabo, Ismaila (March 2021, Applied Sciences)

   null (Ed.)

   Accurate computational predictions of band gaps are of practical importance to the modeling and development of semiconductor technologies, such as (opto)electronic devices and photoelectrochemical cells. Among available electronic-structure methods, density-functional theory (DFT) with the Hubbard U correction (DFT+U) applied to band edge states is a computationally tractable approach to improve the accuracy of band gap predictions beyond that of DFT calculations based on (semi)local functionals. At variance with DFT approximations, which are not intended to describe optical band gaps and other excited-state properties, DFT+U can be interpreted as an approximate spectral-potential method when U is determined by imposing the piecewise linearity of the total energy with respect to electronic occupations in the Hubbard manifold (thus removing self-interaction errors in this subspace), thereby providing a (heuristic) justification for using DFT+U to predict band gaps. However, it is still frequent in the literature to determine the Hubbard U parameters semiempirically by tuning their values to reproduce experimental band gaps, which ultimately alters the description of other total-energy characteristics. Here, we present an extensive assessment of DFT+U band gaps computed using self-consistent ab initio U parameters obtained from density-functional perturbation theory to impose the aforementioned piecewise linearity of the total energy. The study is carried out on 20 compounds containing transition-metal or p-block (group III-IV) elements, including oxides, nitrides, sulfides, oxynitrides, and oxysulfides. By comparing DFT+U results obtained using nonorthogonalized and orthogonalized atomic orbitals as Hubbard projectors, we find that the predicted band gaps are extremely sensitive to the type of projector functions and that the orthogonalized projectors give the most accurate band gaps, in satisfactory agreement with experimental data. This work demonstrates that DFT+U may serve as a useful method for high-throughput workflows that require reliable band gap predictions at moderate computational cost. 

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