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1. A deep learning framework to emulate density functional theory

   https://doi.org/10.1038/s41524-023-01115-3  

   del Rio, Beatriz G. ; Phan, Brandon ; Ramprasad, Rampi ( August 2023 , npj Computational Materials)

   Density functional theory (DFT) has been a critical component of computational materials research and discovery for decades. However, the computational cost of solving the central Kohn–Sham equation remains a major obstacle for dynamical studies of complex phenomena at-scale. Here, we propose an end-to-end machine learning (ML) model that emulates the essence of DFT by mapping the atomic structure of the system to its electronic charge density, followed by the prediction of other properties such as density of states, potential energy, atomic forces, and stress tensor, by using the atomic structure and charge density as input. Our deep learning model successfully bypasses the explicit solution of the Kohn-Sham equation with orders of magnitude speedup (linear scaling with system size with a small prefactor), while maintaining chemical accuracy. We demonstrate the capability of this ML-DFT concept for an extensive database of organic molecules, polymer chains, and polymer crystals.

    

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2. Measuring Density-Driven Errors Using Kohn–Sham Inversion

   https://doi.org/doi.org/10.1021/acs.jctc.0c00391  

   Nam, Seungsoo ; Song, Suhwan ; Sim, Eunji ; and Burke, Kieron ( July 2020 , Journal of chemical theory and computation)

   Kohn–Sham (KS) inversion, that is, the finding of the exact KS potential for a given density, is difficult in localized basis sets. We study the precision and reliability of several inversion schemes, finding estimates of density-driven errors at a useful level of accuracy. In typical cases of substantial density-driven errors, Hartree–Fock density functional theory (HF-DFT) is almost as accurate as DFT evaluated on CCSD(T) densities. A simple approximation in practical HF-DFT also makes errors much smaller than the density-driven errors being calculated. Two paradigm examples, stretched NaCl and the HO·Cl– radical, illustrate just how accurate HF-DFT is. 

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3. Reformulation of thermally assisted-occupation density functional theory in the Kohn–Sham framework

   https://doi.org/10.1063/5.0087012  

   Yeh, Shu-Hao ; Yang, Weitao ; Hsu, Chao-Ping ( May 2022 , The Journal of Chemical Physics)

   We reformulate the thermally assisted-occupation density functional theory (TAO-DFT) into the Kohn–Sham single-determinant framework and construct two new post-self-consistent field (post-SCF) static correlation correction schemes, named rTAO and rTAO-1. In contrast to the original TAO-DFT with the density in an ensemble form, in which each orbital density is weighted with a fractional occupation number, the ground-state density is given by a single-determinant wavefunction, a regular Kohn–Sham (KS) density, and total ground state energy is expressed in the normal KS form with a static correlation energy formulated in terms of the KS orbitals. In post-SCF calculations with rTAO functionals, an efficient energy scanning to quantitatively determine θ is also proposed. The rTAOs provide a promising method to simulate systems with strong static correlation as original TAO, but simpler and more efficient. We show that both rTAO and rTAO-1 is capable of reproducing most results from TAO-DFT without the additional functional Eθ used in TAO-DFT. Furthermore, our numerical results support that, without the functional Eθ, both rTAO and rTAO-1 can capture correct static correlation profiles in various systems. 

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4. Numerical methods for Kohn–Sham density functional theory

   https://doi.org/10.1017/S0962492919000047  

   Lin, Lin ; Lu, Jianfeng ; Ying, Lexing ( May 2019 , Acta Numerica)

   Kohn–Sham density functional theory (DFT) is the most widely used electronic structure theory. Despite significant progress in the past few decades, the numerical solution of Kohn–Sham DFT problems remains challenging, especially for large-scale systems. In this paper we review the basics as well as state-of-the-art numerical methods, and focus on the unique numerical challenges of DFT. 

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5. A molecular orbital selection approach for fast calculations of specific rotation with density functional theory

   https://doi.org/10.1002/chir.23158  

   Aharon, Tal ; Caricato, Marco ( December 2019 , Chirality)

   In this work, we describe a simple approach to select the most important molecular orbitals (MOs) to compute the optical rotation tensor through linear response (LR) Kohn‐Sham density functional theory (KS‐DFT). Taking advantage of the iterative nature of the algorithms commonly used to solve the LR equations, we select the MOs with contributions to the guess perturbed density that are larger than a certain threshold and solve the LR equations with the selected MOs only. We propose two criteria for the selection, and two definitions of the selection threshold. We then test the approach with two functionals (B3LYP and CAM‐B3LYP) and two basis sets (aug‐cc‐pVDZ and aug‐cc‐pVTZ) on a set of 51 organic molecules with specific rotation spanning five orders of magnitude, 10⁰–10⁴deg (dm⁻¹(g/mL)⁻¹). We show that this approach indeed can provide very accurate values of specific rotation with estimated speedup that ranges from 2 to 8× with the most conservative selection criterion, and up to 20 to 30× with the intermediate criterion.

    

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