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.

Characterization of the Hydrogen-Bond Network in High-Pressure Water by Deep Potential Molecular Dynamics.

The hydrogen-bond (H-bond) network of high-pressure water is investigated by neural-network-based molecular dynamics (MD) simulations with first-principles accuracy. The static structure factors (SSFs) of water at three densities, i.e., 1, 1.115, and 1.24 g/cm3, are directly evaluated from 512 water MD trajectories, which are in quantitative agreement with the experiments. We propose a new method to decompose the computed SSF and identify the changes in the SSF with respect to the changes in H-bond structures. We find that a larger water density results in a higher probability for one or two non-H-bonded water molecules to be inserted into the inner shell, explaining the changes in the tetrahedrality of water under pressure. We predict that the structure of the accepting end of water molecules is more easily influenced by the pressure than by the donating end. Our work sheds new light on explaining the SSF and H-bond properties in related fields.

Solvation structures of calcium and magnesium ions in water with the presence of hydroxide: a study by deep potential molecular dynamics.

The solvation structures of calcium (Ca2+) and magnesium (Mg2+) ions with the presence of hydroxide (OH-) ion in water are essential for understanding their roles in biological and chemical processes but have not been fully explored. Ab initio molecular dynamics (AIMD) is an important tool to address this issue, but two challenges exist. First, an accurate description of OH- from AIMD needs an appropriate exchange-correlation functional. Second, a long trajectory is needed to reach an equilibrium state for the Ca2+-OH- and Mg2+-OH- ion pairs in aqueous solutions. Herein, we adopt a deep potential molecular dynamics (DPMD) method to simulate 1 ns trajectories for the Ca2+-OH- and Mg2+-OH- ion pairs in water; the DPMD method provides efficient machine-learning-based models that have the accuracy of the SCAN exchange-correlation functional within the framework of density functional theory. The solvation structures of the cations and the OH- in terms of three different species have been systematically investigated. On the one hand, we find that OH- have more significant effects on the solvation structure of Ca2+ than that of Mg2+. We observe that the OH- substantially affects the orientation angles of water molecules surrounding the cation. Through the time correlation functions, we conclude that the water molecules in the first solvation shell of Ca2+ change their preferred orientation faster than those of Mg2+. On the other hand, with the presence of the cation in the first solvation shell of OH-, we find that the hydrogen bonds of OH- are severely altered, and the adjacent water molecules of OH- are squeezed. The two cations have substantially different effects on the solvation structure of OH-. Our work provides new insight into the solvation structures of Ca2+ and Mg2+ in water with the presence of OH-.

DeePKS + ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials.

Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for different levels of QM methods, such as density functional theory (DFT) at the meta-GGA level and/or with exact exchange, quantum Monte Carlo, etc., generating a sufficient amount of data for training an ML potential has remained computationally challenging due to their high cost. In this work, we demonstrate that this issue can be largely alleviated with Deep Kohn-Sham (DeePKS), an ML-based DFT model. DeePKS employs a computationally efficient neural network-based functional model to construct a correction term added upon a cheap DFT model. Upon training, DeePKS offers closely matched energies and forces compared with high-level QM method, but the number of training data required is orders of magnitude less than that required for training a reliable ML potential. As such, DeePKS can serve as a bridge between expensive QM models and ML potentials: one can generate a decent amount of high-accuracy QM data to train a DeePKS model and then use the DeePKS model to label a much larger amount of configurations to train an ML potential. This scheme for periodic systems is implemented in a DFT package ABACUS, which is open source and ready for use in various applications.

Structural and dynamic properties of solvated hydroxide and hydronium ions in water from ab initio modeling.

Predicting the asymmetric structure and dynamics of solvated hydroxide and hydronium in water from ab initio molecular dynamics (AIMD) has been a challenging task. The difficulty mainly comes from a lack of accurate and efficient exchange-correlation functional in elucidating the amphiphilic nature and the ubiquitous proton transfer behaviors of the two ions. By adopting the strongly constrained and appropriately normed (SCAN) meta-generalized gradient approximation functional in AIMD simulations, we systematically examine the amphiphilic properties, the solvation structures, the electronic structures, and the dynamic properties of the two water ions. In particular, we compare these results to those predicted by the PBE0-TS functional, which is an accurate yet computationally more expensive exchange-correlation functional. We demonstrate that the general-purpose SCAN functional provides a reliable choice for describing the two water ions. Specifically, in the SCAN picture of water ions, the appearance of the fourth and fifth hydrogen bonds near hydroxide stabilizes the pot-like shape solvation structure and suppresses the structural diffusion, while the hydronium stably donates three hydrogen bonds to its neighbors. We apply a detailed analysis of the proton transfer mechanism of the two ions and find the two ions exhibit substantially different proton transfer patterns. Our AIMD simulations indicate that hydroxide diffuses more slowly than hydronium in water, which is consistent with the experimental results.

Photoelectrochemical immunoassay platform based on MoS2 nanosheets integrated with gold nanostars for neuron-specific enolase assay.

MoS2 nanosheets were prepared by exfoliating MoS2 bulk crystals with ultrasonication in N-methylpyrrolidone and were integrated with gold nanostars (AuNS) to fabricate an AuNS/MoS2 nanocomposite. All nanomaterials were characterized by transmission electron microscope, scanning electron microscope, ultraviolet-visible spectroscopy, X-ray diffraction, and X-ray photoelectron spectroscopy. AuNS/MoS2 nanocomposites were coated onto a glassy carbon electrode (GCE) surface to construct a nanointerface for immobilizing neuron-specific enolase antibody (anti-NSE) thus forming a photoelectrochemical immunoassay system. AuNS can significantly promote the photoelectric conversion of MoS2 nanosheets improving the performance for a photoelectrochemical assay. Being illuminated with white light LED and controlling the potential at 0.05 V (vs. SCE), the photocurrent generated from anti-NSE(BSA)/AuNS/MoS2/GCE using 0.15 mol L-1 ascorbic acid as electron donor can be recorded with amperometry and used as an output signal for NSE quantitative assay. Under optimized experimental conditions, the photocurrent variation for the affinity-binding NSE is proportional to the logarithm of NSE concentration in the range 5.0 pg mL-1   to 1.5 ng mL-1 with a detection limit of 3.5 pg mL-1 (S/N = 3). The practicability of the PEC immunoassay system was evaluated by determining NSE in clinical serum samples. The recoveries ranged from 93.0 to 103% for the determination of NSE in serum samples with a standard addition method. The PEC immunoassay system possesses good accuracy for determining NSE in real samples. Graphical abstract.