Artificial intelligence "sees" split electrons

The Source of Some Empirical Density Functionals van der Waals Forces

Density functional approximations became indispensable tools in many fields of chemistry due to their excellent cost-to-accuracy ratio. Still, consideration is required to select an appropriate approximation for each task. Highly parameterized Minnesota functionals are known for their excellent accuracy in reproducing thermochemical properties and, in particular, weak medium-range interactions. Here, we show that the latter ability of many Minnesota functionals comes from exploiting the basis set incompleteness. This finding shows how empirical functionals can trick their makers by learning to operate in a physics-defying way and likely explains the previously observed tendency of Minnesota functionals to distort electron densities. Thus, satisfaction of the Hellmann-Feynman theorem should be considered an important test and parameterization goal for the future generations of highly parameterized density functionals, including those based on neural networks.

Orbital-Free Density Functional Theory: An Attractive Electronic Structure Method for Large-Scale First-Principles Simulations

Kohn-Sham Density Functional Theory (KSDFT) is the most widely used electronic structure method in chemistry, physics, and materials science, with thousands of calculations cited annually. This ubiquity is rooted in the favorable accuracy vs cost balance of KSDFT. Nonetheless, the ambitions and expectations of researchers for use of KSDFT in predictive simulations of large, complicated molecular systems are confronted with an intrinsic computational cost-scaling challenge. Particularly evident in the context of first-principles molecular dynamics, the challenge is the high cost-scaling associated with the computation of the Kohn-Sham orbitals. Orbital-free DFT (OFDFT), as the name suggests, circumvents entirely the explicit use of those orbitals. Without them, the structural and algorithmic complexity of KSDFT simplifies dramatically and near-linear scaling with system size irrespective of system state is achievable. Thus, much larger system sizes and longer simulation time scales (compared to conventional KSDFT) become accessible; hence, new chemical phenomena and new materials can be explored. In this review, we introduce the historical contexts of OFDFT, its theoretical basis, and the challenge of realizing its promise via approximate kinetic energy density functionals (KEDFs). We review recent progress on that challenge for an array of KEDFs, such as one-point, two-point, and machine-learnt, as well as some less explored forms. We emphasize use of exact constraints and the inevitability of design choices. Then, we survey the associated numerical techniques and implemented algorithms specific to OFDFT. We conclude with an illustrative sample of applications to showcase the power of OFDFT in materials science, chemistry, and physics.

Outstanding improvement in removing the delocalization error by global natural orbital functional

This work assesses the performance of the recently proposed global natural orbital functional (GNOF) against the charge delocalization error. GNOF provides a good balance between static and dynamic electronic correlations leading to accurate total energies while preserving spin, even for systems with a highly multi-configurational character. Several analyses were applied to the functional, namely, (i) how the charge is distributed in super-systems of two fragments, (ii) the stability of ionization potentials while increasing the system size, and (iii) potential energy curves of a neutral and charged diatomic system. GNOF was found to practically eliminate the charge delocalization error in many of the studied systems or greatly improve the results obtained previously with PNOF7.

Neural network training method for materials science based on multi-source databases

The fourth paradigm of science has achieved great success in material discovery and it highlights the sharing and interoperability of data. However, most material data are scattered among various research institutions, and a big data transmission will consume significant bandwidth and tremendous time. At the meanwhile, some data owners prefer to protect the data and keep their initiative in the cooperation. This dilemma gradually leads to the “data island” problem, especially in material science. To attack the problem and make full use of the material data, we propose a new strategy of neural network training based on multi-source databases. In the whole training process, only model parameters are exchanged and no any external access or connection to the local databases. We demonstrate its validity by training a model characterizing material structure and its corresponding formation energy, based on two and four local databases, respectively. The results show that the obtained model accuracy trained by this method is almost the same to that obtained from a single database combining all the local ones. Moreover, different communication frequencies between the client and server are also studied to improve the model training efficiency, and an optimal frequency is recommended.

Split electrons in partition density functional theory

Partition density functional theory is a density embedding method that partitions a molecule into fragments by minimizing the sum of fragment energies subject to a local density constraint and a global electron-number constraint. To perform this minimization, we study a two-stage procedure in which the sum of fragment energies is lowered when electrons flow from fragments of lower electronegativity to fragments of higher electronegativity. The global minimum is reached when all electronegativities are equal. The non-integer fragment populations are dealt with in two different ways: (1) An ensemble approach (ENS) that involves averaging over calculations with different numbers of electrons (always integers) and (2) a simpler approach that involves fractionally occupying orbitals (FOO). We compare and contrast these two approaches and examine their performance in some of the simplest systems where one can transparently apply both, including simple models of heteronuclear diatomic molecules and actual diatomic molecules with two and four electrons. We find that, although both ENS and FOO methods lead to the same total energy and density, the ENS fragment densities are less distorted than those of FOO when compared to their isolated counterparts, and they tend to retain integer numbers of electrons. We establish the conditions under which the ENS populations can become fractional and observe that, even in those cases, the total charge transferred is always lower in ENS than in FOO. Similarly, the FOO fragment dipole moments provide an upper bound to the ENS dipoles. We explain why and discuss the implications.

Materials Data toward Machine Learning: Advances and Challenges

Machine learning (ML) is believed to have enabled a paradigm shift in materials research, and in practice, ML has demonstrated its power in speeding up the cost-efficient discovery of new materials and autonomizing materials laboratories. In this Perspective, current research progress in materials data which are the backbones of ML are reviewed, focusing on high-throughput data generation, standardized data storage, and data representation. More importantly, the challenging issues in materials data that should be overcome to unlock the full potential of ML in materials research and development, including classic 5V (volume, velocity, variety, veracity, and value) issues, 3M (multicomponent, multiscale, and multistage) challenges, co-mining of experimental and computational data, and materials data toward transferable/explainable ML or causal ML, are discussed.