Machine learning electronic structure methods

All-solid-state batteries present a promising alternative to traditional Li-ion batteries, offering higher energy density and enhanced safety. However, their widespread application is impeded by challenges such as high interfacial resistance. Both experimental and computational studies have identified cation interdiffusion as a significant phenomenon at these interfaces[1], exemplified by Co-diffusion from the cathode LiCoO2 to the solid electrolyte Li1+xAlxTi2-x(PO4)3 (LATP). However, the impact of cation interdiffusion on interfacial resistance, particularly Li-ion transport, remains unclear. Therefore, our study employs first-principles calculations to analyze Co insertion into LATP and its effect on Li-ion conductivity. Although ab initio molecular dynamics (AIMD) provides precise descriptions of electron interactions and atomic forces[2], it is computationally expensive. To balance accuracy and efficiency, a pre-trained machine learning interatomic potential, CHGNet, and fine-tuned with single-point calculations as the training data. In previous work[3], we attempted to use machine learning potentials to rapidly screen energetically favorable structures, laying the groundwork for the present study. With the fine-tuned model, we conducted machine learning molecular dynamics (MLMD) simulations, which can perform long-timescales simulations. The results indicate that Co insertion notably impedes Li-ion transport in LATP near the LATP/LCO interface. The AIMD results indicate increased activation energy during the charging and discharging processes, along with a decrease in ionic conductivity. The activation energy results also demonstrate that MLMD can achieve precision comparable to AIMD, effectively bridging the gap between electronic structure methods and empirical potentials. Therefore, we can further simulate long-time and large-scale interfacial structures to analyze interfacial composition and ion migration mechanisms, to address the interfacial issues in all-solid-state batteries. These suggests that at the LATP/LiCoO2 interface, Co migration trapped Li-ions in local lattices, raising interfacial impedance. Therefore, preventing Co migrating from the electrode material to the solid electrolyte is key to enhancing interfacial impedance. These findings offer valuable insights for enhancing interfaces in all-solid-state batteries performance. The AIMD results indicate increased activation energy during the charging and discharging processes, along with a decrease in ionic conductivity. The results also demonstrate that MLMD can achieve precision comparable to AIMD, effectively bridging the gap between electronic structure methods and empirical potentials. This enables further simulations of long-term and large-scale interfacial structures to analyze interfacial composition and ion migration mechanisms. The findings suggest that at the LATP/LiCoO₂ interface, Co migration traps Li-ions in local lattice sites, thereby increasing interfacial impedance. Consequently, preventing Co migration from the electrode material to the solid electrolyte is essential for improving interfacial performance. These insights provide valuable guidance for enhancing the interfaces and overall performance of all-solid-state batteries.

Simulations of electronically nonadiabatic processes may employ either the adiabatic or diabatic representation. Direct dynamics calculations are usually carried out in the adiabatic basis because the energy, force, and state coupling can be evaluated directly by many electronic structure methods. However, although its straightforwardness is appealing, direct dynamics is expensive when combined with quantitatively accurate electronic structure theories. This generates interest in analytically fitted surfaces to cut the expense, but the cuspidal ridges of the potentials and the singularities and vector nature of the couplings at high-dimensional, nonsymmetry-determined intersections in the adiabatic representation make accurate fitting almost impossible. This motivates using diabatic representations, where the surfaces are smooth and the couplings are also smooth and-importantly-scalar. In a recent previous work, we have developed a method called diabatization by deep neural network (DDNN) that takes advantage of the smoothness and nonuniqueness of diabatic bases to obtain them by machine learning. The diabatic potential energy matrices (DPEMs) learned by the DDNN method yield not only diabatic potential energy surfaces (PESs) and couplings in an analytic form useful for dynamics calculations, but also adiabatic surfaces and couplings in the adiabatic representation can be calculated inexpensively from the transformation. In the present work, we show how to extend the DDNN method to produce good approximations to global permutationally invariant adiabatic PESs simultaneously with DPEMs. The extended method is called permutationally restrained DDNN.

ABACUS (Atomic-orbital Based Ab initio Computation at USTC) is an open-source software for first-principles electronic structure calculations and molecular dynamics simulations. It mainly features density functional theory (DFT) and molecular dynamics functions and is compatible with both plane wave basis sets and numerical atomic orbital basis sets. ABACUS serves as a platform that facilitates the integration of various electronic structure methods, such as Kohn-Sham DFT, stochastic DFT, orbital-free DFT, real-time time-dependent DFT, etc. In addition, with the aid of high-performance computing, ABACUS is designed to perform efficiently and provide massive amounts of first-principles data for generating general-purpose machine learning potentials, such as deep potential with attention models. Furthermore, ABACUS serves as an electronic structure platform that interfaces with several artificial intelligence-assisted algorithms and packages, such as DeePKS-kit, DeePMD, DP-GEN, DeepH, DeePTB, HamGNN, etc.

Once the level of theory (DFT-LDA, Hartree–Fock, or other) has been chosen, the differences between electronic structure methods are essentially due to the choice of basis set. Pseudopotentials may or may not be part of the package. The main difference is the replacement of the bare Coulomb potential of the nucleus by a softer potential and some technical issues regarding the angular dependence of the pseudopotential, but the abundance of electronic structure methods in the market is mostly due to the quest for the ultimate basis set. The central and computationally most intensive aspect of an electronic structure calculation is the self-consistent solution of the one-electron eigenvalue equation. This involves the calculation of the Kohn–Sham or the Fock matrix elements and the corresponding energy. In addition, geometry optimization and molecular dynamics simulations require the calculation of forces on the nuclear degrees of freedom. In solid-state applications, the optimization of lattice parameters and constant-pressure molecular dynamics simulations require also the calculation of the stress tensor. In this chapter we shall describe how the Hamiltonian and the total energy are calculated in practice, in the most widely used methods. We start in Section 9.1 by introducing the KKR method as an approach derived from multiple scattering theory, where basis sets expansions are bypassed by using Green's function techniques. Section 9.2 is devoted to describing the most relevant aspects of allelectron schemes based on augmentation spheres. These are considered amongst the most accurate approaches because they do not approximate the behavior of core electrons through pseudopotentials, and the basis sets are flexible and adjust themselves according to the eigenvalue energies.

The main goal of electronic structure methods is to solve the Schroedinger equation for the electrons in a molecule or solid, to evaluate the resulting total energies, forces, response functions and other quantities of interest. In this paper we describe the basic ideas behind the main electronic structure methods such as the pseudopotential and the augmented wave methods and provide selected pointers to contributions that are relevant for a beginner. We give particular emphasis to the Projector Augmented Wave (PAW) method developed by one of us, an electronic structure method for ab-initio molecular dynamics with full wavefunctions. We feel that it allows best to show the common conceptional basis of the most widespread electronic structure methods in materials science.

Chapter 2 Explicitly Correlated Approaches for Electronic Structure Computations

Amorphous materials underlie the functionality of many devices in photocatalysis, electronics, and other technological applications. The performance of such devices is largely altered by the interfacial characteristics of the material motivating better understanding of their structure function relationships. However, open questions remain about how to generate atomistic representations of amorphous surfaces that are realistic while being amenable to computational study using electronic structure methods. Here, model parameters are explored to generate accurate amorphous surface models using prototypical amorphous titanium dioxide and a melt‐quench approach. In particular, non‐standard model considerations such as minimum sample size, unit cell size, and quench conditions are varied to efficiently explore amorphous structural space. The results indicate different modeling parameters have a substantial effect on surface morphology and electronic structure that significantly alters the interpretations gained by computational study of amorphous interfaces. Critically, it is shown that the structural motifs that contribute to such differences are not detectable by short range structural analysis that has traditionally been used to assess the quality of melt‐quench derived amorphous structures.

Over the past decade, there has been a significant growth in the development and application of methods for performing global optimization (GO) of cluster and nanoparticle structures using first‐principles electronic structure methods coupled to sophisticated search algorithms. This has in part been driven by the desire to avoid the use of empirical potentials (EPs), especially in cases where no reliable potentials exist to guide the search toward reasonable regions of configuration space. This has been facilitated by improvements in the reliability of the search algorithms, increased efficiency of the electronic structure methods, and the development of faster, multiprocessor high‐performance computing architectures. In this review, we give a brief overview of GO algorithms, though concentrating mainly on genetic algorithm and basin hopping techniques, first in combination with EPs. The major part of the review then deals with details of the implementation and application of these search methods to allow exploration for global minimum cluster structures directly using electronic structure methods and, in particular, density functional theory. Example applications are presented, ranging from isolated monometallic and bimetallic clusters to molecular clusters and ligated and surface supported metal clusters. Finally, some possible future developments are highlighted. © 2013 Wiley Periodicals, Inc.

Theory-Guided Machine Learning Finds Geometric Structure-Property Relationships for Chemisorption on Subsurface Alloys

We present a new method called the effective fragment molecular orbital (EFMO) method. The EFMO method is a hybrid between the fragment molecular orbital (FMO) electronic structure method ( Kitaura , K. ; Ikeo , E. ; Asada , T. ; Nakano , T. ; Uebayasi , M. Chem. Phys. Lett. 1999 , 313 , 701 - 706 ) and the effective fragment potential multipole-based polarizable force field ( Day , P. N. ; Jensen , J. H. ; Gordon , M. S. ; Webb , S. P. ; Stevens , W. J. ; Krauss , M. ; Garmer , D. ; Basch , H. ; Cohen , D. J. Chem. Phys. 1996 , 105 , 1968 - 1986 ). The EFMO method is based on the FMO molecular fragmentation scheme and the many-body energy expression but uses the EFP multipole-based energy expressions for long-range interactions and for evaluating the many-body polarization. The accuracy and performance of the EFMO method is compared to FMO and conventional electronic structure theory for water clusters. The difference in the EFMO energy compared to that of conventional Hartree-Fock theory is roughly 0.5 kcal/mol per hydrogen using the 6-31G(d) basis set but less than 0.1 kcal/mol using the 6-31+G(d) basis set. The EFMO method is roughly two times faster than the FMO2 method using Hartree-Fock and five times when computing Hartree-Fock energy and gradients; preliminary density functional theory results are also presented.

The joint automated repository for various integrated simulations (JARVIS) infrastructure at the National Institute of Standards and Technology is a large-scale collection of curated datasets and tools with more than 80 000 materials and millions of properties. JARVIS uses a combination of electronic structure, artificial intelligence, advanced computation, and experimental methods to accelerate materials design. Here, we report some of the new features that were recently included in the infrastructure, such as (1) doubling the number of materials in the database since its first release, (2) including more accurate electronic structure methods such as quantum Monte Carlo, (3) including graph neural network-based materials design, (4) development of unified force-field, (5) development of a universal tight-binding model, (6) addition of computer-vision tools for advanced microscopy applications, (7) development of a natural language processing tool for text-generation and analysis, (8) debuting a large-scale benchmarking endeavor, (9) including quantum computing algorithms for solids, (10) integrating several experimental datasets, and (11) staging several community engagement and outreach events. New classes of materials, properties, and workflows added to the database include superconductors, two-dimensional (2D) magnets, magnetic topological materials, metal-organic frameworks, defects, and interface systems. The rich and reliable datasets, tools, documentation, and tutorials make JARVIS a unique platform for modern materials design. JARVIS ensures the openness of data and tools to enhance reproducibility and transparency and to promote a healthy and collaborative scientific environment.

We present a perspective on the use of diffuse basis functions for electronic structure calculations by density functional theory and wave function theory. We especially emphasize minimally augmented basis sets and calendar basis sets. We base our conclusions on our previous experience with commonly computed quantities, such as bond energies, barrier heights, electron affinities, noncovalent (van der Waals and hydrogen bond) interaction energies, and ionization potentials, on Stephens et al.'s results for optical rotation and on our own new calculations (presented here) of polarizabilities and of potential energy curves of van der Waals complexes. We emphasize the benefits of partial augmentation of the higher-zeta basis sets in preference to full augmentation at a lower ζ level. Benefits and limitations of the use of fully, partially, and minimally augmented basis sets are reviewed for different electronic structure methods and molecular properties. We have found that minimal augmentation is almost always enough for density functional theory (DFT) when applied to ionization potentials, electron affinities, atomization energies, barrier heights, and hydrogen-bond energies. For electric dipole polarizabilities, we find that augmentation beyond minimal has an average effect of 8% at the polarized triple-ζ level and 5% at the polarized quadruple-ζ level. The effects are larger for potential energy curves of van der Waals complexes. The effects are also larger for wave function theory (WFT). Even for WFT though, full augmentation is not needed for most purposes, and a level of augmentation between minimal and full is optimal for most problems. The calendar basis sets named after the months provide a convergent sequence of partially augmented basis sets that can be used for such calculations. The jun-cc-pV(T+d)Z basis set is very useful for MP2-F12 calculations of barrier heights and hydrogen bond strengths.

Electronic structure of platinum(II)-phosphine-tin(II)trihalide complexes

Sampling potential energy surfaces (PES) is pivotal for understanding chemical structure, energetics and reactivity and is of special importance for complex condensed-phase systems. Until recently such simulations based on electronic structure theory have been performed only by density functional theory and semiempirical methods. Many-body electronic structure methods, almost routinely used for molecules, have been practically unavailable for sampling PES in the condensed-phase. This has changed during the last few years, as efficient algorithms and software implementations for the evaluation of electronic energies and forces on atoms have been developed, allowing for geometry optimization, molecular dynamics and Monte-Carlo simulations, which was previously unthinkable. Herein, we introduce the theory and software developments and overview the applications in the field, the most encouraging results being obtained for aqueous chemistry. Requiring state-of-the-art computer resources PES sampling with many-body electronic structure methods in the condensed phase provides high-quality benchmarks and will gradually become more available due to fast progress in reduced scaling algorithms and computational technologies.

We demonstrate the existence of different density-density functionals designed to retain selected properties of the many-body ground state in a non-interacting solution starting from the standard density functional theory ground state. We focus on diffusion quantum Monte Carlo applications that require trial wave functions with optimal Fermion nodes. The theory is extensible and can be used to understand current practices in several electronic structure methods within a generalized density functional framework. The theory justifies and stimulates the search of optimal empirical density functionals and effective potentials for accurate calculations of the properties of real materials, but also cautions on the limits of their applicability. The concepts are tested and validated with a near-analytic model.