DFT-based 背景

对一些论文中关于从头算和经典分子模拟的描述做一些笔记

Liquid–liquid transition and critical point in sulfur | Nature volume 584, pages382–386 (2020)
The liquid–liquid transition (LLT), in which a single-component liquid transforms into another one via a first-order phase transition, is an intriguing phenomenon that has changed our perception of the liquid state. LLTs have been predicted from computer simulations of water1,2, silicon3, carbon dioxide4, carbon5, hydrogen6 and nitrogen7. Experimental evidence has been found mostly in supercooled (that is, metastable) liquids such as Y2O3–Al2O3 mixtures8, water9 and other molecular liquids10,11,12. However, the LLT in supercooled liquids often occurs simultaneously with crystallization, making it difficult to separate the two phenomena13. A liquid–liquid critical point (LLCP), similar to the gas–liquid critical point, has been predicted at the end of the LLT line that separates the low- and high-density liquids in some cases, but has not yet been experimentally observed for any materials. This putative LLCP has been invoked to explain the thermodynamic anomalies of water1. Here we report combined in situ density, X-ray diffraction and Raman scattering measurements that provide direct evidence for a first-order LLT and an LLCP in sulfur. The transformation manifests itself as a sharp density jump between the low- and high-density liquids and by distinct features in the pair distribution function. We observe a non-monotonic variation of the density jump with increasing temperature: it first increases and then decreases when moving away from the critical point. This behaviour is linked to the competing effects of density and entropy in driving the transition. The existence of a first-order LLT and a critical point in sulfur could provide insight into the anomalous behaviour of important liquids such as water.

Folded network and structural transition in molten tin | Nature Communications volume 13, Article number: 126 (2022)
The fundamental relationships between the structure and properties of liquids are far from being well understood. For instance, the structural origins of many liquid anomalies still remain unclear, but liquid-liquid transitions (LLT) are believed to hold a key. However, experimental demonstrations of LLTs have been rather challenging. Here, we report experimental and theoretical evidence of a second-order-like LLT in molten tin, one which favors a percolating covalent bond network at high temperatures. The observed structural transition originates from the fluctuating metallic/covalent behavior of atomic bonding, and consequently a new paradigm of liquid structure emerges. The liquid structure, described in the form of a folded network, bridges two well-established structural models for disordered systems, i.e., the random packing of hard-spheres and a continuous random network, offering a large structural midground for liquids and glasses. Our findings provide an unparalleled physical picture of the atomic arrangement for a plethora of liquids, shedding light on the thermodynamic and dynamic anomalies of liquids but also entailing far-reaching implications for studying liquid polyamorphism and dynamical transitions in liquids.

Low viscosity of the Earth’s inner core | Nature Communications volume 10, Article number: 2483 (2019)
The Earth’s solid inner core is a highly attenuating medium. It consists mainly of iron. The high attenuation of sound wave propagation in the inner core is at odds with the widely accepted paradigm of hexagonal close-packed phase stability under inner core conditions, because sound waves propagate through the hexagonal iron without energy dissipation. Here we show by first-principles molecular dynamics that the body-centered cubic phase of iron, recently demonstrated to be thermodynamically stable under the inner core conditions, is considerably less elastic than the hexagonal phase. Being a crystalline phase, the body-centered cubic phase of iron possesses the viscosity close to that of a liquid iron. The high attenuation of sound in the inner core is due to the unique diffusion characteristic of the body-centered cubic phase. The low viscosity of iron in the inner core enables the convection and resolves a number of controversies.

Computational methods to simulate molten salt thermophysical properties | Communications Chemistry volume 5, Article number: 69 (2022)
Increased computational power and theoretical insights advanced inter-atomic potentials and density functional theory to the level of usefulness and reliability. Both fields were developed by different research groups whose insights influenced each other. Here, we will first review the progression of DFT-based methods, resulting in dispersion corrected ab-initio molecular dynamics (AIMD) methods. Afterward, we will discuss the advancements of inter-atomic potentials, as they were strongly influenced by the increase in accuracy and feasibility of DFT models.
In 1993, Barnnet and Lanmarn introduced Born-Oppenheimer molecular dynamics with DFT which enabled larger simulation timesteps resulting in a better temporal sampling of still very restricted simulations23. Later that year, Kresse and Hafner introduced the method of initializing Car-Parrinello Molecular Dynamics with energy minimization schemes for metals, resulting in additional speed up24. In 1998, Alfe extracted the diffusion coefficients using CPMD for liquid aluminum and thereby demonstrated the feasibility of DFT methods to extract transport properties in condensed materials25. In 2003, Aguado et al. developed an ab-initio process using many condensed phases of MgO with CATSTEP DFT to parametrize coefficients for the aspherical ion model (AIM) representing a breakthrough for polarizable models26. In 2005, Hazebroucq used a tight-binding density functional to calculate and investigate diffusion in NaCl and KCl for a specific experimental volume, a step towards full AIMD27.
In 2006 Madden et al. highlighted the need to control the dispersion interaction as it—despite being only a tiny fraction of the interaction energies of an ion pair—strongly impacted phase transition behavior, such as transition pressures28. It had been a well-known problem up to this time that dispersion interactions in DFT calculations were not accurate. Grimme tackled the problem of dispersion and published a first empirical correction in 2006 for DFT followed by a second in 2010, practically resolving the issue29. In 2006, Klix investigated the diffusion of tritium in Flibe, using CPMD, and named the method ab-initio molecular dynamics30. This simulation was the first time that a molten salt had dynamical behavior derived using ab-intio methods.

Deep-learning density functional theory Hamiltonian for efficient ab initio electronic-structure calculation | Nature Computational Science volume 2, pages367–377 (2022)
The marriage of density functional theory (DFT) and deep-learning methods has the potential to revolutionize modern computational materials science. Here we develop a deep neural network approach to represent the DFT Hamiltonian (DeepH) of crystalline materials, aiming to bypass the computationally demanding self-consistent field iterations of DFT and substantially improve the efficiency of ab initio electronic-structure calculations. A general framework is proposed to deal with the large dimensionality and gauge (or rotation) covariance of the DFT Hamiltonian matrix by virtue of locality, and this is realized by a message-passing neural network for deep learning. High accuracy, high efficiency and good transferability of the DeepH method are generally demonstrated for various kinds of material system and physical property. The method provides a solution to the accuracy–efficiency dilemma of DFT and opens opportunities to explore large-scale material systems, as evidenced by a promising application in the study of twisted van der Waals materials.

Augmenting zero-Kelvin quantum mechanics with machine learning for the prediction of chemical reactions at high temperatures | Nature Communications volume 12, Article number: 7012 (2021)
The prediction of temperature effects from first principles is computationally demanding and typically too approximate for the engineering of high-temperature processes. Here, we introduce a hybrid approach combining zero-Kelvin first-principles calculations with a Gaussian process regression model trained on temperature-dependent reaction free energies. We apply this physics-based machine-learning model to the prediction of metal oxide reduction temperatures in high-temperature smelting processes that are commonly used for the extraction of metals from their ores and from electronics waste and have a significant impact on the global energy economy and greenhouse gas emissions. The hybrid model predicts accurate reduction temperatures of unseen oxides, is computationally efficient, and surpasses in accuracy computationally much more demanding first-principles simulations that explicitly include temperature effects. The approach provides a general paradigm for capturing the temperature dependence of reaction free energies and derived thermodynamic properties when limited experimental reference data is available.

Ab initio mechanism revealing for tricalcium silicate dissolution | Nature Communications volume 13, 1253 (2022)
Dissolution of minerals in water is ubiquitous in nature and industry, especially for the calcium silicate species. However, the behavior of such a complex chemical reaction is still unclear at atomic level. Here, we show that the ab initio molecular dynamics and metadynamics simulations enable quantitative analyses of reaction pathways, thermodynamics and kinetics of the calcium ion dissolution from the tricalcium silicate (Ca3SiO5) surface. The calcium sites with different coordination environments lead to different reaction pathways and free energy barriers. The low free energy barriers result in that the detachment of the calcium ion is a ligand exchange and auto-catalytic process. Moreover, the water adsorption, proton exchange and diffusion of water into the surface layer accelerate the leaching of the calcium ion from the surface step by step. The discovery in this work thus would be a landmark for revealing the mechanism of tricalcium silicate hydration.

The top 100 papers | Nature 514, 550–553 (2014).
When theorists want to model a piece of matter — be it a drug molecule or a slab of metal — they often use software to calculate the behaviour of the material’s electrons. From this knowledge flows an understanding of numerous other properties: a protein’s reactivity, for instance, or how easily Earth’s liquid iron outer core conducts heat.
Most of this software is built on density functional theory (DFT), easily the most heavily cited concept in the physical sciences. Twelve papers on the top-100 list relate to it, including 2 of the top 10. At its heart, DFT is an approximation that makes impossible mathematics easy, says Feliciano Giustino, a materials physicist at the University of Oxford, UK. To study electronic behaviour in a silicon crystal by taking account of how every electron and every nucleus interacts with every other electron and nucleus, a researcher would need to analyse one sextillion (1021) terabytes of data, he says — far beyond the capacity of any conceivable computer. DFT reduces the data requirement to just a few hundred kilobytes, well within the capacity of a standard laptop.
Theoretical physicist Walter Kohn led the development of DFT half a century ago in papers20, 21 that now rank as numbers 34 and 39. Kohn realized that he could calculate a system’s properties, such as its lowest energy state, by assuming that each electron reacts to all the others not as individuals, but as a smeared-out average. In principle, the mathematics are straightforward: the system behaves like a continuous fluid with a density that varies from point to point. Hence the theory’s name.
But a few decades passed before researchers found ways to implement the idea for real materials, says Giustino. Two22, 23 top-100 papers are technical recipes on which the most popular DFT methods and software packages are built. One (number 8) is by Axel Becke, a theoretical chemist at Dalhousie University in Halifax, Canada, and the other (number 7) is by US-based theoretical chemists Chengteh Lee, Weitao Yang and Robert Parr. In 1992, computational chemist John Pople (who would share the 1998 Nobel prize with Kohn) included a form of DFT in his popular Gaussian software package.
Software users probably cite the original theoretical papers even if they do not fully understand the theory, says Becke. “The theory, mathematics and computer software are specialized and are the concern of quantum physicists and chemists,” he says. “But the applications are endless. At a fundamental level, DFT can be used to describe all of chemistry, biochemistry, biology, nanosystems and materials. Everything in our terrestrial world depends on the motions of electrons — therefore, DFT literally underlies everything.”

Electronic-structure methods for materials design | Nature Materials, volume 20, pages736–749 (2021)
Applications of electronic-structure methods range from nanotechnology to planetary science, from metallurgy to quantum materials, and the current push and excitement to accelerate or complement experiments with simulations makes it even more urgent to highlight not only their capabilities but also their limitations. Simulations do not fail in spectacular ways, but can subtly shift from being invaluable to barely good enough to just useless. The reasons for failure are manifold, from stretching the capabilities of the methods to forsaking the complexity of real materials. But simulations are also irreplaceable: they can assess materials at conditions of pressure and temperature so extreme that no experiment on Earth is able to replicate, they can explore with ever-increasing nimbleness the vast space of materials phases and compositions in the search for that elusive materials breakthrough, and they can directly identify the microscopic causes and origin of a macroscopic property. Last, they share with all branches of computational science a key element of research: they can be made reproducible and open and shareable in ways that no physical infrastructure will ever be.

Ab initio molecular dynamics: Concepts, recent developments, and future trends | PNAS May 3, 2005
AIMD is a rapidly evolving and growing technique that constitutes one of the most important theoretical tools developed in the last decades. In an AIMD calculation, finite-temperature dynamical trajectories are generated by using forces obtained directly from electronic structure calculations performed “on the fly” as the simulation proceeds. Thus, AIMD permits chemical bond breaking and forming events to occur and accounts for electronic polarization effects (3, 4). AIMD has been successfully applied to a wide variety of important problems in physics and chemistry and is now beginning to influence biology as well. In numerous studies, new physical phenomena have been revealed and microscopic mechanisms elucidated that could not have been uncovered by using empirical methods, often leading to new interpretations of experimental data and even suggesting new experiments to perform.

Ab Initio Molecular Dynamics Simulations | J. Phys. Chem. 1996
Classical molecular dynamics (MD), which has its origins in the 1950s and 1960s, is now widely used to investigate condensed phase systems, ranging from micellar solutions to biomolecules, polymers, and inorganic materials. The standard MD technique, which is based on the use of empirical interatomic potential functions parametrized to experimental data, has also proved its worth in the study of ionic solutions, electrochemistry, tribology, and cluster science. One of the most exciting developments of the past decade is the advent of ab initio molecular dynamics, which, rather than requiring an empirical interaction potential as input, utilizes interatomic forces computed directly from the electronic structure. This new approach has now become established as an important tool in the investigation of chemically complex environments. In the Car−Parrinello (CP) approach 1,2 to ab initio MD, the electronic structure is described using the Kohn−Sham formulation 3 of the density functional theory, 4 and the Kohn−Sham orbitals are expanded in a plane wave basis. The expansion coefficients are treated as a set of fictitious dynamical variables that are propagated adiabatically with respect to the nuclei, so that, at each time step, they describe the instantaneous ground state Born−Oppenheimer surface. In this way, the need to solve the Kohn−Sham equations explicitly is avoided. The CP approach has proved useful in a wide variety of physical and chemical applications. The present article illustrates the versatility of the CP approach to MD simulations by considering a variety of condensed phase systems.

Discovering and understanding materials through computation | Nature Materials volume 20, pages728–735 (2021)
Parallel to developments in computational electronic structure, first-principles methods were advanced to explore atomic motions. As electrons are much lighter than nuclei, to a high degree of accuracy, the electrons may be assumed to follow the nuclei instantly in the Born–Oppenheimer adiabatic approximation. However, solving for the electronic structures at each nuclear configuration remains a complicated problem even with the advent of DFT, as it introduces many new degrees of freedom owing to the motion of the nuclei. Moreover, the coupling of electrons to the nuclei going beyond the Born–Oppenheimer approximation is central to many important processes.
Over the past half century, DFT has been arguably the most dominant and successful method for the ab initio computational study of materials’ ground-state properties. The foundations of DFT were laid down in the work of Hohenberg and Kohn6, which showed that the electronic ground-state total energy can be expressed as a functional of the ground-state charge density, and of Kohn and Sham7, which showed that the ground-state charge density can be determined by a set of self-consistent one-body equations. Within Kohn–Sham DFT, the difficult problem of many interacting electrons is mapped to a one-electron Schrödinger equation of a fictitious system of non-interacting particles with the same density. In principle, DFT is an exact theory for ground-state properties—such as molecular and crystal structure, elastic constants and vibrational properties, and the relative stability of different structural phases, among others2. In practice, an approximation for the effective one-particle exchange-correlation potential (a term from the interacting electrons) is needed. Earlier works approximate the exchange-correlation potential as a function of the local charge density in the local density approximation7,8,9. Later developments introduce additional features (from theory or empiricism) based on the gradient of the density or inclusion of a Hartree–Fock-like exchange term. The development of more accurate and universal density functionals is an active research direction. These advances, combined with the implementation of increasingly sophisticated DFT computer codes and algorithms through the years, have tremendously broadened the scope of physical systems that can be studied10. Moreover, DFT results are frequently used as input for the parameterization of coarse-grained models for extended spatial and timescale phenomena, opening the doorway for multiscale modelling rooted in ab initio theory, as discussed in the four Review Articles2,3,4,5.

Self-consistent determination of long-range electrostatics in neural network potentials | Nature Communications volume 13, 1572 (2022)
Computer simulations have transformed our understanding of molecular systems by providing atomic-level insights into phenomena of widespread importance. The earliest models used efficient empirical descriptions of interatomic interactions, and similar force field-based simulations form the foundation of molecular simulations today1. However, it is difficult to describe processes like chemical reactions that involve bond breakage and formation, as well as electronic polarization effects within empirical force fields. The development of quantum mechanics-based ab initio simulations enabled the description of these complex processes, leading to profound insights across scientific disciplines2,3,4,5,6,7,8,9. The vast majority of these first principles approaches rely on density functional theory (DFT), and the development of increasingly accurate density functionals has greatly improved the reliability of ab initio predictions10,11,12,13,14,15. But, performing electronic structure calculations are expensive, and first-principles simulations are limited to small system sizes and short time scales.
The prohibitive expense of ab initio simulations can be overcome through machine learning. Armed with a set of ab initio data, machine learning can be used to train neural network (NN) potentials that describe interatomic interactions at the same level of accuracy as the ab initio methods, but with a fraction of the cost. Consequently, NN potentials enable ab initio quality simulations to reach the large system sizes and long time scales needed to model complex phenomena, such as phase diagrams16,17,18,19,20 and nucleation21,22.

cp2k: atomistic simulations of condensed matter systems
Computer simulation of matter with atomistic detail has become a very prominent tool in chemistry, physics, life sciences, and materials sciences. In these fields, simulation results can yield the insights needed to interpret experimental measurements, can be used to predict material properties, or to design new compounds. A precise picture of the structures and dynamical processes at the atomic scale is a valuable starting point to rationally design new experiments and new systems. With sustained exponential growth in computer resources, the impact of simulation will continue to increase.
CP2K has a large impact in the field of density functional theory (DFT)-based molecular dynamics (MD) simulation, particularly with its capability to describe the dynamics of systems containing hundreds of atoms with relative ease, but has a broader range of capabilities.
To study processes dominated by rare events,like reactions and structural transformations, MD is typically not sufficient due to too slow sampling of the configurations space. Constraints and restraints can be employed to reconstruct the free energy profile along specific reaction pathways by applying methods like thermodynamic integration or umbrella sampling.8 Metadynamics is another powerful method to accelerate the sampling and reconstruct the free energy surfaces in terms of a few collective variables.24,25 In CP2K, different versions of metadynamics are implemented, such as extended Lagrangian metadynamics, well-tempered metadynamics, and the multiwalker scheme.25

Ab initio simulation: The correlation between the local melt structure and segregation behavior of Fe, V, Ti and Si in liquid Al
The rapid development of computer technology has allowed researchers to study melt structures and their solid–liquid interface with atomic level simulations. In particular, simulations based on ab initio molecular dynamics (AIMD) are widely used because of the higher accuracy of AIMD compared to other computational methods. The AIMD simulation method has been proven to be a powerful technique for simulating the properties of molten metal [5], [6], [7], [8].This is especially true for Al and Al alloy melts, which have relatively simple crystalline structures; thus, extensive and deep insights into these systems have been gained [9], [10], [11].

The migration behavior of the fourth period transition metals in liquid Al: An ab initio molecular dynamics study
In this study, for extending previous work, we investigated the local structure characters around all FPTMs solute atoms in the Al melt and researched the correlation between the variation of the diffusivity and changing of local structure of the FPTMs solute atoms, then tried to explain the influence law of diffusivity affected by local structure. However, the challenges of directly detecting molten structure have been beyond the capabilities of experimentalists. Characterization of the local structures around a certain atom in the melt is harder than one can imagine. Ab initio molecular dynamics (AIMD) make researching of the metallic melt at atomic level become possible. In previous work, it was proved that AIMD is powerful to research the melt characters [16], [17], [18], [19], [20], [21], [22], [23] and widely accepted.

Melts of CrCoNi-based high-entropy alloys: Atomic diffusion and electronic/atomic structure from ab initio simulation
Despite the importance of liquid-state properties, their experimental measurement in high-temperature melts is challenging, and ab initio molecular-dynamics (AIMD) simulations have emerged as a powerful framework for their calculation.

An ab initio molecular dynamics exploration of associates in Ba-Bi liquid with strong ordering trends
In a recent CALPHAD (calculation of phase diagram) modeling [24] of the Ba-Bi system, Liu et al. [10] used two fictive associates of Ba4Bi3 and BaBi3 in the liquid phase, which were empirically selected based on the intermetallic compounds with the two highest congruent melting points. The present investigation aims to use the ab initio molecular dynamics (AIMD) simulations to study the presence and the characters of associates in the Ba-Bi liquid phase. The AIMD approach [25] uses the interatomic interactions calculated on the fly based on density functional theory (DFT), avoiding the errors due to empirical potentials.

Quickstep: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
Density functional theory [1], [2] (DFT) is a well established method to perform electronic structure calculations. The accuracy of the method is such that many properties of systems of interest to chemistry, physics, material science, and biology can be predicted in a parameter free way. The standard computational approach to DFT is already efficient and thus appropriate for fairly large systems, currently about 100 atoms. Nevertheless, the computation of the Hartree (Coulomb) energy and the orthogonalisation of the wave functions are not scaling linearly with system size, and these terms therefore dominate the computational cost for larger systems [3]. The hybrid Gaussian and plane waves (GPW) method [4] provides an efficient way to treat these terms accurately at a significantly reduced cost. We present here the implementation of this method in Quickstep, which is part of the freely available program package CP2K [5].

A hybrid Gaussian and plane wave density functional scheme
Calculations based on density functional theory (DFT) [1] have enjoyed great success in recent years, with applications that range from materials science to chemistry and biochemistry. While conventional quantum chemical methods are amply used, an increasing number of applications make use of pseudo- potentials and the expansion of the Kohn±Sham (KS) [2] orbitals in plane waves (PWs), especially in the context of ab initio molecular dynamics simulations [3]. PW as a basis set for quantum chemical problems is a rather unusual and unnatural choice. However, PWs have a series of advantages that are at the heart of their success. PWs are atomic position independent; this makes the calculation of the Hellmann±Feynman forces very simple. PWs are totally unbiased and do not lead to basis set superposition errors. The calculation of the Hartree potential is very simple and checking the con- vergence of the calculation is trivial. Furthermore, the use of the fast Fourier transform technique considerably simplies many algebraic manipulations. There are, however, signi®cant disadvantages in using PWs. Most noticeably, a large number of PWs is needed to repro- duce the rapid variations of the wavefunctions close to the nuclei. This is alleviated by the use of pseudo- potentials, but for several elements unreasonably large basis sets are still needed.

Ab Initio Molecular Dynamics Study of 45S5 Bioactive Silicate Glass
Classical molecular dynamics (MD) simulations are well suited to model simple silicate and phosphate glasses; 12-17 however, multicomponent phosphosilicate glasses may represent a challenge for classical MD, due to the difficulty of incorporating many different interactions and complex effects in a reliable force field. An alternative computational approach, unhindered by the need to develop an accurate potential model due to its first-principle calculation of energy and ionic forces, is represented by ab initio molecular dynamics (AIMD), such as the Car−Parrinello method. 18,19 This approach has been successfully applied to investigate structural and electronic effects in silica and modified silicate glasses. 20-24 The large computational resources needed by the explicit inclusion of electronic degrees of freedom limit the properties which can be effectively explored in AIMD simulations of glasses:  structural features beyond local order, such as network connectivity or the Qn distribution, as well as long-range ionic migration pathways, lie outside the space/time ranges accessible with AIMD. On the other hand, the ionic vibrational motion in condensed phases can be adequately sampled in AIMD simulations, and they have been successfully employed to determine vibrational and elastic properties of silicate glasses.22,25,26 In addition, AIMD simulations give straightforward access to the electronic properties of glasses, 27,28 which are essential to complete the picture of the bulk properties of these materials related to their bioactivity.

First principle study of electronic structural and physical properties of CaO-SiO2-Al2O3 ternary slag system by using Ab Initio molecular and lattice dynamics
As most of the properties on melts would be explained through understanding the behavior of electrons, which can hold atoms together by making bonds. The electronic structure theory and ab initio electronic structure calculations can predict the physical and chemical properties as well as structure of slag [8]. To understand the electronic properties the density of state (DOS), electron density difference (EDD), atomic and bond population are calculated for CSA slag system by using ab initio lattice dynamics (AILD), first principle simulation technique. The modern computational technology has made ab initio molecular dynamics (AIMD) accessible, and emerging simulation method [9] to calculate the physical properties of slags. The Classical molecular dynamics (CMD) simulations based on empirical interatomic potentials, are inexpensive in computer time and simulate the large systems with number of atoms, (N > 1000) but the quality of the results depends on the accuracy of the input force field. While the ab initio DFT simulations which uses the electron’s density for the calculation of properties, gives the more precise results. However, it is expensive in computer time and restricted to small systems (N ~ 100 atoms) [10].

Comparison of desulfurization mechanism in liquid CaO-SiO2 and MnO-SiO2: An ab initio molecular dynamics simulation
With the rapid progress of computer science in recent years, a considerable number of simulation studies on silicate structures have been conducted [19], [20], [21], [22], [23], [24]. For example, in silicate systems, classical molecular dynamics (MD) is frequently utilized to provide structural and coordination information [23], [25], [26], [27], [28], [29]. However, it can only explain molecular interactions in the ground state and not information about atom interactions, such as charge distribution. Ab Initio molecular dynamics (AIMD) based on quantum mechanics theory, which can direct calculation of all molecular and molecular interactions through quantum chemistry methods, no need to input empirical mechanical models. It makes up for the shortcomings of classical molecular dynamics simulation and can have a more essential understanding of the melting structure and charge information of silicate under high-temperature conditions. This method is widely used in materials and chemistry [30], [31], [32] and can deepen understanding of the existing state mechanism of trace elements. At the same time, AIMD simulation has mature applications for the melting process of liquid metal and oxide systems [20], [33], [34], [35], [36], [37], [38], [39], [40], [41], [42], [43], [44]. For the silicate oxide system, Koler [38] and Georg [45] studied thermodynamic properties and structural information of MgO-SiO2 by AIMD. Huang [46] investigated the Fe-Si-O system from 3800 K to 4800 K under high pressure. For CaO-SiO2 and MnO-SiO2 systems, researchers [47] have used DFT-MD calculations to study the structural properties of CaO-SiO2 with different proportions.

Modelling the local atomic structure of molybdenum in nuclear waste glasses with ab initio molecular dynamics simulations
Molecular dynamics (MD) is a computational method of choice for efficiently probing the various heterogeneous local environments found in glasses, as it provides insight into the material properties from the atomistic level.13 However, classical MD simulations are hampered by the lack of reliable force fields to describe the complex interactions in multicomponent borosilicate glasses,14 even though reliable interatomic potentials have been developed to model pure silica and mixed cation silicate glasses.15 An alternative computational approach is the ab initio molecular dynamics technique (AIMD), a parameter free approach, where the forces are computed from a quantum mechanical representation of the electronic structure. Despite being computationally demanding, as compared to classical MD simulations, this approach enables accurate modelling of many-body systems, and it can account for switching chemical bonds and electron density polarisation. AIMD simulations have previously been used to model the structural properties of pure silica and alkali silicate glasses,16–20 as well as, sodium borosilicate glass21 and bioactive phosphate glasses.22–25

Molecular Dynamics Modeling of the Structure and Na+-Ion Transport in Na2S + SiS2 Glassy Electrolytes
Ab initio molecular dynamics (MD), which performs quantum calculations to determine the forces on atoms and solves classical equations of motion at specific temperatures, is therefore well suited to analyze ion migration within these glasses and relate them to the local structure. Furthermore, ab initio MD can capture complex chemical reactions during the formation of glasses by melt-quench processes and can generate representative structures, as evidenced from previous work of Islam et al. (34−36) and Ceder et al. (37−39) on lithium oxide- and lithium sulfide-based glasses. Shah et al. summarized different multiscale modeling techniques addressing the complex issues for developing high-performance lithium-ion batteries. (40)

Coordination of Zr4+/Hf4+/Nb5+/Ta5+ in silicate melts: insight from first principles molecular dynamics simulations
Numerous FPMD simulations of various melts including oxides (e.g., Karki et al., 2007; Verma et al., 2011), silicates (e.g., Karki and Stixrude, 2010a; Ni and de Koker, 2011; Sun et al., 2019) and carbonates (e.g., Vuilleumier et al., 2014; Zhang and Liu, 2015) have been reported. These studies focused on the physical properties of melts, but less attention has been paid to the geochemical behavior of ore-forming metals in melts (e.g., Wagner et al., 2017, Wagner et al., 2017b). To the best of our knowledge, the coordination chemistry of Zr, Hf, Nb and Ta in silicate melts has not been investigated by using FPMD.

Ab initio molecular dynamics assessment of thermodynamic and transport properties in (K,Li)Cl and (K, Na)Cl molten salt mixtures
However, measuring properties of MSs at very high temperatures under hazardous or corrosive conditions is difficult and costly. In addition, MSs are liquid-phase multi-component mixtures whose local structure and speciation are very difficult to determine. Luckily, computer simulations using theoretical modeling techniques such as molecular dynamics or Monte Carlo provide a low-cost alternative approach [[8], [9], [10]]. For atomistic simulations of MS systems, the treatment of inter-atomic interactions is crucial. Since the early days of computer-based molecular simulations, MS modeling has been largely done using force field potentials [8,9,11]. Most commonly, the inter-atomic forces are described with additive pairwise potentials consisting of terms like Coulombic attraction/repulsion, van der Waals dipole-dipole/dipole-quadrupole interactions [12,13]. These so-called rigid ion models omit inter-atomic forces arising from polarization. Rahman et al. showed that on top of these two-body potentials, the polarization, treated in a shell-model type fashion [14], leads to a significant increase in ionic diffusion coefficient, and in a reduction in the characteristic frequencies [15]. The parameterization of these potentials largely depends on reproducing experimental data. More recently, sophisticated procedures based on first principles for potential parameterization assessing polarization have been applied and showed certain success in reproducing static and dynamic properties of MSs system [9,[16], [17], [18]]. However, such a procedure based on the fitting with first principles potentials becomes challenging as the time scale and the complexity of multicomponent systems increase. One can always question the transferability of these potentials as physical and chemical properties of an ion can change significantly from on coordination environment to another. Furthermore, classical force fields implicitly ignore the electronic degrees of freedom when ions change their coordination environments. As such, processes including charge transfer are not captured, and the most obvious consequence is that important chemical processes such as redox cannot be described.
Recently quantum mechanics-based molecular dynamics has been applied to study MSs [[19], [20], [21], [22], [23], [24], [25]]. Galamba et al. [19,20]., by employing density functional theory (DFT) – based molecular dynamics (MD) simulations to study molten NaCl and NaI, found that the main differences in structural and transport properties between results from the rigid ion and ab initio approaches are related to polarization effects. Bengtson et al. [22], performing ab initio molecular dynamics (AIMD) simulations on the eutectic (K, Li)Cl mixture, showed that AIMD is a useful predictive tool for properties such as bulk modulus of which experimental data are not available, or complex thermodynamics properties like the free energy of mixing which help understand phase stability.

Properties of Negatively Charged Ruthenium Clusters in Molten Sodium Chloride
In this study, we use ab initio molecular dynamics (AIMD) to investigate the stability of negatively charged ruthenium clusters in molten sodium chloride and their ability to stabilize negatively charged adsorbates/intermediates. The study builds on a recent study from our group, where the reactivity of solvated electrons was investigated in molten alkali chloride.

Alternative insight into aluminium-phosphate glass network from ab initio molecular dynamics simulations
Depending on the method of description of the interatomic interactions it can be divided on classical or ab initio [26,27,29,[37], [38], [39], [40], [41], [42]]. The classical molecular dynamics (MD) use interatomic potentials based on empirical data or electronic structure calculations to determine the forces between ions [43,44]. The big advantage of the classical MD is the ability to simulate large systems (1 000 000 ions) at current computer performance [41,45]. The main problem of the classical molecular dynamics is matching the potential so that it accurately describes the interaction between ions. This problem does not occur in ab initio MD. This method relies on calculating the forces acting on the nuclei from electron structure calculations. The calculations of electron structure are performed during generating the trajectory of nuclei. One of the ab initio MD methods is Car-Parrinello molecular dynamics (CPMD). This method was used to study the structures of phosphate glasses and gave more accurate results than classical MD [29,[46], [47], [48]]. The ab initio methods are very computationally demanding and are limited to only hundreds of atoms.