Melting Si: Beyond Density Functional Theory

A unified moment tensor potential for silicon, oxygen, and silica

Si and its oxides have been extensively explored in theoretical research due to their technological importance. Simultaneously describing interatomic interactions within both Si and SiO2 without the use of ab initio methods is considered challenging, given the charge transfers involved. Herein, this challenge is overcome by developing a unified machine learning interatomic potentials describing the Si/SiO2/O system, based on the moment tensor potential (MTP) framework. This MTP is trained using a comprehensive database generated using density functional theory simulations, encompassing diverse crystal structures, point defects, extended defects, and disordered structure. Extensive testing of the MTP is performed, indicating it can describe static and dynamic features of very diverse Si, O, and SiO2 atomic structures with a degree of fidelity approaching that of DFT.

Radiogenic heating sustains long-lived volcanism and magnetic dynamos in super-Earths

Radiogenic heat production is fundamental to the energy budget of planets. Roughly half of the heat that Earth loses through its surface today comes from the three long-lived, heat-producing elements (potassium, thorium, and uranium). These three elements have long been believed to be highly lithophile and thus concentrate in the mantle of rocky planets. However, our study shows that they all become siderophile under the pressure and temperature conditions relevant to the core formation of large rocky planets dubbed super-Earths. Mantle convection in super-Earths is then primarily driven by heating from the core rather than by a mix of internal heating and cooling from above as in Earth. Partitioning these sources of radiogenic heat into the core remarkably increases the core-mantle boundary (CMB) temperature and the total heat flow across the CMB in super-Earths. Consequently, super-Earths are likely to host long-lived volcanism and strong magnetic dynamos.

Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5

Herein, we propose a novel computational protocol that enables calculating free energies with improved accuracy by combining the best available techniques for enthalpy and entropy calculation. While the entropy is described by enhanced sampling molecular dynamics techniques, the energy is calculated using ab initio methods. We apply the method to assess the stability of isobutene adsorption intermediates in the zeolite H-SSZ-13, a prototypical problem that is computationally extremely challenging in terms of calculating enthalpy and entropy. We find that at typical operating conditions for zeolite catalysis (400 °C), the physisorbed π-complex, and not the tertiary carbenium ion as often reported, is the most stable intermediate. This method paves the way for sampling-based techniques to calculate the accurate free energies in a broad range of chemistry-related disciplines, thus presenting a big step forward toward predictive modeling.

It's Complicated: On Relativistic Effects and Periodic Trends in the Melting and Boiling Points of the Group 11 Coinage Metals

While the color of metallic gold is a prominent and well-investigated example for the impact of relativistic effects, much less is known regarding the influence on its melting and boiling point (MP/BP). To remedy this situation, this work takes on the challenging task of exploring the phase transitions of the Group 11 coinage metals Cu, Ag, and Au through nonrelativistic (NR) and scalar/spin-orbit relativistic (SR/SOR) Gibbs energy calculations with λ-scaled density-functional theory (λDFT). At the SOR level, the calculations provide BPs in excellent agreement with experimental values (1%), while MPs exhibit more significant deviations (2-10%). Comparing SOR calculations to those conducted in the NR limit reveals some remarkably large and, at the same time, some surprisingly small relativistic shifts. Most notably, the BP of Au increases by about 800 K due to relativity, which is in line with the strong relativistic increase of the cohesive energy, whereas the MP of Au is very similar at the SOR and NR levels, defying the typically robust correlation between MP and cohesive energy. Eventually, an inspection of thermodynamic quantities traces the trend-breaking behavior of Au back to phase-specific effects in liquid Au, which render NR Au more similar to SOR Ag, in line with a half-a-century-old hypothesis of Pyykkö.

Accurate acid dissociation constant (pKa) calculation for the sulfachloropyridazine and similar molecules

Accurate calculation of the acid dissociation constant (pK_a) has fundamental importance for the description of molecular systems with pharmacological activities. The search for a more appropriate procedure for its determination is always welcome and has aroused increasing interest from the scientific community. In this sense, this work presents a computational study involving the combination of ten DFT functionals (M062X, M06L, B3LYP, BLYP, PBEPBE, BP86, LC-BLYP, SPBE, CAM-B3LYP, LC-PBEPBE) and HF method, eight basis set functions (6-311G, 6-311 + G, 6-311G(d,p), 6-311 + G(d,p), 6-311+ +G(d,p), 6-311(2d,2p), 6-311+ +G(2d,2p), and aug-cc-pVDZ), and three solvation models (SMD, PCM, and CPCM) for an accurate sulfachloropyridazine (SCR) pK_a determination. It was found that the smallest deviation (0.02 unit of pK_a) between the current study and experimental result was achieved with the BLYP/6-311 + G(d,p)/PCM combination. Therefore, this combination was extended to calculate the pK_a of six SCR similar molecules selected through the eletroshape similarity method. For all these molecules, the difference between the obtained results and experimental data ranged between 0.14 and 0.69 units of pK_a. This feature suggests that the obtained combination can determine pK_a with experimental precision for complexes that are formed by sulfonamide functional group (SO₂NHR). Graphical Abstract A computational study involving the combination of different levels of theory, basis sets and solvation models for an accurate sulfanamide pK_a determination.

Atomistic Mechanism Underlying the Si(111)-(7×7) Surface Reconstruction Revealed by Artificial Neural-Network Potential

The 7×7 reconstruction of the Si(111) surface represents arguably the most fascinating surface reconstruction so far observed in nature. Yet, the atomistic mechanism underpinning its formation remains unclear after it was discovered sixty years ago. Experimentally, it is observed post priori so that analysis of its formation mechanism can only be carried out in analogy with archaeology. Theoretically, density-functional theory (DFT) correctly predicts the Si(111)-(7×7) ground state but is impractical to simulate its formation process; while empirical potentials failed to produce it as the ground state. Developing an artificial neural-network potential of DFT quality, we carried out accurate large-scale simulations to unravel the formation of the Si(111)-(7×7) surface. We reveal a possible step-mediated atom-pop rate-limiting process that triggers massive nonconserved atomic rearrangements, most remarkably, a critical process of collective vacancy diffusion that mediates a sequence of selective dimer, corner-hole, stacking-fault, and dimer-line pattern formation, to fulfill the 7×7 reconstruction. Our findings may not only solve the long-standing mystery of this famous surface reconstruction but they also illustrate the power of machine learning in studying complex structures.

Anharmonic effects on the dynamics of solid aluminium fromab initiosimulations

Two approaches to simulations of phonon properties of solids beyond the harmonic approximation, the self-consistentab initiolattice dynamics (SCAILD) and decoupled anharmonic mode approximation (DAMA) are critically benchmarked against each other and molecular dynamics simulations using a density-functional-theory description of electronic states, and compared to experimental data for fcc aluminium. The temperature-dependence of phonon dispersion and the phonon density-of-states, heat capacity, and the mean atomic displacement for fcc aluminium are examined with these approaches at ambient pressure. A comparison of results obtained with the harmonic approximation to the ones predicted by SCAILD and DAMA reveal a negligible anharmonic contribution to phonon frequencies, a small, but significant influence on heat capacity, and a strong effect on atomic mean-square displacement. The phase space accessed with SCAILD and DAMA is reduced relative to molecular and harmonic lattice dynamics simulations. In particular the DAMA results are in good agreement with displacement amplitudes determined by the Debye-Waller factor in x-ray diffraction experiments.

Exclusively Relativistic: Periodic Trends in the Melting and Boiling Points of Group 12

First-principles simulations can advance our understanding of phase transitions but are often too costly for the heavier elements, which require a relativistic treatment. Addressing this challenge, we recently composed an indirect approach: A precise incremental calculation of absolute Gibbs energies for the solid and liquid with a relativistic Hamiltonian that enables an accurate determination of melting and boiling points (MPs and BPs). Here, we apply this approach to the Group 12 elements Zn, Cd, Hg, and Cn, whose MPs and BPs we calculate with a mean absolute deviation of only 5 % and 1 %, respectively, while we confirm the previously predicted liquid aggregate state of Cn. At a non-relativistic level of theory, we obtain surprisingly similar MPs and BPs of 650±30 K and 1250±20 K, suggesting that periodic trends in this group are exclusively relativistic in nature. Ultimately, we discuss these results and their implication for Groups 11 and 14.

First-principles hydration free energies of oxygenated species at water-platinum interfaces

The hydration free energy of atoms and molecules adsorbed at liquid-solid interfaces strongly influences the stability and reactivity of solid surfaces. However, its evaluation is challenging in both experiments and theories. In this work, a machine learning aided molecular dynamics method is proposed and applied to oxygen atoms and hydroxyl groups adsorbed on Pt(111) and Pt(100) surfaces in water. The proposed method adopts thermodynamic integration with respect to a coupling parameter specifying a path from well-defined non-interacting species to the fully interacting ones. The atomistic interactions are described by a machine-learned inter-atomic potential trained on first-principles data. The free energy calculated by the machine-learned potential is further corrected by using thermodynamic perturbation theory to provide the first-principles free energy. The calculated hydration free energies indicate that only the hydroxyl group adsorbed on the Pt(111) surface attains a hydration stabilization. The observed trend is attributed to differences in the adsorption site and surface morphology.

Oganesson: A Noble Gas Element That Is Neither Noble Nor a Gas

Oganesson (Og) is the last entry into the Periodic Table completing the seventh period of elements and group 18 of the noble gases. Only five atoms of Og have been successfully produced in nuclear collision experiments, with an estimate half-life for294 118 Og of 0. 69 + 0 . 64 - 0 . 22  ms.[1] With such a short lifetime, chemical and physical properties inevitably have to come from accurate relativistic quantum theory. Here, we employ two complementary computational approaches, namely parallel tempering Monte-Carlo (PTMC) simulations and first-principles thermodynamic integration (TI), both calibrated against a highly accurate coupled-cluster reference to pin-down the melting and boiling points of this super-heavy element. In excellent agreement, these approaches show Og to be a solid at ambient conditions with a melting point of ≈325 K. In contrast, calculations in the nonrelativistic limit reveal a melting point for Og of 220 K, suggesting a gaseous state as expected for a typical noble gas element. Accordingly, relativistic effects shift the solid-to-liquid phase transition by about 100 K.

Accurate elemental boiling points from first principles

The normal boiling point (NBP) is a fundamental property of liquids and marks the intersection of the Gibbs energies of the liquid and the gas-phase at ambient pressure. This work provides the first comprehensive demonstration of the calculation of boiling points of atomic liquids through first-principles molecular-dynamics simulations. To this end, thermodynamic integration (TDI) and perturbation theory (TPT) are combined with a density-functional theory (DFT) Hamiltonian, which provides absolute Gibbs energies, internal energies, and entropies of atomic liquids with an accuracy of a few meV/atom. Linear extrapolation to the intersection with the Gibbs energy of a non-interacting gas-phase eventually pins-down the NBPs. While these direct results can already be quite accurate, they are susceptible to a systematic over or underbinding of the employed density functional. It is shown how this dependency can be strongly reduced and the robustness of the method increased through a simple linear correction termed λ-scaling. Eventually, by carefully tuning of the technical parameters of the approach, the walltime per element is reduced from weeks to about a day (10-20k core-hours), enabling extensive testing for B, Al, Na, K, Ca, Sr, Ba, Mn, Cu, Xe, and Hg. This comprehensive benchmark demonstrates the excellent performance and robustness of the approach with a mean absolute deviation (MAD) of less than 2% from experimental NBPs and very similar accuracy for liquid entropies (MAD 2.3 J (mol K)-1, 2% relative). In some cases, the uncertainties in the predictions are several times smaller than the variation between literature values, allowing us to clear out long-standing ambiguities in the NBPs of B and Ba.

Ab initio phase diagram and nucleation of gallium

Elemental gallium possesses several intriguing properties, such as a low melting point, a density anomaly and an electronic structure in which covalent and metallic features coexist. In order to simulate this complex system, we construct an ab initio quality interaction potential by training a neural network on a set of density functional theory calculations performed on configurations generated in multithermal–multibaric simulations. Here we show that the relative equilibrium between liquid gallium, α-Ga, β-Ga, and Ga-II is well described. The resulting phase diagram is in agreement with the experimental findings. The local structure of liquid gallium and its nucleation into α-Ga and β-Ga are studied. We find that the formation of metastable β-Ga is kinetically favored over the thermodinamically stable α-Ga. Finally, we provide insight into the experimental observations of extreme undercooling of liquid Ga.

Exploring nucleation processes of gallium by molecular simulation is extremely challenging due to its structural complexity. Here the authors demonstrate a neural network potential trained on a multithermal–multibaric DFT data for the study of the phase diagram of gallium in a wide temperature and pressure range.

Graphene thermal break-down induced by anharmonic bending mode

A novel approach is proposed allowing us to prove, self-consistently, that free-standing graphene reaching a certain temperature loses its mechanical stability resulting in abrupt breakdown, which can be interpreted as melting. Our study is based on the idea of the crucial role of the anomalously soft bending 'sound' mode in the jump transition of graphene from the state with relatively small bending fluctuations to a state with fluctuations close in amplitude to the graphene lattice constant. The acme of the developed theory is in establishing a quantitative relationship connecting the graphene elastic moduli of second, third (negative!), and fourth orders at the melting temperature T _m that permits us to calculate T _m. The results obtained lay a theoretical foundation for an analog of Lindemann criterion for graphene.

Machine Learning Interatomic Potentials as Emerging Tools for Materials Science

Atomic-scale modeling and understanding of materials have made remarkable progress, but they are still fundamentally limited by the large computational cost of explicit electronic-structure methods such as density-functional theory. This Progress Report shows how machine learning (ML) is currently enabling a new degree of realism in materials modeling: by "learning" electronic-structure data, ML-based interatomic potentials give access to atomistic simulations that reach similar accuracy levels but are orders of magnitude faster. A brief introduction to the new tools is given, and then, applications to some select problems in materials science are highlighted: phase-change materials for memory devices; nanoparticle catalysts; and carbon-based electrodes for chemical sensing, supercapacitors, and batteries. It is hoped that the present work will inspire the development and wider use of ML-based interatomic potentials in diverse areas of materials research.

Copernicium: A Relativistic Noble Liquid

The chemical nature and aggregate state of superheavy copernicium (Cn) have been subject of speculation for many years. While strong relativistic effects render Cn chemically inert, which led Pitzer to suggest a noble-gas-like behavior in 1975, Eichler and co-workers in 2008 reported substantial interactions with a gold surface in atom-at-a-time experiments, suggesting a metallic character and a solid aggregate state. Herein, we explore the physicochemical properties of Cn by means of first-principles free-energy calculations, which confirm Pitzer's original hypothesis: With predicted melting and boiling points of 283±11 K and 340±10 K, Cn is indeed a volatile liquid and exhibits a density very similar to that of mercury. However, in stark contrast to mercury and the lighter Group 12 metals, we find bulk Cn to be bound by dispersion and to exhibit a large band gap of 6.4 eV, which is consistent with a noble-gas-like character. This non-group-conforming behavior is eventually traced back to strong scalar-relativistic effects, and in the non-relativistic limit, Cn appears as a common Group 12 metal.

Regularized SCAN functional

We propose modifications to the functional form of the Strongly Constrained and Appropriately Normed (SCAN) density functional to eliminate numerical instabilities. This is necessary to allow reliable, automatic generation of pseudopotentials (including projector augmented-wave potentials). The regularized SCAN is designed to match the original form very closely, and we show that its performance remains comparable.