Force-Free Identification of Minimum-Energy Pathways and Transition States for Stochastic Electronic Structure Theories.

The accurate mapping of potential energy surfaces (PESs) is crucial to our understanding of the numerous physical and chemical processes mediated by atomic rearrangements, such as conformational changes and chemical reactions, and the thermodynamic and kinetic feasibility of these processes. Stochastic electronic structure theories, e.g., Quantum Monte Carlo (QMC) methods, enable highly accurate total energy calculations that in principle can be used to construct the PES. However, their stochastic nature poses a challenge to the computation and use of forces and Hessians, which are typically required in algorithms for minimum-energy pathway (MEP) and transition state (TS) identification, such as the nudged elastic band (NEB) algorithm and its climbing image formulation. Here, we present strategies that utilize the surrogate Hessian line-search method, previously developed for QMC structural optimization, to efficiently identify MEP and TS structures without requiring force calculations at the level of the stochastic electronic structure theory. By modifying the surrogate Hessian algorithm to operate in path-orthogonal subspaces and at saddle points, we show that it is possible to identify MEPs and TSs by using a force-free QMC approach. We demonstrate these strategies via two examples, the inversion of the ammonia (NH3) molecule and the nucleophilic substitution (SN2) reaction F- + CH3F → FCH3 + F-. We validate our results using Density Functional Theory (DFT)- and Coupled Cluster (CCSD, CCSD(T))-based NEB calculations. We then introduce a hybrid DFT-QMC approach to compute thermodynamic and kinetic quantities, free energy differences, rate constants, and equilibrium constants that incorporates stochastically optimized structures and their energies, and show that this scheme improves upon DFT accuracy. Our methods generalize straightforwardly to other systems and other high-accuracy theories that similarly face challenges computing energy gradients, paving the way for highly accurate PES mapping, transition state determination, and thermodynamic and kinetic calculations at significantly reduced computational expense.

Alkali cation stabilization of defects in 2D MXenes at ambient and elevated temperatures.

Transition metal carbides have been adopted in energy storage, conversion, and extreme environment applications. Advancements in their 2D counterparts, known as MXenes, enable the design of unique structures at the ~1 nm thickness scale. Alkali cations have been essential in MXenes manufacturing processing, storage, and applications, however, exact interactions of these cations with MXenes are not fully understood. In this study, using Ti3C2Tx, Mo2TiC2Tx, and Mo2Ti2C3Tx MXenes, we present how transition metal vacancy sites are occupied by alkali cations, and their effect on MXene structure stabilization to control MXene's phase transition. We examine this behavior using in situ high-temperature x-ray diffraction and scanning transmission electron microscopy, ex situ techniques such as atomic-layer resolution secondary ion mass spectrometry, and density functional theory simulations. In MXenes, this represents an advance in fundamentals of cation interactions on their 2D basal planes for MXenes stabilization and applications. Broadly, this study demonstrates a potential new tool for ideal phase-property relationships of ceramics at the atomic scale.

DFT+U and quantum Monte Carlo study of electronic and optical properties of AgNiO2 and AgNi1-xCoxO2 delafossite.

As the only semimetallic d10-based delafossite, AgNiO2 has received a great deal of attention due to both its unique semimetallicity and its antiferromagnetism in the NiO2 layer that is coupled with a lattice distortion. In contrast, other delafossites such as AgCoO2 are insulating. Here we study how the electronic structure of AgNi1-xCoxO2 alloys vary with Ni/Co concentration, in order to investigate the electronic properties and phase stability of the intermetallics. While the electronic and magnetic structure of delafossites have been studied using density functional theory (DFT), earlier studies have not included corrections for strong on-site Coulomb interactions. In order to treat these interactions accurately, in this study we use Quantum Monte Carlo (QMC) simulations to obtain accurate estimates for the electronic and magnetic properties of AgNiO2. By comparison to DFT results we show that these electron correlations are critical to account for. We show that Co doping on the magnetic Ni sites results in a metal-insulator transition near x ∼0.33, and reentrant behavior near x ∼ 0.66.

Development of Heteroatomic Constant Potential Method with Application to MXene-Based Supercapacitors.

We describe a method for modeling constant-potential charges in heteroatomic electrodes, keeping pace with the increasing complexity of electrode composition and nanostructure in electrochemical research. The proposed "heteroatomic constant potential method" (HCPM) uses minimal added parameters to handle differing electronegativities and chemical hardnesses of different elements, which we fit to density functional theory (DFT) partial charge predictions in this paper by using derivative-free optimization. To demonstrate the model, we performed molecular dynamics simulations using both HCPM and conventional constant potential method (CPM) for MXene electrodes with Li-TFSI/AN (lithium bis(trifluoromethane sulfonyl)imide/acetonitrile)-based solvent-in-salt electrolytes. Although the two methods show similar accumulated charge storage on the electrodes, the results indicated that HCPM provides a more reliable depiction of electrode atom charge distribution and charge response compared with CPM, accompanied by increased cationic attraction to the MXene surface. These results highlight the influence of elemental composition on electrode performance, and the flexibility of our HCPM opens up new avenues for studying the performance of diverse heteroatomic electrodes including other types of MXenes, two-dimensional materials, metal-organic frameworks (MOFs), and doped carbonaceous electrodes.

Evaluation of the excitation spectra with diffusion Monte Carlo on an auxiliary bosonic ground state.

We aim to improve upon the variational Monte Carlo (VMC) approach for excitations replacing the Jastrow factor by an auxiliary bosonic (AB) ground state and multiplying it by a fermionic component factor. The instantaneous change in imaginary time of an arbitrary excitation in the original interacting fermionic system is obtained by measuring observables via the ground-state distribution of walkers of an AB system that is subject to an auxiliary effective potential. The effective potential is used to (i) drive the AB system's ground-state configuration space toward the configuration space of the excitations of the original fermionic system and (ii) subtract from a diffusion Monte Carlo (DMC) calculation contributions that can be included in conventional approximations, such as mean-field and configuration interaction (CI) methods. In this novel approach, the AB ground state is treated statistically in DMC, whereas the fermionic component of the original system is expanded in a basis. The excitation energies of the fermionic eigenstates are obtained by sampling a fermion-boson coupling term on the AB ground state. We show that this approach can take advantage of and correct for approximate eigenstates obtained via mean-field calculations or truncated interactions. We demonstrate that the AB ground-state factor incorporates the correlations missed by standard Jastrow factors, further reducing basis truncation errors. Relevant parts of the theory have been tested in soluble model systems and exhibit excellent agreement with exact analytical data and CI and VMC approaches. In particular, for limited basis set expansions and sufficient statistics, AB approaches outperform CI and VMC in terms of basis size for the same systems. The implementation of this method in current codes, despite being demanding, will be facilitated by reusing procedures already developed for calculating ground-state properties with DMC and excitations with VMC.

Existence of La-site antisite defects in [Formula: see text] ([Formula: see text], Fe, and Co) predicted with many-body diffusion quantum Monte Carlo.

The properties of [Formula: see text] (M: 3d transition metal) perovskite crystals are significantly dependent on point defects, whether introduced accidentally or intentionally. The most studied defects in La-based perovskites are the oxygen vacancies and doping impurities on the La and M sites. Here, we identify that intrinsic antisite defects, the replacement of La by the transition metal, M, can be formed under M-rich and O-poor growth conditions, based on results of an accurate many-body ab initio approach. Our fixed-node diffusion Monte Carlo (FNDMC) calculations of [Formula: see text] ([Formula: see text], Fe, and Co) find that such antisite defects can have low formation energies and are magnetized. Complementary density functional theory (DFT)-based calculations show that Mn antisite defects in [Formula: see text] may cause the p-type electronic conductivity. These features could affect spintronics, redox catalysis, and other broad applications. Our bulk validation studies establish that FNDMC reproduces the antiferromagnetic state of [Formula: see text], whereas DFT with PBE (Perdew-Burke-Ernzerhof), SCAN (strongly constrained and appropriately normed), and the LDA+U (local density approximation with Coulomb U) functionals all favor ferromagnetic states, at variance with experiment.

Importance of Nuclear Quantum Effects on Aqueous Electrolyte Transport under Confinement in Ti3C2 MXenes.

Protons display a high chemical activity and strongly affect the charge storage capability in confined interlayer spaces of two-dimensional (2D) materials. As such, an accurate representation of proton dynamics under confinement is important for understanding and predicting charge storage dynamics in these materials. While often ignored in atomistic-scale simulations, nuclear quantum effects (NQEs), e.g., tunneling, can be significant under confinement even at room temperature. Using the thermostatted ring polymer molecular dynamics implementation of path integral molecular dynamics (PIMD) in conjunction with the ReaxFF force field, density functional tight binding (DFTB), and NequIP neural network potential simulations, we investigate the role of NQEs on proton and water transport in bulk water and aqueous electrolytes under confinement in Ti3C2 MXenes. Although overall NQEs are relatively small, especially in bulk, we find that they can alter both quantitative values and qualitative trends on both proton transport and water self-diffusion under confinement relative to classical MD predictions. Therefore, our results suggest the need for NQEs to be considered to simulate aqueous systems under confinement for both qualitative and quantitative accuracy.

Novel boron nitride MXenes as promising energy storage materials.

MXenes are promising materials for rechargeable metal ion batteries and supercapacitors due to their high energy storage capacities, high electrical and ionic conductivities, and ease of synthesis. In this study, we predict the structure and properties of hitherto unexplored Ti-boron nitride MXenes (Ti3BN and Ti3BNT2 where T = F, O, OH) using high-throughput density functional theory calculations. We identify multiple stable structures exhibiting high thermodynamic and mechanical stability with B and N atoms evenly dispersed in the lattice sites. The predicted properties of the BN MXenes show remarkable similarities to their carbide counterparts, including in their metallicity, elastic constants, and cation absorption properties. Significantly, these novel MXene compounds display high lithium storage capacities (>250 mA h g-1), as well as suitability for non-lithium ion storage (Na, K, Ca, Mg), making them attractive candidates for both batteries and supercapacitors. This class of MXenes therefore merits further theoretical and experimental investigation.

Surrogate Hessian accelerated structural optimization for stochastic electronic structure theories.

We present an efficient energy-based method for structural optimization with stochastic electronic structure theories, such as diffusion quantum Monte Carlo (DMC). This method is based on robust line-search energy minimization in reduced parameter space, exploiting approximate but accurate Hessian information from a surrogate theory, such as density functional theory. The surrogate theory is also used to characterize the potential energy surface, allowing for simple but reliable ways to maximize statistical efficiency while retaining controllable accuracy. We demonstrate the method by finding the minimum DMC energy structures of the selected flake-like aromatic molecules, such as benzene, coronene, and ovalene, represented by 2, 6, and 19 structural parameters, respectively. In each case, the energy minimum is found within two parallel line-search iterations. The method is near-optimal for a line-search technique and suitable for a broad range of applications. It is easily generalized to any electronic structure method where forces and stresses are still under active development and implementation, such as diffusion Monte Carlo, auxiliary-field Monte Carlo, and stochastic configuration interaction, as well as deterministic approaches such as the random-phase approximation. Accurate and efficient means of geometry optimization could shed light on a broad class of materials and molecules, showing high sensitivity of induced properties to structural variables.

Investigating the Accuracy of Water Models through the Van Hove Correlation Function.

We present molecular-simulation-based calculations of the Van Hove correlation function (VHF) of water using multiple modeling approaches: classical molecular dynamics with simple three-site nonpolarizable models, with a polarizable model, and with a reactive force field; density functional tight-binding molecular dynamics; and ab initio molecular dynamics. Due to the many orders of magnitude difference in the computational cost of these approaches, we investigate how small and short the simulations can be while still yielding sufficiently accurate and interpretable results for the VHF. We investigate the accuracy of the different models by comparing them to recently published inelastic X-ray scattering measurements of the VHF. We find that all of the models exhibit qualitative agreement with the experiments, and in some models and for some properties, the agreement is quantitative. This work lays the foundation for future simulation approaches to calculating the VHF for aqueous solutions in bulk and under nanoconfinement.

Toward a systematic improvement of the fixed-node approximation in diffusion Monte Carlo for solids-A case study in diamond.

While Diffusion Monte Carlo (DMC) is in principle an exact stochastic method for ab initio electronic structure calculations, in practice, the fermionic sign problem necessitates the use of the fixed-node approximation and trial wavefunctions with approximate nodes (or zeros). This approximation introduces a variational error in the energy that potentially can be tested and systematically improved. Here, we present a computational method that produces trial wavefunctions with systematically improvable nodes for DMC calculations of periodic solids. These trial wavefunctions are efficiently generated with the configuration interaction using a perturbative selection made iteratively (CIPSI) method. A simple protocol in which both exact and approximate results for finite supercells are used to extrapolate to the thermodynamic limit is introduced. This approach is illustrated in the case of the carbon diamond using Slater-Jastrow trial wavefunctions including up to one million Slater determinants. Fixed-node DMC energies obtained with such large expansions are much improved, and the fixed-node error is found to decrease monotonically and smoothly as a function of the number of determinants in the trial wavefunction, a property opening the way to a better control of this error. The cohesive energy extrapolated to the thermodynamic limit is in close agreement with the estimated experimental value. Interestingly, this is also the case at the single-determinant level, thus, indicating a very good error cancellation in carbon diamond between the bulk and atomic total fixed-node energies when using single-determinant nodes.

Perspectives on van der Waals Density Functionals: The Case of TiS2.

The van der Waals interaction is of foundational importance for a wide variety of physical systems. In particular, van der Waals forces lie at the heart of potential device technologies that may be realized from the functional organization of layered two-dimensional (2D) nanomaterials. For intermediate to large-scale applications modeling, van der Waals density functionals have become the de facto choice for first-principles calculations. In particular, the vdW-DF family of functionals have provided a systematic approach to this theoretically challenging problem. While much progress has been made, there remains room for improvement in the microscopic description of vdW forces from these density functionals. In this work, we compute benchmark results for the binding energy and the electronic density response to binding in TiS2 via accurate diffusion quantum Monte Carlo calculations. We compare these benchmark data to results obtained from local, semilocal, and van der Waals functionals. In particular, we gauge the quality of the original vdW-DF/vdW-DF2 functionals, as well as updated variants such as vdW-DF-C09, vdW-DF-optB88, vdW-DF-optB86b, and vdW-DF2-B86R. We find a close relationship between the accuracy of predicted interlayer separation distances and binding energies for TiS2, with the vdW-DF-optB88 functional performing very well in terms of both quantities. In general, the more recently developed functionals are systematic improvements over older ones. However, when considering the response of the electron density to binding, we find that local-density approximation (LDA) and PBEsol generally outperform the vdW-DF functionals in describing the interlayer charge accumulation with vdW-DF-C09 variants performing the best overall.

Metal-insulator transition tuned by oxygen vacancy migration across TiO2/VO2 interface.

Oxygen defects are essential building blocks for designing functional oxides with remarkable properties, ranging from electrical and ionic conductivity to magnetism and ferroelectricity. Oxygen defects, despite being spatially localized, can profoundly alter global properties such as the crystal symmetry and electronic structure, thereby enabling emergent phenomena. In this work, we achieved tunable metal-insulator transitions (MIT) in oxide heterostructures by inducing interfacial oxygen vacancy migration. We chose the non-stoichiometric VO2-δ as a model system due to its near room temperature MIT temperature. We found that depositing a TiO2 capping layer on an epitaxial VO2 thin film can effectively reduce the resistance of the insulating phase in VO2, yielding a significantly reduced ROFF/RON ratio. We systematically studied the TiO2/VO2 heterostructures by structural and transport measurements, X-ray photoelectron spectroscopy, and ab initio calculations and found that oxygen vacancy migration from TiO2 to VO2 is responsible for the suppression of the MIT. Our findings underscore the importance of the interfacial oxygen vacancy migration and redistribution in controlling the electronic structure and emergent functionality of the heterostructure, thereby providing a new approach to designing oxide heterostructures for novel ionotronics and neuromorphic-computing devices.

Effects of Surface Terminations of 2D Bi2WO6 on Photocatalytic Hydrogen Evolution from Water Splitting.

Two-dimensional (2D)-structured photocatalysts with atomically thin layers not only have the potential to enhance hydrogen generation efficiency but also allow more direct investigations of the effects of surface terminations on photocatalytic activity. Taking 2D Bi2WO6 as a model, we found that the configuration of bilayer Bi2O2 sandwiched by alternating WO4 layers enabled the thermodynamic driving potential for photocatalytic hydrogen evolution. Without Pt deposition, the H2 generation efficiency can reach to 56.9 µmol/g/h by 2D Bi2WO6 as compared with no activity of Bi2WO6 nanocrystals under simulated solar light. This configuration is easily functionalized by adsorption of Cl-/Br- to form Bi-Cl/Bi-Br bonds, which leads to the decrease of recombination in photogenerated charge carriers and narrower band gaps. This work highlights an effective way to design photocatalysts with efficient hydrogen evolution by tuning the surface terminations.

Exascale applications: skin in the game.

As noted in Wikipedia, skin in the game refers to having 'incurred risk by being involved in achieving a goal', where 'skin is a synecdoche for the person involved, and game is the metaphor for actions on the field of play under discussion'. For exascale applications under development in the US Department of Energy Exascale Computing Project, nothing could be more apt, with the skin being exascale applications and the game being delivering comprehensive science-based computational applications that effectively exploit exascale high-performance computing technologies to provide breakthrough modelling and simulation and data science solutions. These solutions will yield high-confidence insights and answers to the most critical problems and challenges for the USA in scientific discovery, national security, energy assurance, economic competitiveness and advanced healthcare. This article is part of a discussion meeting issue 'Numerical algorithms for high-performance computational science'.

Proton Redox and Transport in MXene-Confined Water.

The redox reaction of intercalated protons is key to the pseudocapacitance of MXenes (two-dimensional (2D) carbides and nitrides) in H2SO4. However, an atomistic understanding of proton redox and transfer in water confined between MXene layers is still lacking. Here, we use first-principles molecular dynamics (FPMD) simulations to reveal the proton-transfer mechanism in MXene-confined water layers of different thicknesses by using O-terminated Ti3C2 as a prototypical MXene. We found that the proton redox process takes place reversibly between surface -O sites and interfacial water molecules, intermitted by the more frequent in-water proton-transfer events. The surface redox rate is much higher in the highly confined one-layer water than in the two or three layers of water. Proton mobility increases with the water-layer number and already approaches the bulk value in the three-layer water. The proton transfer still follows the Eigen-Zundel-Eigen mechanism in the 2D-like confined water (regardless of the thickness) as in the 3D bulk water via the special pair dance. Our model in the case of two layers of water is in excellent agreement with the experimental interlayer spacing after charging the Ti3C2O2 electrode in H2SO4. Our finding from FPMD of fast surface redox and in-water transfer for the intercalated protons implies that other processes such as the intercalating step are likely the bottleneck for the ionic transport.

Computational Discovery and Design of MXenes for Energy Applications: Status, Successes, and Opportunities.

MXenes (Mn+1Xn, e.g., Ti3C2) are the largest 2D material family developed in recent years. They exhibit significant potential in the energy sciences, particularly for energy storage. In this review, we summarize the progress of the computational work regarding the theoretical design of new MXene structures and predictions for energy applications including their fundamental, energy storage, and catalytic properties. We also outline how high-throughput computation, big data, and machine-learning techniques can help broaden the MXene family. Finally, we present some of the major remaining challenges and future research directions needed to mature this novel materials family.

Edge Segregated Polymorphism in 2D Molybdenum Carbide.

Molybdenum carbide (Mo2 C), a class of unterminated MXene, is endowed with rich polymorph chemistry, but the growth conditions of the various polymorphs are not understood. Other than the most commonly observed T-phase Mo2 C, little is known about other phases. Here, Mo2 C crystals are successfully grown consisting of mixed polymorphs and polytypes via a diffusion-mediated mechanism, using liquid copper as the diffusion barrier between the elemental precursors of Mo and C. By controlling the thickness of the copper diffusion barrier layer, the crystal growth can be controlled between a highly uniform AA-stacked T-phase Mo2 C and a "wedding cake" like Mo2 C crystal with spatially delineated zone in which the Bernal-stacked Mo2 C predominate. The atomic structures, as well as the transformations between distinct stackings, are simulated and analyzed using density functional theory (DFT)-based calculations. Bernal-stacked Mo2 C has a d band closer to the Fermi energy, leading to a promising performance in catalysis as verified in hydrogen evolution reaction (HER).

Hybrid DFT investigation of the energetics of Mg ion diffusion in α-MoO3.

Rechargeable batteries that utilize divalent Mg ions as the charge carrier species can in principle achieve substantially greater volumetric energy densities than conventional Li-ion batteries. One significant impediment to the development of commercially viable Mg-ion batteries is the slow rate of Mg ion diffusion through otherwise promising cathode materials. Accurate prediction of the activation energies associated with this diffusion process using density functional theory (DFT) is especially challenging due to self-interaction errors intrinsic to DFT that lead to over-delocalization of the d-electrons. One effective but highly computationally demanding approach to reducing self-interaction errors is the use of hybrid functionals, which incorporate a fraction of exact Hartree-Fock exchange. In this work, we assess the effects of exact exchange on computed activation energies for ion diffusion in one potential cathode material, α-MoO3. In contrast to previous studies that primarily utilize non-hybrid functionals, we perform nudged elastic band calculations in which the nuclear coordinates are fully converged using both hybrid functionals and k-point sampling. It is found that while non-hybrid functionals indicate the existence of thermodynamically accessible channels for bulk Mg ion diffusion in all three dimensions, hybrid functionals predict that some of these channels are largely inaccessible under typical charge/discharge conditions. Furthermore, it is demonstrated that certain commonly used approximations for incorporating the effects of Hartree-Fock exchange are inadequate for this system, including DFT+U calculations and the use of single-point hybrid calculations using atomic positions obtained using non-hybrid functionals.

An efficient hybrid orbital representation for quantum Monte Carlo calculations.

The scale and complexity of the quantum system to which real-space quantum Monte Carlo (QMC) can be applied in part depends on the representation and memory usage of the trial wavefunction. B-splines, the computationally most efficient basis set, can have memory requirements exceeding the capacity of a single computational node. This situation has traditionally forced a difficult choice of either using slow internode communication or a potentially less accurate but smaller basis set such as Gaussians. Here, we introduce a hybrid representation of the single particle orbitals that combine a localized atomic basis set around atomic cores and B-splines in the interstitial regions to reduce the memory usage while retaining the high speed of evaluation and either retaining or increasing overall accuracy. We present a benchmark calculation for NiO demonstrating a superior accuracy while using only one eighth of the memory required for conventional B-splines. The hybrid orbital representation therefore expands the overall range of systems that can be practically studied with QMC.