Enhanced Twist-Averaging Technique for Magnetic Metals: Applications Using Quantum Monte Carlo.

We propose an improved twist-averaging (TA) scheme for quantum Monte Carlo methods that use converged Kohn-Sham or Hartree-Fock orbitals as the reference. This TA technique is tailored to sample the Brillouin zone of magnetic metals, although it naturally extends to nonmagnetic (NM) conducting systems. The proposed scheme aims to reproduce the reference magnetization and achieves charge neutrality by construction, thus avoiding the large energy fluctuations and the postprocessing needed to correct the energies. It shows the most robust convergence of total energy and magnetism to the thermodynamic limit (TDL) when compared to four other TA schemes. Diffusion Monte Carlo applications are shown on NM Al and ferromagnetic α-Fe. The cohesive energy of Al in the TDL shows an excellent agreement with the experimental result. Furthermore, the magnetic moments in α-Fe exhibit rapid convergence with an increasing number of twists.

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.

Predictions of delafossite-hosted honeycomb and kagome phases.

Delafossites, typically denoted by the formula ABO2, are a class of layered materials that exhibit a wide range of electronic and optical properties. Recently, the idea of modifying these delafossites into ordered kagome or honeycomb phases via strategic doping has emerged as a potential way to tailor these properties. In this study, we use high-throughput density functional theory calculations to explore many possible candidate kagome and honeycomb phases by considering dopants selected from the parent compounds of known ternary delafossite oxides from the inorganic crystal structure database. Our results indicate that while A-site in existing delafossites can host a limited range of elemental specifies, and display a low propensity for mixing or ordering, the oxide sub-units in the BO2 much more readily admit guest species. Our study identifies four candidate B-site kagome and fifteen candidate B-site honeycombs with a formation energy more than 50 meV f.u.-1 below other competing phases. The ability to predict and control the formation of these unique structures offers exciting opportunities in materials design, where innovative properties can be engineered through the selection of specific dopants. A number of these constitute novel correlated metals, which may be of interest for subsequent efforts in synthesis. These novel correlated metals may have significant implications for quantum computing, spintronics, and high-temperature superconductivity, thus inspiring future experimental synthesis and characterization of these proposed materials.

Locality error free effective core potentials for 3d transition metal elements developed for the diffusion Monte Carlo method.

Pseudopotential locality errors have hampered the applications of the diffusion Monte Carlo (DMC) method in materials containing transition metals, in particular oxides. We have developed locality error free effective core potentials, pseudo-Hamiltonians, for transition metals ranging from Cr to Zn. We have modified a procedure published by some of us in Bennett et al. [J. Chem. Theory Comput. 18, 828 (2022)]. We carefully optimized our pseudo-Hamiltonians and achieved transferability errors comparable to the best semilocal pseudopotentials used with DMC but without incurring in locality errors. Our pseudo-Hamiltonian set (named OPH23) bears the potential to significantly improve the accuracy of many-body-first-principles calculations in fundamental science research of complex materials involving transition metals.

Stacking Faults and Topological Properties in MnBi2Te4: Reconciling Gapped and Gapless States.

Despite theoretical predictions of a gapped surface state for the magnetic topological insulator MnBi2Te4 (MBT), there has been a series of experimental evidence pointing toward gapless states. Here, we theoretically explore how stacking faults could influence the topological characteristics of MBT. We envisage a scenario that a stacking fault exists at the surface of MBT, causing the uppermost layer to deviate from the ground state and its interlayer separation to be expanded. This stacking fault with modulated interlayer couplings hosts a nearly gapless state within the topmost layer due to charge redistribution as the outermost layer recedes. Furthermore, we find evidence of spin-momentum locking and preservation of weak band inversion in the gapless surface state, suggesting the nontrivial topological surface states in the presence of the stacking fault. Our findings provide a plausible elucidation to the long-standing conundrum of reconciling the observation of gapped and gapless states on MBT surfaces.

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.

Emergent Magnetism with Continuous Control in the Ultrahigh-Conductivity Layered Oxide PdCoO2.

The current challenge to realizing continuously tunable magnetism lies in our inability to systematically change properties, such as valence, spin, and orbital degrees of freedom, as well as crystallographic geometry. Here, we demonstrate that ferromagnetism can be externally turned on with the application of low-energy helium implantation and can be subsequently erased and returned to the pristine state via annealing. This high level of continuous control is made possible by targeting magnetic metastability in the ultrahigh-conductivity, nonmagnetic layered oxide PdCoO2 where local lattice distortions generated by helium implantation induce the emergence of a net moment on the surrounding transition metal octahedral sites. These highly localized moments communicate through the itinerant metal states, which trigger the onset of percolated long-range ferromagnetism. The ability to continuously tune competing interactions enables tailoring precise magnetic and magnetotransport responses in an ultrahigh-conductivity film and will be critical to applications across spintronics.

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.

A Quantum Monte Carlo Study of the Structural, Energetic, and Magnetic Properties of Two-Dimensional H and T Phase VSe2.

Previous works have controversially claimed near-room-temperature ferromagnetism in two-dimensional (2D) VSe2, with conflicting results throughout the literature. These discrepancies in magnetic properties between both phases (T and H) of 2D VSe2 are most likely due to the structural parameters being coupled to the magnetic properties. Specifically, both phases have a close lattice match and similar total energies, which makes it difficult to determine which phase is being observed experimentally. In this study, we used a combination of density functional theory, highly accurate diffusion Monte Carlo (DMC), and a surrogate Hessian line-search optimization technique to resolve the previously reported discrepancy in structural parameters and relative phase stability. With DMC accuracy, we determined the free-standing geometry of both phases and constructed a phase diagram. Our findings demonstrate the successes of the DMC method coupled with the surrogate Hessian structural optimization technique when applied to a 2D magnetic system.

Toward DMC Accuracy Across Chemical Space with Scalable Δ-QML.

In the past decade, quantum diffusion Monte Carlo (DMC) has been demonstrated to successfully predict the energetics and properties of a wide range of molecules and solids by numerically solving the electronic many-body Schrödinger equation. With O(N3) scaling with the number of electrons N, DMC has the potential to be a reference method for larger systems that are not accessible to more traditional methods such as CCSD(T). Assessing the accuracy of DMC for smaller molecules becomes the stepping stone in making the method a reference for larger systems. We show that when coupled with quantum machine learning (QML)-based surrogate methods, the computational burden can be alleviated such that quantum Monte Carlo (QMC) shows clear potential to undergird the formation of high-quality descriptions across chemical space. We discuss three crucial approximations necessary to accomplish this: the fixed-node approximation, universal and accurate references for chemical bond dissociation energies, and scalable minimal amons-set-based QML (AQML) models. Numerical evidence presented includes converged DMC results for over 1000 small organic molecules with up to five heavy atoms used as amons and 50 medium-sized organic molecules with nine heavy atoms to validate the AQML predictions. Numerical evidence collected for Δ-AQML models suggests that already modestly sized QMC training data sets of amons suffice to predict total energies with near chemical accuracy throughout chemical space.

Phase Transition Dynamics in a Complex Oxide Heterostructure.

Understanding the behavior of defects in the complex oxides is key to controlling myriad ionic and electronic properties in these multifunctional materials. The observation of defect dynamics, however, requires a unique probe-one sensitive to the configuration of defects as well as its time evolution. Here, we present measurements of oxygen vacancy ordering in epitaxial thin films of SrCoO_{x} and the brownmillerite-perovskite phase transition employing x-ray photon correlation spectroscopy. These and associated synchrotron measurements and theory calculations reveal the close interaction between the kinetics and the dynamics of the phase transition, showing how spatial and temporal fluctuations of heterointerface evolve during the transformation process. The energetics of the transition are correlated with the behavior of oxygen vacancies, and the dimensionality of the transformation is shown to depend strongly on whether the phase is undergoing oxidation or reduction. The experimental and theoretical methods described here are broadly applicable to in situ measurements of dynamic phase behavior and demonstrate how coherence may be employed for novel studies of the complex oxides as enabled by the arrival of fourth-generation hard x-ray coherent light sources.

Machine Learning Diffusion Monte Carlo Energies.

We present two machine learning methodologies that are capable of predicting diffusion Monte Carlo (DMC) energies with small data sets (≈60 DMC calculations in total). The first uses voxel deep neural networks (VDNNs) to predict DMC energy densities using Kohn-Sham density functional theory (DFT) electron densities as input. The second uses kernel ridge regression (KRR) to predict atomic contributions to the DMC total energy using atomic environment vectors as input (we used atom-centered symmetry functions, atomic environment vectors from the ANI models, and smooth overlap of atomic positions). We first compare the methodologies on pristine graphene lattices, where we find that the KRR methodology performs best in comparison to gradient boosted decision trees, random forest, Gaussian process regression, and multilayer perceptrons. In addition, KRR outperforms VDNNs by an order of magnitude. Afterward, we study the generalizability of KRR to predict the energy barrier associated with a Stone-Wales defect. Lastly, we move from 2D to 3D materials and use KRR to predict total energies of liquid water. In all cases, we find that the KRR models are more accurate than Kohn-Sham DFT and all mean absolute errors are less than chemical accuracy.

Correlative Nanoscale Imaging of Strained hBN Spin Defects.

Spin defects like the negatively charged boron vacancy color center (VB-) in hexagonal boron nitride (hBN) may enable new forms of quantum sensing with near-surface defects in layered van der Waals heterostructures. Here, the effect of strain on VB- color centers in hBN is revealed with correlative cathodoluminescence and photoluminescence microscopies. Strong localized enhancement and redshifting of the VB- luminescence is observed at creases, consistent with density functional theory calculations showing VB- migration toward regions with moderate uniaxial compressive strain. The ability to manipulate spin defects with highly localized strain is critical to the development of practical 2D quantum devices and quantum sensors.

A new generation of effective core potentials from correlated and spin-orbit calculations: Selected heavy elements.

We introduce new correlation consistent effective core potentials (ccECPs) for the elements I, Te, Bi, Ag, Au, Pd, Ir, Mo, and W with 4d, 5d, 6s, and 6p valence spaces. These ccECPs are given as a sum of spin-orbit averaged relativistic effective potential (AREP) and effective spin-orbit (SO) terms. The construction involves several steps with increasing refinements from more simple to fully correlated methods. The optimizations are carried out with objective functions that include weighted many-body atomic spectra, norm-conservation criteria, and SO splittings. Transferability tests involve molecular binding curves of corresponding hydride and oxide dimers. The constructed ccECPs are systematically better and in a few cases on par with previous effective core potential (ECP) tables on all tested criteria and provide a significant increase in accuracy for valence-only calculations with these elements. Our study confirms the importance of the AREP part in determining the overall quality of the ECP even in the presence of sizable spin-orbit effects. The subsequent quantum Monte Carlo calculations point out the importance of accurate trial wave functions that, in some cases (mid-series transition elements), require treatment well beyond a single-reference.

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.

High Accuracy Transition Metal Effective Cores for the Many-Body Diffusion Monte Carlo Method.

Practical applications of the real-space diffusion Monte Carlo (DMC) method require the removal of core electrons, where currently localization approximations of semilocal potentials are generally used in the projector. Accurate calculations of complex solids and large molecules demand minimizing the impact of approximated atomic cores. Prior works have shown that the errors from such approximations can be sizable in both finite and periodic systems. In this work, we show that a class of differential pseudopotentials, known as pseudo-Hamiltonians, can be constructed for the 3d transition metal atoms, entirely removing the need for any localization scheme in the DMC projector. As a proof of principle, we demonstrate the approach for the case of Co. In order to minimize errors in the pseudo-Hamiltonian at the many-body level, we generalize the recently proposed correlation-consistent pseudopotential generation scheme to successively close semilocal representations of the differential potentials. Our generation scheme successfully produces potentials tailored specifically for real space projector quantum Monte Carlo methods with low error at the many-body level, i.e., with many-body scattering properties very close to relativistic all-electron results. In particular, we show that the agreement with respect to atomic and molecular quantities reach chemical accuracy in many cases─on par with the most accurate semilocal pseudopotentials available. Further, our pseudo-Hamiltonian generation scheme utilizes standard quantum chemistry codes designed only to work with semilocal pseudopotentials, enabling straightforward generation of pseudo-Hamiltonians for additional elements in future works.

Toward quantum Monte Carlo forces on heavier ions: Scaling properties.

Quantum Monte Carlo (QMC) forces have been studied extensively in recent decades because of their importance with spectroscopic observables and geometry optimization. Here, we benchmark the accuracy and computational cost of QMC forces. The zero-variance zero-bias (ZVZB) force estimator is used in standard variational and diffusion Monte Carlo simulations with mean-field based trial wavefunctions and atomic pseudopotentials. Statistical force uncertainties are obtained with a recently developed regression technique for heavy tailed QMC data [P. Lopez Rios and G. J. Conduit, Phys. Rev. E 99, 063312 (2019)]. By considering selected atoms and dimers with elements ranging from H to Zn (1 ≤ Zeff ≤ 20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Zeff, increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Zeff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Zeff 6.5(3) for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Zeff -2, insensitive to model assumptions or the use of the "space warp" variance-reduction technique. Our results predict the practical cost of obtaining forces for a range of materials, such as transition metal oxides where QMC forces have yet to be applied, and underscore the importance of further developing force variance-reduction techniques, particularly for atoms with high Zeff.

From Molecules to Solids: A vdW-DF-C09 Case Study of the Mercury Dihalides.

The mercury dihalides show a remarkable diversity in the structural preferences in their minimum energy structure types, spanning molecular to strongly bound ionic solids. A challenge in the development of density functional methods for extended systems is to arrive at strategies that serve equally well such a broad range of bonding modes or structural preferences. The chemical bonding and the stabilities of mercury dihalides and the general utility and reliability of the van der Waals density functional with C09 exchange (vdW-DF-C09) in predicting or describing the energetics and structural preferences in these metal dihalides is examined. We show that, in contrast with the uncorrected generalized gradient approximation of the Perdew-Burke-Erzenhoff (PBE) exchange-correlation functional, qualitative and quantitative patterns in the bonding of the mercury dihalide solids are well reproduced with vdW-DF-C09 for the full series of HgX2 systems for X = F, Cl, Br, and I. The possible existence of a low-temperature cotunnite polymorph for HgF2 and PbF2 is posited.

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.