Discovering correlated fermions using quantum Monte Carlo

Diffusion Monte Carlo method for barrier heights of multiple proton exchanges and complexation energies in small water, ammonia, and hydrogen fluoride clusters

Proton exchange reactions are of key importance in many processes in water. However, it is nontrivial to achieve reliable barrier heights for multiple proton exchanges and complexation energies in hydrogen-bonded systems theoretically. Performance of the fixed-node diffusion quantum Monte Carlo (FN-DMC) with the single-Slater-Jastrow trial wavefunction on total energies, barrier heights of multiple proton exchanges, and complexation energies of small water, ammonia, and hydrogen fluoride clusters is investigated in this study. Effects of basis sets and those of locality approximation (LA), T-move approximation (T-move), and determinant localization approximation (DLA) schemes in dealing with the nonlocal part of pseudopotentials on FN-DMC results are evaluated. According to our results, diffuse basis functions are important in achieving reliable barrier heights and complexation energies with FN-DMC, although the cardinal number of the basis set is more important than diffuse basis functions on total energies of these systems. Our results also show that the time step bias with DLA and LA is smaller than T-move; however, the time step bias of DMC energies with respect to time steps using the T-move is roughly linear up to 0.06 a.u., while this is not the case with LA and DLA. Barrier heights and complexation energies with FN-DMC using these three schemes are always within chemical accuracy. Taking into account the fact that T-move and DLA are typically more stable than LA, FN-DMC calculations with the T-move or DLA scheme and basis sets containing diffuse basis functions are suggested for barrier heights of multiple proton exchanges and complexation energies of hydrogen-bonded clusters.

Dynamic and Nondynamic Electron Correlation Energy Decomposition Based on the Node of the Hartree-Fock Slater Determinant

Distinguishing between dynamic and nondynamic electron correlation energy is a fundamental concept in quantum chemistry. It can be challenging to make a clear distinction between the two types of correlation energy or to determine their actual contributions in specific cases using wave function theory. This is because both single-reference and multireference methods cover both types of correlation energy to some extent. Fixed-node diffusion quantum Monte Carlo (FNDMC) accurately covers dynamic correlations, but it is limited in overall accuracy by the node of the trial wave function. We introduce a methodology for partitioning an exact electron correlation energy into its dynamic and nondynamic components. This is accomplished by restricting a ground-state solution from sharing its node with a spin-restricted Hartree-Fock Slater determinant. The FNDMC method is used as a tool to conveniently project out a lowest-energy state obeying such a boundary condition. The proposed approach provides an unambiguous and useful procedure for separating electron correlation energy, as demonstrated on multiple systems, including the He atom, bond breaking of H2, the parametric H2-H2 system, the Be-Ne atomic series with low- and high-spin states for C, N, and O atoms, and small molecules such as BH, HF, and CO at both equilibrium and elongated configurations, respectively.

PyQMC: An all-Python real-space quantum Monte Carlo module in PySCF

We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.

Benchmarking fundamental gap of Sc2C(OH)2 MXene by many-body methods

Sc₂C(OH)₂ is a prototypical non-magnetic member of MXenes, a promising transition-metal-based 2D material family, with a direct bandgap. We provide here a benchmark of its fundamental gap Δ obtained from many-body GW and fixed-node diffusion Monte Carlo methods. Both approaches independently arrive at a similar value of Δ ∼ 1.3 eV, suggesting the validity of both methods. Such a bandgap makes Sc₂C(OH)₂ a 2D semiconductor suitable for optoelectronic applications. The absorbance spectra and the first exciton binding energy (0.63 eV), based on the Bethe-Salpeter equation, are presented as well. The reported results may serve to delineate experimental uncertainties and enable selection of reasonable approximations such as density functional theory functionals, for use in modeling of related MXenes.

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

We present a stable and systematically improvable quantum Monte Carlo (QMC) approach to calculating excited-state energies, which we implement using our fast randomized iteration method for the full configuration interaction problem (FCI-FRI). Unlike previous excited-state quantum Monte Carlo methods, our approach, which is based on an asymmetric variant of subspace iteration, avoids the use of dot products of random vectors and instead relies upon trial vectors to maintain orthogonality and estimate eigenvalues. By leveraging recent advances, we apply our method to calculate ground- and excited-state energies of challenging molecular systems in large active spaces, including the carbon dimer with 8 electrons in 108 orbitals (8e,108o), an oxo-Mn(salen) transition metal complex (28e,28o), ozone (18e,87o), and butadiene (22e,82o). In the majority of these test cases, our approach yields total excited-state energies that agree with those from state-of-the-art methods─including heat-bath CI, the density matrix renormalization group approach, and FCIQMC─to within sub-milliHartree accuracy. In all cases, estimated excitation energies agree to within about 0.1 eV.

Barrier heights, reaction energies and bond dissociation energies for RH + HO2 reactions with coupled-cluster theory, density functional theory and diffusion quantum Monte Carlo methods

Hydrogen abstraction reactions by the HO₂ radical from hydrocarbon molecules are an important class of reactions in the autoignition of hydrocarbon fuels. Performance of DLPNO-CC and DFT methods using three hybrids and four double hybrids as well as FN-DMC with the single-Slater-Jastrow trial wavefunction on barrier heights and reaction energies of RH + HO₂ reactions as well as bond dissociation energies of the involved X-H molecules is evaluated by comparison with the highly accurate CCSD(T)-F12b/CBS results in this study. Our results show that the DLPNO-CCSD(T)-F12 method can achieve highly accurate barrier heights, reaction energies and X-H bond energies for RH + HO₂ reactions at a relatively low computational cost, and it is applicable to the H-abstraction reactions of larger molecules. Among all DFAs, MN15 and the employed double hybrids can achieve accurate barrier heights and reaction energies with MADs of less than or around 2 kJ mol^-1, but their error on X-H bond energies is more pronounced. Only DSD-BLYP and DSD-PBEB95 can provide X-H bond energies with MADs less than 4 kJ mol^-1. Considering dispersion correction in DFT calculations does not improve these barrier heights and reaction energies. The error of FN-DMC on barrier heights and reaction energies is slightly larger than that of MN15 and those of double hybrids, but it can achieve results within chemical accuracy for these reactions and the X-H bond energies.

Ground-state properties of the narrowest zigzag graphene nanoribbon from quantum Monte Carlo and comparison with density functional theory

By means of quantum Monte Carlo (QMC) calculations from first-principles, we study the ground-state properties of the narrowest zigzag graphene nanoribbon with an infinite linear acene structure. We show that this quasi-one-dimensional system is correlated and its ground state is made of localized π electrons whose spins are antiferromagnetically ordered. The antiferromagnetic (AFM) stabilization energy [36(3) meV per carbon atom] and the absolute magnetization [1.13(0.11) μ B per unit cell] predicted by QMC are sizable, and they suggest the survival of antiferromagnetic correlations above room temperature. These values can be reproduced to some extent by density functional theory (DFT) within the DFT+U framework or by using hybrid functionals. Based on our QMC results, we then provide the strength of Hubbard repulsion in DFT+U suitable for this class of systems.

Stochastic Vector Techniques in Ground-State Electronic Structure

We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss highly effective techniques to reduce statistical errors. Finally, we review the use of stochastic vector techniques for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Machine Learning Discovery of Computational Model Efficacy Boundaries

Computational models are formulated in hierarchies of variable fidelity, often with no quantitative rule for defining the fidelity boundaries. We have constructed a dataset from a wide range of atomistic computational models to reveal the accuracy boundary between higher-fidelity models and a simple, lower-fidelity model. The symbolic decision boundary is discovered by optimizing a support vector machine on the data through iterative feature engineering. This data-driven approach reveals two important results: (i) a symbolic rule emerges that is independent of the algorithm, and (ii) the symbolic rule provides a deeper understanding of the fidelity boundary. Specifically, our dataset is composed of radial distribution functions from seven high-fidelity methods that cover wide ranges in the features (element, density, and temperature); high-fidelity results are compared with a simple pair-potential model to discover the nonlinear combination of the features, and the machine learning approach directly reveals the central role of atomic physics in determining accuracy.

Itinerant-Electron Magnetism: The Importance of Many-Body Correlations

Do electrons become ferromagnetic just because of their repulsive Coulomb interaction? Our calculations on the three-dimensional electron gas imply that itinerant ferromagnetism of delocalized electrons without lattice and band structure, the most basic model considered by Stoner, is suppressed due to many-body correlations as speculated already by Wigner, and a possible ferromagnetic transition lowering the density is precluded by the formation of the Wigner crystal.

Open System Tensor Networks and Kramers' Crossover for Quantum Transport

Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes-such as quantum transport or quenches-where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.

Adsorption and diffusion of sulfur on the (111), (100), (110), and (211) surfaces of FCC metals: Density functional theory calculations

We have studied the adsorption and diffusion of sulfur at the low-coverage regime of 0.25 ML on the (111), (100), (110), and (211) surfaces of Ni, Cu, Rh, Pd, Ag, Ir, Pt, and Au using density functional theory calculations. Sulfur adsorbed preferentially on three-fold or four-fold high-coordination sites over most of the studied surfaces. On the Ir(110), Pt(110), and Au(110) surfaces, sulfur is more stable on the two-fold sites. Calculations of the minimum energy diffusion pathway show that the energy barrier for the surface diffusion of sulfur depends on the orientation and nature of the metal surfaces. On the (100), sulfur shows the highest diffusion energy, ranging from 0.47 eV in Au(100) to 1.22 eV in Pd(100). In the (110) surface, the diffusion of sulfur is along the channel for Ni, Cu, Rh, Pd, and Ag, and across the channel for Ir, Pt, and Au. In the case of the (211) surfaces, the diffusion is preferentially along the terrace or step-edge sites. Our work provides data for the adsorption of sulfur on many surfaces not previously reported. The present work is a reference point for future computational studies of sulfur and sulfur-containing molecules absorbed on face center cubic metal surfaces.

Toward a predictive theory of correlated materials

Correlated electron materials display a rich variety of notable properties ranging from unconventional superconductivity to metal-insulator transitions. These properties are of interest from the point of view of applications but are hard to treat theoretically, as they result from multiple competing energy scales. Although possible in more weakly correlated materials, theoretical design and spectroscopy of strongly correlated electron materials have been a difficult challenge for many years. By treating all the relevant energy scales with sufficient accuracy, complementary advances in Green's functions and quantum Monte Carlo methods open a path to first-principles computational property predictions in this class of materials.

Kinetic energy classification and smoothing for compact B-spline basis sets in quantum Monte Carlo

Quantum Monte Carlo calculations of defect properties of transition metal oxides have become feasible in recent years due to increases in computing power. As the system size has grown, availability of on-node memory has become a limiting factor. Saving memory while minimizing computational cost is now a priority. The main growth in memory demand stems from the B-spline representation of the single particle orbitals, especially for heavier elements such as transition metals where semi-core states are present. Despite the associated memory costs, splines are computationally efficient. In this work, we explore alternatives to reduce the memory usage of splined orbitals without significantly affecting numerical fidelity or computational efficiency. We make use of the kinetic energy operator to both classify and smooth the occupied set of orbitals prior to splining. By using a partitioning scheme based on the per-orbital kinetic energy distributions, we show that memory savings of about 50% is possible for select transition metal oxide systems. For production supercells of practical interest, our scheme incurs a performance penalty of less than 5%.

QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids

QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.