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.

Quantification of electron correlation for approximate quantum calculations.

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrödinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains.

Frontiers of stochastic electronic structure calculations.

In recent years there has been a rapid growth in the development and application of new stochastic methods in electronic structure. These methods are quite diverse, from many-body wave function techniques in real space or determinant space to being used to sum perturbative expansions. This growth has been spurred by the more favorable scaling with the number of electrons and often better parallelization over large numbers of central processing unit (CPU) cores or graphical processing units (GPUs) than for high-end non-stochastic wave function based methods.

Excited states in variational Monte Carlo using a penalty method.

In this article, the authors present a technique using variational Monte Carlo to solve for excited states of electronic systems. This technique is based on enforcing orthogonality to lower energy states, which results in a simple variational principle for the excited states. Energy optimization is then used to solve for the excited states.

Identifying materials with charge-spin physics using charge-spin susceptibility computed from first principles.

The authors present a quantity termed charge-spin susceptibility, which measures the charge response to spin degrees of freedom in strongly correlated materials. This quantity is simple to evaluate using both standard density functional theory and many-body electronic structure techniques, enabling comparison between different levels of theory. A benchmark on 28 layered magnetic materials shows that large values of charge-spin susceptibility correlate with unconventional ground states such as disordered magnets and unconventional superconductivity.

Recent developments in the PySCF program package.

PySCF is a Python-based general-purpose electronic structure platform that supports first-principles simulations of molecules and solids as well as accelerates the development of new methodology and complex computational workflows. This paper explains the design and philosophy behind PySCF that enables it to meet these twin objectives. With several case studies, we show how users can easily implement their own methods using PySCF as a development environment.

Non-orthogonal determinants in multi-Slater-Jastrow trial wave functions for fixed-node diffusion Monte Carlo.

The accuracy and efficiency of Quantum Monte Carlo (QMC) algorithms benefit greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial wave functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C molecule.

High Hole Mobility and Nonsaturating Giant Magnetoresistance in the New 2D Metal NaCuSe Synthesized by a Unique Pathway.

The new compound NaCuSe forms by the reaction of CuO and Cu in a molten sodium polyselenide flux, with the existence of CuO being unexpectedly critical to its synthesis. It adopts a layered hexagonal structure (space group P6/ mmc with cell parameters a = 3.9931(6) Å and c = 25.

Erratum: Computation of the Correlated Metal-Insulator Transition in Vanadium Dioxide from First Principles [Phys. Rev. Lett. 114, 176401 (2015)].

This corrects the article DOI: 10.1103/PhysRevLett.114.

Semiconducting BaSnSb and Metallic BaSnSb (x = 0.4, y = 0.6) Zintl Phases.

We report the discovery of two ternary Zintl phases BaSnSb and BaSnSb (x = 0.4, y = 0.6).

Importance of σ Bonding Electrons for the Accurate Description of Electron Correlation in Graphene.

Electron correlation in graphene is unique because of the interplay between the Dirac cone dispersion of π electrons and long-range Coulomb interaction. Because of the zero density of states at Fermi level, the random phase approximation predicts no metallic screening at long distance and low energy, so one might expect that graphene should be a poorly screened system. However, empirically graphene is a weakly interacting semimetal, which leads to the question of how electron correlations take place in graphene at different length scales.

Charge Density Wave and Narrow Energy Gap at Room Temperature in 2D PbSbSTe with Square Te Sheets.

We report a new two-dimensional compound, PbSbSTe, that has a charge density wave (CDW) at room temperature. The CDW is incommensurate with q-vector of 0.248(6)a* + 0.

Accurate barrier heights using diffusion Monte Carlo.

Fixed nodediffusion Monte Carlo (DMC) has been performed on a test set of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions, and the nodal error has been assessed. The DMC results are robust to changes in the nodal surface, as assessed by using different mean-field techniques to generate single determinant wave functions. Using these single determinant nodal surfaces, DMC results in errors of 1.

Using local operator fluctuations to identify wave function improvements.

A method is developed that allows analysis of quantum Monte Carlo simulations to identify errors in trial wave functions. The purpose of this method is to allow for the systematic improvement of variational wave functions by identifying degrees of freedom that are not well described by an initial trial state. We provide proof of concept implementations of this method by identifying the need for a Jastrow correlation factor and implementing a selected multideterminant wave function algorithm for small dimers that systematically decreases the variational energy.

Discovering correlated fermions using quantum Monte Carlo.

It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.

Diffusion Monte Carlo Perspective on the Spin-State Energetics of [Fe(NCH)6](2.).

The energy difference between the high spin and the low spin state of the model compound [Fe(NCH)6](2+) is investigated by means of Diffusion Monte Carlo (DMC), where special attention is dedicated to analyzing the effect of the fix node approximation on the accuracy of the results. For this purpose, we compare several Slater-Jastrow and multireference Slater-Jastrow trial wave functions. We found that a Slater-Jastrow trial wave function constructed with the generalized Kohn-Sham orbitals from hybrid DFT represents the optimal choice.

Diffusion Monte Carlo for Accurate Dissociation Energies of 3d Transition Metal Containing Molecules.

Transition metals and transition metal compounds are important to catalysis, photochemistry, and many superconducting systems. We study the performance of diffusion Monte Carlo (DMC) applied to transition metal containing dimers (TMCDs) using single-determinant Slater-Jastrow trial wavefunctions and investigate the possible influence of the locality and pseudopotential errors. We find that the locality approximation can introduce nonsystematic errors of up to several tens of kilocalories per mole in the absolute energy of Cu and CuH if Ar or Mg core pseudopotentials (PPs) are used for the 3d transition metal atoms.

Hexagonal boron nitride and water interaction parameters.

The study of hexagonal boron nitride (hBN) in microfluidic and nanofluidic applications at the atomic level requires accurate force field parameters to describe the water-hBN interaction. In this work, we begin with benchmark quality first principles quantum Monte Carlo calculations on the interaction energy between water and hBN, which are used to validate random phase approximation (RPA) calculations. We then proceed with RPA to derive force field parameters, which are used to simulate water contact angle on bulk hBN, attaining a value within the experimental uncertainties.

Towards a systematic assessment of errors in diffusion Monte Carlo calculations of semiconductors: Case study of zinc selenide and zinc oxide.

The fixed node diffusion Monte Carlo (DMC) method has attracted interest in recent years as a way to calculate properties of solid materials with high accuracy. However, the framework for the calculation of properties such as total energies, atomization energies, and excited state energies is not yet fully established. Several outstanding questions remain as to the effect of pseudopotentials, the magnitude of the fixed node error, and the size of supercell finite size effects.

Density-matrix based determination of low-energy model Hamiltonians from ab initio wavefunctions.

We propose a way of obtaining effective low energy Hubbard-like model Hamiltonians from ab initio quantum Monte Carlo calculations for molecular and extended systems. The Hamiltonian parameters are fit to best match the ab initio two-body density matrices and energies of the ground and excited states, and thus we refer to the method as ab initio density matrix based downfolding. For benzene (a finite system), we find good agreement with experimentally available energy gaps without using any experimental inputs.

The interaction between hexagonal boron nitride and water from first principles.

The use of hexagonal boron nitride (h-BN) in microfluidic and nanofluidic applications requires a fundamental understanding of the interaction between water and the h-BN surface. A crucial component of the interaction is the binding energy, which is sensitive to the treatment of electron correlation. In this work, we use state of the art quantum Monte Carlo and quantum chemistry techniques to compute the binding energy.

Computation of the correlated metal-insulator transition in vanadium dioxide from first principles.

Vanadium dioxide (VO2) is a paradigmatic example of a strongly correlated system that undergoes a metal-insulator transition at a structural phase transition. To date, this transition has necessitated significant post hoc adjustments to theory in order to be described properly. Here we report standard state-of-the-art first principles quantum Monte Carlo (QMC) calculations of the structural dependence of the properties of VO2.

Origins of structural hole traps in hydrogenated amorphous silicon.

The inherently disordered nature of hydrogenated amorphous silicon (a-Si:H) obscures the influence of atomic features on the trapping of holes. To address this, we have created a set of over two thousand ab initio structures of a-Si:H and explored the influence of geometric factors on the occurrence of deep hole traps using density-functional theory. Statistical analysis of the relative contribution of various structures to the trap distribution shows that floating bonds and ionization-induced displacements correlate most strongly with hole traps in our ensemble.

Types of single particle symmetry breaking in transition metal oxides due to electron correlation.

Very accurate wave functions are calculated for small transition metal oxide molecules. These wave functions are decomposed using reduced density matrices to study the underlying correlation of electrons. The correlation is primarily of left-right type between the transition metals and the oxygen atoms, which is mediated by excitations from the nominal single Slater ground state into antibonding and d-type orbitals.