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.

Bio-Inspired Deaminative Hydroxylation of Aminoheterocycles and Electron-Deficient Anilines.

Among the tools available to chemists for drug design of bioactive compounds, the bioisosteric replacement of atoms or groups of atoms is the cornerstone of modern strategies. Despite the undeniable interest in amino-to-hydroxyl interchange, enzymatic deaminative hydroxylation remains unmatched. Herein, we report a user friendly and safe procedure to selectively convert aminoheterocycles to their hydroxylated analogues by means of a simple pyrylium tetrafluoroborate salt. The hydroxylation step relies on a Lossen-type rearrangement under mild conditions thus avoiding the use of strong hydroxide bases. In addition to biorelevant heterocycles, the deaminative hydroxylation of electron-deficient anilines was also demonstrated. Finally, mechanistic experiments allowed the identification of the key intermediates, thus unveiling a rather unusual mechanism for this formal aromatic substitution.

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. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater-Jastrow wave functions.

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. This special issue of the Journal of Chemical Physics includes 33 papers that describe recent developments and applications in this area. As seen from the articles in the issue, stochastic electronic structure methods are applicable to both molecules and solids and can accurately describe systems with strong electron correlation. This issue was motivated, in part, by the 2019 Telluride Science Research Center workshop on Stochastic Electronic Structure Methods that we organized. Below we briefly describe each of the papers in the special issue, dividing the papers into six subtopics.

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. This technique is applied to the well-characterized benzene molecule, in which ∼10 000 parameters are optimized for the first 12 excited states. Agreement within ∼0.2 eV is obtained with higher scaling coupled cluster methods; small disagreements with experiment are likely due to vibrational effects.

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. We then summarize the capabilities of PySCF for molecular and solid-state simulations. Finally, we describe the growing ecosystem of projects that use PySCF across the domains of quantum chemistry, materials science, machine learning, and quantum information science.

High Hole Mobility and Nonsaturating Giant Magnetoresistance in the New 2D Metal NaCu4Se4 Synthesized by a Unique Pathway.

The new compound NaCu4Se4 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 P63/ mmc with cell parameters a = 3.9931(6) Å and c = 25.167(5) Å), consisting of infinite two-dimensional [Cu4Se4]- slabs separated by Na+ cations. X-ray photoelectron spectroscopy suggests that NaCu4Se4 is mixed-valent with the formula (Na+)(Cu+)4(Se2-)(Se-)(Se2)2-. NaCu4Se4 is a p-type metal with a carrier density of ∼1021 cm-3 and a high hole mobility of ∼808 cm2 V-1 s-1 at 2 K based on electronic transport measurements. First-principles calculations suggest the density of states around the Fermi level are composed of Cu-d and Se-p orbitals. At 2 K, a very large transverse magnetoresistance of ∼1400% was observed, with a nonsaturating, linear dependence on field up to 9 T. Our results indicate that the use of metal oxide chemical precursors can open reaction paths to new low-dimensional compounds.

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.114.176401.

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

The accuracy and efficiency of ab initio 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 C2 molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. In some cases, fewer non-orthogonal determinants are required compared to orthogonal ones in order to achieve similar accuracy in FN-DMC. Our calculations indicate that trial wave functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.

Charge Density Wave and Narrow Energy Gap at Room Temperature in 2D Pb3-xSb1+xS4Te2-δ with Square Te Sheets.

We report a new two-dimensional compound, Pb3-xSb1+xS4Te2-δ, that has a charge density wave (CDW) at room temperature. The CDW is incommensurate with q-vector of 0.248(6)a* + 0.246(8)b* + 0.387(9)c* for x = 0.29(2) and δ = 0.37(3) due to positional and occupational long-range ordering of Te atoms in the sheets. The modulated structure was refined from the single-crystal X-ray diffraction data with a superspace group P1̅(αßγ)0 using (3 + 1)-dimensional crystallography. The resistivity increases with decreasing temperature, suggesting semiconducting behavior. The transition temperature (TCDW) of the CDW is ∼345 K, above which the Te square sheets become disordered with no q-vector. First-principles density functional theory calculations on the undistorted structure and an approximate commensurate supercell reveal that the gap is due to the structure modulation.

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. We address this question by computing the equal time and dynamic structure factor S(q) and S(q,ω) of freestanding graphene using ab initio fixed-node diffusion Monte Carlo simulations and the random phase approximation. We find that the σ electrons contribute strongly to S(q,ω) for relevant experimental values of ω even at distances up to around 80 Å. These findings illustrate how the emergent physics from underlying Coulomb interactions results in the observed weakly correlated semimetal.

Semiconducting Ba3Sn3Sb4 and Metallic Ba7-xSn11Sb15-y (x = 0.4, y = 0.6) Zintl Phases.

We report the discovery of two ternary Zintl phases Ba3Sn3Sb4 and Ba7-xSn11Sb15-y (x = 0.4, y = 0.6). Ba3Sn3Sb4 adopts the monoclinic space group P21/c with a = 14.669(3) Å, b = 6.9649(14) Å, c = 13.629(3) Å, and ß = 104.98(3)°. It features a unique corrugated two-dimensional (2D) structure consisting of [Sn3Sb4]6- layers extending along the ab-plane with Ba2+ atoms sandwiched between them. The nonstoichiometric Ba6.6Sn11Sb14.4 has a complex one-dimensional (1D) structure adopting the orthorhombic space group Pnma, with unit cell parameters a = 37.964(8) Å, b = 4.4090(9) Å, and c = 24.682(5) Å. It consists of large double Sn-Sb ribbons separated by Ba2+ atoms. Ba3Sn3Sb4 is an n-type semiconductor which has a narrow energy gap of ∼0.18 eV and a room temperature carrier concentration of ∼4.2 × 1018 cm-3. Ba6.6Sn11Sb14.4 is determined to be a metal with electrons being the dominant carriers.

Interpolated energy densities, correlation indicators and lower bounds from approximations to the strong coupling limit of DFT.

We investigate the construction of approximated exchange-correlation functionals by interpolating locally along the adiabatic connection between the weak- and the strong-coupling regimes, focussing on the effect of using approximate functionals for the strong-coupling energy densities. The gauge problem is avoided by dealing with quantities that are all locally defined in the same way. Using exact ingredients at weak coupling we are able to isolate the error coming from the approximations at strong coupling only. We find that the nonlocal radius model, which retains some of the non-locality of the exact strong-coupling regime, yields very satisfactory results. We also use interpolation models and quantities from the weak- and strong-coupling regimes to define a correlation-type indicator and a lower bound to the exact exchange-correlation energy. Open problems, related to the nature of the local and global slope of the adiabatic connection at weak coupling, are also discussed.

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 1.5(1) kcal/mol on barrier heights. Using the large data set of DMC energies, we attempted to find good descriptors of the fixed node error. It does not correlate with a number of descriptors including change in density but does show some correlation with the gap between the highest occupied and lowest unoccupied orbital energies in the mean-field calculation.

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.

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. This paper demonstrates that end-to-end multiscale modeling, starting at detailed many-body quantum mechanics and ending with macroscopic properties, with the approximations controlled along the way, is feasible for these systems.

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. Using this technique, we simulate the interactions between electrons explicitly, which allows for the metal-insulator transition to naturally emerge, importantly without ad hoc adjustments. The QMC calculations show that the structural transition directly causes the metal-insulator transition and a change in the coupling of vanadium spins. This change in the spin coupling results in a prediction of a momentum-independent magnetic excitation in the insulating state. While two-body correlations are important to set the stage for this transition, they do not change significantly when VO2 becomes an insulator. These results show that it is now possible to account for electron correlations in a quantitatively accurate way that is also specific to materials.

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. Here, we consider in detail the semiconductors ZnSe and ZnO and carry out systematic studies to assess the magnitude of the energy differences arising from controlled and uncontrolled approximations in DMC. The former include time step errors and supercell finite size effects for ground and optically excited states, and the latter include pseudopotentials, the pseudopotential localization approximation, and the fixed node approximation. We find that for these compounds, the errors can be controlled to good precision using modern computational resources and that quantum Monte Carlo calculations using Dirac-Fock pseudopotentials can offer good estimates of both cohesive energy and the gap of these systems. We do however observe differences in calculated optical gaps that arise when different pseudopotentials are used.

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. For graphene, a two dimensional solid (extended system) with periodic boundary conditions, we find the effective on-site Hubbard U(∗)/t to be 1.3 ± 0.2, comparable to a recent estimate based on the constrained random phase approximation. For molecules, such parameterizations enable calculation of excited states that are usually not accessible within ground state approaches. For solids, the effective Hamiltonian enables large-scale calculations using techniques designed for lattice models.