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.

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.

Hydrogen separation with a graphenylene monolayer: Diffusion Monte Carlo study.

We performed fixed-node diffusion Monte Carlo (DMC) calculations to investigate structural and energetic properties of graphenylene (GPNL), a two-dimensional network of sp2-bonded carbon atoms with large near-circular pores, and its H2 separation performance for gas mixtures. We have found that the energetic stability of a GPNL monolayer is comparable to that of γ-graphyne, as evidenced by its large cohesive energy of 6.755(3) eV/atom. Diffusion barriers of several gas molecules, including hydrogen, through a GPNL membrane were determined from the analysis of their adsorption energies depending on the adsorption distance, which led to our estimation for hydrogen selectivity with respect to other target molecules. DMC hydrogen selectivity of a GPNL monolayer was found to be exceptionally high at 300 K, as high as 1010-1011 against CO and N2 gases. This, along with high hydrogen permeance due to its generic pore structure, leads us to conclude that GPNL is a promising membrane to be used as a high-performance hydrogen separator from gas mixtures. We find that when compared to our DMC results, DFT calculations tend to overestimate H2 selectivity, which is mostly due to their inaccurate description of short-range repulsive interactions.

The binding of atomic hydrogen on graphene from density functional theory and diffusion Monte Carlo calculations.

In this work, density functional theory (DFT) and diffusion Monte Carlo (DMC) methods are used to calculate the binding energy of a H atom chemisorbed on the graphene surface. The DMC value of the binding energy is about 16% smaller in magnitude than the Perdew-Burke-Ernzerhof (PBE) result. The inclusion of exact exchange through the use of the Heyd-Scuseria-Ernzerhof functional brings the DFT value of the binding energy closer in line with the DMC result. It is also found that there are significant differences in the charge distributions determined using PBE and DMC approaches.

Metastable Metallic Phase of a Bilayer Blue Phosphorene Induced by Interlayer Bonding and Intralayer Charge Redistributions.

We have carried out diffusion Monte Carlo calculations for an A1B-1-stacked bilayer blue phosphorene to find that it undergoes a semiconductor-metal transition as the interlayer distance decreases. While the most stable bilayer structure is a semiconducting one with two monolayers coupled through a weak van der Waals interaction, the metallic bilayer at a shorter interlayer distance is found to be only metastable. This is in contrast to a recent theoretical prediction based on a random phase approximation that the metallic phase would be the most stable bilayer configuration of blue phosphorene. Our analysis of charge density distributions reveals that the metastable metallic phase is induced by interlayer chemical bonding and intralayer charge redistributions. This study enriches our understanding of interlayer binding of a blue phosphorene and contributes to the establishment of correct energetic order between its different phases, which will be essential in devising an experimental pathway for a metallic phosphorene.

Importance of Van der Waals Interactions in Hydrogen Adsorption on a Silicon-carbide Nanotube Revisited with vdW-DFT and Quantum Monte Carlo.

Density functional theory (DFT) is a valuable tool for calculating adsorption energies toward designing materials for hydrogen storage. However, dispersion forces being absent from the local/semi-local theory, it remains unclear as to how the consideration of van der Waals (vdW) interactions affects such calculations. For the first time, we applied diffusion Monte Carlo (DMC) to evaluate the adsorption characteristics of a hydrogen molecule on a (5,5) armchair silicon-carbide nanotube (H2-SiCNT). Within the DFT framework, we benchmarked various exchange-correlation functionals, including those recently developed for treating dispersion or vdW interactions. We found that the vdW-corrected DFT methods agree well with DMC, whereas the local (semilocal) functional significantly over (under)-binds. Furthermore, we fully optimized the H2-SiCNT geometry within the DFT framework and investigated the correlation between the structure and charge density. The vdW contribution to the adsorption was found to be non-negligible at ∼1 kcal/mol per hydrogen molecule, which amounts to 9-29% of the ideal adsorption energy required for hydrogen storage applications.

Adsorption of a single Pt atom on graphene: spin crossing between physisorbed triplet and chemisorbed singlet states.

Diffusion Monte Carlo (DMC) calculations have been performed to study the adsorption of a single Pt atom on pristine graphene. We obtain the adsorption energy curves of a single Pt atom adsorbed at three different adsorption sites (bridge, on-top, hollow) as functions of the vertical distance from a graphene surface for both spin singlet and triplet states. The bridge-site adsorption in a singlet spin state is found to be energetically most stable, which is consistent with previous theoretical predictions. As the Pt atom moves away from a graphene surface, spin triplet states are favored over spin singlet states for all three adsorption sites, reflecting that the ground state of an isolated Pt atom is in a spin triplet state. Furthermore, our DMC calculations reveal local-minimum features in the triplet region which is understood to be due to van der Waals interaction between the Pt atom and graphene. This provides a comprehensive understanding for a spin crossing from a physisorbed triplet state to a chemisorbed singlet state in the adsorption process of a single Pt atom on graphene.

Quantum Monte Carlo benchmarking of large noncovalent complexes in the L7 benchmark set.

We have used diffusion Monte Carlo (DMC) to perform calculations on the L7 benchmark set. DMC is a stochastic numerical integration scheme in real-space and part of a larger set of quantum Monte Carlo methods. The L7 set was designed to test the ability of electronic structure methods to include dispersive interactions. While the agreement between DMC and quantum-chemical state-of-the-art methods is excellent for some of the structures, there are significant differences in others. In contrast to wavefunction-based quantum chemical methods, DMC is a first-principle many-body method with the many-body wavefunction evolving in real space. It includes explicitly all electron-electron interactions and is relatively insensitive to the size of the basis set.

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.

Taming the fixed-node error in diffusion Monte Carlo via range separation.

By combining density-functional theory (DFT) and wave function theory via the range separation (RS) of the interelectronic Coulomb operator, we obtain accurate fixed-node diffusion Monte Carlo (FN-DMC) energies with compact multi-determinant trial wave functions. In particular, we combine here short-range exchange-correlation functionals with a flavor of selected configuration interaction known as configuration interaction using a perturbative selection made iteratively (CIPSI), a scheme that we label RS-DFT-CIPSI. One of the take-home messages of the present study is that RS-DFT-CIPSI trial wave functions yield lower fixed-node energies with more compact multi-determinant expansions than CIPSI, especially for small basis sets. Indeed, as the CIPSI component of RS-DFT-CIPSI is relieved from describing the short-range part of the correlation hole around the electron-electron coalescence points, the number of determinants in the trial wave function required to reach a given accuracy is significantly reduced as compared to a conventional CIPSI calculation. Importantly, by performing various numerical experiments, we evidence that the RS-DFT scheme essentially plays the role of a simple Jastrow factor by mimicking short-range correlation effects, hence avoiding the burden of performing a stochastic optimization. Considering the 55 atomization energies of the Gaussian-1 benchmark set of molecules, we show that using a fixed value of µ = 0.5 bohr-1 provides effective error cancellations as well as compact trial wave functions, making the present method a good candidate for the accurate description of large chemical systems.

QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo.

We review recent advances in the capabilities of the open source ab initio Quantum Monte Carlo (QMC) package QMCPACK and the workflow tool Nexus used for greater efficiency and reproducibility. The auxiliary field QMC (AFQMC) implementation has been greatly expanded to include k-point symmetries, tensor-hypercontraction, and accelerated graphical processing unit (GPU) support. These scaling and memory reductions greatly increase the number of orbitals that can practically be included in AFQMC calculations, increasing the accuracy. Advances in real space methods include techniques for accurate computation of bandgaps and for systematically improving the nodal surface of ground state wavefunctions. Results of these calculations can be used to validate application of more approximate electronic structure methods, including GW and density functional based techniques. To provide an improved foundation for these calculations, we utilize a new set of correlation-consistent effective core potentials (pseudopotentials) that are more accurate than previous sets; these can also be applied in quantum-chemical and other many-body applications, not only QMC. These advances increase the efficiency, accuracy, and range of properties that can be studied in both molecules and materials with QMC and QMCPACK.

Competition between Hückel's Rule and Jahn-Teller Distortion in Small Carbon Rings: A Quantum Monte Carlo Study.

Structural properties and energetics of carbon rings are studied with the diffusion Monte Carlo (DMC) method. Our DMC-based geometry optimization reveals that both polyynic C4n and cumulenic C4n + 2 rings exhibit bond length alternations for n ≥ 3, which is understood to be due to Jahn-Teller distortions. The bond length alternation even in a cumulenic (4n + 2) carbon ring was experimentally observed in a recently synthesized C18 molecule. From a comparison of the DMC cohesive energies of C4n with those of C4n + 2, we present a comprehensive picture of the competition between Hückel's rule and Jahn-Teller distortion in small carbon rings; the former is more dominant than the latter for n < 5 where C4n + 2 rings are more stable than C4n, while C4n rings are as stable as C4n + 2 for n < 5 where dimerization effects due to Jahn-Teller distortion are more important.

Quantum Package 2.0: An Open-Source Determinant-Driven Suite of Programs.

Quantum chemistry is a discipline which relies heavily on very expensive numerical computations. The scaling of correlated wave function methods lies, in their standard implementation, between O(N5) and O(eN) , where N is proportional to the system size. Therefore, performing accurate calculations on chemically meaningful systems requires (i) approximations that can lower the computational scaling and (ii) efficient implementations that take advantage of modern massively parallel architectures. Quantum Package is an open-source programming environment for quantum chemistry specially designed for wave function methods. Its main goal is the development of determinant-driven selected configuration interaction (sCI) methods and multireference second-order perturbation theory (PT2). The determinant-driven framework allows the programmer to include any arbitrary set of determinants in the reference space, hence providing greater methodological freedom. The sCI method implemented in Quantum Package is based on the CIPSI (Configuration Interaction using a Perturbative Selection made Iteratively) algorithm which complements the variational sCI energy with a PT2 correction. Additional external plugins have been recently added to perform calculations with multireference coupled cluster theory and range-separated density-functional theory. All the programs are developed with the IRPF90 code generator, which simplifies collaborative work and the development of new features. Quantum Package strives to allow easy implementation and experimentation of new methods, while making parallel computation as simple and efficient as possible on modern supercomputer architectures. Currently, the code enables, routinely, to realize runs on roughly 2 000 CPU cores, with tens of millions of determinants in the reference space. Moreover, we have been able to push up to 12 288 cores in order to test its parallel efficiency. In the present manuscript, we also introduce some key new developments: (i) a renormalized second-order perturbative correction for efficient extrapolation to the full CI limit and (ii) a stochastic version of the CIPSI selection performed simultaneously to the PT2 calculation at no extra cost.

Excitation energies from diffusion Monte Carlo using selected configuration interaction nodes.

Quantum Monte Carlo (QMC) is a stochastic method that has been particularly successful for ground-state electronic structure calculations but mostly unexplored for the computation of excited-state energies. Here, we show that within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using selected configuration interaction (sCI) expansions, one is able to obtain accurate excitation energies at the fixed-node diffusion Monte Carlo (FN-DMC) level. This evidences that the fixed-node errors in the ground and excited states obtained with sCI wave functions cancel out to a large extent. Our procedure is tested on two small organic molecules (water and formaldehyde) for which we report all-electron FN-DMC calculations. For both the singlet and triplet manifolds, accurate vertical excitation energies are obtained with relatively compact multideterminant expansions built with small (typically double-ζ) basis sets.

Benchmarks and Reliable DFT Results for Spin Gaps of Small Ligand Fe(II) Complexes.

All-electron fixed-node diffusion Monte Carlo provides benchmark spin gaps for four Fe(II) octahedral complexes. Standard quantum chemical methods (semilocal DFT and CCSD(T)) fail badly for the energy difference between their high- and low-spin states. Density-corrected DFT is both significantly more accurate and reliable and yields a consistent prediction for the Fe-Porphyrin complex.

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.

Nature of Interlayer Binding and Stacking of sp-sp2 Hybridized Carbon Layers: A Quantum Monte Carlo Study.

α-Graphyne is a two-dimensional sheet of sp-sp2 hybridized carbon atoms in a honeycomb lattice. While the geometrical structure is similar to that of graphene, the hybridized triple bonds give rise to electronic structure that is different from that of graphene. Similar to graphene, α-graphyne can be stacked in bilayers with two stable configurations, but the different stackings have very different electronic structures: one is predicted to have gapless parabolic bands, and the other, a tunable band gap which is attractive for applications. In order to realize applications, it is crucial to understand which stacking is more stable. This is difficult to model, as the stability is a result of weak interlayer van der Waals interactions which are not well captured by density functional theory (DFT). We have used quantum Monte Carlo simulations that accurately include van der Waals interactions to calculate the interlayer binding energy of bilayer graphyne and to determine its most stable stacking mode. Our results show that interlayer bindings of sp- and sp2-bonded carbon networks are significantly underestimated in a Kohn-Sham DFT approach, even with an exchange-correlation potential corrected to include, in some approximation, van der Waals interactions. Finally, our quantum Monte Carlo calculations reveal that the interlayer binding energy difference between the two stacking modes is only 0.9(4) meV/atom. From this we conclude that the two stable stacking modes of bilayer α-graphyne are almost degenerate with each other, and both will occur with about the same probability at room temperature unless there is a synthesis path that prefers one stacking over the other.

Quantum Monte Carlo analysis of a charge ordered insulating antiferromagnet: the Ti4O7 Magnéli phase.

The Magnéli phase Ti4O7 is an important transition metal oxide with a wide range of applications because of its interplay between charge, spin, and lattice degrees of freedom. At low temperatures, it has non-trivial magnetic states very close in energy, driven by electronic exchange and correlation interactions. We have examined three low-lying states, one ferromagnetic and two antiferromagnetic, and calculated their energies as well as Ti spin moment distributions using highly accurate quantum Monte Carlo methods. We compare our results to those obtained from density functional theory-based methods that include approximate corrections for exchange and correlation. Our results confirm the nature of the states and their ordering in energy, as compared with density-functional theory methods. However, the energy differences and spin distributions differ. A detailed analysis suggests that non-local exchange-correlation functionals, in addition to other approximations such as LDA+U to account for correlations, are needed to simultaneously obtain better estimates for spin moments, distributions, energy differences and energy gaps.

Application of Diffusion Monte Carlo to Materials Dominated by van der Waals Interactions.

van der Waals forces are notoriously difficult to account for from first principles. We have performed extensive calculations to assess the usefulness and validity of diffusion quantum Monte Carlo when predicting van der Waals forces. We present converged results for noble gas solids and clusters, archetypical van der Waals dominated systems, as well as the highly relevant π-π stacking supramolecular complex: DNA + intercalating anticancer drug ellipticine. Analysis of the calculated binding energies underscores the existence of significant interatomic many-body contributions.