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.

The transition to the metallic state in low density hydrogen.

Solid atomic hydrogen is one of the simplest systems to undergo a metal-insulator transition. Near the transition, the electronic degrees of freedom become strongly correlated and their description provides a difficult challenge for theoretical methods. As a result, the order and density of the phase transition are still subject to debate. In this work, we use diffusion quantum Monte Carlo to benchmark the transition between paramagnetic and anti-ferromagnetic body centered cubic atomic hydrogen in its ground state. We locate the density of the transition by computing the equation of state for these two phases and identify the phase transition order by computing the band gap near the phase transition. These benchmark results show that the phase transition is continuous and occurs at a Wigner-Seitz radius of rs = 2.27(3) a0. We compare our results to previously reported density functional theory, Hedin's GW approximation, and dynamical mean field theory results.

Structural stability and defect energetics of ZnO from diffusion quantum Monte Carlo.

We have applied the many-body ab initio diffusion quantum Monte Carlo (DMC) method to study Zn and ZnO crystals under pressure and the energetics of the oxygen vacancy, zinc interstitial, and hydrogen impurities in ZnO. We show that DMC is an accurate and practical method that can be used to characterize multiple properties of materials that are challenging for density functional theory (DFT) approximations. DMC agrees with experimental measurements to within 0.3 eV, including the band-gap of ZnO, the ionization potential of O and Zn, and the atomization energy of O2, ZnO dimer, and wurtzite ZnO. DMC predicts the oxygen vacancy as a deep donor with a formation energy of 5.0(2) eV under O-rich conditions and thermodynamic transition levels located between 1.8 and 2.5 eV from the valence band maximum. Our DMC results indicate that the concentration of zinc interstitial and hydrogen impurities in ZnO should be low under n-type and Zn- and H-rich conditions because these defects have formation energies above 1.4 eV under these conditions. Comparison of DMC and hybrid functionals shows that these DFT approximations can be parameterized to yield a general correct qualitative description of ZnO. However, the formation energy of defects in ZnO evaluated with DMC and hybrid functionals can differ by more than 0.5 eV.

Successes and failures of Hubbard-corrected density functional theory: the case of Mg doped LiCoO2.

We have evaluated the successes and failures of the Hubbard-corrected density functional theory approach to study Mg doping of LiCoO2. We computed the effect of the U parameter on the energetic, geometric, and electronic properties of two possible doping mechanisms: (1) substitution of Mg onto a Co (or Li) site with an associated impurity state and (2) formation of impurity-state-free complexes of substitutional Mg and point defects in LiCoO2. We find that formation of impurity states results in changes on the valency of Co in LiCoO2. Variation of the Co U shifts the energy of the impurity state, resulting in energetic, geometric, and electronic properties that depend significantly on the specific value of U. In contrast, the properties of the impurity-state-free complexes are insensitive to U. These results identify reasons for the strong dependence on the doping properties on the chosen value of U and for the overall difficulty of achieving agreement with the experimentally known energetic and electronic properties of doped transition metal oxides such as LiCoO2.

Cohesion energetics of carbon allotropes: quantum Monte Carlo study.

We have performed quantum Monte Carlo calculations to study the cohesion energetics of carbon allotropes, including sp(3)-bonded diamond, sp(2)-bonded graphene, sp-sp(2) hybridized graphynes, and sp-bonded carbyne. The computed cohesive energies of diamond and graphene are found to be in excellent agreement with the corresponding values determined experimentally for diamond and graphite, respectively, when the zero-point energies, along with the interlayer binding in the case of graphite, are included. We have also found that the cohesive energy of graphyne decreases systematically as the ratio of sp-bonded carbon atoms increases. The cohesive energy of γ-graphyne, the most energetically stable graphyne, turns out to be 6.766(6) eV/atom, which is smaller than that of graphene by 0.698(12) eV/atom. Experimental difficulty in synthesizing graphynes could be explained by their significantly smaller cohesive energies. Finally, we conclude that the cohesive energy of a newly proposed graphyne can be accurately estimated with the carbon-carbon bond energies determined from the cohesive energies of graphene and three different graphynes considered here.

Generalizing the self-healing diffusion Monte Carlo approach to finite temperature: a path for the optimization of low-energy many-body bases.

A statistical method is derived for the calculation of thermodynamic properties of many-body systems at low temperatures. This method is based on the self-healing diffusion Monte Carlo method for complex functions [F. A. Reboredo, J. Chem. Phys. 136, 204101 (2012)] and some ideas of the correlation function Monte Carlo approach [D. M. Ceperley and B. Bernu, J. Chem. Phys. 89, 6316 (1988)]. In order to allow the evolution in imaginary time to describe the density matrix, we remove the fixed-node restriction using complex antisymmetric guiding wave functions. In the process we obtain a parallel algorithm that optimizes a small subspace of the many-body Hilbert space to provide maximum overlap with the subspace spanned by the lowest-energy eigenstates of a many-body Hamiltonian. We show in a model system that the partition function is progressively maximized within this subspace. We show that the subspace spanned by the small basis systematically converges towards the subspace spanned by the lowest energy eigenstates. Possible applications of this method for calculating the thermodynamic properties of many-body systems near the ground state are discussed. The resulting basis can also be used to accelerate the calculation of the ground or excited states with quantum Monte Carlo.

Quantum Monte Carlo Benchmark of Exchange-Correlation Functionals for Bulk Water.

The accurate description of the thermodynamic and dynamical properties of liquid water from first-principles is a very important challenge to the theoretical community. This represents not only a critical test of the predictive capabilities of first-principles methods, but it will also shed light into the microscopic properties of such an important substance. Density Functional Theory, the main workhorse in the field of first-principles methods, has been so far unable to properly describe water and its unusual properties in the liquid state. With the recent introduction of exact exchange and an improved description of dispersion interaction, the possibility of an accurate description of the liquid is finally within reach. Unfortunately, there is still no way to systematically improve exchange-correlation functionals, and the number of available functionals is very large. In this article we use highly accurate quantum Monte Carlo calculations to benchmark a selection of exchange-correlation functionals typically used in Density Functional Theory simulations of bulk water. This allows us to test the predictive capabilities of these functionals in water, giving us a way to choose optimal functionals for first-principles simulations. We compare and contrast the importance of different features of functionals, including the hybrid component, the vdW component, and their importance within different aspects of the PES. In addition, in order to correct the inaccuracies in the description of short-range interactions in the liquid, we test a recently introduced scheme that combines Density Functional Theory with Coupled Cluster calculations through a Many-Body expansion of the energy.

Binding and Diffusion of Lithium in Graphite: Quantum Monte Carlo Benchmarks and Validation of van der Waals Density Functional Methods.

Highly accurate diffusion quantum Monte Carlo (QMC) studies of the adsorption and diffusion of atomic lithium in AA-stacked graphite are compared with van der Waals-including density functional theory (DFT) calculations. Predicted QMC lattice constants for pure AA graphite agree with experiment. Pure AA-stacked graphite is shown to challenge many van der Waals methods even when they are accurate for conventional AB graphite. Highest overall DFT accuracy, considering pure AA-stacked graphite as well as lithium binding and diffusion, is obtained by the self-consistent van der Waals functional vdW-DF2, although errors in binding energies remain. Empirical approaches based on point charges such as DFT-D are inaccurate unless the local charge transfer is assessed. The results demonstrate that the lithium-carbon system requires a simultaneous highly accurate description of both charge transfer and van der Waals interactions, favoring self-consistent approaches.

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.

Multideterminant Wave Functions in Quantum Monte Carlo.

Quantum Monte Carlo (QMC) methods have received considerable attention over past decades due to their great promise for providing a direct solution to the many-body Schrodinger equation in electronic systems. Thanks to their low scaling with the number of particles, QMC methods present a compelling competitive alternative for the accurate study of large molecular systems and solid state calculations. In spite of such promise, the method has not permeated the quantum chemistry community broadly, mainly because of the fixed-node error, which can be large and whose control is difficult. In this Perspective, we present a systematic application of large scale multideterminant expansions in QMC and report on its impressive performance with first row dimers and the 55 molecules of the G1 test set. We demonstrate the potential of this strategy for systematically reducing the fixed-node error in the wave function and for achieving chemical accuracy in energy predictions. When compared to traditional quantum chemistry methods like MP2, CCSD(T), and various DFT approximations, the QMC results show a marked improvement over all of them. In fact, only the explicitly correlated CCSD(T) method with a large basis set produces more accurate results. Further developments in trial wave functions and algorithmic improvements appear promising for rendering QMC as the benchmark standard in large electronic systems.

Computing the energy of a water molecule using multideterminants: a simple, efficient algorithm.

Quantum Monte Carlo (QMC) methods such as variational Monte Carlo and fixed node diffusion Monte Carlo depend heavily on the quality of the trial wave function. Although Slater-Jastrow wave functions are the most commonly used variational ansatz in electronic structure, more sophisticated wave functions are critical to ascertaining new physics. One such wave function is the multi-Slater-Jastrow wave function which consists of a Jastrow function multiplied by the sum of Slater determinants. In this paper we describe a method for working with these wave functions in QMC codes that is easy to implement, efficient both in computational speed as well as memory, and easily parallelized. The computational cost scales quadratically with particle number making this scaling no worse than the single determinant case and linear with the total number of excitations. Additionally, we implement this method and use it to compute the ground state energy of a water molecule.

Momentum distribution and renormalization factor in sodium and the electron gas.

We present experimental and theoretical results on the momentum distribution and the quasiparticle renormalization factor in sodium. From an x-ray Compton-profile measurement of the valence-electron-momentum density, we derive its discontinuity at the Fermi wave vector. This yields an accurate measure of the renormalization factor that we compare with quantum Monte Carlo and G0W0 calculations performed both on crystalline sodium and on the homogeneous electron gas.

Fundamental high-pressure calibration from all-electron quantum Monte Carlo calculations.

We develop an all-electron quantum Monte Carlo (QMC) method for solids that does not rely on pseudopotentials, and use it to construct a primary ultra-high-pressure calibration based on the equation of state of cubic boron nitride. We compute the static contribution to the free energy with the QMC method and obtain the phonon contribution from density functional theory, yielding a high-accuracy calibration up to 900 GPa usable directly in experiment. We compute the anharmonic Raman frequency shift with QMC simulations as a function of pressure and temperature, allowing optical pressure calibration. In contrast to present experimental approaches, small systematic errors in the theoretical EOS do not increase with pressure, and no extrapolation is needed. This all-electron method is applicable to first-row solids, providing a new reference for ab initio calculations of solids and benchmarks for pseudopotential accuracy.

Molecular hydrogen adsorbed on benzene: Insights from a quantum Monte Carlo study.

We present a quantum Monte Carlo study of the hydrogen-benzene system where binding is very weak. We demonstrate that the binding is well described at both variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) levels by a Jastrow correlated single determinant geminal wave function with an optimized compact basis set that includes diffuse orbitals. Agreement between VMC and fixed-node DMC binding energies is found to be within 0.18 mhartree, suggesting that the calculations are well converged with respect to the basis. Essentially the same binding is also found in independent DMC calculations using a different trial wave function of a more conventional Slater-Jastrow form, supporting our conclusion that the binding energy is accurate and includes all effects of correlation. We compare with previous calculations, and we discuss the physical mechanisms of the interaction, the role of diffuse basis functions, and the charge redistribution in the bond.

Complexity of small silicon self-interstitial defects.

The combination of long-time, tight-binding molecular dynamics and real-time multiresolution analysis techniques reveals the complexity of small silicon interstitial defects. The stability of identified structures is confirmed by ab initio relaxations. The majority of structures were previously unknown, demonstrating the effectiveness of the approach. A new, spatially extended tri-interstitial ground state structure is identified as a probable nucleation site for larger extended defects and may be key for the compact-to-extended transition.