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The accurate treatment of non-covalent interactions is necessary to model a wide range of applications, from molecular crystals to surface catalysts to aqueous solutions and many more. Quantum diffusion Monte Carlo (DMC) and coupled cluster theory with single, double and perturbative triple excitations [CCSD(T)] are considered two widely-trusted methods for treating non-covalent interactions. However, while they have been well-validated for small molecules, recent work has indicated that these two methods can disagree by more than $7.5\,$kcal/mol for larger systems. The origin of this discrepancy remains unknown. Moreover, the lack of systematic comparisons, particularly for medium-sized complexes, has made it difficult to identify which systems may be prone to such disagreements and the potential scale of these differences. In this work, we leverage the latest developments in DMC to compute interaction energies for the entire S66 dataset, containing 66 medium-sized complexes with a balanced representation of dispersion and electrostatic interactions. Comparison to previous CCSD(T) references reveals systematic trends, with DMC predicting stronger binding than CCSD(T) for electrostatic-dominated systems, while the binding becomes weaker for dispersion-dominated systems. We show that the relative strength of this discrepancy is correlated to the ratio of electrostatic and dispersion interactions, as obtained from energy decomposition analysis methods. Finally, we pinpoint systems in the S66 dataset where these discrepancies are particularly prominent, offering cost-effective benchmarks to guide future developments in DMC, CCSD(T) as well as the wider electronic structure theory community.

Quantum Monte Carlo (QMC) methods represent a powerful family of computational techniques for tackling complex quantum many-body problems and performing calculations of stationary state properties. QMC is among the most accurate and powerful approaches to the study of electronic structure, but its application is often hindered by a steep learning curve, hence it is rarely addressed in undergraduate and postgraduate classes. This tutorial is a step towards filling this gap. We offer an introduction to the diffusion Monte Carlo (DMC) method, which aims to solve the imaginary time Schr\"odinger equation through stochastic sampling of the configuration space. Starting from the theoretical foundations, the discussion leads naturally to the formulation of a step-by-step algorithm. To illustrate how the method works in simplified scenarios, examples such as the harmonic oscillator and the hydrogen atom are provided. The discussion extends to the fixed-node approximation, a crucial approach for addressing the fermionic sign problem in multi-electron systems. In particular, we examine the influence of trial wavefunction nodal surfaces on the accuracy of DMC energy by evaluating results from a non-interacting two-fermion system. Extending the method to excited states is feasible in principle, but some additional considerations are needed, supported by practical insights. By addressing the fundamental concepts from a hands-on perspective, we hope this tutorial will serve as a valuable guide for researchers and students approaching DMC for the first time.

Basis set incompleteness error (BSIE) is a common source of error in quantum chemistry (QC) calculations, but it has not been comprehensively studied in fixed-node Diffusion Monte Carlo (FN-DMC) calculations. FN-DMC, being a projection method, is often considered minimally affected by basis set biases. Here, we show that this assumption is not always valid. While the relative error introduced by a small basis set in the total FN-DMC energy is minor, it can become significant in binding energy ($E_{\rm b}$) evaluations of weakly interacting systems. We systematically investigated BSIEs in FN-DMC-based binding energy ($E_{\rm b}$) evaluations using the A24 dataset, a well-known benchmark set of 24 non-covalently bound dimers. Contrary to common expectations, we found that BSIEs in FN-DMC evaluations of $E_{\rm b}$ are indeed significant when small localized basis sets, such as cc-pVDZ, are employed. We observed that BSIEs are larger in dimers with hydrogen-bonding interactions and smaller in dispersion-dominated interactions. We also found that augmenting the basis sets with diffuse orbitals, using counterpoise (CP) correction, or both, effectively mitigates BSIEs., Comment: 49 pages

Water confined in nanoscale cavities plays a crucial role in everyday phenomena in geology and biology, as well as technological applications at the water-energy nexus. However, even understanding the basic properties of nano-confined water is extremely challenging for theory, simulations, and experiments. In particular, determining the melting temperature of quasi-one-dimensional ice polymorphs confined in carbon nanotubes has proven to be an exceptionally difficult task, with previous experimental and classical simulations approaches report values ranging from $\sim 180 \text{ K}$ up to $\sim 450 \text{ K}$ at ambient pressure. In this work, we use a machine learning potential that delivers first principles accuracy to study the phase diagram of water for confinement diameters $ 9.5 < d < 12.5 \text{ \AA}$. We find that several distinct ice polymorphs melt in a surprisingly narrow range between $\sim 280 \text{ K}$ and $\sim 310 \text{ K}$, with a melting mechanism that depends on the nanotube diameter. These results shed new light on the melting of ice in one-dimension and have implications for the operating conditions of carbon-based filtration and desalination devices.

CO$_2$ capture using carbon-based materials, particularly graphene and graphene-like materials, is a promising strategy to deal with CO$_2$ emissions. However, significant gaps remain in our understanding of the molecular-level interaction between CO$_2$ molecules and graphene, particularly, in terms of chemical bonding and electron transfer. In this work, we employ random structure search and density functional theory to understand the adsorption of CO$_2$ molecules on Ca, Sr, Na, K, and Ti decorated graphene surfaces. Compared to the pristine material, we observe enhanced CO$_2$ adsorption on the decorated graphene surfaces. Particularly on group 2 metals and titanium decorated graphene, CO$_2$ can be strongly chemisorbed as a bent CO$_2$ anion or as an oxalate, depending on the number of CO$_2$ molecules. Electronic structure analysis reveals the adsorption mechanism to involve an ionic charge transfer from the metal adatom to the adsorbed CO$_2$. Overall, this study suggests that reducing CO$_2$ to oxalate on group 2 metals and titanium metal-decorated graphene surfaces is a potential strategy for CO$_2$ storage., Comment: Main manuscript and Supplementary information provided

Molecular crystals play a central role in a wide range of scientific fields, including pharmaceuticals and organic semiconductor devices. However, they are challenging systems to model accurately with computational approaches because of a delicate interplay of intermolecular interactions such as hydrogen bonding and van der Waals dispersion forces. Here, by exploiting recent algorithmic developments, we report the first set of diffusion Monte Carlo lattice energies for all 23 molecular crystals in the popular and widely used X23 dataset. Comparisons with previous state-of-the-art lattice energy predictions (on a subset of the dataset) and a careful analysis of experimental sublimation enthalpies reveals that high-accuracy computational methods are now at least as reliable as (computationally derived) experiments for the lattice energies of molecular crystals. Overall, this work demonstrates the feasibility of high-level explicitly correlated electronic structure methods for broad benchmarking studies in complex condensed phase systems, and signposts a route towards closer agreement between experiment and simulation.

Diffusion Monte Carlo (DMC) is an exact technique to project out the ground state (GS) of a Hamiltonian. Since the GS is always bosonic, in fermionic systems the projection needs to be carried out while imposing anti-symmetric constraints, which is a nondeterministic polynomial hard problem. In practice, therefore, the application of DMC on electronic structure problems is made by employing the fixed-node (FN) approximation, consisting of performing DMC with the constraint of having a fixed predefined nodal surface. How do we get the nodal surface? The typical approach, applied in systems having up to hundreds, or even thousands of electrons, is to obtain the nodal surface from a preliminary mean-field approach (typically, a density functional theory calculation) used to obtain a single Slater determinant. This is known as {\emph{single reference}}. In this paper, we propose a new approach, applicable to systems as large as the C$_{60}$ fullerene, which improves the nodes by going beyond the single reference. In practice, we employ an implicitly multireference ansatz (Antisymmetrized Geminal power wavefunction constraint with molecular orbitals), initialized on the preliminary mean-field approach, which is relaxed by optimizing a few parameters of the wave function determining the nodal surface by minimizing the FN-DMC energy. We highlight the improvements of the proposed approach over the standard single reference method on several examples and, where feasible, the computational gain over the standard multireference ansatz, which makes the methods applicable to large systems. We also show that physical properties relying on relative energies, such as binding energies, are affordable and reliable within the proposed scheme.

Molecular hydrogen is at the core of hydrogen energy applications and has the potential to significantly reduce the use of carbon dioxide emitting energy processes. However, hydrogen gas storage is a major bottleneck for its large-scale use as current storage methods are energy intensive. Among different storage methods, physisorbing molecular hydrogen at ambient pressure and temperatures is a promising alternative - particularly thanks to tuneable lightweight nanomaterials and high throughput screening methods. Nonetheless, understanding hydrogen adsorption in well-defined nanomaterials remains experimentally challenging and reference information is scarce despite the proliferation of works predicting hydrogen adsorption. In this work, we focus on Li, Na, Ca, and K, decorated graphene sheets as substrates for hydrogen adsorption and compute the most accurate adsorption energies available to date using quantum diffusion Monte Carlo (DMC). Building on our previous insights at the density functional theory (DFT) level, we find that a weak covalent chemisorption of molecular hydrogen, known as Kubas binding, is feasible on Ca decorated graphene according to DMC, in agreement with DFT. This finding is in contrast to previous DMC predictions of the 4H$_2$/Ca$^+$ gas cluster where chemisorption is not favoured. However, we find that the adsorption energy of hydrogen on metal decorated graphene according to a widely-used DFT method is not fully consistent with DMC and the discrepancies are not systematic. The reference adsorption energies reported herein can be used to find better work-horse methods for application in large-scale modelling of hydrogen adsorption. Furthermore, the implications of this work affect strategies for finding suitable hydrogen storage materials and high-throughput methods.

The occurrence of a noncollinear magnetic structure at a Mn monolayer grown epitaxially on Fe(100) is predicted theoretically, using spinor density-functional theory, and observed experimentally, using x-ray magnetic circular dichroism (XMCD) and linear dichroism (XMLD) spectroscopies. The combined use of XMCD and XMLD at the Mn-absorption edge allows us to assess the existence of ferromagnetic and antiferromagnetic order at the interface, and also to determine the moment orientations with element specificity. The experimental results thus obtained are in excellent agreement with the magnetic structure determined theoretically.

A two-dimensional layer of oxide reveals itself as a essential element to drive the photocatalytic activity in a nanostructured hybrid material, which combines high-quality epitaxial graphene and titanium dioxide nanoparticles. In particular, it has been revealed that the addition of a 2D Ti oxide layer sandwiched between graphene and metal induces a p-doping of graphene and a consistent shift in the Ti d states. These modifications induced by the interfacial oxide layer induce a reduction of the probability of charge carrier recombination and enhance the photocatalytic activity of the heterostructure. This is indicative of a capital role played by thin oxide films in fine-tuning the properties of heterostructures based on graphene and pave the way to new combinations of graphene/oxides for photocatalysis-oriented applications.

Knowing the transport properties of iron under realistic conditions present in the Earth's core is essential for the geophysical modeling of Earth's magnetic field generation. Besides by extreme pressures and temperatures, transport may be influenced importantly also by the presence of light elements. Using a combination of molecular dynamics, density functional theory, and dynamical mean-field theory methods we investigate how oxygen impurities influence the electronic correlations and transport in the liquid outer Earth's core. We consider a case with an oxygen content of ~10 atomic%, a value that is believed to be close to the composition of the core. We find that the electronic correlations are enhanced but their effect on conductivities is moderate (compared to pure Fe, electrical conductivity drops by 10% and thermal conductivity by 18%). The effect of electron-electron scattering alone, whereas not large, is comparable to effects of the compositional disorder. We reveal the mechanism behind the larger suppression of the thermal conductivity and associated reduction of the Lorenz ratio and discuss its geophysical significance., Comment: 8 pages, 7 figures

Hydrogen is a key player in global strategies to reduce greenhouse gas emissions. In order to make hydrogen a widely-used fuel, we require more efficient methods of storing it than the current standard of pressurized cylinders. An alternative method is to adsorb H$_2$ in a material and avoid the use of high pressures. Among many potential materials, layered materials such as graphene present a practical advantage as they are lightweight. However, graphene and other 2D materials typically bind H$_2$ too weakly to store it at the typical operating conditions of a hydrogen fuel cell. Modifying the material, for example by decorating graphene with adatoms, can strengthen the adsorption energy of H$_2$ molecules, but the underlying mechanisms are still not well understood. In this work, we systematically screen alkali and alkaline earth metal decorated graphene sheets for the adsorption of hydrogen gas from first principles, and focus on the mechanisms of binding. We show that there are three mechanisms of adsorption on metal decorated graphene and each leads to distinctly different hydrogen adsorption structures. The three mechanisms can be described as weak van der Waals physisorption, metal adatom facilitated polarization, and Kubas adsorption. Among these mechanisms, we find that Kubas adsorption is easily perturbed by an external electric field, providing a way to tune H$_2$ adsorption.

Ice is one of the most important and interesting molecular crystals exhibiting a rich and evolving phase diagram. Recent discoveries mean that there are now twenty distinct polymorphs; a structural diversity that arises from a delicate interplay of hydrogen bonding and van der Waals dispersion forces. This wealth of structures provides a stern test of electronic structure theories, with Density Functional Theory (DFT) often not able to accurately characterise the relative energies of the various ice polymorphs. Thanks to recent advances that enable the accurate and efficient treatment of molecular crystals with Diffusion Monte Carlo (DMC), we present here the DMC-ICE13 dataset; a dataset of lattice energies of 13 ice polymorphs. This dataset encompasses the full structural complexity found in the ambient and high-pressure molecular ice polymorphs and when experimental reference energies are available our DMC results deliver sub-chemical accuracy. Using this dataset we then perform an extensive benchmark of a broad range of DFT functionals. Of the functionals considered, we find revPBE-D3 and RSCAN to reproduce reference absolute lattice energies with the smallest error, whilst optB86b-vdW and SCAN+rVV10 have the best performance on the relative lattice energies. Our results suggest that a single functional achieving reliable performance for all phases is still missing, and that care is needed in the selection of the most appropriate functional for the desired application. The insights obtained here may also be relevant to liquid water and other hydrogen bonded and dispersion bonded molecular crystals.

The race to meet the challenges of the global pandemic has served as a reminder that the existing drug discovery process is expensive, inefficient and slow. There is a major bottleneck screening the vast number of potential small molecules to shortlist lead compounds for antiviral drug development. New opportunities to accelerate drug discovery lie at the interface between machine learning methods, in this case developed for linear accelerators, and physics-based methods. The two in silico methods, each have their own advantages and limitations which, interestingly, complement each other. Here, we present an innovative infrastructural development that combines both approaches to accelerate drug discovery. The scale of the potential resulting workflow is such that it is dependent on supercomputing to achieve extremely high throughput. We have demonstrated the viability of this workflow for the study of inhibitors for four COVID-19 target proteins and our ability to perform the required large-scale calculations to identify lead antiviral compounds through repurposing on a variety of supercomputers.

Transition metal surfaces catalyse a broad range of thermally-activated reactions involving carbon-containing-species -- from atomic carbon to small hydrocarbons or organic molecules, and polymers. These reactions yield well-separated phases, for instance graphene and the metal surface, or, on the contrary, alloyed phases, such as metal carbides. Here, we investigate carbon phases on a rhenium (0001) surface, where the former kind of phase can transform into the latter. We find that this transformation occurs with increasing annealing time, which is hence not suitable to increase the quality of graphene. Our scanning tunneling spectroscopy and reflection high-energy electron diffraction analysis reveal that repeated short annealing cycles are best suited to increase the lateral extension of the structurally coherent graphene domains. Using the same techniques and with the support of density functional theory calculations, we next unveil, in real space, the symmetry of the many variants (two six-fold families) of a rhenium surface carbide observed with diffraction since the 1970s, and finally propose models of the atomic details. One of these models, which nicely matches the microscopy observations, consists of parallel rows of eight aligned carbon trimers with a so-called $(7\times\sqrt{\mathrm{19}})$ unit cell with respect to Re(0001)., Comment: 12 pages, 6 figures

COVID-19 has claimed more 1 million lives and resulted in over 40 million infections. There is an urgent need to identify drugs that can inhibit SARS-CoV-2. In response, the DOE recently established the Medical Therapeutics project as part of the National Virtual Biotechnology Laboratory, and tasked it with creating the computational infrastructure and methods necessary to advance therapeutics development. We discuss innovations in computational infrastructure and methods that are accelerating and advancing drug design. Specifically, we describe several methods that integrate artificial intelligence and simulation-based approaches, and the design of computational infrastructure to support these methods at scale. We discuss their implementation and characterize their performance, and highlight science advances that these capabilities have enabled.

The drug discovery process currently employed in the pharmaceutical industry typically requires about 10 years and $2-3 billion to deliver one new drug. This is both too expensive and too slow, especially in emergencies like the COVID-19 pandemic. In silicomethodologies need to be improved to better select lead compounds that can proceed to later stages of the drug discovery protocol accelerating the entire process. No single methodological approach can achieve the necessary accuracy with required efficiency. Here we describe multiple algorithmic innovations to overcome this fundamental limitation, development and deployment of computational infrastructure at scale integrates multiple artificial intelligence and simulation-based approaches. Three measures of performance are:(i) throughput, the number of ligands per unit time; (ii) scientific performance, the number of effective ligands sampled per unit time and (iii) peak performance, in flop/s. The capabilities outlined here have been used in production for several months as the workhorse of the computational infrastructure to support the capabilities of the US-DOE National Virtual Biotechnology Laboratory in combination with resources from the EU Centre of Excellence in Computational Biomedicine.

Due to their current and future technological applications, including realisation of water filters and desalination membranes, water adsorption on graphitic sp$^{2}$-bonded carbon is of overwhelming interest. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and non-covalent interactions in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed \textbf{WaC18}), which includes a single water molecule interacting with a broad range of carbon structures, and various bulk (3D) and two dimensional (2D) ice polymorphs. The performance of 28 approaches, including semi-local exchange-correlation functionals, non-local (Fock) exchange contributions, and long-range van der Waals (vdW) treatments, are tested by computing the deviations from the reference interaction energies. The calculated mean absolute deviations on the WaC18 set depends crucially on the DFT approach, ranging from 135 meV for LDA to 12 meV for PBE0-D4. We find that modern vdW corrections to DFT significantly improve over their precursors. Within the 28 tested approaches, we identify the best performing within the functional classes of: generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, which are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, respectively.

Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate electronic structure approaches for its favorable cubic scaling with system size, which often makes FN-DMC the only computationally affordable high-quality method in large condensed phase systems with more than 100 atoms. In such systems FN-DMC deploys pseudopotentials to substantially improve efficiency. In order to deal with non-local terms of pseudopotentials, the FN-DMC algorithm must use an additional approximation, leading to the so-called localization error. However, the two available approximations, the locality approximation (LA) and the T-move approximation (TM), have certain disadvantages and can make DMC calculations difficult to reproduce. Here we introduce a third approach, called the determinant localization approximation (DLA). DLA eliminates reproducibility issues and systematically provides good quality results and stable simulations that are slightly more efficient than LA and TM. When calculating energy differences -- such as interaction and ionization energies -- DLA is also more accurate than the LA and TM approaches. We believe that DLA paves the way to the automization of FN-DMC and its much easier application in large systems.

We combine state-of-the-art large-scale first principles calculations with a low-energy continuum model to describe the nearly flat bands of twisted bilayer graphene at the first magic angle $\theta =1.08^\circ$. We show that the energy width of the flat band manifold, as well as the energy gap separating it from the valence and conduction bands, can be obtained only if the out-of-plane relaxations are fully taken into account. The results agree both qualitatively and quantitatively with recent experimental outcomes., Comment: Published in Phys. Rev. B 99, 195419 (2019)

Molecular adsorption on surfaces plays a central role in catalysis, corrosion, desalination, and many other processes of relevance to industry and the natural world. Few adsorption systems are more ubiquitous or of more widespread importance than those involving water and carbon, and for a molecular level understanding of such interfaces water monomer adsorption on graphene is a fundamental and representative system. This system is particularly interesting as it calls for an accurate treatment of electron correlation effects, as well as posing a practical challenge to experiments. Here, we employ many-body electronic structure methodologies that can be rigorously converged and thus provide faithful references for the molecule-surface interaction. In particular, we use diffusion Monte-Carlo (DMC), coupled cluster (CCSD(T)), as well as the random phase approximation (RPA) to calculate the strength of the interaction between water and an extended graphene surface. We establish excellent, sub-chemical, agreement between the complementary high-level methodologies, and an adsorption energy estimate in the most stable configuration of approximately -100\,meV is obtained. We also find that the adsorption energy is rather insensitive to the orientation of the water molecule on the surface, despite different binding motifs involving qualitatively different interfacial charge reorganisation. In producing the first demonstrably accurate adsorption energies for water on graphene this work also resolves discrepancies amongst previously reported values for this widely studied system. It also paves the way for more accurate and reliable studies of liquid water at carbon interfaces with cheaper computational methods, such as density functional theory and classical potentials.

Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated \emph{ab initio} electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers sub-chemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high accuracy methods.

We present an accurate interatomic potential for graphene, constructed using the Gaussian Approximation Potential (GAP) machine learning methodology. This GAP model obtains a faithful representation of a density functional theory (DFT) potential energy surface, facilitating highly accurate (approaching the accuracy of ab initio methods) molecular dynamics simulations. This is achieved at a computational cost which is orders of magnitude lower than that of comparable calculations which directly invoke electronic structure methods. We evaluate the accuracy of our machine learning model alongside that of a number of popular empirical and bond-order potentials, using both experimental and ab initio data as references. We find that whilst significant discrepancies exist between the empirical interatomic potentials and the reference data - and amongst the empirical potentials themselves - the machine learning model introduced here provides exemplary performance in all of the tested areas. The calculated properties include: graphene phonon dispersion curves at 0 K (which we predict with sub-meV accuracy), phonon spectra at finite temperature, in-plane thermal expansion up to 2500 K as compared to NPT ab initio molecular dynamics simulations and a comparison of the thermally induced dispersion of graphene Raman bands to experimental observations. We have made our potential freely available online at [http://www.libatoms.org]., Comment: 20 Pages (Main text), 6 figures v2. Edited Abstract, removed typos. v3. Changed Figure 3

Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature. As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems. The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods. Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension. Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation (RPA), and second order M{\o}ller-Plesset (MP2) theory. These explicitly correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is $-107\pm7$ meV from FNQMC. In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions but interestingly, this is not the case here. This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DFT). Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems. In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods.

We present a comprehensive benchmark study of the adsorption energy of a single water molecule on the (001) LiH surface using periodic coupled cluster and quantum Monte Carlo theories. We benchmark and compare different implementations of quantum chemical wave function based theories in order to verify the reliability of the predicted adsorption energies and the employed approximations. Furthermore we compare the predicted adsorption energies to those obtained employing widely-used van der Waals density-functionals. Our findings show that quantum chemical approaches are becoming a robust and reliable tool for condensed phase electronic structure calculations, providing an additional tool that can also help in potentially improving currently available van der Waals density-functionals.

The interaction strength of molecular hydrogen and water to carbon nanomaterials is relevant to, among many applications, hydrogen storage, water treatment, and water flow. However, accurate interaction energies for hydrogen and water with carbon nanotubes(CNTs) remain scarce despite the importance of having reliable benchmark data to inform experiments and to validate computational models. Here, benchmark fixed-node diffusion Monte Carlo (DMC) interaction energies are provided for hydrogen and water monomers, inside and outside a typical zigzag CNT. The DMC interaction energies provide valuable insight into molecular interactions with CNTs in general, and are also expected to be particularly relevant to gas uptake studies on CNTs. In addition, a selection of density functional theory (DFT) exchangecorrelation(xc) functionals and force field potentials that ought to be suitable for these systems, is compared. An unexpected variation is found in the performance of DFT van der Waals (vdW) models in particular. An analysis of the peculiar discrepancy between different vdW models indicates that medium-range correlation (at circa 3 to 5 \r{A}) plays a key role inside CNTs, and is poorly predicted by some vdW models. Using accurate reference information, this work reveals which xc functionals and force fields perform well for molecules interacting with CNTs. The findings will be valuable to future work on these and related systems, that involve molecules interacting with low-dimensional systems.

Recent experiments on ice formed by water under nanoconfinement provide evidence for a two-dimensional (2D) `square ice' phase. However, the interpretation of the experiments has been questioned and the stability of square ice has become a matter of debate. Partially this is because the simulation approaches employed so far (force fields and density functional theory) struggle to accurately describe the very small energy differences between the relevant phases. Here we report a study of 2D ice using an accurate wave-function based electronic structure approach, namely Diffusion Monte Carlo (DMC). We find that at relatively high pressure square ice is indeed the lowest enthalpy phase examined, supporting the initial experimental claim. Moreover, at lower pressures a `pentagonal ice' phase (not yet observed experimentally) has the lowest enthalpy, and at ambient pressure the `pentagonal ice' phase is degenerate with a `hexagonal ice' phase. Our DMC results also allow us to evaluate the accuracy of various density functional theory exchange correlation functionals and force field models, and in doing so we extend the understanding of how such methodologies perform to challenging 2D structures presenting dangling hydrogen bonds.

Clay minerals are ubiquitous in nature, and the manner in which they interact with their surroundings has important industrial and environmental implications. Consequently, a molecular-level understanding of the adsorption of molecules on clay surfaces is crucial. In this regard computer simulations play an important role, yet the accuracy of widely used empirical force fields (FF) and density functional theory (DFT) exchange-correlation functionals is often unclear in adsorption systems dominated by weak interactions. Herein we present results from quantum Monte Carlo (QMC) for water and methanol adsorption on the prototypical clay kaolinite. To the best of our knowledge, this is the first time QMC has been used to investigate adsorption at a complex, natural surface such as a clay. As well as being valuable in their own right, the QMC benchmarks obtained provide reference data against which the performance of cheaper DFT methods can be tested. Indeed using various DFT exchange-correlation functionals yields a very broad range of adsorption energies, and it is unclear a priori which evaluation is better. QMC reveals that in the systems considered here it is essential to account for van der Waals (vdW) dispersion forces since this alters both the absolute and relative adsorption energies of water and methanol. We show, via FF simulations, that incorrect relative energies can lead to significant changes in the interfacial densities of water and methanol solutions at the kaolinite interface. Despite the clear improvements offered by the vdW-corrected and the vdW-inclusive functionals, absolute adsorption energies are often overestimated, suggesting that the treatment of vdW forces in DFT is not yet a solved problem., Comment: in J. Phys. Chem. C, (2016)

Density functional theory (DFT) studies of weakly interacting complexes have recently focused on the importance of van der Waals dispersion forces whereas, the role of exchange has received far less attention. Here, by exploiting the subtle binding between water and a boron and nitrogen doped benzene derivative (1,2-azaborine) we show how exact exchange can alter the binding conformation within a complex. Benchmark values have been calculated for three orientations of the water monomer on 1,2-azaborine from explicitly correlated quantum chemical methods, and we have also used diffusion quantum Monte Carlo. For a host of popular DFT exchange-correlation functionals we show that the lack of exact exchange leads to the wrong lowest energy orientation of water on 1,2-azaborine. As such, we suggest that a high proportion of exact exchange and the associated improvement in the electronic structure could be needed for the accurate prediction of physisorption sites on doped surfaces and in complex organic molecules. Meanwhile to predict correct absolute interaction energies an accurate description of exchange needs to be augmented by dispersion inclusive functionals, and certain non-local van der Waals functionals (optB88- and optB86b-vdW) perform very well for absolute interaction energies. Through a comparison with water on benzene and borazine (B$_3$N$_3$H$_6$) we show that these results could have implications for the interaction of water with doped graphene surfaces, and suggest a possible way of tuning the interaction energy.

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard to provide high quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Green function to avoid singularities near the nodal surface of the trial wavefunction. We show that these modifications affect the DMC energies in a way that is not size-consistent, resulting in large time-step errors. Building on the modifications of Umrigar {\em et al.} and of DePasquale {\em et al.} we propose a simple Green function modification that restores size-consistency to large values of time-step; substantially reducing the time-step errors. The new algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.

Novel uses for 2-dimensional materials like graphene and hexagonal boron nitride (h-BN) are being frequently discovered especially for membrane and catalysis applications. Still however, a great deal remains to be understood about the interaction of environmentally and industrially elevant molecules such as water with these materials. Taking inspiration from advances in hybridising graphene and h-BN, we explore using density functional theory, the dissociation of water, hydrogen, methane, and methanol on graphene, h-BN, and their isoelectronic doped counterparts: BN doped graphene and C doped h-BN. We find that doped surfaces are considerably more reactive than their pristine counterparts and by comparing the reactivity of several small molecules we develop a general framework for dissociative adsorption. From this a particularly attractive consequence of isoelectronic doping emerges: substrates can be doped to enhance their reactivity specifically towards either polar or non-polar adsorbates. As such, these substrates are potentially viable candidates for selective catalysts and membranes, with the implication that a range of tuneable materials can be designed.

Despite a recent flurry of experimental and simulation studies, an accurate estimate of the interaction strength of water molecules with hexagonal boron nitride is lacking. Here we report quantum Monte Carlo results for the adsorption of a water monomer on a periodic hexagonal boron nitride sheet, which yield a water monomer interaction energy of -84 +/- 5 meV. We use the results to evaluate the performance of several widely used density functional theory (DFT) exchange correlation functionals, and find that they all deviate substantially. Differences in interaction energies between different adsorption sites are however better reproduced by DFT.

High quality reference data from diffusion Monte Carlo calculations are presented for bulk sI methane hydrate, a complex crystal exhibiting both hydrogen-bond and dispersion dominated interactions. The performance of some commonly used exchange-correlation functionals and all-atom point charge force fields is evaluated. Our results show that none of the exchange-correlation functionals tested are sufficient to describe both the energetics and the structure of methane hydrate accurately, whilst the point charge force fields perform badly in their description of the cohesive energy but fair well for the dissociation energetics. By comparing to ice Ih, we show that a good prediction of the volume and cohesive energies for the hydrate relies primarily on an accurate description of the hydrogen bonded water framework, but that to correctly predict stability of the hydrate with respect to dissociation to ice Ih and methane gas, accuracy in the water-methane interaction is also required. Our results highlight the difficulty that density functional theory faces in describing both the hydrogen bonded water framework and the dispersion bound methane., Comment: 8 pages, 4 figures, 1 table. Minor typos corrected and clarification added in Methods

The computational cost of quantum Monte Carlo (QMC) calculations of realistic periodic systems depends strongly on the method of storing and evaluating the many-particle wave function. Previous work [A. J. Williamson et al., Phys. Rev. Lett. 87, 246406 (2001); D. Alf\`e and M. J. Gillan, Phys. Rev. B 70, 161101 (2004)] has demonstrated the reduction of the O(N^3) cost of evaluating the Slater determinant with planewaves to O(N^2) using localized basis functions. We compare four polynomial approximations as basis functions -- interpolating Lagrange polynomials, interpolating piecewise-polynomial-form (pp-) splines, and basis-form (B-) splines (interpolating and smoothing). All these basis functions provide a similar speedup relative to the planewave basis. The pp-splines have eight times the memory requirement of the other methods. To test the accuracy of the basis functions, we apply them to the ground state structures of Si, Al, and MgO. The polynomial approximations differ in accuracy most strongly for MgO and smoothing B-splines most closely reproduce the planewave value for of the variational Monte Carlo energy. Using separate approximations for the Laplacian of the orbitals increases the accuracy sufficiently to justify the increased memory requirement, making smoothing B-splines, with separate approximation for the Laplacian, the preferred choice for approximating planewave-represented orbitals in QMC calculations.

The melting curve of Ni up to 100 GPa has been calculated using first principles methods based on density functional theory (DFT). We used two complementary approaches: i) coexistence simulations with a reference system and then free energy corrections between DFT and the reference system, and ii) direct DFT coexistence using simulation cells including 1000 atoms. The calculated zero pressure melting temperature is slightly underestimated at $1637 \pm 10$ K (experimental value is 1728 K), and at high pressure is significantly higher than recent measurements in diamond anvil cell experiments [Phys. Rev. B {\bf 87}, 054108 (2013)]. The zero pressure DFT melting slope is calculated to be $30 \pm 2$ K, in good agreement with the experimental value of 28 K., Comment: 5 pages, 2 figures

Density-functional theory (DFT) has been widely used to study water and ice for at least 20 years. However, the reliability of different DFT exchange-correlation (xc) functionals for water remains a matter of considerable debate. This is particularly true in light of the recent development of DFT based methods that account for van der Waals (vdW) dispersion forces. Here, we report a detailed study with several xc functionals (semi-local, hybrid, and vdW inclusive approaches) on ice Ih and six proton ordered phases of ice. Consistent with our previous study [Phys. Rev. Lett. 107, 185701 (2011)] which showed that vdW forces become increasingly important at high pressures, we find here that all vdW inclusive methods considered improve the relative energies and transition pressures of the high-pressure ice phases compared to those obtained with semi-local or hybrid xc functionals. However, we also find that significant discrepancies between experiment and the vdW inclusive approaches remain in the cohesive properties of the various phases, causing certain phases to be absent from the phase diagram. Therefore, room for improvement in the description of water at ambient and high pressures remains and we suggest that because of the stern test the high pressure ice phases pose they should be used in future benchmark studies of simulation methods for water., Comment: 13 pages, 5 figures, 4 tables

We report on the thermal and electrical conductivities of two liquid silicon-oxygen-iron mixtures (Fe$_{0.82}$Si$_{0.10}$O$_{0.08}$ and Fe$_{0.79}$Si$_{0.08}$O$_{0.13}$), representative of the composition of the Earth's outer core at the relevant pressure-temperature conditions, obtained from density functional theory calculations with the Kubo-Greenwood formulation. We find thermal conductivities $k$ =100 (160) W m$^{-1}$ K$^{-1}$, and electrical conductivities $\sigma = 1.1 (1.3) \times 10^6 \Omega^{-1}$ m$^{-1}$ at the top (bottom) of the outer core. These new values are between 2 and 3 times higher than previous estimates, and have profound implications for our understanding of the Earth's thermal history and the functioning of the Earth's magnetic field, including rapid cooling rate for the whole core or high level of radiogenic elements in the core. We also show results for a number of structural and dynamic properties of the mixtures, including the partial radial distribution functions, mean square displacements, viscosities and speeds of sound., Comment: 16 pages, 12 figures

Spin crossover molecules have recently emerged as a family of compounds potentially useful for implementing molecular spintronics devices. The calculations of the electronic properties of such molecules is a formidable theoretical challenge as one has to describe the spin ground state of a transition metal as the legand field changes. The problem is dominated by the interplay between strong electron correlation at the transition metal site and charge delocalization over the ligands, and thus it fits into a class of problems where density functional theory may be inadequate. Furthermore, the crossover activity is extremely sensitive to environmental conditions, which are difficult to fully characterize. Here we discuss the phase transition of a prototypical spin crossover molecule as obtained with diffusion Monte Carlo simulations. We demonstrate that the ground state changes depending on whether the molecule is in the gas or in the solid phase. As our calculation provides a solid benchmark for the theory we then assess the performances of density functional theory. We find that the low spin state is always over-stabilized, not only by the (semi-)local functionals, but even by the most commonly used hybrids (such as B3LYP and PBE0). We then propose that reliable results can be obtained by using hybrid functionals containing about 50% of exact-exchange.

The Earth acts as a gigantic heat engine driven by decay of radiogenic isotopes and slow cooling, which gives rise to plate tectonics, volcanoes, and mountain building. Another key product is the geomagnetic field, generated in the liquid iron core by a dynamo running on heat released by cooling and freezing to grow the solid inner core, and on chemical convection due to light elements expelled from the liquid on freezing. The power supplied to the geodynamo, measured by the heat-flux across the core-mantle boundary (CMB), places constraints on Earth's evolution. Estimates of CMB heat-flux depend on properties of iron mixtures under the extreme pressure and temperature conditions in the core, most critically on the thermal and electrical conductivities. These quantities remain poorly known because of inherent difficulties in experimentation and theory. Here we use density functional theory to compute these conductivities in liquid iron mixtures at core conditions from first principles- the first directly computed values that do not rely on estimates based on extrapolations. The mixtures of Fe, O, S, and Si are taken from earlier work and fit the seismologically-determined core density and inner-core boundary density jump. We find both conductivities to be 2-3 times higher than estimates in current use. The changes are so large that core thermal histories and power requirements must be reassessed. New estimates of adiabatic heat-flux give 15-16 TW at the CMB, higher than present estimates of CMB heat-flux based on mantle convection; the top of the core must be thermally stratified and any convection in the upper core driven by chemical convection against the adverse thermal buoyancy or lateral variations in CMB heat flow. Power for the geodynamo is greatly restricted and future models of mantle evolution must incorporate a high CMB heat-flux and explain recent formation of the inner core., Comment: 11 pages including supplementary information, two figures. Scheduled to appear in Nature, April 2012

One of the salient features of graphene is the very high carrier mobility that implies tremendous potential for use in electronic devices. Unfortunately, transport measurements find the expected high mobility only in freely suspended graphen. When supported on a surface, graphene shows a strongly reduced mobility, and an especially severe reduction for temperatures above 200 K. A temperature-dependent mobility reduction could be explained by scattering of carriers with phonons, but this is expected to be weak for pristine, weakly-doped graphene. The mobility reduction has therefore been ascribed to the interaction with confined ripples or substrate phonons. Here we study the temperature-dependent electronic structure of supported graphene by angle-resolved photoemission spectroscopy, a technique that can reveal the origin of the phenomena observed in transport measurements. We show that the electron-phonon coupling for weakly-doped, supported graphene on a metal surface is indeed extremely weak, reaching the lowest value ever reported for any material. However, the temperature-dependent dynamic interaction with the substrate leads to a complex and dramatic change in the carrier type and density that is relevant for transport. Using ab initio molecular dynamics simulations, we show that these changes in the electronic structure are mainly caused by fluctuations in the graphene-substrate distance., Comment: 14 pages, 2 figures