On the accuracy of van der Waals inclusive density-functional theory exchange-correlation functionals for ice at ambient and high pressures

Toward Accurate Adsorption Energetics on Clay Surfaces

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.

Evaluating dispersion forces for optimization of van der Waals complexes using a non-empirical functional

Modelling dispersion interactions with traditional density functional theory (DFT) is a challenge that has been extensively addressed in the past decade. The exchange-dipole moment (XDM), among others, is a non-empirical add-on dispersion correction model in DFT. The functional PW86+PBE+XDM for exchange, correlation and dispersion, respectively, compromises an accurate functional for thermochemistry and for van der Waals (vdW) complexes at equilibrium and non-equilibrium geometries. To use this functional in optimizing vdW complexes, rather than computing single point energies, it is necessary to evaluate accurate forces. The purpose of this paper is to validate that, along the potential energy surface, the distance at which the energy is minimum is commensurate with the distance at which the forces vanish to zero. This test was validated for 10 rare gas diatomic molecules using various integration grids and different convergence criteria. It was found that the use of either convergence criterion, 10^-6 or 10^-8, in Gaussian09, does not affect the accuracy of computed optimal distances and binding energies. An ultra-fine grid needs to be used when computing accurate energies using generalized gradient approximation functionals.This article is part of the themed issue 'Multiscale modelling at the physics-chemistry-biology interface'.

Raman and IR Spectra of Ice Ih and Ice XI with an Assessment of DFT Methods

IR and Raman spectroscopic technology can be directly used to identify the occurrence of ferroelectric ice XI in laboratory or extraterrestrial settings. The performance of 16 different DFT methods applied on the ice Ih, VIII, IX, and XI crystal phases is evaluated. Based on a selected DFT computational scheme, the IR and Raman spectra of ice Ih and XI are derived and compared. When the spectra, both IR and Raman, of ice Ih and ice XI are compared, the librational vibrations are found to be the most affected by the proton ordering. The spectroscopic fingerprint of ice XI can be used to distinguish ferroelectric ice XI from ice Ih in the universe. Furthermore, the existence of only one kind of H-bond in ice Ih is demonstrated from the overlapping subspectra for different types of H-bonded pair configurations in 16 isomers of ice Ih, which provides an illustration to the historic debate on whether one or two kinds of H-bonds existed in ice.

Effect of packing motifs on the energy ranking and electronic properties of putative crystal structures of tricyano-1,4-dithiino[c]-isothiazole

We present an analysis of putative structures of tricyano-1,4-dithiino[c]-isothiazole (TCS3), generated within the sixth crystal structure prediction blind test. Typical packing motifs are identified and characterized in terms of distinct patterns of close contacts and regions of electrostatic and dispersion interactions. We find that different dispersion-inclusive density functional theory (DFT) methods systematically favor specific packing motifs, which may affect the outcome of crystal structure prediction efforts. The effect of crystal packing on the electronic and optical properties of TCS3 is investigated using many-body perturbation theory within the GW approximation and the Bethe-Salpeter equation (BSE). We find that a structure with Pna21 symmetry and a bilayer packing motif exhibits intermolecular bonding patterns reminiscent of π-π stacking and has markedly different electronic and optical properties than the experimentally observed P21/n structure with a cyclic dimer motif, including a narrower band gap, enhanced band dispersion and broader optical absorption. The Pna21 bilayer structure is close in energy to the observed structure and may be feasible to grow.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Active sites and mechanisms for H₂O₂ decomposition over Pd catalysts

A combination of periodic, self-consistent density functional theory (DFT-GGA-PW91) calculations, reaction kinetics experiments on a SiO2-supported Pd catalyst, and mean-field microkinetic modeling are used to probe key aspects of H2O2 decomposition on Pd in the absence of cofeeding H2 We conclude that both Pd(111) and OH-partially covered Pd(100) surfaces represent the nature of the active site for H2O2 decomposition on the supported Pd catalyst reasonably well. Furthermore, all reaction flux in the closed catalytic cycle is predicted to flow through an O-O bond scission step in either H2O2 or OOH, followed by rapid H-transfer steps to produce the H2O and O2 products. The barrier for O-O bond scission is sensitive to Pd surface structure and is concluded to be the central parameter governing H2O2 decomposition activity.

Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs

Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm(3) and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3(atm) gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3%.

Structure prediction of the solid forms of methanol: an ab initio random structure searching approach

Liquid methanol and methanol clusters have been comprehensively studied to reveal their local structure and hydrogen bond networks.

Water adsorption in SAPO-34: elucidating the role of local heterogeneities and defects using dispersion-corrected DFT calculations

The chabazite-type silicoaluminophosphate SAPO-34 is a promising adsorbent for applications in thermal energy storage using water adsorption-desorption cycles. In order to develop a microscopic understanding of the impact of local heterogeneities and defects on the water adsorption properties, the interaction of different models of SAPO-34 with water was studied using dispersion-corrected density-functional theory (DFT-D) calculations. In addition to SAPO-34 with isolated silicon atoms, the calculations considered models incorporating two types of heterogeneities (silicon islands, aluminosilicate domains), and two defect-containing (partially and fully desilicated) systems. DFT-D optimisations were performed for systems with small amounts of adsorbed water, in which all H2O molecules can interact with framework protons, and systems with large amounts of adsorbed water (30 H2O molecules per unit cell). At low loadings, the host-guest interaction energy calculated for SAPO-34 with isolated Si atoms amounts to approximately -90 kJ mol(-1). While the presence of local heterogeneities leads to the creation of some adsorption sites that are energetically slightly more favourable, the interaction strength is drastically reduced in systems with defects. At high water loadings, energies in the range of -70 kJ mol(-1) are obtained for all models. The DFT-D interaction energies are in good agreement with experimentally measured heats of water adsorption. A detailed analysis of the equilibrium structures was used to gain insights into the binding modes at low coverages, and to assess the extent of framework deprotonation and changes in the coordination environment of aluminium atoms at high water loadings.

Probing the structural and dynamical properties of liquid water with models including non-local electron correlation

Water is a ubiquitous liquid that displays a wide range of anomalous properties and has a delicate structure that challenges experiment and simulation alike. The various intermolecular interactions that play an important role, such as repulsion, polarization, hydrogen bonding, and van der Waals interactions, are often difficult to reproduce faithfully in atomistic models. Here, electronic structure theories including all these interactions at equal footing, which requires the inclusion of non-local electron correlation, are used to describe structure and dynamics of bulk liquid water. Isobaric-isothermal (NpT) ensemble simulations based on the Random Phase Approximation (RPA) yield excellent density (0.994 g/ml) and fair radial distribution functions, while various other density functional approximations produce scattered results (0.8-1.2 g/ml). Molecular dynamics simulation in the microcanonical (NVE) ensemble based on Møller-Plesset perturbation theory (MP2) yields dynamical properties in the condensed phase, namely, the infrared spectrum and diffusion constant. At the MP2 and RPA levels of theory, ice is correctly predicted to float on water, resolving one of the anomalies as resulting from a delicate balance between van der Waals and hydrogen bonding interactions. For several properties, obtaining quantitative agreement with experiment requires correction for nuclear quantum effects (NQEs), highlighting their importance, for structure, dynamics, and electronic properties. A computed NQE shift of 0.6 eV for the band gap and absorption spectrum illustrates the latter. Giving access to both structure and dynamics of condensed phase systems, non-local electron correlation will increasingly be used to study systems where weak interactions are of paramount importance.

Consistent structures and interactions by density functional theory with small atomic orbital basis sets

A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of "low-cost" electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust "high-speed" computational tool in theoretical chemistry and physics.

Elucidating the fundamental forces in protein crystal formation: the case of crambin

This study demonstrates the feasibility of periodic all-electron hybrid density functional theory calculations in the description of protein crystals, using crambin as a test case.

Molecular simulations of proteins have been usually accomplished through empirical or semi-empirical potentials, due to the large size and inherent complexity of these biological systems. On the other hand, a theoretical description of proteins based on quantum-mechanical methods would however provide an unbiased characterization of their electronic properties, possibly offering a link between these and the ultimate biological activity. Yet, such approaches have been historically hindered by the large amount of requested computational power. Here we demonstrate the feasibility of periodic all-electron density functional theory calculations in the description of the crystal of the protein crambin (46 aminoacids), which is determined with exceptional structural accuracy. We have employed the hybrid B3LYP functional, coupled to an empirical description of London interactions (D*) to simulate the crambin crystal with an increasing amount of lattice water molecules in the cell (up to 172H₂O per cell). The agreement with the experiment is good for both protein geometry and protein–water interactions. The energetics was computed to predict crystal formation energies, protein–water and protein–protein interaction energies. We studied the role of dispersion interactions which are crucial for holding the crambin crystal in place. B3LYP-D* electrostatic potential and dipole moment of crambin as well as the electronic charge flow from crambin to the solvating water molecules (0.0015e per H₂O) have also been predicted. These results proved that quantum-mechanical simulations of small proteins, both free and in their crystalline state, are now feasible in a reasonable amount of time, by programs capable of exploiting high performance computing architectures, allowing the study of protein properties not easily amenable through classical force fields.

Water on BN doped benzene: a hard test for exchange-correlation functionals and the impact of exact exchange on weak binding

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 (B3N3H6) 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.

Density and Compressibility of Liquid Water and Ice from First-Principles Simulations with Hybrid Functionals

We determined the equilibrium density and compressibility of water and ice from first-principles molecular dynamics simulations using gradient-corrected (PBE) and hybrid (PBE0) functionals. Both functionals predicted the density of ice to be larger than that of water, by 15 (PBE) and 35% (PBE0). The PBE0 functional yielded a lower density of both ice and water with respect to PBE, leading to better agreement with experiment for ice but not for liquid water. Approximate inclusion of dispersion interactions on computed molecular-dynamics trajectories led to a substantial improvement of the PBE0 results for the density of liquid water, which, however, resulted to be slightly lower than that of ice.

Structure and energetics of hydrogen-bonded networks of methanol on close packed transition metal surfaces

Methanol is a versatile chemical feedstock, fuel source, and energy storage material. Many reactions involving methanol are catalyzed by transition metal surfaces, on which hydrogen-bonded methanol overlayers form. As with water, the structure of these overlayers is expected to depend on a delicate balance of hydrogen bonding and adsorbate-substrate bonding. In contrast to water, however, relatively little is known about the structures methanol overlayers form and how these vary from one substrate to another. To address this issue, herein we analyze the hydrogen bonded networks that methanol forms as a function of coverage on three catalytically important surfaces, Au(111), Cu(111), and Pt(111), using a combination of scanning tunneling microscopy and density functional theory. We investigate the effect of intermolecular interactions, surface coverage, and adsorption energies on molecular assembly and compare the results to more widely studied water networks on the same surfaces. Two main factors are shown to direct the structure of methanol on the surfaces studied: the surface coverage and the competition between the methanol-methanol and methanol-surface interactions. Additionally, we report a new chiral form of buckled hexamer formed by surface bound methanol that maximizes the interactions between methanol monomers by sacrificing interactions with the surface. These results serve as a direct comparison of interaction strength, assembly, and chirality of methanol networks on Au(111), Cu(111), and Pt(111) which are catalytically relevant for methanol oxidation, steam reforming, and direct methanol fuel cells.

The individual and collective effects of exact exchange and dispersion interactions on the ab initio structure of liquid water

In this work, we report the results of a series of density functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid water using a hierarchy of exchange-correlation (XC) functionals to investigate the individual and collective effects of exact exchange (Exx), via the PBE0 hybrid functional, non-local van der Waals/dispersion (vdW) interactions, via a fully self-consistent density-dependent dispersion correction, and an approximate treatment of nuclear quantum effects, via a 30 K increase in the simulation temperature, on the microscopic structure of liquid water. Based on these AIMD simulations, we found that the collective inclusion of Exx and vdW as resulting from a large-scale AIMD simulation of (H2O)128 significantly softens the structure of ambient liquid water and yields an oxygen-oxygen structure factor, SOO(Q), and corresponding oxygen-oxygen radial distribution function, gOO(r), that are now in quantitative agreement with the best available experimental data. This level of agreement between simulation and experiment demonstrated herein originates from an increase in the relative population of water molecules in the interstitial region between the first and second coordination shells, a collective reorganization in the liquid phase which is facilitated by a weakening of the hydrogen bond strength by the use of a hybrid XC functional, coupled with a relative stabilization of the resultant disordered liquid water configurations by the inclusion of non-local vdW/dispersion interactions. This increasingly more accurate description of the underlying hydrogen bond network in liquid water also yields higher-order correlation functions, such as the oxygen-oxygen-oxygen triplet angular distribution, POOO(θ), and therefore the degree of local tetrahedrality, as well as electrostatic properties, such as the effective molecular dipole moment, that are in much better agreement with experiment.

Benchmarking the performance of density functional theory and point charge force fields in their description of sI methane hydrate against diffusion Monte Carlo

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, while 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.

The accurate calculation of the band gap of liquid water by means of GW corrections applied to plane-wave density functional theory molecular dynamics simulations

Knowledge about the intrinsic electronic properties of water is imperative for understanding the behaviour of aqueous solutions that are used throughout biology, chemistry, physics, and industry.

Periodic MP2, RPA, and Boundary Condition Assessment of Hydrogen Ordering in Ice XV

Ice XV is the hydrogen-ordered form of the ice VI phase whose structure was predicted to be Cc and ferroelectric using periodic DFT approaches. However, neutron diffraction and Raman spectroscopy data show the structure to have P1̅ symmetry and to be antiferroelectric. Recent work1 using fragment-based MP2 and CCSD(T) approaches predicts the experimental structure as the ground state. We have reconsidered this problem using fully periodic MP2 and RPA approaches and find that the ferroelectric Cc structure is the lowest energy configuration. However, ubiquitously employed tinfoil boundary conditions stabilize polar structures. We suggest that ferroelectric Cc crystals can grow within a paraelectric ice VI matrix but may become unstable once a fraction of the matrix has become hydrogen-ordered. The reduction in dielectric constant causes P1̅ and other structures with small polarization to become favored, providing a possible resolution between observation and theoretical predictions.