Towards an assessment of the accuracy of density functional theory for first principles simulations of water. II

A series of 20 ps ab initio molecular dynamics simulations of water at ambient density and temperatures ranging from 300 to 450 K are presented. Car-Parrinello (CP) and Born-Oppenheimer (BO) molecular dynamics techniques are compared for systems containing 54 and 64 water molecules. At 300 K, an excellent agreement is found between radial distribution functions (RDFs) obtained with BO and CP dynamics, provided an appropriately small value of the fictitious mass parameter is used in the CP simulation. However, we find that the diffusion coefficients computed from CP dynamics are approximately two times larger than those obtained with BO simulations for T>400 K, where statistically meaningful comparisons can be made. Overall, both BO and CP dynamics at 300 K yield overstructured RDFs and slow diffusion as compared to experiment. In order to understand these discrepancies, the effect of proton quantum motion is investigated with the use of empirical interaction potentials. We find that proton quantum effects may have a larger impact than previously thought on structure and diffusion of the liquid.     

On the accuracy of density functional theory for iron-sulfur clusters

A simple, yet powerful wave function manipulation method was introduced utilizing a generalized ionic fragment approach that allows for systematic mapping of the wave function space for multispin systems with antiferromagnetic coupling. The use of this method was demonstrated for developing ground state electronic wave function for [2Fe-2S] and [Mo-3Fe-4S] clusters. Using well-defined ionic wave functions for ferrous and ferric irons, sulfide, and thiolate fragments, the accuracy of various density functionals and basis sets including effective core potentials were evaluated on a [4Fe-4S] cluster by comparing the calculated geometric and electronic structures with crystallographic data and experimental atomic spin densities from X-ray absorption spectroscopy, respectively. We found that the most reasonable agreement for both geometry and atomic spin densities is obtained by a hybrid functional with 5% HF exchange and 95% density functional exchange supplemented with Perdew's 1986 correlation functional. The basis set seems to saturate only at the triple-zeta level with polarization and diffuse functions. Reasonably preoptimized structures can be obtained by employing computationally less expensive effective core potentials, such as the Stuttgart-Dresden potential with a triple-zeta valence basis set. The extension of the described calibration methodology to other biologically important and more complex iron-sulfur clusters, such as hydrogenase H-cluster and nitrogenase FeMo-co will follow.     

Addressing an instability in unrestricted density functional theory direct dynamics simulations

In Density Functional Theory (DFT) direct dynamics simulations with Unrestricted Hartree Fock (UHF) theory, triplet instability often emerges when numerically integrating a classical trajectory. A broken symmetry initial guess for the wave function is often used to obtain the unrestricted DFT potential energy surface (PES), but this is found to be often insufficient for direct dynamics simulations. An algorithm is described for obtaining smooth transitions between the open-shell and the closed-shell regions of the unrestricted PES, and thus stable trajectories, for direct dynamics simulations of dioxetane and its •O CH₂-CH₂ O• singlet diradical. © 2018 Wiley Periodicals, Inc.     

Assessing the accuracy of quantum Monte Carlo and density functional theory for energetics of small water clusters

We present a detailed study of the energetics of water clusters (H(2)O)(n) with n ≤ 6, comparing diffusion Monte Carlo (DMC) and approximate density functional theory (DFT) with well converged coupled-cluster benchmarks. We use the many-body decomposition of the total energy to classify the errors of DMC and DFT into 1-body, 2-body and beyond-2-body components. Using both equilibrium cluster configurations and thermal ensembles of configurations, we find DMC to be uniformly much more accurate than DFT, partly because some of the approximate functionals give poor 1-body distortion energies. Even when these are corrected, DFT remains considerably less accurate than DMC. When both 1- and 2-body errors of DFT are corrected, some functionals compete in accuracy with DMC; however, other functionals remain worse, showing that they suffer from significant beyond-2-body errors. Combining the evidence presented here with the recently demonstrated high accuracy of DMC for ice structures, we suggest how DMC can now be used to provide benchmarks for larger clusters and for bulk liquid water.     

Characterization of methoxy adsorption on some transition metals: a first principles density functional theory study

Based on the gradient-density functional theory, calculation results of methoxy adsorption on Au(111), Ag(111), Cu(111), Pt(111), Pd(111), Ni(111), Rh(111), and Fe(100) surfaces are presented, and a consistent picture for some key physical properties determining the reactivity of metals appears. These eight metals belong to two groups: either with filled d electrons (group IB) or with unfilled but more than half filled d electrons (group VIII). The calculated adsorption energies are quite in agreement with the experimental data as well as the previous theoretical calculation results. Importantly, using the analysis of B. Hammer and J. K. Norskov, Nature (London) 376, 232 (1995) and in Chemisorption and Reactivity on Supported Clusters and Thin Films, edited by R. M. Lambert and G. Pacchioni (Kluwer Academic, Dordrecht, 1997), pp. 285-351, the binding energies have selectively been linearly correlated to the d-band center and to the size of the metal d-band orbital overlapping with the adsorbate (coupling matrix element) for these two groups of metals. And by analyzing the nature of the adsorption bonding, the possible reason of this difference is suggested.     

Liquid structures of water, methanol, and hydrogen fluoride at ambient conditions from first principles molecular dynamics simulations with a dispersion corrected density functional

Using first principles molecular dynamics simulations in the isobaric-isothermal ensemble (T = 300 K, p = 1 atm) with the Becke-Lee-Yang-Parr exchange/correlation functional and a dispersion correction due to Grimme, the hydrogen bonding networks of pure liquid water, methanol, and hydrogen fluoride are probed. Although an accurate density is found for water with this level of electronic structure theory, the average liquid densities for both hydrogen fluoride and methanol are overpredicted by 50 and 25%, respectively. The radial distribution functions indicate somewhat overstructured liquid phases for all three compounds. The number of hydrogen bonds per molecule in water is about twice as high as for methanol and hydrogen fluoride, though the ratio of cohesive energy over number of hydrogen bonds is lower for water. An analysis of the hydrogen-bonded aggregates revealed the presence of mostly linear chains in both hydrogen fluoride and methanol, with a few stable rings and chains spanning the simulation box in the case of hydrogen fluoride. Only an extremely small fraction of smaller clusters was found for water, indicating that its hydrogen bond network is significantly more extensive. A special form of water with on average about two hydrogen bonds per molecule yields a hydrogen-bonding environment significantly different from the other two compounds.     

The relationship between formate adsorption energy and electronic properties: A first principles density functional theory study

First principles density functional theory calculations have been performed for the chemisorption of formate adsorption on some metal surfaces. For the most stable adsorption site of short-bridge, the calculated formate adsorption energy follows the order of Au(110) < Ag(110) < Cu(110) < Pd(110) < Pt(110) < Ni(110) < Rh(110) < Fe(100) < Mo(100), and a clear linear correlation exists between the adsorption energy and the corresponding heat of formation of metal oxides. Moreover, it has been found that the fo...     

Clustering in the absence of attractions: density functional theory and computer simulations

We numerically investigate the formation of stable clusters of overlapping particles in certain systems interacting via purely repulsive, bounded pair potentials. In close vicinity of a first-order phase transition between a disordered and an ordered structure, clusters are encountered already in the fluid phase which then freeze into crystals with multiply occupied lattice sites. These hyper-crystals are characterized by a number of remarkable features that are in clear contradiction to our experience with harshly repulsive systems: upon compression, the lattice constant remains invariant, leading to a concomitant linear growth in the cluster population with density; further, the freezing and melting lines are to high accuracy linear in the density-temperature plane, and the conventional indicator that announces freezing, that is, the Hansen-Verlet value of the first peak of the structure factor, attains for these soft systems much higher values than for their hard-matter counterparts. Our investigations are based on the generalized exponential model of index 4 (i.e., Phi(r) approximately exp[-(r/sigma)4]). The properties of the phases involved are calculated via liquid state theory and classical density functional theory. Monte Carlo simulations for selected states confirm the theoretical results for the structural and thermodynamic properties of the system. These numerical data, in turn, fully corroborate an approximate theoretical framework that was recently put forward to explain the clustering phenomenon for systems of this kind (Likos, C. N.; Mladek, B. M.; Gottwald, D.; Kahl, G. J. Chem. Phys. 2007, 126, 224502).     

Resolving the CO/CN ligand arrangement in CO-inactivated [FeFe] hydrogenase by first principles density functional theory calculations

The currently presumed assignment of CO/CN ligands in the structure of the active cluster in CO-inactivated [FeFe] hydrogenase is shown to be inconsistent with the available IR data in the enzyme from Clostridium pasteurianum I. A different arrangement has the correct qualitative and quantitative features, reproducing the observed line spacing and intensities and the observed line shift consequent to inactivation with labeled 13CO instead of 12CO. The new assignment is also consistent with the observed change from rhombic to axial symmetry of the electron paramagnetic resonance g tensor upon inactivation.     

Fitting properties from density functional theory based molecular dynamics simulations to parameterize a rigid water force field

In the quest towards coarse-grained potentials and new water models, we present an extension of the force matching technique to parameterize an all-atom force field for rigid water. The methodology presented here allows to improve the matching procedure by first optimizing the weighting exponents present in the objective function. A new gauge for unambiguously evaluating the quality of the fit has been introduced; it is based on the root mean square difference of the distributions of target properties between reference data and fitted potentials. Four rigid water models have been parameterized; the matching procedure has been used to assess the role of the ghost atom in TIP4P-like models and of electrostatic damping. In the former case, burying the negative charge inside the molecule allows to fit better the torques. In the latter, since short-range interactions are damped, a better fit of the forces is obtained. Overall, the best performing model is the one with a ghost atom and with electrostatic damping. The approach shown in this paper is of general validity and could be applied to any matching algorithm and to any level of coarse graining, also for non-rigid molecules.     

Thermodynamics of symmetric dimers: lattice density functional theory predictions and simulations

A new lattice density functional theory (DFT) approach is proposed for symmetric dimers taking into account all possible configurations for molecules adjacent to a central dimer. Comparison with Monte Carlo simulations shows significant improvement of the proposed model compared to previously developed version of lattice DFT for dimers. It is shown that the new model gives accurate analytical solutions over a wide range of densities and temperatures. Phase transitions in dimers are analyzed and fundamental differences between dimers and monomers are discussed.     

A density functional theory for studying ionization processes in water clusters

A generalized Kohn-Sham (GKS) approach to density functional theory (DFT), based on the Baer-Neuhauser-Livshits range-separated hybrid, combined with ab initio motivated range-parameter tuning is used to study properties of water dimer and pentamer cations. The water dimer is first used as a benchmark system to check the approach. The present brand of DFT localizes the positive charge (hole), stabilizing the proton transferred geometry in agreement with recent coupled-cluster calculations. Relative energies of various conformers of the water dimer cation compare well with previously published coupled cluster results. The GKS orbital energies are good approximations to the experimental ionization potentials of the system. Low-lying excitation energies calculated from time-dependent DFT based on the present method compare well with recently published high-level "equation of motion-coupled-cluster" calculations. The harmonic frequencies of the water dimer cation are in good agreement with experimental and wave function calculations where available. The method is applied to study the water pentamer cation. Three conformers are identified: two are Eigen type and one is a Zundel type. The structure and harmonic vibrational structure are analyzed. The ionization dynamics of a pentamer water cluster at 0 K shows a fast <50 fs transient for transferring a proton from one of the water molecules, releasing a hydroxyl radical and creating a protonated tetramer carrying the excess hole.     

Frontiers in first principles modelling of electrochemical simulations

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Real-time, local basis-set implementation of time-dependent density functional theory for excited state dynamics simulations

We present a method suitable for large-scale accurate simulations of excited state dynamics within the framework of time-dependent density functional theory (DFT). This is achieved by employing a local atomic basis-set representation and real-time propagation of excited state wave functions. We implement the method within SIESTA, a standard ground-state DFT package with local atomic basis, and demonstrate its potential for realistic and accurate excited state dynamics simulations using small and medium-sized molecules as examples (H(2), CO, O(3), and indolequinone). The method can be readily applied to problems involving nanostructures and large biomolecules.     

Exact-exchange density functional theory for hyperpolarizabilities

Time-dependent density functional theory (TDDFT) employing the exact-exchange functional (TDDFTx) has been formulated using the optimized effective potential method for the beta static hyperpolarizabilities, where it reduces to coupled-perturbed Kohn-Sham theory. A diagrammatic technique is used to take the functional derivatives for the derivation of the adiabatic second kernel, which is required for the analytical calculation of the beta static hyperpolarizabilities with DFT. The derived formulas have been implemented using Gaussian basis sets. The structure of the adiabatic exact-exchange second kernel is described and numerical examples are presented. It is shown that no current DFT functional satisfies the correct properties of the second kernel. Not surprisingly, TDDFTx, which corrects the self-interaction error in standard DFT methods and has the correct long-range behavior, provides results close to those of time-dependent Hartree-Fock in the static limit.     

Energies of ions in water and nanopores within density functional theory

Accurate calculations of electrostatic potentials and treatment of substrate polarizability are critical for predicting the permeation of ions inside water-filled nanopores. The ab initio molecular dynamics method, based on density functional theory (DFT), accounts for the polarizability of materials, water, and solutes, and it should be the method of choice for predicting accurate electrostatic energies of ions. In practice, DFT coupled with the use of periodic boundary conditions in a charged system leads to large energy shifts. Results obtained using different DFT packages may vary because of the way pseudopotentials and long-range electrostatics are implemented. Using maximally localized Wannier functions, we apply robust corrections that yield relatively unambiguous ion energies in select molecular and aqueous systems and inside carbon nanotubes. Large binding energies are predicted for ions in metallic carbon nanotube arrays, while Na+ and Cl- energies are found to exhibit asymmetry in water that is smaller than but comparable with those computed using nonpolarizable water force fields.     

Generalized density functional theory for degenerate states

An extension of density functional theory is proposed for degenerate states. There are suitably selected basic variables beyond the subspace density. Generalized Kohn-Sham equations are derived. A direct method is proposed to ensure the fixed value of ensemble quantities. Then the Kohn-Sham equations are similar to the conventional Kohn-Sham equations. But the Kohn-Sham potential is different for different ensembles. A simple local expression is proposed for the correlation energy.     

Incremental solver for orbital-free density functional theory

First-principle calculations are still a challenge since they require a great amount of computational time. In this article, we introduce a new algorithm to perform orbital-free density functional theory (OF-DFT) calculations. Our new algorithm focuses computational efforts on important parts of the particle system, which, in the context of adaptively restrained particle simulations (ARPS) allows us to accelerate particle simulations. © 2019 Wiley Periodicals, Inc.