Nonlocal Density Functionals Research Articles

Ab initio and classical atomistic modelling of structure and defects in crystalline orthorhombic polyethylene: Twin boundaries, slip interfaces, and nature of barriers

We study the stability of twin boundaries and slip in crystalline orthorhombic polyethylene by means of density functional theory (DFT), using a nonempirical, truly nonlocal density function, and by means of classical molecular dynamics (MD). The results show that, in accordance with experimental observations, there is a clear preference to chain slip over transverse slip for all considered slip planes. The activation energy for pure chain slip lies in the range 10–20 mJ/m2 while that for transverse slip corresponds to 40–280 mJ/m2. For the (11¯0)-slip plane the energy landscape is non-convex with multiple potential energy minima, indicating the presence of stable stacking faults. This suggests that dissociation of perfect dislocations into partials may occur. For the two low-energy twin boundaries considered in this work, {110} and {310}, we find that the former is more stable than the latter, with ground state energies corresponding to 8.9 and 28 mJ/m2, respectively. We have also evaluated how well the empirical MD simulations with the all-atom optimized potential for liquid MD simulations (OPLS-AA) and the coarse-grained united atom (UA) potential concur with the DFT results. It is found that an all-atom potential is necessary to partially capture the γ-surface energy landscapes obtained from the DFT calculations. The OPLS-AA predicts chain slip activation energies comparable with DFT data, while the transverse slip energy thresholds are low in comparison, which is attributed to weak close ranged monomer repulsion. Finally, we find that the H-H interaction dominates the slip activation. While not explicitly represented in the UA potential, its key role is revealed by correlating the DFT energy landscape with changes in the electron distributions and by MD simulations in which components of the OPLS-AA intermolecular potential are selectively silenced.

Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy.

From a simplified version of the mathematical structure of the strong coupling limit of the exact exchange-correlation functional, we construct an approximation for the electronic repulsion energy at physical coupling strength, which is fully nonlocal. This functional is self-interaction free and yields energy densities within the definition of the electrostatic potential of the exchange-correlation hole that are locally accurate and have the correct asymptotic behavior. The model is able to capture strong correlation effects that arise from chemical bond dissociation, without relying on error cancellation. These features, which are usually missed by standard density functional theory (DFT) functionals, are captured by the highly nonlocal structure, which goes beyond the “Jacob’s ladder” framework for functional construction, by using integrals of the density as the key ingredient. Possible routes for obtaining the full exchange-correlation functional by recovering the missing kinetic component of the correlation energy are also implemented and discussed.

Nonlocal energy density functionals for pairing and beyond-mean-field calculations

We propose to use two-body regularized finite-range pseudopotential to generate nuclear energy density functional (EDF) in both particle–hole and particle–particle channels, which makes it free from self-interaction and self-pairing, and also free from singularities when used beyond mean field. We derive a sequence of pseudopotentials regularized up to next-to-leading order and next-to-next-to-leading order, which fairly well describe infinite-nuclear-matter properties and finite open-shell paired and/or deformed nuclei. Since pure two-body pseudopotentials cannot generate sufficiently large effective mass, the obtained solutions constitute a preliminary step towards future implementations, which will include, e.g., EDF terms generated by three-body pseudopotentials.

Vapor Liquid Equilibria of Hydrofluorocarbons Using Dispersion-Corrected and Nonlocal Density Functionals.

Recent developments in dispersion corrected and nonlocal density functionals are aimed at accurately capturing dispersion interactions, a key shortcoming of local and semilocal approximations of density functional theory. These functionals have shown significant promise for dimers and small clusters of molecules as well as crystalline materials. However, their efficacy for predicting vapor liquid equilibria is largely unexplored. In this work, we examine the accuracy of dispersion-corrected and nonlocal van der Waals functionals by computing the vapor liquid coexistence curves (VLCCs) of hydrofluoromethanes. Our results indicate that the PBE-D3 functional performs significantly better in predicting saturated liquid densities than the rVV10 functional. With the PBE-D3 functional, we also find that as the number of fluorine atoms increase in the molecule, the accuracy of saturated liquid density prediction improves as well. All the functionals significantly underpredict the saturated vapor densities, which also result in an underprediction of saturated vapor pressure of all compounds. Despite the differences in the bulk liquid densities, the local microstructures of the liquid CFH3 and CF2H2 are relatively insensitive to the density functional employed. For CF3H, however, rVV10 predicts slightly more structured liquid than the PBE-D3 functional.

Phonons in nonlocal van der Waals density functional theory

We extend the formulation of density functional perturbation theory to treat nonlocal density functionals, accounting for van der Waals interactions, in a rigorous and efficient way. We provide a general formalism, suitable for any functional in this family, and give specific equations for the most widely used ones. We then study the lattice dynamics of graphite, comparing several nonlocal functionals and the local density approximation, showing that our recent revision of the VV10 functional [R. Sabatini et al., Phys. Rev. B 87, 041108(R) (2013)] gives the best comparison with experiments.

Density Functional Methods for Fast Screening of Metal–Organic Frameworks for Hydrogen Storage

Classical density functional theory (DFT) has been routinely used for the characterization of pore size distribution and specific surface area of porous materials by gas physisorption. However, its application to large-scale screening of materials for gas storage has been largely unexplored because it is commonly believed that the DFT calculations are applicable only to one-dimensional systems and highly sensitive to the approximations introduced in the free-energy functionals. In this work, we have investigated four representative versions of nonlocal density functionals for predicting H2 adsorption using both the slit pore model and a large library of metal–organic frameworks (MOFs) under a broad range of temperatures and pressures. The four versions of DFT share a common functional from the modified fundamental measure theory to account for the molecular excluded volume effects while differing in their approximations to represent the intermolecular attractions, viz., mean-field approximation, two versi...

Role of van der Waals Forces in Thermodynamics and Kinetics of Layered Transition Metal Oxide Electrodes: Alkali and Alkaline-Earth Ion Insertion into V2O5

Layered transition metal oxides (LTMOs) have a long tradition of success as effective electrode materials for power storage applications. However, the growing demand for improved technologies has motivated a strong interest in developing new generations of this class of materials. First-principles calculations, in particular density functional theory (DFT), have become an important tool to gain atomic-level understanding and speed up the search of new materials in general. An important structural ingredient of LTMOs is the weak van der Waals (vdW) forces that hold layers together. Unfortunately, conventional DFT approaches have serious shortcomings to treat these dispersion interactions. This is an uneasy position for the role of DFT in describing such layered-type structural materials. Recent exciting developments in DFT allow us now to tackle this problem head on. Here we have employed newly developed vdW-inclusive methods based on improved nonlocal density functionals to thoroughly explore the role of ...

Nonlocal energy density functionals for low-energy nuclear structure

We introduce a finite-range pseudopotential built as an expansion in derivatives up to next-to-next-to-next-to-leading order and we calculate the corresponding nonlocal energy density functional (EDF). The coupling constants of the nonlocal EDF, for both finite nuclei and infinite nuclear matter, are expressed through the parameters of the pseudopotential. All central, spin-orbit, and tensor terms of the pseudopotential are derived both in the spherical-tensor and Cartesian representation. At next-to-leading order, we also derive relations between the nonlocal EDF expressed in the spherical-tensor and Cartesian formalism. Finally, a simplified version of the finite-range pseudopotential is considered, which generates the EDF identical to that generated by a local potential.

Insight into the description of van der Waals forces for benzene adsorption on transition metal (111) surfaces

Exploring the role of van der Waals (vdW) forces on the adsorption of molecules on extended metal surfaces has become possible in recent years thanks to exciting developments in density functional theory (DFT). Among these newly developed vdW-inclusive methods, interatomic vdW approaches that account for the nonlocal screening within the bulk [V. G. Ruiz, W. Liu, E. Zojer, M. Scheffler, and A. Tkatchenko, Phys. Rev. Lett. 108, 146103 (2012)] and improved nonlocal functionals [J. Klimeš, D. R. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010)] have emerged as promising candidates to account efficiently and accurately for the lack of long-range vdW forces in most popular DFT exchange-correlation functionals. Here we have used these two approaches to compute benzene adsorption on a range of close-packed (111) surfaces upon which it either physisorbs (Cu, Ag, and Au) or chemisorbs (Rh, Pd, Ir, and Pt). We have thoroughly compared the performance between the two classes of vdW-inclusive methods and when available compared the results obtained with experimental data. By examining the computed adsorption energies, equilibrium distances, and binding curves we conclude that both methods allow for an accurate treatment of adsorption at equilibrium adsorbate-substrate distances. To this end, explicit inclusion of electrodynamic screening in the interatomic vdW scheme and optimized exchange functionals in the case of nonlocal vdW density functionals is mandatory. Nevertheless, some discrepancies are found between these two classes of methods at large adsorbate-substrate separations.

Fundamental studies of H2 interaction with MAl3 clusters [M = Li, Sc, Ti, Zr

Complex metal hydride is a promising hydrogen storage material for automobile applications due to its reversible storage capacity. The presence of transition metal halide is found to improve significantly the kinetics of H2 adsorption and desorption processes. Experimental studies have indicated the formation of distorted MAl3 phase where M=Sc, Ti, Zr. In this study, a first-principles density functional study has been performed to investigate the hydrogen interaction and saturation on stable tetrahedral MAl3 clusters [M=Li, Sc, Ti, and Zr] by employing spin-polarized hybrid and non-local density functionals. On saturation, the first H2 molecule undergoes chemisorption in the transition metals while further loading results in physisorption with the Kubas-type H2 interaction. Activation energy barrier for the H2 dissociation over the cluster is calculated to be ∼0.2eV for the transition metals. Effect of external electric field on the MAl3H4 cluster with molecular H2 is studied which leads to polarization of physisorbed H2 and the cluster. The results offer an explanation for catalysts role in improving the kinetics of H2 sorption process in complex metal hydrides.

Towards nonlocal density functionals by explicit modeling of the exchange-correlation hole in inhomogeneous systems

We put forward new approach for the development of a non-local density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc-energy and an accurate corresponding xc-potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains -1 electron, (2) the xc-potential has the asymptotic -1/r behavior outside finite systems and (3) the xc-potential has the correct step structure related to the derivative discontinuities of the xc-energy functional. None of the currently existing functionals satisfies all these requirements. These demands are achieved by screening the exchange hole in such a way that the pair-correlation function is symmetric and satisfies the sum-rule. These two features immediately imply (1) and (2) while the explicit dependence of the exchange hole on the Kohn-Sham orbitals implies (3). Preliminary calculations show an improved physical description of the dissociating hydrogen molecule. Though the total energy is still far from perfect, the binding curve from our non-local density functional provides a significant improvement over the local density approximation.

Nuclear Quantum Effects and Nonlocal Exchange-Correlation Functionals Applied to Liquid Hydrogen at High Pressure

Using first-principles molecular dynamics, we study the influence of nuclear quantum effects (NQEs) and nonlocal exchange-correlation density functionals (DFs) near molecular dissociation in liquid hydrogen. NQEs strongly influence intramolecular properties, such as bond stability, and are thus an essential part of the dissociation process. Moreover, by including DFs that account for either the self-interaction error or dispersion interactions, we find a much better description of molecular dissociation and metallization than previous studies based on classical protons and/or local or semilocal DFs. We obtain excellent agreement with experimentally measured optical properties along Hugoniot curves for precompressed states, and while we still find a first-order liquid-liquid transition at low temperatures, transition pressures are increased by more than 100GPa.

The role of van der Waals forces in water adsorption on metals

The interaction of water molecules with metal surfaces is typically weak and as a result van der Waals (vdW) forces can be expected to be of importance. Here we account for the systematic poor treatment of vdW forces in most popular density functional theory exchange-correlation functionals by applying accurate non-local vdW density functionals. We have computed the adsorption of a variety of exemplar systems including water monomer adsorption on Al(111), Cu(111), Cu(110), Ru(0001), Rh(111), Pd(111), Ag(111), Pt(111), and unreconstructed Au(111), and small clusters (up to 6 waters) on Cu(110). We show that non-local correlations contribute substantially to the water-metal bond in all systems, whilst water-water bonding is much less affected by non-local correlations. Interestingly non-local correlations contribute more to the adsorption of water on the reactive transition metal substrates than they do on the noble metals. The relative stability, adsorption sites, and adsorption geometries of competing water adstructures rarely differ when comparing results obtained with semi-local functionals and the non-local vdW density functionals, which explains the previous success of semi-local functionals in characterizing adsorbed water structures on a number of metal surfaces.

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps.

Generalized nonlocal kinetic energy density functionals based on the von Weizsäcker functional

We generalize the ideas behind the procedure for the construction of kinetic energy density functionals with a nonlocal term based on the structure of the von Weizsäcker functional, and present several types of nonlocal terms. In all cases, the functionals are constructed such that they reproduce the linear response function of the homogeneous electron gas. These functionals are designed by rewriting the von Weizsäcker functional with the help of a parameter β that determines the power of the electron density in the expression, a strategy we have previously used in the generalization of Thomas-Fermi nonlocal functionals. Benchmark calculations in localized systems have been performed with these functionals to test both their relative errors and the quality of their local behavior. We have obtained competitive results when compared to semilocal and previous nonlocal functionals, the generalized nonlocal von Weizsäcker functionals giving very good results for the total kinetic energies and improving the local behavior of the kinetic energy density. In addition, all the functionals discussed in this paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, resulting in a quasilinear scaling for the computational cost.

Evaluation of density functionals, SCC-DFTB, neglect of diatomic differential overlap (NDDO) models and molecular mechanics methods for prolyl-leucyl-glycinamide (PLG) and structural analogs

Prolyl-leucyl-glycinamide (PLG) is a unique endogenous peptide that modulates dopamine receptor subtypes of the D 2 receptor family within the CNS. We seek to elucidate the structural basis and molecular mechanism by which PLG and its analogs modulate dopamine receptors, toward the development of new therapeutics to treat Parkinson’s disease, tardive dyskinesia and schizophrenia. As a first step toward establishing a validated protocol for accurate computational modeling of PLG and associated peptidomimetic analogs, we evaluated the accuracy of density functional theory (DFT), wave function theory (WFT), and molecular mechanics (MM) calculations for PLG and for a library of structurally related small molecules. We first tested 12 local and nonlocal density functionals, Hartree–Fock (HF) theory, four “semiempirical” methods of the neglect of diatomic differential overlap (NDDO) type, and one self-consistent-charge nonorthogonal tight-binding (SCC-DFTB) method as implemented in two software suites, against coupled-cluster benchmark geometries for 4-methylthiazolidine, a small molecule that comprises key structural features present in our PLG-analog library. DFT and HF calculations were done with the MG3S augmented polarized triple-zeta basis set. We find that for 4-methylthiazolidine bond distances, DFT significantly outperforms NDDO, and both SCC-DFTB versions we evaluated perform worse than HF theory and are less accurate than 83% of the density functionals tested. The top five functionals for 4-methylthiazolidine were M05-2X, mPW1PW, B97-2, M06-2X, and PBEh, with mean unsigned errors (MUEs) in bond length of 0.0017, 0.0020, 0.0023, 0.0025 and 0.0027 Å, respectively. The widely used B3LYP functional ranked 11th out of 12 functionals evaluated, slightly below SCC-DFTB, and is significantly less accurate for 4-methylthiazolidine bond distances (MUE = 0.0095 Å) than the best local functional (M06-L, MUE = 0.0030 Å), which is far less computationally costly. Based on that initial analysis, we obtained new M05-2X benchmark geometric parameters for PLG and a library of 11 peptidomimetic derivatives, which we in turn used to examine the accuracy of thirty-four popular molecular mechanics (MM) force fields, four NDDO approaches, and SCC-DFTB for the full compound structures. Here, we found that ∼70% of the MM force fields tested superior to the best semiempirical and SCC-DFTB codings. Moreover, AMBER-type force fields proved most accurate among MM methods for this class of small-molecule peptidomimetics; the AMBER-type methods comprised eight out of the top 10 molecular mechanics options we tested.

Fully nonlocal kinetic energy density functionals: A proposal and a general assessment for atomic systems

Following some recent ideas on the construction of kinetic energy density functionals that reproduce the linear response function of the homogeneous electron gas, a family of them with a nonlocal term based on the von Weizsacker functional and with a dependence on the logarithm of the density is presented. As localized systems are the most difficult to study with explicit kinetic functionals, in this paper we apply to atomic systems a number of families of fully nonlocal kinetic functionals. We have put our attention in both the total kinetic energy and the local behavior of the kinetic energy density, and the results clearly show the quality of these fully nonlocal functionals. They make a good description of the local behavior of the kinetic energy density and maintain good results for the total kinetic energies. We must remark that almost all the functionals discussed in the paper, when using an adequate reference density, can be evaluated as a single integral in momentum space, with a quasilinear scaling for the computational cost.

Assessment of density functionals, semiempirical methods, and SCC-DFTB for protonated creatinine geometries

Creatinine concentrations in blood and urine can be used to detect renal insufficiencies and muscle diseases, but current chemical sensors cannot measure creatinine with sufficient selectivity and robustness because they lack a receptor that binds protonated creatinine (creatininium) selectively enough. As a first step toward identifying potential receptors for creatininium, we examine the accuracy of density functional theory (DFT) and wave function theory (WFT) calculations for creatininium cation geometries, evaluated against reference parameters from experiment. We tested twenty-one local and nonlocal density functionals, Hartree-Fock theory, four semiempirical molecular orbital (SEMO) methods of the neglect of differential overlap (NDO) type, and one self-consistent-field nonorthogonal tight-binding method (SCC-DFTB) as implemented in two closely related software packages. DFT and HF calculations were carried out with the MG3S augmented polarized triple-zeta basis set. We find that DFT significantly outperforms SEMO methods for our dataset, and both SCC-DFTB releases we tested (which gave almost identical results) were less accurate than 81% of the density functionals evaluated. The top five functionals for the creatininium structures we examined were MPW1B95, PBEh, mPW1PW, SVWN5, and B97-2, with MMUEs in bond length of 0.0126, 0.0129, 0.0133, 0.0142, and 0.0144 Å respectively, which indicates that all five functionals are similarly suitable for creatininium. The popular B3LYP functional has a MMUE of 0.0178 Å, which ranks it 16th overall. B3LYP also performs less favorably than the best local functional (SVWN5), which is less expensive.

Novel Binary Room-Temperature Complex System Based on LiTFSI and 2-Oxazolidinone and Its Characterization as Electrolyte

Binary room-temperature complex system has been prepared based on lithium bis(trifluoromethane sulfonyl) imide (LiN(SO2CF3)2, LiTFSI) and 2-oxazolidinone (C3H5NO2, OZO). Both LiTFSI and OZO are solid at room temperature, but their mixture is a liquid with a liquidus temperature about −58.4 °C at a molar ratio of 1:4.0 characterized by differential scanning calorimetry. Thermogravimetry analysis shows that the complex system possesses high thermal stability over a wide range of temperature. Infrared and Raman spectroscopic studies have been carried out to understand the interactions between the precursors, LiTFSI and OZO, of the complex system. It is shown that the OZO can coordinate with the Li+ cation and the TFSI- anion via their polar groups (the CO and NH groups). Such strong interactions lead to the dissociation of LiTFSI and the breakage of the hydrogen bonds among the OZO molecules, resulting in the formation of the complex. To have a comprehensive understanding to the above interactions, quantum chemistry calculations with nonlocal density function theory have also been performed on the free ions or organic molecule by determining their Mulliken charges, equilibrium configuration, binding energy, and the coordination number of Li+ ion. The calculations indicate that the ionic conductivity of the LiTFSI−OZO complex with different molar ratios depends strongly on the ionic species in the complex system. Electrochemical performances of the complex electrolyte are evaluated with ac impedance spectroscopy, cyclic voltammetry (CV), and in a test electric double layer capacitor, respectively. The complex at a molar ratio of 1:4.5 exhibits the highest ionic conductivity due to the relatively large amount of “free” ions at room temperature. The analysis for the CV behavior indicates that the electrochemical stability window of the electrolyte is about 3V. This kind of complex system proves to be a promising candidate of electrolytes for supercapacitor and other electrochemical devices.

The structure–activity relationship studies of binary room temperature complex electrolytes based on LiTFSI and organic compounds with acylamino group

Binary room temperature complex electrolytes based on lithium bis(trifluoromethane sulfone) imide (LiN(SO 2CF 3) 2, LiTFSI) and organic molecules with acylamino (amide) groups, such as ethyleneurea, acetamide, etc., have been synthesized and evaluated with differential scanning calorimetry (DSC) and ac impedance spectroscopy. Most of the complex systems with proper molar ratio have excellent thermal stability and electrochemical performance. Infrared (IR) and Raman spectroscopic studies have been carried out to understand the formation these electrolytes. It is shown that the organic compounds with amide group can coordinate with the Li + cation and the TFSI − anion via their polar groups (the C O and NH groups). Such strong interactions lead to the dissociation of LiTFSI and the breaking of the hydrogen bonds among the organic molecules, resulting in the formation of the complex systems. In order to have a comprehensive understanding of the above interactions and the structure–activity relationship of these complex systems, the Mulliken charges on the O and N atoms, the equilibrium configuration and the bonding energy of the systems have been determined by quantum chemistry calculations with non-local density function theory (DFT). The calculations indicate that the structure and the substitution group of organic molecules influence the charge density and coordination strength of the carbonyl oxygen of these molecules. In addition, the strength of hydrogen bonding between the organic molecules influences the physico-chemical properties of the complex electrolyte.