Implementation Of Density Functional Theory Research Articles

Strongly constrained and appropriately normed density functional theory exchange-correlation functional applied to rare earth oxides

Density functional theory (DFT) is one of the main tools for studying the electronic structure of solids and molecules. Nevertheless, one of the main drawbacks of the implementation of DFT is the so-called self-interaction error (SIE) that can yield undesired delocalization errors and ultimately results in the prediction of metals instead of experimentally observed insulators. These SIEs can be amended by using more evolved exchange-correlation functionals than standard local density approximation such as the recent meta-generalized gradient approximation strongly constrained and appropriately normalized (SCAN) functional that is successful in describing electronic properties of $3d$ transition metal oxides. Nevertheless, the ability of such a functional to describe electronic properties of materials involving more localized states such as $4f$ orbitals is rather elusive. Here, we show that, even though SCAN can sometimes predict the insulating character of some compounds, it often fails in predicting the correct band edge orbital character of insulators. By comparing our SCAN results with benchmark simulations obtained with more accurate hybrid DFT calculations, we ascribe this failure to insufficiently amended SIEs by SCAN that results in an underestimation of Hund's splitting associated with $4f$ states. Thus, although appropriate for $3d$ transition metal elements, the SCAN functional is not yet a sufficient platform for studying electronic properties of materials involving rare-earth elements where $4f$ states play a key role in the properties.

Electronic properties and carrier mobilities of nanocarbons formed by non-benzoidal building blocks.

Exotic 1D and 2D carbon nanostructures have been grown in the laboratory in the last few years by means of surface-assisted chemical routes. In these processes, the strategical choice of a molecular precursor plays a dominant role in the determination of the synthesized nanocarbon. Further variations of these techniques are able to produce non-benzoidal carbon quantum-dots (QDs). Considering this experimental scenario as motivation, we propose a series of nanoribbon systems based on concatenating recently synthesized carbon QDs containing pentagonal, hexagonal, and heptagonal rings. We use density functional theory (DFT) simulations to reveal their properties can range from metallic to semiconducting depending on the concatenation hierarchy used to form the nanoribbons. This DFT implementation is based on a LCAO approach to describe valence wavefunctions and most of the simulations employ the PBE-GGA functional. Since this functional is known to underestimate band gaps, we also use the B3LYP functional in a plane-wave DFT approach for a selected case for comparison purposes. These systems show a different gap versus width relationship compared to conventional graphene nanoribbons setups and a particular set of carrier mobility values. We further discuss the interplay between the QD's frontier states and the electronic properties of the nanoribbons in light of their structural details.

Tensor-structured algorithm for reduced-order scaling large-scale Kohn\u2013Sham density functional theory calculations

We present a tensor-structured algorithm for efficient large-scale density functional theory (DFT) calculations by constructing a Tucker tensor basis that is adapted to the Kohn–Sham Hamiltonian and localized in real-space. The proposed approach uses an additive separable approximation to the Kohn–Sham Hamiltonian and an L1 localization technique to generate the 1-D localized functions that constitute the Tucker tensor basis. Numerical results show that the resulting Tucker tensor basis exhibits exponential convergence in the ground-state energy with increasing Tucker rank. Further, the proposed tensor-structured algorithm demonstrated sub-quadratic scaling with system-size for both systems with and without a gap, and involving many thousands of atoms. This reduced-order scaling has also resulted in the proposed approach outperforming plane-wave DFT implementation for systems beyond 2000 electrons.

Electrode-molecule energy level offsets in a gold-benzene diamine-gold single molecule tunnel junction.

One means for describing electron transport across single molecule tunnel junctions (MTJs) is to use density functional theory (DFT) in conjunction with a nonequilibrium Green's function formalism. This description relies on interpreting solutions to the Kohn-Sham (KS) equations used to solve the DFT problem as quasiparticle (QP) states. Many practical DFT implementations suffer from electron self-interaction errors and an inability to treat charge image potentials for molecules near metal surfaces. For MTJs, the overall effect of these errors is typically manifested as an overestimation of electronic currents. Correcting KS energies for self-interaction and image potential errors results in MTJ current-voltage characteristics in close agreement with measured currents. An alternative transport approach foregoes a QP picture and solves for a many-electron wavefunction on the MTJ subject to open system boundary conditions. It is demonstrated that this many-electron method provides similar results to the corrected QP picture for electronic current. The analysis of these two distinct approaches is related through corrections to a junction's electronic structure beyond the KS energies for the case of a benzene diamine molecule bonded between two gold electrodes.

Ising-like models for stacking faults in a free electron metal.

We propose an extension of the axial next nearest neighbour Ising (ANNNI) model to a general number of interactions between spins. We apply this to the calculation of stacking fault energies in magnesium—particularly challenging due to the long-ranged screening of the pseudopotential by the free electron gas. We employ both density functional theory (DFT) using highest possible precision, and generalized pseudopotential theory (GPT) in the form of an analytic, long ranged, oscillating pair potential. At the level of first neighbours, the Ising model is reasonably accurate, but higher order terms are required. In fact, our ‘ ANNNI model’ is slow to converge—an inevitable feature of the free electron-like electronic structure. In consequence, the convergence and internal consistency of the ANNNI model is problematic within the most precise implementation of DFT. The GPT shows the convergence and internal consistency of the DFT bandstructure approach with electron temperature, but does not lead to loss of precision. The GPT is as accurate as a full implementation of DFT but carries the additional benefit that damping of the oscillations in the ANNNI model parameters are achieved without entailing error in stacking fault energies. We trace this to the logarithmic singularity of the Lindhard function.

At the Limits of Isolobal Bonding: π-Based Covalent Magnetism in Mn2Hg5.

Magnetic ordering in inorganic materials is generally considered to be a mechanism for structures to stabilize open shells of electrons. The intermetallic phase Mn2Hg5 represents a remarkable exception: its crystal structure is in accordance with the 18-n bonding scheme and non-spin-polarized density functional theory (DFT) calculations show a corresponding pseudogap near its Fermi energy. Nevertheless, it exhibits strong antiferromagnetic ordering virtually all the way up to its decomposition temperature. In this Article, we examine how these two features of Mn2Hg5 coexist through the development of a DFT implementation of the reversed approximation Molecular Orbital (raMO) analysis. In the non-spin-polarized electronic structure, the DFT-raMO approach confirms that Mn2Hg5 adheres to the 18-n rule: its chains of Mn atoms are linked through isolobal triple bonds, with three electron pairs being shared at each Mn-Mn contact in one σ-type and two π-type functions. Because each Mn atom has 6 isolobal Mn-Mn bonds, it achieves a filled 18-electron count at the compound's electron concentration of 18 - 6 = 12 electrons/Mn. A pseudogap thus occurs at the Fermi energy. Upon the introduction of antiferromagnetic order, the original pseudogap widens and deepens, suggesting enhancement of a stabilizing effect already present in the nonmagnetic state. A raMO analysis reveals that antiferromagnetism enlarges the gap by allowing diradical character to enter into the Mn-Mn isolobal π bonds, reminiscent of the dissociation of a classic covalent bond. Antiferromagnetism is accompanied by residual bonding in the π system, making Mn2Hg5 a vivid realization of the concept of covalent magnetism.

On the study of the vapor-liquid interface of associating fluids with classical density functional theory

Classical density functional theory (DFT) is applied to study the vapor-liquid interface of associating fluids. Our classical DFT implementation uses a Helmholtz free energy functional that reduces to the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state in the bulk limit. We apply a new association functional, presented in one of our previous works, based on the weighted density approximation to calculate the interfacial tension of associating fluids and compare them with two of the most used association functionals from literature. It is found that classical DFT with the three association functionals and the current molecular parameters of PC-SAFT is not able to predict satisfactorily the interfacial tension of alkanols. Therefore, the experimental interfacial tension of alkanols and some associating fluids is included in the determination of the pure molecular parameters of PC-SAFT. With this approach the determination of interfacial tension of pure associating fluids can be greatly improved with the new parameters, but at the expense of slightly higher deviations in the vapor pressure. The new parameters are tested for the determination of vapor-liquid equilibria (VLE) and the prediction of interfacial tension of binary mixtures containing at least one associating compound. Good agreement is found between experimental data of VLE and interfacial tension of the binary mixtures and the three association functionals. Furthermore, we discuss about the limitations and capabilities of the current classical DFT implementation in the study of the vapor-liquid interface of associating fluids.

Projector Augmented Wave Method with Gauss-Type Atomic Orbital Basis: Implementation of the Generalized Gradient Approximation and Mesh Grid Quadrature.

The projector augmented wave (PAW) method is a powerful numerical algorithm that serves as a backend, enabling efficient density functional theory (DFT) calculations through the smoothing of valence electronic descriptions. Although it is mainly used in conjunction with plane-wave basis for solid-state systems, its generality permits the combination with other types of basis functions. In the previous study, we proposed a scheme to incorporate the PAW method into the conventional quantum chemical DFT implementation based on Gauss-type function (GTF) basis (Xiong et al., J. Chem. Theory Comput. 2017, 13, 3236-3249). The potentially high usability of the GTF-based PAW method, referred to as GTF-PAW, was previously shown, while its implementation was limited to the local density approximation (LDA). Here, we present a development of two technical extensions in this method toward practical DFT calculations. The GTF-PAW-based formulation and implementation to raise the level of the functional treatment to the generalized gradient approximation (GGA) is presented for improving reliability. In addition, we attempt to use the uniform mesh grid for DFT's quadrature in place of the conventional Becke grid, which was previously used. With the test calculations performed on illustrative molecules, it is confirmed that the conventional approach to implement GGA within GTF basis code can be straightforwardly integrated into the GTF-PAW method, allowing for the numerically stable treatment of the gradients of density. It is demonstrated that the uniform mesh grid can be used as an efficient numerical quadrature approach, which may be advantageous for handling larger systems.

Defect states in monolayer hexagonal BN: A comparative DFT and DFT-1/2 study

Hexagonal boron nitride (h-BN) acts like a semiconductor vacuum to point defects enabling stable and controllable spin states at room temperature which qualifies them for quantum technological applications. To characterize their properties first-principles techniques constitute indispensable tools. The currently established paradigm for such solid-state electronic structure calculations is the density functional theory (DFT). Recently its variant, so-called DFT-1/2 method was introduced with the promise of accurate band gaps without a computational overhead with respect to ordinary DFT. Here, for the monolayer h-BN we contrast DFT and DFT-1/2 results for carbon substitutional impurities (CB, CN), boron and nitrogen single vacancies (VB, VN), divacancy, and Stone-Wales defects. Comparisons with more sophisticated, yet computationally costly techniques namely, hybrid functional DFT and the GW are also made, where available. From the standpoint of defect states embedded in the band gap region we demonstrate a clear advantage of DFT-1/2 in revealing the localized states otherwise buried within either the valence or conduction band continuum due to well-known gap underestimation syndrome of the standard DFT implementations. Thus, DFT-1/2 can serve for the rapid screening of candidate defect systems before more demanding considerations.

Finite Temperatures by Means of Zero Kelvin Kohn-Sham Formalism of Density-Functional Theory

During the last decades, density-functional theory (DFT) has been specially employed in cases with temperature T= 0 K. Even though the interest is growing rapidly, in situations with T> 0 K, the implementation of the so-called thermal DFT (thDFT) remains not so widely explored. In this context, we here present an alternative procedure of including thermal effects in a Kohn-Sham DFT calculation: using the T= 0 K formalism, we propose the construction of an effective potential which incorporates, beyond electronic interaction, temperature effects.

Gas Adsorption and Interfacial Tension with Classical Density Functional Theory

A classical density functional theory (DFT) that reduces to the perturbed chain statistical associating fluid theory equation of state has been implemented. This DFT implementation allows the use of molecular and binary interaction parameters fitted to the vapor–liquid equilibria of pure compounds and binary mixtures, respectively. Different functionals of dispersion forces are investigated and applied to the calculation of interfacial tension and adsorption of pure gases and their mixtures. The predictions of interfacial tension have been compared with both molecular simulations and experimental data, and good agreements have been seen. The DFT approaches also show good performance in correlating and predicting gas adsorption, and they are further compared with the multicomponent potential theory of adsorption and other DFT approaches available in the literature.

Projector Augmented Wave Method Incorporated into Gauss-Type Atomic Orbital Based Density Functional Theory.

The Projector Augmented Wave (PAW) method developed by Blöchl is well recognized as an efficient, accurate pseudopotential approach in solid-state density functional theory (DFT) calculations with the plane-wave basis. Here we present an approach to incorporate the PAW method into the Gauss-type function (GTF) based DFT implementation, which is widely used for molecular quantum chemistry calculations. The nodal and high-exponent GTF components of valence molecular orbitals (MOs) are removed or pseudized by the ultrasoft PAW treatment, while there is elaborate transparency to construct an accurate and well-controlled pseudopotential from all-electron atomic description and to reconstruct an all-electron form of valence MOs from the pseudo MOs. The smoothness of the pseudo MOs should benefit the efficiency of GTF-based DFT calculations in terms of elimination of high-exponent primitive GTFs and reduction of grid points in the numerical quadrature. The processes of the PAW method are divided into basis-independent and -dependent parts. The former is carried out using the previously developed PAW libraries libpaw and atompaw. The present scheme is implemented by incorporating libpaw into the conventional GTF-based DFT solver. The details of the formulations and implementations of GTF-related PAW procedures are presented. The test calculations are shown for illustrating the performance. With the near-complete GTF basis at the cc-pVQZ level, the total energies obtained using our PAW method with suited frozen core treatments converge to those with the conventional all-electron GTF-based method with a rather small absolute error.

On the accuracy of population analyses based on fitted densities.

Population analyses are part of the theoretical chemist's toolbox. They provide means to extract information about the repartition of the electronic density among molecules or solids. The values of atomic multipoles in a molecule can shed light on its electrostatic properties and may help to predict how different molecules could interact or to rationalize chemical reactivity for instance. Not being physical observables to which a quantum mechanical operator can be associated, atomic charges and higher order atomic multipoles cannot be defined unambiguously in a molecule, and therefore, several population schemes (PS) have been devised in the last decades. In the context of density functional theory (DFT), PS based on the electron density seem to be best grounded. In particular, some groups have proposed various iterative schemes the outcomes of which are very encouraging. Modern implementations of DFT that are for example based on density fitting techniques permit the investigation of molecular systems comprising of hundreds of atoms. However, population analyses following iterative schemes may become very CPU time consuming for such large systems. In this article, we investigate if the computationally less expensive analyses of the variationally fitted electronic densities can be safely carried out instead of the Kohn-Sham density. It is shown that as long as flexible auxiliary function sets including f and g functions are used, the multipoles extracted from the fitted densities are extremely close to those obtained from the KS density. We further assess if the multipoles obtained through the Hirshfeld's approach, in its standard or iterative form, can be a useful approach to calculate interaction energies in non-covalent complexes. Relative energies computed with the AMOEBA polarizable forced field combined to iterative Hirshfeld multipoles are encouraging.

Metadynamics combined with auxiliary density functional and density functional tight-binding methods: alanine dipeptide as a case study.

Application of ab initio molecular dynamics to study free energy surfaces (FES) is still not commonly performed because of the extensive sampling required. Indeed, it generally necessitates computationally costly simulations of more than several hundreds of picoseconds. To achieve such studies, efficient density functional theory (DFT) formalisms, based on various levels of approximate computational schemes, have been developed, and provide a good alternative to commonly used DFT implementations. We report benchmark results on the conformational change FES of alanine dipeptide obtained with auxiliary density functional theory (ADFT) and second- and third-order density functional tight-binding (DFTB) methods coupled to metadynamics simulations. The influence of an explicit water solvent is also studied with DFTB, which was made possible by its lower computational cost compared to ADFT. Simulations lengths of 2.1 and 15 ns were achieved with ADFT and DFTB, respectively, in a reasonably short computational time. ADFT leads to a free energy difference (ΔF eq-ax) of ∼ -3kcalmol-1 between the two low energy conformers, C7eq and C7ax, which is lower by only 1.5 kcalmol-1 than the ΔF eq-ax computed with DFTB. The two minima in ADFT FES are separated by an energy barrier of 9 kcalmol-1, which is higher than the DFTB barriers by 2-4kcalmol-1. Despite these small quantitative differences, the DFTB method reveals FES shapes, confor-mation geometries and energies of the stationary points in good agreement with these found with ADFT. This validates the promising applicability of DFTB to FES of reactions occurring in larger-size systems placed in complex environments.

Electronic Coupling Calculations for Bridge-Mediated Charge Transfer Using Constrained Density Functional Theory (CDFT) and Effective Hamiltonian Approaches at the Density Functional Theory (DFT) and Fragment-Orbital Density Functional Tight Binding (FODFTB) Level.

In this article, four methods to calculate charge transfer integrals in the context of bridge-mediated electron transfer are tested. These methods are based on density functional theory (DFT). We consider two perturbative Green's function effective Hamiltonian methods (first, at the DFT level of theory, using localized molecular orbitals; second, applying a tight-binding DFT approach, using fragment orbitals) and two constrained DFT implementations with either plane-wave or local basis sets. To assess the performance of the methods for through-bond (TB)-dominated or through-space (TS)-dominated transfer, different sets of molecules are considered. For through-bond electron transfer (ET), several molecules that were originally synthesized by Paddon-Row and co-workers for the deduction of electronic coupling values from photoemission and electron transmission spectroscopies, are analyzed. The tested methodologies prove to be successful in reproducing experimental data, the exponential distance decay constant and the superbridge effects arising from interference among ET pathways. For through-space ET, dedicated π-stacked systems with heterocyclopentadiene molecules were created and analyzed on the basis of electronic coupling dependence on donor-acceptor distance, structure of the bridge, and ET barrier height. The inexpensive fragment-orbital density functional tight binding (FODFTB) method gives similar results to constrained density functional theory (CDFT) and both reproduce the expected exponential decay of the coupling with donor-acceptor distances and the number of bridging units. These four approaches appear to give reliable results for both TB and TS ET and present a good alternative to expensive ab initio methodologies for large systems involving long-range charge transfers.

Partitioning the DFT exchange-correlation energy in line with the interacting quantum atoms approach

The interacting quantum atoms (IQA) energy partition has given important insights about different systems and processes in theoretical chemistry. Given its intrinsic dependence on first- and second-order density matrices, IQA is only cleanly defined within wavefunction methods. This means that, despite the importance of density functional theory (DFT) in electronic structure methods, a neat IQA–DFT implementation is not straightforward. This work addresses this issue through a new implementation of IQA within the Kohn–Sham formalism of DFT in conjunction with hybrid and non-hybrid functionals that contributes further to that already presented (Maxwell et al. in Phys Chem Chem Phys, 2016. doi:10.1039/C5CP07021J). For this purpose, we use additive exchange-correlation (xc) energies, defined within the IQA approach, to scale the one- and two-atom terms of the Kohn–Sham xc energy. This leads to an exact partition of the xc DFT energy of a molecule into intra-atomic and inter-atomic contributions. The suggested method is illustrated with several molecules together with some of the most popular local and hybrid DFT functionals. Overall, we anticipate that the approach put forward in this work will prove useful in getting further insights of phenomena in chemistry which are properly described with DFT .

TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials

We present the TRIQS/DFTTools package, an application based on the TRIQS library that connects this toolbox to realistic materials calculations based on density functional theory (DFT). In particular, TRIQS/DFTTools together with TRIQS allows an efficient implementation of DFT plus dynamical mean-field theory (DMFT) calculations. It supplies tools and methods to construct Wannier functions and to perform the DMFT self-consistency cycle in this basis set. Post-processing tools, such as band-structure plotting or the calculation of transport properties are also implemented. The package comes with a fully charge self-consistent interface to the Wien2k band structure code, as well as a generic interface that allows to use TRIQS/DFTTools together with a large variety of DFT codes. It is distributed under the GNU General Public License (GPLv3). Program summaryProgram title: TRIQS/DFTToolsProject homepage:https://triqs.ipht.cnrs.fr/applications/dft_toolsCatalogue identifier: AFAF_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AFAF_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3npNo. of lines in distributed program, including test data, etc.: 164018No. of bytes in distributed program, including test data, etc.: 4916969Distribution format: tar.gzProgramming language: Fortran/Python.Computer: Any architecture with suitable compilers including PCs and clusters.Operating system: Unix, Linux, OSX.RAM: Highly problem dependentClassification: 6.5, 7.3, 7.7, 7.9.External routines: TRIQS, cmakeNature of problem: Setting up state-of-the-art methods for an ab initio description of correlated systems from scratch requires a lot of code development. In order to make these calculations possible for a larger community there is need for high-level methods that allow the construction of DFT+DMFT calculations in a modular and efficient way.Solution method: We present a Fortran/Python open-source computational library that provides high-level abstractions and modules for the combination of DFT with many-body methods, in particular the dynamical mean-field theory. It allows the user to perform fully-fledged DFT+DMFT calculations using simple and short Python scripts.Running time: Tests take less than a minute; otherwise highly problem dependent.

Using the GVB Ansatz to develop ensemble DFT method for describing multiple strongly correlated electron pairs.

Ensemble density functional theory (DFT) furnishes a rigorous theoretical framework for describing the non-dynamic electron correlation arising from (near) degeneracy of several electronic configurations. Ensemble DFT naturally leads to fractional occupation numbers (FONs) for several Kohn-Sham (KS) orbitals, which thereby become variational parameters of the methodology. The currently available implementation of ensemble DFT in the form of the spin-restricted ensemble-referenced KS (REKS) method was originally designed for systems with only two fractionally occupied KS orbitals, which was sufficient to accurately describe dissociation of a single chemical bond or the singlet ground state of biradicaloid species. To extend applicability of the method to systems with several dissociating bonds or to polyradical species, more fractionally occupied orbitals must be included in the ensemble description. Here we investigate a possibility of developing the extended REKS methodology with the help of the generalized valence bond (GVB) wavefunction theory. The use of GVB enables one to derive a simple and physically transparent energy expression depending explicitly on the FONs of several KS orbitals. In this way, a version of the REKS method with four electrons in four fractionally occupied orbitals is derived and its accuracy in the calculation of various types of strongly correlated molecules is investigated. We propose a possible scheme to ameliorate the partial size-inconsistency that results from perfect spin-pairing. We conjecture that perfect pairing natural orbital (NO) functionals of reduced density matrix functional theory (RDMFT) should also display partial size-inconsistency.

Quantum Monte Carlo for Ab Initio calculations of energy-relevant materials

Humanity faces one of its greatest challenges in the move from fossil-fuel based energy sources to alternative sources that do not produce greenhouse gases. New materials design is an important facet of the overall solution, since designed materials have the potential to increase efficiency in areas ranging from solar electricity generation to energy storage and distribution technologies. In that context, it is vital to be able to predict the properties of materials from basic physical principles. While traditional electronic structure techniques such as the ubiquitous density functional theory (DFT) are very important in this goal, there are many cases where current implementations of DFT fail in a design-important way. Among other solutions, quantum Monte Carlo techniques have emerged as a practical way to obtain predictive power for challenging materials. This perspective highlights some recent advances in this field, concentrating in particular on the effect that quantum Monte Carlo methods have and will have on our energy challenge. © 2013 Wiley Periodicals, Inc.

Probabilistic Approach to the Length-Scale Dependence of the Effect of Water Hydrogen Bonding on Hydrophobic Hydration

We present a probabilistic approach to water-water hydrogen bonding that allows one to obtain an analytic expression for the number of bonds per water molecule as a function of both its distance to a hydrophobic particle and hydrophobe radius. This approach can be used in density functional theory (DFT) and computer simulations to examine particle size effects on the hydration of particles and on their solvent-mediated interaction. For example, it allows one to explicitly identify a water hydrogen bond contribution to the external potential, whereto a water molecule is subjected near a hydrophobe. The DFT implementation of the model predicts the hydration free energy per unit area of a spherical hydrophobe to be sharply sensitive to the hydrophobe radius for small radii and weakly sensitive thereto for large ones; this corroborates the vision of the hydration of small and large length-scale particles as occurring via different mechanisms. On the other hand, the model predicts that the hydration of even apolar particles of small enough radii may become thermodynamically favorable owing to the interplay of the energies of pairwise (dispersion) water-water and water-hydrophobe interactions. This sheds light on previous counterintuitive observations (both theoretical and simulational) that two inert gas molecules would prefer to form a solvent-separated pair rather than a contact one.