Recent Developments in Multiple Scattering Theory and Density Functional Theory for Molecules and Solids

This study demonstrates the capability of the density functional theory (DFT) formalism to predict contact angles and density profiles of model fluids and of real substances in good quantitative agreement with molecular simulations and experimental data. The DFT problem is written in cylindrical coordinates, and the solid-fluid interactions are defined as external potentials toward the fluid phase. Monte Carlo (MC) molecular simulations are conducted in order to assess the density profiles resulting from the Helmholtz energy functional used in the DFT formalism. Good quantitative agreement between DFT predictions and MC results for Lennard-Jones and ethane nanodroplets is observed, both for density profiles and for contact angles. That comparison suggests, first, that the Helmholtz energy functional proposed in a previous study [ Sauer , E. ; Gross , J. Ind. Eng. Chem. Res. 56 , 2017 , 4119 - 4135 ] is suitable for three-phase contact lines and, second, that Lagrange multipliers can be used to constrain the number of molecules, similar to a canonical ensemble. Experiments of sessile droplets on solid surfaces are performed to assess whether a real solid with its microscopic roughness can be described through a simple model potential. Comparison of DFT results to experimental data is done for a Teflon surface because Teflon can be regarded as a substrate exhibiting only attractive interactions of van der Waals type. It is shown that the real solid can be described as a perfectly planar solid with effective solvent-to-solid interactions, defined through a single adjustable parameter for the solid. Subsequent predictions for the contact angle of eight solvents, including polar components such as water, are found in very good agreement to experimental data using simple Berthelot-Lorentz combining rules. For the eight investigated solvents, we find mean absolute deviations of 3.77°.

RECENT PROGRESS IN ELECTRONIC STRUCTURE CALCULATIONS FOR DEFECTS IN METALS

In the beginning of quantum mechanical Density-Functional Theory (DFT), there was the Thomas-Fermi (TF) model, which uses the electron density p(r) (a function of only 3 coordinates) as the only physical variable. Calculations with this model were inexpensive but yielded poor numerical results due to a lack of understanding of exchange-correlation effects and the kinetic-energy density functional. Many years later, Hohenberg and Kohn (HK) established the formal foundation for DFT; Kohn and Sham (KS) devised a practical implementation and brought DFT into mainstream calculations of electronic structure. Although the KS formulation allows exact evaluation of the KS kinetic energy (Ts [p]), the one-electron orbitals introduced by the KS scheme inevitably encumber the formulation in three ways: (i) 3N (vs. 3) degrees of freedom, (ii) orbital orthonormalization, and (iii) Brillouin-zone (k-point) sampling in condensed phases. Given the accuracy of DFT with present exchange-correlation density functionals, it is logical to conclude that the last frontier in DFT is a better representation of the kinetic energy solely in terms of the density. If this is true, KS orbitals will be completely eliminated from DFT formulation, and the density can be solved directly from the TF-HK equation. This is certainly superior to the KS scheme because all energy terms can be computed in momentum space with an effectively linear scaling, O(MlnM), where M is the integration grid size. This work reviews major ideas in the design of such optimal orbital-free kinetic-energy density functionals and their applications.

Density functional theory (DFT) was used to study polymer chains, tethered to a surface and in the presence of a solvent. For reasons of computational practicality, it is common practice to remove the explicit solvent molecules from the problem. Contact was made with two such models, which we call the “implicit-solvent” and “continuum-solvent” approximations. First, DFT was applied to tethered chains in an implicit solvent. Using the equation of state of bead–spring chains as input, we found excellent agreement of the theory with density profiles obtained in molecular dynamics simulations on the same model as a function of temperature. Next, DFT was applied to tethered chains in an incompressible, continuum solvent. Using the Flory–Huggins theory as input, our DFT equations reduced to conventional self-consistent field theory. From our DFT formalism, we demonstrated that the implicit-solvent problem, at a given temperature, is equivalent to the continuum-solvent problem, provided the χ parameter and total density are interpreted appropriately.

We develop a quantum kinetic theory of the dynamic response of typical noble metals. Our approach is based on the density functional theory (DFT) and incorporates new important elements as compared to the conventional time-dependent DFT formalism. The kinetic DFT is derived starting from the master equation of motion for the density matrix, which involves both momentum and energy relaxation processes. Therefore, the quantum system is described by two relaxation parameters, unlike the conventional time-dependent DFT incorporating only one relaxation parameter. This allows us to describe both the absorption of light and the generation of hot plasmonic electrons. Using our kinetic DFT theory, we also observe the transition from the multiple peaks in small size-quantized systems to the intensive plasmonic resonance in large classical systems. Unlike the standard picture of collisional broadening of the plasmon peak in small systems, we observe a very different scenario: the formation of multiple plasmonic-like peaks in small quantized systems. These peaks are the result of a hybridization of the collective plasmon mode and the single-particle transitions in a quantized electron gas. There are a few experimental observations that seem to correlate with such a scenario of the plasmonic broadening in small systems. Our approach also incorporates the interband transitions, which are important for a qualitative description of gold and silver. Although this paper gives an application of our kinetic DFT only to the slab geometry, our theory can be applied to nanocrystals of arbitrary shape. The kinetic DFT formalism developed here can be employed to model and predict a variety of metal and hybrid nanostructures for applications in photocatalysis, sensors, photodetectors, metamaterials, etc.

Conceptual Density Functional Theory and Some Recent Developments

A Multiple Scattering Theory Approach to Solving the Time-Dependent Schrödinger Equation with an Asymmetric Rectangular Potential

The results of first principles calculations of band structure, density of states and electron density topology of CdC2O4 and Ag2C2O4 crystals are presented. The calculations have been performed with WIEN2k ab initio program, using highly precise full potential linearized augmented plane wave (FP LAPW) method within Density Functional Theory formalism. The obtained SCF electron density has been used in calculations of Bader’s AIM (atoms in molecules) topological properties of the electron density in crystal. The obtained results show important similarities in electronic structure and electron density topology of both compounds and allow supposing, that during the thermal decomposition process these compounds should behave similarly, which is in agreement with the experiment.

This article is part-I of a review of density-functional theory (DFT) that is the most widely used method for calculating electronic structure of materials. The accuracy and ease of numerical implementation of DFT methods has resulted in its extensive use for materials design and discovery and has thus ushered in the new field of computational material science. In this article, we start with an introduction to Schrödinger equation and methods of its solutions. After presenting exact results for some well-known systems, difficulties encountered in solving the equation for interacting electrons are described. How these difficulties are handled using the variational principle for the energy to obtain approximate solutions of the Schrödinger equation is discussed. The resulting Hartree and Hartree–Fock theories are presented along with results they give for atomic and solid-state systems. We then describe Thomas–Fermi theory and its extensions which were the initial attempts to formulate many-electron problem in terms of electronic density of a system. Having described these theories, we introduce modern DFT by discussing Hohenberg–Kohn theorems that form its foundations. We then go on to discuss Kohn–Sham (KS) formulation of DFT in its exact form. Next, local density approximation (LDA) is introduced and solutions of KS equation for some representative systems, obtained using the LDA, are presented. We end part-I of the review describing the contents of part-II.

We present and discuss main results of the calculations for the surface relaxation and rumpling of SrTiO3 surfaces with TiO2 and SrO terminations using a wide variety of methods of modern computational physics and chemistry, including the shell model (SM) and ab initio methods based on Hartree-Fock (HF) and Density Functional Theory (DFT). The HF and DFT formalisms with different exchange-correlation functionals are implemented into Crystal-98 computer code using a Gaussian-type basis set. We demonstrate that a hybrid B3PW formalism gives the best results for the bulk SrTiO3 properties. Results are compared with previous ab initio plane-wave LDA calculations and LEED experiments. Our calculations demonstrate an increase of the covalency effects between Ti and O atoms near the surface.

We used a recently developed classical Density Functional Theory (DFT) method to study the structures, phase transitions, and electrochemical behaviours of two coarse-grained ionic fluid models, in the presence of a perfectly conducting model electrode. Common to both is that the charge of the cationic component is able to approach the electrode interface more closely than the anion charge. This means that the cations are specifically attracted to the electrode, due to surface polarization effects. Hence, for a positively charged electrode, there is competition at the surface between cations and anions, where the latter are attracted by the positive electrode charge. This generates demixing, for a range of positive voltages, where the two phases are structurally quite different. The surface charge density is also different between the two phases, even at the same potential. The DFT formulation contains an approximate treatment of ion correlations, and surface polarization, where the latter is modelled via screened image interactions. Using a mean-field DFT, where ion correlations are neglected, causes the phase transition to vanish for both models, but there is still a dramatic drop in the differential capacitance as proximal cations are replaced by anions, for increasing surface potentials. While these findings were obtained for relatively crude coarse-grained models, we argue that the findings can also be relevant in "real" systems, where we note that many ionic liquids are composed of a spherically symmetric anion, and a cation that is asymmetric both from a steric and a charge distribution point of view.

The formalism of (nonlocal) density functional theory provides an attractive way to describe the physical adsorption process at the fluid-solid interface. It provides numerical results of analytic precision in a small fraction of the time required by a simulation technique. In particular, the ability to model adsorption in a pore space of slit-like or cylindrical geometry has led to useful methods for extracting pore size distribution information from experimental adsorption isotherms. However, critical comparisons of experimental isotherms with the isotherms predicted by density functional theory have shown important differences when using the usual prescription for the nonlocal free energy density functional. It is clear that these differences would affect the accuracy of such pore size information. We show in this paper how a small modification to the mean field computation of the intermolecular attractive potential results in excellent agreement with experiment for the systems studied.

A form of full-potential multiple-scattering theory for electrons in solids or molecules has recently been proposed in which the structure constants characteristic of standard theory (Korringa-Kohn-Rostoker) do not occur. This formalism was derived from the Lippmann-Schwinger integral equation and has been called the Green-function cellular method. It is shown here that this formalism is a restatement of the tail-cancellation condition of Andersen, applied originally in the context of his muffin-tin-orbital construction, using a local spherical approximation to the potential function in the Schr\"odinger equation. This was generalized to the atomic-cell orbital (ACO) construction for the full-potential problem by the present author. The equations of this method are derived here directly from the ACO tail-cancellation condition for boundary matching on the surface of each cell in a set of space-filling atomic cells, making no use of the free-particle or Helmholtz Green function. It is also shown here that these equations correspond to a restricted variation of trial functions on the surfaces of atomic cells in the context of the variational cellular method of Leite and collaborators, derived from the variational principle of Schlosser and Marcus.

The aim of the present work was to show that full-potential multiple-scattering theory can be used to solve the density-functional one-particle equations for free and eigenvectors are needed as in basis-set methods based on the Rayleigh-Ritz variational principle. Compared to systems like bulk solids, impurities in the bulk or at the surface, where states with energies near the chemical potential are continuous, in free clusters the states are discrete and partially filled and require special techniques like the use of finite temperatures and integration contours in the complex-energy plane.

We investigate a reduced scaling full-potential DFT method based on the multiple scattering theory (MST) code MuST, which is released online (https://github.com/mstsuite/MuST) very recently. First, we test the accuracy by calculating structural properties of typical body-centered cubic (BCC) metals (V, Nb, and Mo). It is shown that the calculated lattice parameters, bulk moduli, and elastic constants agree with those obtained from the VASP, WIEN2k, EMTO, and Elk codes. Second, we test the locally self-consistent multiple scattering (LSMS) mode, which achieves reduced scaling by neglecting the multiple scattering processes beyond a cut-off radius. In the case of Nb, the accuracy of 0.5 mRy/atom can be achieved with a cut-off radius of 20 Bohr, even when small deformations are imposed on the lattice. Despite that the calculation of valence states based on MST exhibits linear scaling, the whole computational procedure has an overall scaling of about , due to the fact that the updating of Coulomb potential scales almost as . Nevertheless, it can be still expected that MuST would provide a reliable and accessible way to large-scale first-principles simulations of metals and alloys.