Thermodynamics of attractive hard rods: a test of mean field density functional theory

Mean field density functional theory (MFDFT) has been employed to calculate the free energy of a pair of attractive hard rods on a ring. The results for homogeneous and optimal inhomogeneous density profiles have been compared with the exact free energy as a test of the approach. We discuss the problems in applying MFDFT to small systems and suggest modifications which allow a reasonably accurate treatment of this particular, rather extreme, case.     

Dynamical density functional theory and its application to spinodal decomposition

We present an alternative derivation of the dynamical density functional theory for the one-body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys. 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multibody interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our nonlinear theory is equivalent to the (generalized) linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wave number larger than that of the main peak.     

Density functional theory: Approximating quasiparticle density functional

A constructive approach for deriving the approximating quasiparticle energy density functional is proposed. As a matter of fact, the proposed approach is the direct development of the Kohn–Sham quasiparticle concept and the Levy–Valone approach. The approach presented takes into account a pseudopotential character of the exchange-correlation part of the density functional and results in a system of functional equations to obtain ground-state energies of many-electron systems.     

The behavior of fluids near solutes: a density functional theory and computer simulation study

The density distribution of solvent near a solute particle is studied using density functional theory and Monte Carlo simulation. The fluid atoms interact with each other via a hard sphere plus Yukawa potential, and interact with the solute via a hard sphere potential. For small solute sizes, the solvent displays liquidlike ordering near the particle. When the solute become larger, a drying transition is observed at state points near the coexistence conditions of the solvent. These predictions are similar to those of a recent theory for the hydrophobic effect by Lum, Chandler, and Weeks [J. Phys. Chem. 103, 4570 (1999)], although a comparison with simulations shows that the theory of this work is quantitatively more accurate. The connection between density functional methods and the LCW approach is also established.     

Robust acceleration of self consistent field calculations for density functional theory

We show that the type 2 Broyden secant method is a robust general purpose mixer for self consistent field problems in density functional theory. The Broyden method gives reliable convergence for a large class of problems and parameter choices. We directly mix the approximation of the electronic density to provide a basis independent mixing scheme. In particular, we show that a single set of parameters can be chosen that give good results for a large range of problems. We also introduce a spin transformation to simplify treatment of spin polarized problems. The spin transformation allows us to treat these systems with the same formalism as regular fixed point iterations.     

A density functional theory formulation of the reaction field model of solvent effects

It is possible to reformulate the reaction field (RF ) model of continuum solvent effects, by considering an approximate expression describing the energy changes from one ground state to another, in the frame of density functional theory (DFT ). The energy functional for an arbitrary electronic system coupled to a spin-independent electrostatic external perturbation is used to derive the well-known Born expression giving the electrostatic component of the solvation energy of an atomic ion. The approximate RF –DFT model is illustrated for a series of representative singly positive and negatively charged atomic ions. A Kohn–Sham (KS )-like formalism is then proposed to compute solvation energies within a self-consistent field scheme. The extension of the RF -DFT model to molecular systems is also outlined. © 1995 John Wiley & Sons, Inc.     

Modeling fluid diffusion using the lattice density functional theory approach: counterdiffusion in an external field

The dependence of the diffusivity on temperature, pressure, and composition is not understood well; consequently, data is preferred significantly over correlations in most practical situations. Even in dilute gases, the contributions of attractions and repulsions to the diffusivity are difficult to understand on a molecular level without performing simulations. We have developed a Lattice Density Functional Theory (LDFT) approach for modeling diffusion to supplement existing methods that are very rigorous but computationally demanding. The LDFT approach is analogous to the van der Waals equation in how it accounts for molecular interactions in that it has first-order corrections to ideal behavior; it is an extension of the Equilibrium LDFT for adsorption and phase behavior. In this work, the LDFT approach is presented and demonstrated by modeling the problem of color counterdiffusion in an externally-applied potential field. This potential field, in combination with the intermolecular potential function, creates a diffusion regime in which repulsions cause oscillations in the density profile. Using the LDFT approach, the oscillations were described and attributed to nearest-neighbor and next nearest-neighbor interactions. The LDFT approach gives qualitative and quantitative agreement with dual control-volume Grand Canonical Molecular Dynamics simulations.     

A generalized mean field theory of coarse-graining

A general mean field theory is presented for the construction of equilibrium coarse-grained models. Inverse methods that reconstruct microscopic models from low resolution experimental data can be derived as particular implementations of this theory. The theory also applies to the opposite problem of reduction, where relevant information is extracted from available equilibrium ensemble data. Additionally, a complementary approach is presented and problems of representability in coarse-grained modeling analyzed using information theoretic arguments. These problems are central to the construction of coarse-grained representations of complex systems, and commonly used coarse-graining methods and variational principles for coarse-graining are derived as particular cases of the general theory.     

Orbital-corrected orbital-free density functional theory

A new implementation of density functional theory (DFT), namely orbital-corrected orbital-free (OO) DFT, has been developed. With at most two non-self-consistent iterations, OO-DFT accomplishes the accuracy comparable to fully self-consistent Kohn-Sham DFT as demonstrated by its application on the cubic-diamond Si and the face-centered-cubic Ag systems. Our work provides a new impetus to further improve orbital-free DFT method and presents a robust means to significantly lower the cost associated with general applications of linear-scaling Kohn-Sham DFT methods on large systems of thousands of atoms within different chemical bonding environment.     

The role of fluctuations in both density functional and field theory of nanosystems

The role of fluctuations in both the density functional theory (DFT) and the field theory (FT) of nanosystems is studied. It turns out that although fluctuations are rigorously incorporated into the general formalism of DFT, they are often omitted in the choice of an approximate free energy functional that must be constructed in order to solve the basic integral equation appearing in DFT. Aside from the analytical discussion, it is demonstrated, in connection with a particular system (fluid in a nanopore) that the effects of fluctuation are missing when one of the most common functionals for this system is used. The demonstration involves a comparison of the results of Monte Carlo simulation with the predictions of DFT when this free energy functional is used. The applicability of FT and DFT in the context of the theory of nucleation is also discussed.     

Pseudospectral time-dependent density functional theory

Time-dependent density functional theory (TDDFT) is implemented within the Tamm-Dancoff approximation (TDA) using a pseudospectral approach to evaluate two-electron repulsion integrals. The pseudospectral approximation uses a split representation with both spectral basis functions and a physical space grid to achieve a reduction in the scaling behavior of electronic structure methods. We demonstrate here that exceptionally sparse grids may be used in the excitation energy calculation, following earlier work employing the pseudospectral approximation for determining correlation energies in wavefunction-based methods with similar conclusions. The pseudospectral TDA-TDDFT method is shown to be up to ten times faster than a conventional algorithm for hybrid functionals without sacrificing chemical accuracy.     

Magnetogranulometric analysis of ferrocolloids: Second-order modified mean field theory

A statistical model of highly concentrated ferrocolloids is proposed. The model is based on the use of the mean field theory for the single-particle orientational distribution function of the magnetic moments of ferroparticles. The expression for the effective mean field is derived with the method of perturbation theory of the second order with respect to the concentration and intensity of magnetodipole interparticle interaction. It is proposed to apply the magnetogranulometric analysis for describing magnetization curves for highly concentrated ferrocolloids. The high efficiency of the modified mean field theory is demonstrated during the determination of the parameters of disperse composition of ferrocolloids by the magnetogranulometric analysis.     

Perspective on density functional theory

Density functional theory (DFT) is an incredible success story. The low computational cost, combined with useful (but not yet chemical) accuracy, has made DFT a standard technique in most branches of chemistry and materials science. Electronic structure problems in a dazzling variety of fields are currently being tackled. However, DFT has many limitations in its present form: too many approximations, failures for strongly correlated systems, too slow for liquids, etc. This perspective reviews some recent progress and ongoing challenges.     

Time-dependent density functional theory gradients in the Amsterdam density functional package: geometry optimizations of spin-flip excitations

An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH₂ and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C?CC bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.     

Irreversible versus reversible aggregation: mean field theory and experiments

Colloidal aggregation processes arising at different electrolyte concentrations were studied by means of experiments and confronted with theoretical predictions of different kinetic aggregation models. For this purpose, aqueous dispersions of relatively large polystyrene microspheres were chosen as experimental systems. Aggregation was induced by adding KBr electrolyte to the initially stable particle dispersions. During the aggregation processes, the cluster-size distribution was monitored by means of single cluster light scattering. Analyzing the time evolution of the monomer concentration, we found that the processes arising even at moderate electrolyte concentrations cannot be described by pure time-independent irreversible aggregation models. Hence, alternative models such as time-dependent irreversible aggregation and several reversible aggregation models were also tested. The model that considers a time-dependent sticking probability was found to fit the data quite satisfactorily. Nevertheless, the fitted was so slow that it seems not very likely to find such a behavior in real systems. The aggregation-fragmentation models reported in the literature were unable to reproduce the experimental observations. Hence, a more realistic reversible aggregation model was developed. This model accounts also for reenforced or double bonds between the constituent particles. The corresponding fit improved significantly and reached the same quality as the time-dependent model. Moreover, the obtained fitting parameters were in qualitative agreement with the DLVO predictions and so, reversible aggregation seems to be a more reasonable explanation for the experimental data than time-dependent irreversible aggregation. However, no definite statement on the possible secondary bond fragmentation mechanism may be made since both the applied shear stress in the measuring cell and thermal fluctuations can cause weaker bonds to break.     

Estimations of electric field effects on the oxygen reduction reaction based on the density functional theory

By varying the external electric field in density functional theory (DFT) calculations we have estimated the impact of the local electric field in the electric double layer on the oxygen reduction reaction (ORR). Potentially, including the local electric field could change adsorption energies and barriers substantially, thereby affecting the reaction mechanism predicted for ORR on different metals. To estimate the effect of local electric fields on ORR we combine the DFT results at various external electric field strengths with a previously developed model of electrochemical reactions which fully accounts for the effect of the electrode potential. We find that the local electric field only slightly affects the output of the model. Hence, the general picture obtained without inclusion of the electric field still persists. However, for accurate predictions at oxygen reduction potentials close to the volcano top local electric field effects may be of importance.     

Embedding wave function theory in density functional theory

We present a framework for embedding a highly accurate coupled-cluster calculation within a larger density functional calculation. We use a perturbative buffer to help insulate the coupled-cluster region from the rest of the system. Regions are defined, not in real space, but in Hilbert space, though connection between the two can be made by spatial localization of single-particle orbitals. Relations between our embedding approach and some similar techniques are discussed. We present results for small sample systems for which we can extract essentially exact results, demonstrating that our approach seems to work quite well and is generally more reliable than some of the related approaches due to the introduction of additional interaction terms.