Density-functional theory for polymer-carbon dioxide mixtures: A perturbed-chain SAFT approach

We propose a density-functional theory (DFT) describing inhomogeneous polymer-carbon dioxide mixtures based on a perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The weight density functions from fundamental measure theory are used to extend the bulk excess Helmholtz free energy to the inhomogeneous case. The additional long-range dispersion contributions are included using a mean-field approach. We apply our DFT to the interfacial properties of polystyrene-CO(2) and poly(methyl methacrylate) CO(2) systems. Calculated values for both solubility and interfacial tension are in good agreement with experimental data. In comparison with our earlier DFT based on the Peng-Robinson-SAFT EOS, the current DFT produces quantitatively superior agreement with experimental data and is free of the unphysical behavior at high pressures (>35 MPa) in the earlier theory.     

Density-functional theory studies on microscopic processes of gaas growth

Results for the elementary processes of MBE growth of GaAs on the frequently used GaAs(001) substrate are reviewed. We propose a bottom-up approach, where a growth model is constructed from the results of density functional theory (DFT) calculations. The implications of such a model can be tested against the information from STM images. First, the stable surface reconstructions are reviewed. Under the most commonly used conditions for MBE growth, the arsenic-rich β2 (2 × 4) reconstruction, which contains As dimers as basic building blocks, is the most stable. Next, the adsorption and diffusion of Ga atoms and As molecules on this surface is described. The DFT calculations support the picture that adsorbed Ga atoms are quite stable against re-evaporation. Thus, their mobility determines the homogeneity of the growing layer. Incorporation of Ga atoms proceeds by splitting the As dimers. We propose a model where growth proceeds in two stages: filling of trenches in the β2 (2 × 4) reconstruction, followed by nucleation of islands on the surface regions where the trenches are filled. We demonstrate how clusters of incorporated Ga atoms act as nuclei for the process of trench filling. Concerning island formation, the role of step formation energies and attachment probabilities of mobile adatoms at steps is discussed. Knowledge of these is crucial for an understanding of island shapes. Ongoing research is aiming at understanding of the microscopic mechanisms giving rise to the transition between the step-flow mode and the island-nucleation mode of growth.     

Communication: Density-functional theory for inhomogeneous hyperbranched polymeric fluids: polydisperse effect of degree of branching

We developed a new density-functional theory (DFT) for inhomogeneous hyperbranched polymers that is able to describe the polydisperse degree of branching quantitatively. The topological contributions of the polymer chains to the Helmholtz free energy take into account the effect of triple connections that are absent in previous DFT investigations. One key advantage of the new theory is that the computational cost shows only a linear relationship with the molecular weight (rather than an exponential relationship). The practical utility of the new DFT is illustrated by investigating colloidal stability in the presence of monodisperse and polydisperse hyperbranched polymers.     

Density-functional theory study of Iron(III) hydrolysis in aqueous solution

Fe(III) hydrolysis in aqueous solution has been investigated using density-functional methods (DFT). All possible structures arising from different tautomers and multiplicities have been calculated. The solvation energy has been estimated using the UAHF-PCM method. The hydrolysis free energies have been estimated and compared with the available experimental data. The different hydrolysis species have distinct geometries and electronic structures. We have shown that improvement of theory level in calculating the electronic energy does not necessarily improve the estimated free energies in aqueous solution since the UAHF-PCM is a simple method that neglects specific interactions with the solvent. Therefore, it is important to have the correct balance between theory level used in the electronic calculation and the UAHF-PCM. The PBE/TZVP/UAHF-PCM method has been found to describe correctly the hydrolysis energies of Fe(III), deviating about 3.0 kcal mol(-1) from experimental values.     

Density-functional theory calculations of optical rotatory dispersion in the nonresonant and resonant frequency regions

The complex linear response function, which can be employed for calculations of second-order molecular properties in regions of strong absorption, is here extended to encompass the mixed electric-dipole-magnetic-dipole polarizability. The mixed electric-dipole-magnetic-dipole polarizability determines the optical rotation and, when absorption is taken into account, the full anomalous optical rotatory dispersion (ORD) spectra of chiral molecules can be calculated using first-principle quantum-chemical methods. Gauge-origin independence of the results is ensured through the use of London atomic orbitals. To illustrate the importance of taking the absorption process properly into account, we here apply this methodology to the study of the anomalous ORD of hydrogen peroxide, 3R-methylcyclohexanone, 4R-1,1-dimethyl-[3]-(1,2)-ferrocenophan-2-on, and the D(2) isomer of the C(84) fullerene.     

Density-functional theory study of electric and magnetic properties of hexafluorobenzene in the vapor phase

A series of electric and magnetic properties of hexafluorobenzene have been calculated, including the electric dipole polarizability, magnetizability, electric quadrupole moment, and nonlinear mixed electric dipole-magnetic dipole-electric quadrupole hyperpolarizabilities needed to obtain estimates of the Kerr, Cotton-Mouton, Buckingham, Jones, and magnetoelectric birefringences in the vapor phase. Time-dependent density-functional theory was employed for the calculation of linear-, quadratic, and cubic response functions. A number of density functionals have been considered, along with Sadlej's triple-zeta basis set and the augmented correlation-consistent polarized valence double zeta and augmented correlation-consistent polarized valence triple zeta basis sets. Comparisons have been made with experiment where possible. The analysis of results allows for an assessment of the capability of time-dependent density-functional theory for high-order electromagnetic properties of an electron-rich system such as hexafluorobenzene.     

Correlations in anticrossing spectra and scattering theory: Numerical simulations

For the interpretation of experimental results of anticrossing spectroscopy in molecules, the results of numerical simulations are presented. We have focussed our attention on the visibility of the correlation hole. In the formulation of the model, we combine scattering theory and a random-matrix model.     

Density-functional generalized-gradient and hybrid calculations of electromagnetic properties using Slater basis sets

In this paper we extend our density-functional theory calculations, with generalized gradient approximation and hybrid functionals, using Slater-type orbitals (STOs), to the determination of second-order molecular properties. The key to the entire methodology involves the fitting of all STO basis function products to an auxiliary STO basis, through the minimization of electron-repulsion integrals. The selected properties are (i) dipole polarizabilities, (ii) nuclear magnetic shielding constants, and (iii) nuclear spin-spin coupling constants. In all cases the one-electron integrals involving STOs were evaluated by quadrature. The implementation for (ii) involved some complexity because we used gauge-including atomic orbitals. The presence of two-electron integrals on the right-hand side of the coupled equations meant that the fitting procedure had to be implemented. For (iii) in the hybrid case, fitting procedures were again required for the exchange contributions. For each property we studied a number of small molecules. We first obtained an estimate of the basis set limit using Gaussian-type orbitals (GTOs). We then showed how it is possible to reproduce these values using a STO basis set. For (ii) a regular TZ2P quality STO basis was adequate; for (i) the addition of one set of diffuse functions (determined by Slater's rules) gave the required accuracy; for (iii) it was necessary to add a set of 1s functions, including one very tight function, to give the desired result. In summary, we show that it is possible to predict second-order molecular properties using STO basis sets with an accuracy comparable with large GTO basis sets. We did not encounter any major difficulties with either the selection of the bases or the implementation of the procedures. Although the energy code (especially in the hybrid case) may not be competitive with a regular GTO code, for properties we find that STOs are more attractive.     

Density-functional theory (hyper)polarizabilities of push-pull pi-conjugated systems: treatment of exact exchange and role of correlation

The performance of the optimized effective potential procedure for exact exchange in calculating static electric-field response properties of push-pull pi-conjugated systems has been studied, with an emphasis on NO2-(CH=CH)n-NH2 chains. Good agreement with Hartree-Fock dipole moments and (hyper)polarizabilities is obtained; particularly noteworthy is the chain length dependence for beta/n. Thus, the problem that conventional density-functional theory functionals dramatically overestimate these properties is largely solved, although there remains a significant correlation contribution that cannot be accounted for with current correlation functionals.     

Analysis of sample-solvent induced modifier-solute peak interactions in biochromatography using equilibrium theory and detailed simulations

Batch liquid chromatographic columns are often equilibrated with an eluent stream being a mixture of inert compounds and so-called modifiers. The sample injected into the eluent stream usually consists of the solutes to be separated and of a mixture of the same solvents as in the eluent but in general with different concentration values. This results in two groups of peaks moving along the column: the solute peaks and the modifier pertubations. If the adsorptivity of the solute depends strongly on the modifier, as it is often the case in biochromatography, the interference between the two groups of peaks leads to peculiar phenomena like double peaks, split peaks, distorted peaks with anti-Langmurian shape, etc. In this work, these phenomena are analyzed based on an analytical solution of the equilibrium theory model and the results are compared with detailed simulations and experimental data. It is shown that the qualitative behavior is well predicted in the frame of equilibrium theory and general guidelines how to avoid these kinds of interactions are developed.     

Self-diffusion and transport diffusion of light gases in metal-organic framework materials assessed using molecular dynamics simulations

Metal-organic framework (MOF) materials pose an interesting alternative to more traditional nanoporous materials for a variety of separation processes. Separation processes involving nanoporous materials can be controlled by either adsorption equilibrium, diffusive transport rates, or a combination of these factors. Adsorption equilibrium has been studied for a variety of gases in MOFs, but almost nothing is currently known about molecular diffusion rates in MOFs. We have used equilibrium molecular dynamics (MD) to probe the self-diffusion and transport diffusion of a number of small gas species in several MOFs as a function of pore loading at room temperature. Specifically, we have studied Ar, CH4, CO2, N2, and H2 diffusion in MOF-5. The diffusion of Ar in MOF-2, MOF-3, and Cu-BTC has been assessed in a similar manner. Our results greatly expand the range of MOFs for which data describing molecular diffusion is available. We discuss the prospects for exploiting molecular transport properties in MOFs in practical separation processes and the future role of MD simulations in screening families of MOFs for these processes.     

Ab-initio self-consistent field theory for the treatment of interface between two different quasi-one-dimensional chains

The solution of the problem how to treat an interface between two quasi-one-dimensional polymers has been formulated combining Dyson's equation with the mutually consistent field (self-consistent field solutions for the change of the bulk states of the polymers and for the extraband “interface” states) method. A numerical procedure for the implementation of an appropriate program (which needs as input only the ab initio self-consistent field crystal orbital solutions of the two infinite periodic polymers as well as some cluster calculations of the interface and its neighbors at both sides) is outlined. The necessary program is under development.     

Vibronic coupling simulations for linear and nonlinear optical processes: theory

A comprehensive vibronic coupling model based on the time-dependent wavepacket approach is derived to simulate linear optical processes, such as one-photon absorbance and resonance Raman scattering, and nonlinear optical processes, such as two-photon absorbance and resonance hyper-Raman scattering. This approach is particularly well suited for combination with first-principles calculations. Expressions for the Franck-Condon terms, and non-Condon effects via the Herzberg-Teller coupling approach in the independent-mode displaced harmonic oscillator model are presented. The significance of each contribution to the different spectral types is discussed briefly.     

Electrolyte exclusion from charged adsorbent: replica Ornstein-Zernike theory and simulations

Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.     

Argon nucleation: bringing together theory, simulations, and experiment

We present an overview of the current status of experimental, theoretical, molecular dynamics (MD), and density functional theory (DFT) studies of argon vapor-to-liquid nucleation. Since the experimental temperature-supersaturation domain does not overlap with the corresponding MD and DFT domains, separate comparisons have been made: theory versus experiment and theory versus MD and DFT. Three general theoretical models are discussed: Classical nucleation theory (CNT), mean-field kinetic nucleation theory (MKNT), and extended modified liquid drop model-dynamical nucleation theory (EMLD-DNT). The comparisons are carried out for the area below the MKNT pseudospinodal line. The agreement for the nucleation rate between the nonclassical models and the MD simulations is very good--within 1-2 orders of magnitude--while the CNT deviates from simulations by about 3-5 orders of magnitude. Perfect agreement is demonstrated between DFT results and predictions of MKNT (within one order of magnitude), whereas CNT and EMLD-DNT show approximately the same deviation of about 3-5 orders of magnitude. At the same time the agreement between all theoretical models and experiment remains poor--4-8 orders of magnitude for MKNT, 12-14 orders for EMLD-DNT, and up to 26 orders for CNT. We discuss possible reasons for this discrepancy and the ways to carry out experiment and simulations within the common temperature-supersaturation domain in order to produce a unified picture of argon nucleation.     

Charge reversal in real colloids: Experiments, theory and simulations

In the last years, the inclusion of ionic short-range correlations in the study of colloidal stability has led to significant disagreements with the predictions obtained from classical treatments. An example of these discrepancies is the occurrence of charge reversal of charged particles. In order to shed light on this issue, the charge reversal of latex particles in the presence of asymmetric electrolytes has been investigated through Monte Carlo (MC) simulations. In particular, experimental results concerning electrophoretic mobility reversals and the Hyper-Netted-Chain/Mean-Spherical-Approximation (HNC/MSA) predictions have been compared with simulations in which two alternative methods for evaluating energies have been applied. A realistic hydrated ion size is used in the HNC/MSA calculations and simulations. In this way, the existence of a reversal in the electrophoretic mobility due to ion size correlations and without requiring specific counterion adsorption is probed. Moreover, the simulations appears as a useful tool for explaining those results in which the HNC/MSA does not reproduce the experimental trends.     

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.     

Osmotic ensemble methods for predicting adsorption-induced structural transitions in nanoporous materials using molecular simulations

Osmotic framework adsorbed solution theory is a useful molecular simulation method to predict the evolution of structural transitions upon adsorption of guest molecules in flexible nanoporous solids. One challenge with previous uses of this approach has been the estimation of free energy differences between the solid phases of interest in the absence of adsorbed molecules. Here we demonstrate that these free energy differences can be calculated without reference to experimental data via the vibrational density of states of each phase, a quantity that can be obtained from molecular dynamics simulations. We show the applicability of this method through case studies of the swelling behaviors of two representative systems in which swelling upon adsorption of water is of importance: single-walled aluminosilicate nanotube bundles and cesium montmorillonite. The resulting predictions show that the aluminosilicate nanotube bundles swell significantly with increasing interstitial adsorption and that the layer spacing of cesium montmorillonite expands up to about 12.5 A?, giving good agreement with experiments. The method is applicable to a wide range of flexible nanoporous materials, such as zeolites, metal-organic frameworks, and layered oxide materials, when candidate structures can be defined and a force field to describe the material is available.     

Adsorption of gases in metal organic materials: comparison of simulations and experiments

Molecular simulations using standard force fields have been carried out to model the adsorption of various light gases on a number of different metal organic framework-type materials. The results have been compared with the available experimental data to test the validity of the model potentials. We observe good agreement between simulations and experiments for a number of different cases and very poor agreement in other cases. Possible reasons for the discrepancy in simulated and measured isotherms are discussed. We predict hydrogen adsorption isotherms at 77 and 298 K in a number of different metal organic framework materials. The importance of quantum diffraction effects and framework charges on the adsorption of hydrogen at 77 K is discussed. Our calculations indicate that at room temperature none of the materials that we have tested is able to meet the requirements for on-board hydrogen storage for fuel cell vehicles. We have calculated the volume available in a given sorbent at a specified adsorption energy (density of states). We discuss how this density of states can be used to assess the effectiveness of a sorbent material for hydrogen storage.