Mean field density-functional theory

Kierlik, E., Rosinberg, M.L., Fan, Y., and Monson, P. (1994). Prewetting at a liquid mixture-solid interface a comparison of Monte Carlo simulations with mean field density functional theory. J. Chem. Phys., 101, 10947-52. 

Comparison with mean-field density functional theory... 

In dynamic mean field density functional theory, the dynamics of the polymer melt under simple steady shear is described by the time evolution of density fields p/. The dynamics is governed by a diffusion-convection equation with sheared periodic boundary conditions and can readily be extended with (second order) reaction terms in the following manner ... 

Mean-field density functional theory (MF-DFT) calculations have been widely used fin the modeling of gas adsorption experiments in mesoporous materials [24-27]. For our lattice model, the mean-field expression of the grand potential is... 

The mean field density functional theory (DFT) approach was primarily developed by Evans and co-workers [67,68] for studying the interactions of fluids in pores at the molecular level. Recently, DFT methods have been developed specifically with the objective of the estimation of PSD of carbon-based as well as other types of microporous materials. This technique was first proposed by Seaton et al. [16], who used the local-DFT approximation. Later, the theory was modified by Lastoskie et al. [17,18] to incorporate the smoothed or nonlocal DFT approach. The rigorous statistical mechanics basis behind the DFT model has been recently reviewed by Gubbins [34]. Some sahent features of the theory are discussed later in this subsection. The DFT method initially proceeds by estimating the properties of a fluid directly from intermolecular forces such as that between sorbate-sorbent and sorbate-sorbate molecules. The interactions are divided into a short-ranged repulsive part and a long-ranged attractive part, which are both determined separately. 

L. Sarkisov, P. Monson, Lattice model of adsorption in disordered porous materials Mean-field density functional theory and Monte Carlo simulations, Phys. Rev. E 65 (2001) 011202. 

The dynamic mean-field density functional method is similar to DPD in practice, but not in its mathematical formulation. This method is built around the density functional theory of coarse-grained systems. The actual simulation is a... 

Fig. 2. Bead density profiles. Solid line Brushes, mean-field and scaling theory (step function) dashed-dotted line generalization of the Milner et al. theory for brushes in the theta state dashed-double dotted line Milner et al. theory for brushes (EV chains) dashed line EV stars dotted line EV combs. Variable r is scaled to give zero bead density for the smooth curves of brushes at r=l. The brush curves are normalized to show equal areas (same number of units). The comb and star densities are arbitrarily normalized to show similar bead density per volume unit as the step function and EV curves for brushes at the value ol r where these curves intercept...

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

Abbreviations MD, molecular dynamics TST, transition state theory EM, energy minimization MSD, mean square displacement PFG-NMR, pulsed field gradient nuclear magnetic resonance VAF, velocity autocorrelation function RDF, radial distribution function MEP, minimum energy path MC, Monte Carlo GC-MC, grand canonical Monte Carlo CB-MC, configurational-bias Monte Carlo MM, molecular mechanics QM, quantum mechanics FLF, Hartree-Fock DFT, density functional theory BSSE, basis set superposition error DME, dimethyl ether MTG, methanol to gasoline. 

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