Atomistic density functional theory

Keywords solid oxide fuel cell modeling kinetic Monte Carlo frequency response atomistic density functional theory electrochemistry... 

Statistical thermodynamic theories such as atomistic density functional theory (DFT) for the computation of adsorption isotherms in simple pore geometries such as slits [15] or cylindrical capillaries [16] This category also includes integral equation methods for porous matrices [17] and templated porous materials [18],... 

The precursor of such atomistic studies is a description of atomic interactions or, generally, knowledge of the dependence of the total energy of the system on the positions of the atoms. In principle, this is available in ab-initio total energy calculations based on the loc density functional theory (see, for example, Pettifor and Cottrell 1992). However, for extended defects, such as dislocations and interfaces, such calculations are only feasible when the number of atoms included into the calculation is well below one hundred. Hence, only very special cases can be treated in this framework and, indeed, the bulk of the dislocation and interfacial... 

The second contribution spans an even larger range of length and times scales. Two benchmark examples illustrate the design approach polymer electrolyte fuel cells and hard disk drive (HDD) systems. In the current HDDs, the read/write head flies about 6.5 nm above the surface via the air bearing design. Multi-scale modeling tools include quantum mechanical (i.e., density functional theory (DFT)), atomistic (i.e., Monte Carlo (MC) and molecular dynamics (MD)), mesoscopic (i.e., dissipative particle dynamics (DPD) and lattice Boltzmann method (LBM)), and macroscopic (i.e., LBM, computational fluid mechanics, and system optimization) levels. 

Density functional theory (DFT) has become the main technique for the study of matter at the atomistic level. Practical methods of DFT are roughly of the same computational cost as the HF level. Formally DFT methods may scale as or depending of the particular implementation, but in both cases... 

The success of any molecular simulation method relies on the potential energy function for the system of interest, also known as force fields [27]. In case of proteins, several (semi)empirical atomistic force fields have been developed over the years, of which ENCAD [28,29], AMBER [30], CHARMM [31], GRO-MOS [32], and OPLSAA [33] are the most well known. In principle, the force field should include the electronic structure, but for most except the smallest systems the calculation of the electronic structure is prohibitively expensive, even when using approximations such as density functional theory. Instead, most potential energy functions are (semi)empirical classical approximations of the Born-Oppenheimer energy surface. 

In Chapter 4, Professor Donald W. Brenner and his co-workers Olga A. Shenderova and Denis A. Areshkin explore density functional theory and quantum-based analytic interatomic forces as they pertain to simulations of materials. The study of interfaces, fracture, point defects, and the new area of nanotechnology can be aided by atomistic simulations. Atom-level simulations require the use of an appropriate force field model because quantum mechanical calculations, although useful, are too compute-intensive for handling large systems or long simulation times. For these cases, analytic potential energy functions can be used to provide detailed information. Use of reliable quantum mechanical models to derive the functions is explained in this chapter. 

This chapter discusses a staged multi-scale approach for understanding CO electrooxidation on Pt-based electrodes. In this approach, density functional theory (DFT) is used to obtain an atomistic view of reactions on Pt-based surfaces. Based on results from experiments and quantum chemistry calculations, a consistent coarse-grained lattice model is developed. Kinetic Monte Carlo (KMC) simulations are then used to study complex multi-step reaction kinetics on the electrode surfaces at much larger lengthscales and timescales compared to atomistic dimensions. These simulations are compared to experiments. We review KMC results on Pt and PtRu alloy surfaces. 

Static band-structure calculations have recently flourished due to developments in the accuracy and computational efficiency of density functional theory calculations [31]. These calculations were originally developed to evaluate the properties of solids, in a similar way to how molecular orbital theory calculations are used to evaluate the properties of molecules. From a reaction point of view, the electronic and atomistic properties of reactant, product, intermediate, and transition states can also be evaluated using these methods, allowing... 

Useful atomic and subatomic scale information on hydroxylated oxide surfaces and their interaction with aggressive ions (e.g., Cl ) can be provided by theoretical chemistry, whose application to corrosion-related issues has been developed in the context of the metal/liquid interfaces [34 9]. The application of ah initio density functional theory (DFT) and other atomistic methods to the problem of passivity breakdown is, however, limited by the complexity of the systems that must include three phases, metal(alloy)/oxide/electrolyte, then-interfaces, electric field, and temperature effects for a realistic description. Besides, the description of the oxide layer must take into account its orientation, the presence of surface defects and bulk point defects, and that of nanostructural defects that are key actors for the reactivity. Nevertheless, these methods can be applied to test mechanistic hypotheses. 

Zhang X, Lu G, Curtin WA. Multiscale quantum/atomistic couphng using constrained density functional theory. Phys. Rev. B 2013 87 054113. 

The outline of the paper is as follows. In Sect. 2 we describe the basic RISM and PRISM formalisms, and the fundamental approximations invoked that render the polymer problem tractable. The predicticms of PRISM theory for the structure of polymer melts are described in Sect. 3 for a variety of single chain models, including a comparison of atomistic calculations for polyethylene melt with diffraction experiments. The general problem of calculating thermodynamic properties, and particularly the equation-of-state, within the PRISM formalism is described in Sect. 4. A detailed application to polyethylene fluids is summarized and compared with experiment. The develojanent of a density functional theory to treat polymer crystallization is briefly discussed in Sect. 5, and numerical predictions for polyethylene and polytetrafluoroethylene are summarized. 

The bottom left Panel illustrates models used in dynamic density functional theory (DDFT) simulations (a) The chemical structure of repeat unit of sulfonated poly(ether ether ketone) (sPEEK) chain. Hydrophilic blocks A and hydrophobic blocks B correspond to the sulfonated and nonsulfonated monomers, respectively, (b) The atomistic model of sPEEK chain, (c) The mapping of the atomistic chain onto a coarse-grained [ABtxChain and water molecules onto mesoscale solvent particle of type C. 

To bypass the limitations of the Cauchy-Born rule, in 2006, Lu et al. proposed a more involved scheme to couple standard DFT to quasi-continuum calculations. In their method, the part of the system far away from the zone of interest is described using a classical (nonquantum) quasi-continumn approach (see discussion above on QC for details), i.e., considering both local (continuum) and nonlocal (atomistic) terms. Classical potentials (EAM in the applications presented) are used to evaluate the energy within the QC calculations. A third region is considered as well, covering the part of the system that needs a more detailed description. It is in this region that density functional theory is used. 

There is no single, perfect, and all-comprising model for predicting fuel cell properties on all length- and time scales. As shown in Figure 3.2, the density functional theory (DFT) can be applied at the atomistic scale (10 m) chemical reactions in the three-phase boundary (TPB) the molecular Dynamics (MD) and Monte Carlo (MC) methods, based on classical force fields, can be employed to describe individual atoms or clusters of catalyst materials at the nano-Zmicro-scale (10 —10 m) the particle-based methods (e.g. DPD) or mesh-based methods, for example Lattice-Boltzmann (LB), are used to solve the complex fluid flows in the porous media at the meso-scopic scale (10 10 m) and at the macroscopic scale (>10 m), continuum models... 

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