Ab initio thermodynamics

Ab initio thermodynamics, 129-155 Acetaldehyde oxidation, 196-197, 624 Acetic acid, 192-198, 394-395 Active sites in electrocatalysis, 93-124, 159-198, 237,250,253 Adiabatic and non-adiabatic electron transfer, 34... 

EQUILIBRIUM PHASE DIAGRAMS FROM AB INITIO THERMODYNAMICS... 

Figure 7.5 An ab initio phase diagram for O2 interacting with Ag(l 11). [Reprinted with per mission from W. X. Li, C. Stampfl, and M. Scheffler, Insights into the Function of Silver as an Oxidation Catalyst by ab initio Thermodynamics, Phys. Rev. B 68 (2003), 165412 (Copyright 2003 by the American Physical Society).]...

The overprediction of binding energies for simple molecules can have consequences for ab initio thermodynamic calculations involving these species. In Chapter 7 we examined the stability of bulk oxide materials using this approach. In order to quantitatively predict the conditions at which bulk phases were in equilibrium, the chemical potential of 02 had to be calculated using Eq. (7.6), which includes a contribution from the total energy of 02. One way to correct for the imprecision of DFT for total energies of this kind is to use experimental data when it is available. When this approach is used, it is important that it is clearly stated. 

Figure 7.18. Plot of surface energy vs. oxygen chemical potential for different terminations of the a-Fe203 (0001) from ab initio thermodynamic calculations, (from [85]).

In Section 2.1, we remarked that classical thermodynamics does not offer us a means of determining absolute values of thermodynamic state functions. Fortunately, first-principles (FP), or ab initio, methods based on the density-functional theory (DFT) provide a way of calculating thermodynamic properties at 0 K, where one can normally neglect zero-point vibrations. At finite temperatures, vibrational contributions must be added to the zero-kelvin DFT results. To understand how ab initio thermodynamics (not to be confused with the term computational thermochemistry used in Section 2.1) is possible, we first need to discuss the statistical mechanical interpretation of absolute internal energy, so that we can relate it to concepts from ab initio methods. 

The review is broken into three broad sections, each containing three separate topics. The first section highlights three dramatic successes in the application of DFT to heterogeneous catalysis, followed by a discussion of the accuracy of DFT. The second section reviews three areas within heterogeneous catalysis that have attracted large volumes of theoretical effort in recent years, namely ab initio thermodynamics, the catalytic activity of nanoclusters of gold, and the development of bimetallic catalysts. The third section provides recent... 

Reuter, Frenkel, and Scheffler have recently used DFT-based calculations to predict the CO turnover frequency on RuO2(110) as a function of 02 pressure, CO pressure, and temperature.31 This was an ambitious undertaking, and as we will see below, remarkably successful. Much of this work was motivated by the earlier success of ab initio thermodynamics, a topic that is reviewed more fully below in section 3.1. The goal of Reuter et al. s work was to derive a lattice model for adsorption, dissociation, surface diffusion, surface reaction, and desorption on defect-free Ru02(l 10) in which the rates of each elementary step were calculated from DFT via transition state theory (TST). As mentioned above, experimental evidence strongly indicates that surface defects do not play a dominant role in this system, so neglecting them entirely is a reasonable approach. The DFT calculations were performed using a GGA full-potential... 

The success stories reviewed above are, of course, just several of a larger number of areas of heterogeneous catalysis in which DFT-based calculations have made valuable contributions in recent years. In this section, three topics that have attracted considerable attention are described, ab initio thermodynamics, the catalytic activity of nanoclusters of gold, and computational efforts to screen bimetallic catalysts. Again, the choice of these topics does not indicate that they are the only topics of interest in the community, but they give a good representation of current approaches. 

Detailed descriptions of the theory underlying ab initio thermodynamics are available in the review by Stampfl,100 as well as in the papers by Zhang et a/.103 and Reuter and Scheffler.99 Rather than reiterating these discussions, it is more useful to present a simple pedagogical example, which I have modeled on the calculations by Greeley and Mavrikakis of FI adlayers on Ni(lll).104 Similar calculations for FI on Pt(lll) have been performed by Legare.105 Consider the situation where DFT calculations have been used to minimize the energy, E, associated with n different adlayer structures of H on a Ni surface. We would... 

As mentioned briefly above, ab initio thermodynamics have not only been applied to surfaces, but to bulk materials. Stampfl and Freeman have investigated the structure of tantalum nitride in this way.102 These methods are well suited for predicting the solubility of atoms in bulk materials. Calculations of this type have been reported for the solubility of O in Pd114 and H solubility in CuPd alloys.130... 

The more limited geometry and vibrational analyses employed in standard ab initio thermodynamics schemes, such as G3, while typically suitable for thermodynamic evaluations of stable species, lack the accuracy required for quantitative a priori kinetic predictions. In essence, kinetic predictions depend much more strongly on the vibrational analyses than do low temperature thermodynamic predictions. Furthermore, saddle point geometries are more strongly dependent on the electronic structure methodology than are equilibrium geometries. 

AB INITIO THERMODYNAMIC AND STRUCTURAL STUDIES OF CATIONIC DISORDERED MgAl204 SPINEL... 

Drautz, R. and Diaz-Ortiz, A. (2006) Obtaining cluster expansion coefficients in ab initio thermodynamics of multicomponent lattice-gas systems. Phys. Rev. B, 73, 224207. 

The following sections highlight studies employing the computational methods discussed in the previous section to characterize supported metal-oxide systems. It is not intended to be an exhaustive review of the subject, but rather serves to illustrate the strengths and limitations of these methods when applied to supported heterogeneous catalysis. It is broken into three sections corresponding to DFT applied to water-gas-shift (WGS) catalysis (4.3.1), applications of ab initio thermodynamics to assess thermodynamic stability of surfaces (4.3.2), and applications of empirical force-fields (4.3.3). The sections... 

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