First-principles energetics

There are mainly two reasons why so many GO structure models have been proposed in experiment. One reason is that GO samples vary from one batch to another under different synthesis conditions. Another reason is that assignment of spectroscopic data has been based on experiences on other molecules and materials and thus may not be very accurate. Theoretical studies are very useful in these two aspects. First-principles energetics can provide a clean simplified picture on GO structure, without the complexities of experimental conditions involved. On the other hand, computational spectroscopy provides a direct connection to experimental observations. 

First-principles energetics is very powerful for computational structure characterization. The main difficulty in applying this method to GO structure study is the amorphous nature of GO. When the number of atoms is very large, it is not feasible to compare energy for all possible structures. Therefore, first-principles calculations are typically limited to a small system. For this reason, an artificial periodic boundary condition is required for GO structure study. Such an artificial boundary condition of course will weaken the power of predictability of first-principles energetics for GO. However, useful insights can still be obtained from such calculations, especially in prediction of local building blocks. 

As we have shown, based on first principles energetics, many GO stmcture models have been proposed. However, the power of energetics analysis is expected to be limited by the complexity of the GO potential energy surface, especially when artificial periodic boundary condition must be adopted with a small unit cell. In contrast, computational spectroscopy provides information, which can be directly compared with experiments. Therefore, it provides a powerful alternative in computational nanostructure characterization. XPS [37,48-52] and NMR [34-36, 53, 54] are two widely used experimental spectroscopic techniques to characterize local structures, and they are mostly used in GO structure research. 

Nolan M, Parker SC, Watson GW Ce02 catalysed conversion of CO, NOj and NO from first principles energetics, Phys Chem Chem Phys 8(2) 216-218, 2006a. 

Chatteijee, A., Ebina, T., and Iwasaki, T. 2003. Adsorption structures and energetic of fluoro- and chlorofluorocarbons over faujasite—a first principle study. Stud. Surf. Sci. Catal. 145 371-374. 

The structure and dynamics of clean metal surfaces are also of importance for understanding surface reactivity. For example, it is widely held that reactions at steps and defects play major roles in catalytic activity. Unfortunately a lack of periodicity in these configurations makes calculations of energetics and structure difficult. When there are many possible structures, or if one is interested in dynamics, first-principle electronic structure calculations are often too time consuming to be practical. The embedded-atom method (EAM) discussed above has made realistic empirical calculations possible, and so estimates of surface structures can now be routinely made. 

There have been a small number of theoretical studies of cation ordering in LDHs. First principles molecular dynamics calculations [43] on [Mg3Al(OH)8]Cl LDHs discussed in Sect. 3.2.6 suggested that structures with adjacent aluminum cations were energetically less favorable than one without, although the chosen arrangement for the latter lacked either hexagonal or rhombohedral supercell. 

To investigate the STM imaging mechanism further, Ohnishi and Tsukada (1989) made a first-principles calculation of the electronic states for a number of W clusters. From the calculations, they found that on the apex atom of many W clusters, there is a <7--like stale protruding from the apex atom, energetically very close to the Fermi level. Using Green s function methods. 

A commonly used quantity to present the information obtained from a first-principles calculation based on the density-functional method is the local density of states (LDOS) at every energy value below the Fermi level at zero absolute temperature. Because every state has an energy eigenvalue, the information with both spatial and energetic distributions is important for many experiments involving energy information. The LDOS p(r, ) at a point r and at an energy level E is defined as... 

The infancy of these first-principles methods as applied to periodic zeolite lattices means that further detailed work is necessary, particularly in the area of verification of the ability of the pseudopotential to reproduce dynamic as well as static structural properties. However, the results found with these methods demonstrate that the debate concerning the modeling of the activation of methanol within a zeolite is far from concluded. The proton transfer to methanol as a reaction in its own right is, however, of relatively little interest. It does not govern the pathway or energetics of reactions such as dehydration to give dimethyl ether (DME). These are governed instead by the individual transition states that lead to the products, as we discuss in the next section. 

With the advent of first principles computational methods, highly scalable software and parallel computer architectures, more elaborate and accurate classical force fields than those discussed in the preceding section are being developed for predictions of physical and chemical properties of energetic solids. As indicated in section 2 of this chapter there are several... 

The preceding introduction might lead one to believe that this chapter could simply be divided into two basic parts—thermochemical considerations and kinetic considerations—which would cover all the relevant subject matter. However, in the last decade, first-principles (ab initio) computations have become commonplace and their results have often confirmed predictions based on thermochemical approaches, sometimes even surpassing them in accuracy. Hence, there is a need to encompass both thermochemical and ab initio treatments. We group the latter under the heading structural energetics and explore this topic further in Section 2.2. We also talk about the relevant thermodynamic and kinetic factors for specific systems in their respective chapters. For now, we discuss thermodynamics and kinetics in the most general terms. 

In order to calculate adsorbed SO3 configuration on Pt surface, we used the first-principles calculation code PHASE [9] with a slab model in a periodic boundary condition along the surface plane to simulate the Pt (111) surface. A four-layer slab model was used for main calculations. In these calculations, the atoms at the bottom are fixed at a bond distance d=2.83 A, which is the optimized value in Pt fee crystal with PHASE. A p(4 x 4) lateral supercell was used for the computation of the most energetically stable configuration. The p(4 x 4) surface supercell has 16 Pt atoms per layer with a lateral lattice constant of 11.31 A. 

Tinte et al.54 have carried out molecular dynamic simulations of first-principles based effective Hamiltonian for PSN under pressure and of PMN at ambient pressure that clearly exhibit a relaxor state in the paraelectric phase. Analysis of the short-to-medium range polar order allows them to locate Burns temperature Tb. Burns temperature is identified as the temperature below which dynamic nanoscale polar clusters form. Below TB, the relaxor state characterized by enhanced short-to-medium range polar order (PNR) pinned to nanoscale chemically ordered regions. The calculated temperature-pressure phase diagram of PSN demonstrates that the stability of the relaxor state depends on a delicate balance between the energetics that stabilize normal ferroelectricity and the average strength of quenched "random" local fields. 

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