Structure calculations overview

Chapter 1, Computational Models and Model Chemistries, provides an overview of the computational chemistry field and where electronic structure theory fits within it. It also discusses the general theoretical methods and procedures employed in electronic structure calculations (a more detailed treatment of the underlying quantum mechanical theory is given in Appendix A). 

As it was mentioned in Section 9.4.1, 3D structures generated by DG have to be optimized. For this purpose, MD is a well-suited tool. In addition, MD structure calculations can also be performed if no coarse structural model exists. In both cases, pairwise atom distances obtained from NMR measurements are directly used in the MD computations in order to restrain the degrees of motional freedom of defined atoms (rMD Section 9.4.2.4). To make sure that a calculated molecular conformation is rehable, the time-averaged 3D structure must be stable in a free MD run (fMD Sechon 9.4.2.5J where the distance restraints are removed and the molecule is surrounded by expMcit solvent which was also used in the NMR measurement Before both procedures are described in detail the general preparation of an MD run (Section 9.4.2.1), simulations in vacuo (Section 9.4.2.2) and the handling of distance restraints in a MD calculation (Section 9.4.2.3) are treated. Finally, a short overview of the SA technique as a special M D method is given in Sechon 9.4.2.6. 

W. Paul, High Pressure in Semiconductor Physics A Historical Overview N. E. Christensen, Electronic Structure Calculations for Semiconductors under Pressure R. J. Neimes and M. I. McMahon, Structural Transitions in the Group IV, III-V and II-VI Semiconductors Under Pressure... 

The presence of symmetry in a molecule can be used to great advantage in electronic structure calculations, although some care is required to avoid possible pitfalls that are simultaneously introduced (Appendix B provides a brief overview of nomenclature (e.g., the term irrep . 

In the remainder of this chapter, we first give an overview of electronic structure calculations for the donor-acceptor heteroj unction systems under consideration (Sec. 2). We then introduce the electron-phonon coupling model adopted to describe the extended polymer system (Sec. 3), followed by an... 

The overwhelming majority of the theoretical studies were performed on cluster models of the catalytic site, hi spite of the fact that the role of space confinement and the secondary interactions with the framework atoms is well-known, there are only a few electronic structure calculations on lattice models involving hydrocarbons, using either periodic DFT calculations, or embedding methods. In this brief account of the subject we attempt to overview some of the recent computational results of the literature and present some new data obtained from ab initio DFT pseudopotential plane wave calculations on Cl - C4 alkanes in the chabazite framework. 

This paper gives a short overview of density functional calculations mainly based on the DV-Xa approach organized as follows. A short overview of Density Functional Theory, DFT, and Kohn-Sham equations is given in section II followed by a summary of different ways of solution of the Kohn-Sham equations in Sec. III. Comparisons of results from some old and some up-to-date density functional electronic structure calculations made by our group to show applications to clusters, surfaces, adsorbates on surfaces and Ceo are given in Sec. IV. Conclusions and outlook are summarized in Sec. V. 

The aim of this chapter is to provide the reader with an overview of the potential of modern computational chemistry in studying catalytic and electro-catalytic reactions. This will take us from state-of-the-art electronic structure calculations of metal-adsorbate interactions, through (ab initio) molecular dynamics simulations of solvent effects in electrode reactions, to lattice-gas-based Monte Carlo simulations of surface reactions taking place on catalyst surfaces. Rather than extensively discussing all the different types of studies that have been carried out, we focus on what we believe to be a few representative examples. We also point out the more general theory principles to be drawn from these studies, as well as refer to some of the relevant experimental literature that supports these conclusions. Examples are primarily taken from our own work other recent review papers, mainly focused on gas-phase catalysis, can be found in [1-3]. 

The next section gives a brief overview of the main computational techniques currently applied to catalytic problems. These techniques include ab initio electronic structure calculations, (ab initio) molecular dynamics, and Monte Carlo methods. The next three sections are devoted to particular applications of these techniques to catalytic and electrocatalytic issues. We focus on the interaction of CO and hydrogen with metal and alloy surfaces, both from quantum-chemical and statistical-mechanical points of view, as these processes play an important role in fuel-cell catalysis. We also demonstrate the role of the solvent in electrocatalytic bondbreaking reactions, using molecular dynamics simulations as well as extensive electronic structure and ab initio molecular dynamics calculations. Monte Carlo simulations illustrate the importance of lateral interactions, mixing, and surface diffusion in obtaining a correct kinetic description of catalytic processes. Finally, we summarize the main conclusions and give an outlook of the role of computational chemistry in catalysis and electrocatalysis. 

OVERVIEW OF COMPUTATIONAL METHODS 1.2.1 Electronic Structure Calculations... 

Earlier it was mentioned that the relativistic theory of electronic states in solids in many respects is identical to that of atoms. Since this is well described elsewhere, this section will only deal with some features of specific implementations of the theory in actual calculation methods used for solids, and the importance of relativistic effects — apart from those already discussed — will be illustrated by examples. Although Section 3 did refer to results of LMTO calculations, we did not describe how these included relativity. This section will deal with these items in the form of an overview, and the basic band structure calculations described relate to the density-functional theory [62,63]. Since magnetism is one of the most important solid state physics fields we shall discuss the simultaneous inclusion of spin-polarization and relativistic effects, in particular the spin-orbit coupling. In that context it appears that several of the materials where such effects are particularly large and interesting are those where electron... 

Several excellent reviews have been written during the past five years on the application of electronic structure calculations of systems containing transition metal atoms. In the book edited by Dedieu on transition metal hydrides [1], several chapters relate to this subject, and the same is true of the book on the treatment of d and / electrons edited by Salahub and Zemer [2]. A book edited by van Leeuwen et al. on theoretical aspects of homogeneous catalysis [3] covers important areas of application. Furthermore, the review by Veillard [4] has given an overview of the range of systems that have been studied by ab initio... 

This theoretical overview Is divided into three sections (1) pairing mechanism, (2) electronic structure calculations and... 

Overview Over the last few decades, quanmm chemistry has evolved into a predictive tool for the calculation of energy differences. Of equal importance as a driving force for chemical reactions is the entropy that has received less attention from the computational community. The predictive value of computed rate constants depends not only on the accuracy of the electronic structure calculations but also on the correct description of the molecular entropy, including anharmonic effects in the vibrational modes, which is subject of Section 7.3.1.3. 

After this short (and unavoidably selective) overview and introduction we shall now work out the theory of relativistic atomic structure calculations. 

Theoretical chemical research on the heaviest elements is not less challenging than the experimental one. It should be based on the most accurate relativistic electronic structure calculations in order to reliably predict properties and experimental behavior of the new elements and their compounds. It also needs development of special approaches that bridge calculations with quantities that cannot be so easily predicted from calculations. Due to recent spectacular developments in the relativistic quantum theory, computational algorithms and techniques, very accurate calculations of properties of the transactinide elements and their compounds are now possible, which allow for reliable predictions of their experimental behavior. These theoretical works are overviewed here. Special attention is paid to the predictive power of the theoretical studies for the chemical experiments. The role of relativistic effects is discussed in detail. 

In the next sections, we give a general overview how the Density Functional Theory is applied to electronic structure calculations within the framework of the finite-element method. We show how to incorporate pseudopotentials into the equations, explaining some technical difficulties that had to be solved and sorting all the ideas out and presenting them in a fashion applicable to our problem. 

This chapter has given an overview of the structure and dynamics of lipid and water molecules in membrane systems, viewed with atomic resolution by molecular dynamics simulations of fully hydrated phospholipid bilayers. The calculations have permitted a detailed picture of the solvation of the lipid polar groups to be developed, and this picture has been used to elucidate the molecular origins of the dipole potential. The solvation structure has been discussed in terms of a somewhat arbitrary, but useful, definition of bound and bulk water molecules. 

In this section we aim to introduce some of the main theoretical ideas which underlie the strategies for modelling liquid crystal molecules. It is clear that there are a very wide range of methods available and we will not attempt to be comprehensive. Instead, we will begin with a brief overview of traditional semi-empirical approaches and then progress to concentrate on treating fully predictive parameter-free calculations of molecular electronic structure and properties in some depth. 

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