Ab initio electronic structure techniques

Mechanistic Studies of Electron Exchange Kinetics Using Ab Initio Electronic Structure Techniques... 

Vertical Ionization Potentials (VIPs) of small molecules can be accurately computed by a variety of ab initio electronic structure techniques [1-7]. For relatively larger molecules, Density Functional Theory (DFT) possesses a major advantage over more conventional techniques due to its computational expedience and reliability. 

Ab initio molecular orbital theory is concerned with predicting the properties of atomic and molecular systems. It is based upon the fundamental laws of quantum mechanics and uses a variety of mathematical transformation and approximation techniques to solve the fundamental equations. This appendix provides an introductory overview of the theory underlying ab initio electronic structure methods. The final section provides a similar overview of the theory underlying Density Functional Theory methods. 

Calculation of thermochemical data using high-quality ab initio electronic structure calculations has been a long-standing goal. However, the availability of supercomputers and new theoretical techniques now allow the calculation of thermochemical properties with chemical accuracy, i.e., AHf to within... 

In addition to experiments, a range of theoretical techniques are available to calculate thermochemical information and reaction rates for homogeneous gas-phase reactions. These techniques include ab initio electronic structure calculations and semi-empirical approximations, transition state theory, RRKM theory, quantum mechanical reactive scattering, and the classical trajectory approach. Although still computationally intensive, such techniques have proved themselves useful in calculating gas-phase reaction energies, pathways, and rates. Some of the same approaches have been applied to surface kinetics and thermochemistry but with necessarily much less rigor. 

Ten years ago when I attended a Faraday Discussion on Solid State Chemistry New Opportunities from Computer Simulations, interatomic potential methods were well developed and the use of ab initio methods starting to become widespread. In his Introductory Lecture Prof. C. R. A. Catlow asked With the continuing growth of the applicability of electronic structure techniques, can we see them as replacing interatomic potential based methods His reply then was there will be a continuing role for interatomic based potential based methods as the field moves to more complex systems. Over the last decade, ab initio electronic structure methods have progressed rapidly and for many applications plane-wave ab initio methods are now the first choice for calculations. Nevertheless that reply still holds true. 

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. 

For more than three decades, van der Waals (vdW) complexes have become prototypes for studying energy transfer mechanisms and weak intermolecular forces. During these years, the understanding of vdW forces has expanded dramatically. With the development of experimental techniques such as supersonic nozzle expansion, and by performing more accurate ab initio electronic structure calculations, it became possible to study the structure and dynamics of vdW complexes in more detail. 

Calculations of the type reported here are relatively simple and inexpensive. There are clear limitations in that they are based on an ionic model which cannot serve the role of appropriate ab initio electronic structure studies, particularly for electronic defects. Neither can aspects related to the magnetism be addressed. Nevertheless, the approach is highly specific and versatile. It is clear from the results presented here that its particular strength lies in the insight that can be gained from comparative studies of interrelated families of materials with related structures and other similarities in their chemical or physical behaviour. It seems likely that simulation techniques will continue to provide valuable information on these complex materials and in particular on the new superconducting phases prepared by novel synthetic strategies. 

Modern computer hardware, innovative numerical techniques, and novel theoretical approaches have dramatically transformed the character of quantum chemical calculations. Not only can properties of small molecules be computed with better accuracy, but also one can now obtain chemically useful information on large and very large systems almost routinely from ab initio electronic structure calculations. In particular, elimination of the need for storage of ERIs disposed of the 10 bottleneck that inhibited earlier methods from being successfully scaled up. The direct techniques are now commonly employed at the SCF level, and they claim an ever-increasing share of correlated calculations. 

Abstract A new recursive procedure is reported for the evaluation of certain three-body integrals involving exponentially correlated atomic orbitals. The procedure is more rapidly convergent than those reported earlier. The formulas are relevant to ab initio electronic-structure computations on three- and four-body systems. They also illustrate techniques that are useful in the evaluation of summations involving binomial coefficients. 

The importance of the non-pairwise additive components of the interaction energy between atoms and molecules is widely recognized and ab initio electronic structure calculations offer a route to important information about such effects. Attention has recently been drawn to the fact that there is no unique generalization of the Boys-Bernardi function counterpoise technique to clusters of molecules. Two possible generalizations have been introduced, as follows. 

Based on the Dirac-Coulomb-Breit operator, most known methods of quantum-chemical ab initio electronic structure determination have been implemented by now also for four-component spinors. This comprises time-honoured pioneering work on atoms in the Dirac-Hartree-Fock framework, using numerical techniques and basis set expansion techniques, " as well as work for molecules in Dirac-Har tree-Fock approximations with global basis sets " or finite elements and elaborate techniques to treat relativity and correlation on the same footing. " ... 

With the improvement in hardware and software tools, the ab initio electronic structure calculations will gain importance because they can deal with increasingly complex systems and yield higher precision in the result. Along with this trend, the hybrid techniques will grow in relevance. It is expected that the hybrid methods will play an important role in the molecular-level modelling of SOFCs in the near future. 

The next five chapters are each devoted to the study of one particular computational model of ab initio electronic-structure theory Chapter 10 is devoted to the Hartree-Fock model. Important topics discussed are the parametrization of the wave function, stationary conditions, the calculation of the electronic gradient, first- and second-order methods of optimization, the self-consistent field method, direct (integral-driven) techniques, canonical orbitals, Koopmans theorem, and size-extensivity. Also discussed is the direct optimization of the one-electron density, in which the construction of molecular orbitals is avoided, as required for calculations whose cost scales linearly with the size of the system. 

The NMR chemical shift, the most prevalent parameter in NMR spectroscopy, carries a wealth of information regarding the environment and the local electronic structure in the vicinity of the nucleus under study.(i). For example, one normally finds a different chemical shift for the Ca nucleus of each alanine residue in a protein. Ideally, a thorough analysis of the NMR chemical shift can yield information regarding the structure and interactions in the vicinity of the nucleus concerned. To achieve this, a detailed understanding of how geometrical factors and intermolecular interactions influence the chemical shift is crucial. The development and validation of the methods towards this end have combined powerful and efficient ab initio quantum mechanical techniques, which have been... 

Today, the methods presented in the 1981 report are firmly established as the most widely used ab initio quantum chemical technique for molecular electronic structure studies. The theoretical background of the methods are now described in both undergraduate and graduate text books, such as those by P.W. Atkins and R.S. Friedman Molecular quantum mechanics51) and by R. McWeeny Methods of molecular quantum mechanics5 ). 

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