Molecular systems, early models

Actually, the first attempts to use the electron density rather than the wave function for obtaining information about atomic and molecular systems are almost as old as is quantum mechanics itself and date back to the early work of Thomas, 1927 and Fermi, 1927. In the present context, their approach is of only historical interest. We therefore refrain from an in-depth discussion of the Thomas-Fermi model and restrict ourselves to a brief summary of the conclusions important to the general discussion of DFT. The reader interested in learning more about this approach is encouraged to consult the rich review literature on this subject, for example by March, 1975, 1992 or by Parr and Yang, 1989. 

In recent years, there have been many significant advances in our models for the dynamics for proton transfer. However, only a limited number of experimental studies have served to probe the validity of these models for bimolecular systems. The proton-transfer process within the benzophenone-AL A -di methyl aniline contact radical IP appears to be the first molecular system that clearly illustrates non-adiabatic proton transfer at ambient temperatures in the condensed phase. The studies of Pines and Fleming on napthol photoacids-carboxylic base pairs appear to provide evidence for adiabatic proton transfer. Clearly, from an experimental perspective, the examination of the predictions of the various theoretical models is still in the very early stages of development. 

Further analysis is based on the idea that the characteristic experimental behavior of different classes of compounds and the suitability of those or other models used to describe this behavior is ultimately related to the extent to which chromophores responsible for the observed behavior and physically present in the molecular system are reflected in these models by adequate electron groups. The TMCs of interest, can be physically characterized as those bearing the 4-shell chromophores. (The analogy between the chromophore concept and McWeeny s theory for the special case of TMCs has also been noticed early in a remarkable work [149]). The basic features in the electronic structure of TMCs of interest, distinguishing these compounds from others, are the following ... 

We have chosen to concentrate on two of the themes in early twenty-first century science computational and supercomputational molecular modelling and the study of increasingly complex molecular systems. Both trends have their roots in the later decades of the twentieth century but have emerged as dominant themes over recent years. Both trends will impact upon the type of molecule structure problems that will be addressed in the future. We believe that the many-body perturbation theory will play a key role in advancing molecular studies to these new horizons. 

Even from the start of their development, computers were being applied to the study of chemical systems.Early computational models were necessarily crude. For example, rare-gas atoms were first modelled as hard spheres and then later with models including attractive as well as repulsive components, such as the widely-used Lennard-Jones potential. The first simulations of molecular systems were performed on a diatomic molecular liquid in the late 1960s, closely followed by the first simulations of liquid... 

Mixed-valence compounds continue to attract attention, not least because of their occurrence as intermediates of multistep redox systems Mixed-valence species are found in the geo- and biosphere, as evident from minerals such as Fe304 and from metalloproteins, where the Fe /Fe °/Fe, Cu /Cu and Mn / Mn Nn combinations are established Man-made mixed-valence compounds, starting from Prussian Blue in the early 18th century, have raised interest in what is now known as materials science because of their often special optical, electrical and magnetic properties These physical properties then prompted attempts at increasingly sophisticated levels to theoretically understand and computationally reproduce the experimental features of mixed-valence compounds More recent developments involve the application of mixed-valence systems as models and actual components in the areas of molecular electronics and molecular computing ... 

Our aim in this chapter will be to establish the basic elements of those quantum mechanical methods that are most widely used in molecular modelling. We shall assume some familiarity with the elementary concepts of quantum mechanics as found in most general physical chemistry textbooks, but little else other than some basic mathematics (see Section 1.10). There are also many excellent introductory texts to quantum mechanics. In Chapter 3 we then build upon this chapter and consider more advanced concepts. Quantum mechanics does, of course, predate the first computers by many years, and it is a tribute to the pioneers in the field that so many of the methods in common use today are based upon their efforts. The early applications were restricted to atomic, diatomic or highly symmetrical systems which could be solved by hand. The development of quantum mechanical techniques that are more generally applicable and that can be implemented on a computer (thereby eliminating the need for much laborious hand calculation) means that quantum mechanics can now be used to perform calculations on molecular systems of real, practical interest. Quantum mechanics explicitly represents the electrons in a calculation, and so it is possible to derive properties that depend upon the electronic distribution and, in particular, to investigate chemical reactions in which bonds are broken and formed. These qualities, which differentiate quantum mechanics from the empirical force field methods described in Qiapter 4, will be emphasised in our discussion of typical applications. 

The repulsion of fully occupied orbitals in model systems received attention in the earliest application of quantum mechanical methods. From those studies an exponential representation of the energy-distance curve was obtained. This functional form has been used extensively in the simulation of both solids and molecular systems. Also derived from early quantum mechanical results were potentials using inverse power repulsive forms (see, e.g.. Refs. 49 and 50). Such potentials have also been employed with success in the simulation of liquids, molecular solids, and ionic systems. 

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