Correlation methods, molecular similarity measurements

Among the many applications of molecular similarity measures to the analysis of electronic wavefunctions, those associated with the taxonomy of chemical reactions and the assessment of accuracy of various quantum chemical methods are particularly worth mentioning. Quantification of similarities among reactants, products, and transition states of chemical reactions has afforded a rigorous formulation of the Hariimond postulate. Accuracies of Koopmans theorem and various approaches to the electron correlation problem have been assessed with the help of the NOEL similarity measure applied to the one-electron reduced density matrices obtained at the respective levels of theory. The use of similarity measures in analysis of excited-state wavefunctions has already been mentioned in Section 7. 

In this chapter we consider the physics of the positronium atom and what is known, both theoretically and experimentally, of its interactions with other atomic and molecular species. The basic properties of positronium have been briefly mentioned in subsection 1.2.2 and will not be repeated here. Similarly, positronium production in the collisions of positrons with gases, and within and at the surface of solids, has been reviewed in section 1.5 and in Chapter 4. Some of the experimental methods, e.g. lifetime spectroscopy and angular correlation studies of the annihilation radiation, which are used to derive information on positronium interactions, have also been described previously. These will be of most relevance to the discussion in sections 7.3-7.5 on annihilation, slowing down and bound states. Techniques for the production of beams of positronium atoms were introduced in section 1.5. We describe here in more detail the method which has allowed measurements of positronium scattering cross sections to be made over a range of kinetic energies, typically from a few eV up to 100-200 eV, and the first such studies are summarized in section 7.6. 

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