Relative Energies and Thermochemistry
Information about the energetic properties of molecules is at the heart of every quantum chemical investigation. In this chapter we will take a close look at the performance of current approximate density functionals when it comes to the determination of such important energetic properties as atomization energies, ionization energies (IE) and electron affinities (EA). In particular the first quantity is of great value since it provides an idea of the ballpark figure we are talking about when we are interested in computing the thermochemistry of chemical reactions. The energies needed to remove (IE) or add an electron (EA) to an atom or molecule are obviously of significant interest in their own right. For example, the interpretation of photoelectron spectroscopy experiments is greatly facilitated if accurate ionization energies are available. Furthermore, since the computation of all these different quantities poses severe and often different demands on the method chosen, the accuracy with which a functional delivers such energies is a probe for its versatility. Somewhat counterintuitively at first sight, the reliable calculation of energetic information for atoms, in particular for transition-metals, is especially difficult and not without ambiguity. We therefore devote a complete section to this problem. Finally, we take up the discussion on excitation energies from Section 5.3.7 and give an overview of the current state of the art in the determination of electronically excited states and the corresponding transition energies using density functional theory. We conclude with a few remarks about the ability of approximate density functional theory to reproduce singlet-triplet gaps in carbenes and related species.