The Energy Levels of Molecules

Experimental information about the energy levels of molecules is obtained from spectroscopic studies, in the infra-red for the rotational states and in the ultra-violet for the vibrational and most of the dissociation energies. Some thermodynamic data are also obtained for the dissociation energies using mass spectroscopy. 

The most accurate theories of reaction rates come from statistical mechanics. These theories allow one to write the partition function for molecules and thus to formulate a quantitative description of rates. Rate expressions for many homogeneous elementary reaction steps come from these calculations, which use quantum mechanics to calculate the energy levels of molecules and potential energy surfaces over which molecules travel in the transition between reactants and products. These theories give... 

In view of the different ways in which a molecule may absorb quantized energy, spectroscopists often describe the energy levels of molecules using quantum numbers (only very roughly analogous to the quantum... 

For the molecules located at the surface the coordination numbers, Zs, are smaller than for those in the bulk, and hence the interactions between molecules present within the surface layer are not saturated. Due to these factors the decrease in energy upon condensation is smaller within the surface layer, as compared to that in the bulk by the amount oS (where S is the surface area). This essentially means that the energy level of molecules at the surface is higher than that of those in the bulk by the amount oS (Fig. 1-6). In other words, the excess of energy within the surface layer can be regarded as... 

A completely separate branch of science is statistical mechanics which is concerned with microscopic properties. This subject makes use of what quantum mechanics tells us about the energy levels of molecules, and allows us to calculate macroscopic properties on the basis of this information. The area of overlap between statistical mechanics and thermodynamics is known as statistical thermodynamics which allows us, for example, to calculate equilibrium constants for chemical reactions using the molecular properties obtained from quantum mechanics. 

What is symmetry Essentially in lliis book wc shall be interested in two uses of this word. First we shall be interested in the symmetry" of a molecule. When looking at objects we invariably have some feel as to whether they are highly symmetric or alternatively, not very symmetric. This needs to be quantified in some way. Second we will need to be able to classify, in terms of some symmetry description, the energy levels of molecules. Once this has been done we will find that with the use of a couple of mathematical tools we will be in a good position to be able to understand the symmetry control of the orbital structure in molecules. 

The requirement, set out in the previous section, that two orbitals will not interact unless they are of the same symmetry species is an extremely useful one when the energy levels of molecules arc constructed. We will start off by looking at a simple system, that of linear H3. 

As an indication of the importance of charge on the energy levels of molecules, we look at the variation in carbonyl stretching vibrational frequencies in the series Mn(CO)6, Cr(CO)6, and V(CO)6. All arc low spin isoelectronic molecules. The orbital details of the attachment of the carbon mono.xidc ligand to a transition metal are reserved for Section 15.1, but an important part is played by the acceptor behavior of the carbonyl 77 0 (8.12). The more important donation from... 

Linus Pauling, an American chemist, was the first to take a closer look at the electrical difference of bonds. He tested the differences in energies of covalent bonds. In 1939, he published The Nature of the Chemical Bond which discussed the energy levels of molecules. Pauling was recognized for his work with protein structures. His electrochemical valency theory won the Nobel Prize for Chemistry in 1954. 

UV-photoelectron spectroscopy provides a means of studying the energy levels of molecules experimentally. Simple interpretation of PE spectra relies on Koopmans theorem which states that the same order of molecular orbitals... 

There are two approaches for proving the existence of entropy in classical thermodynamics these rely on either molecular-based statistical mechanics or classical thermodynamics. First we employ the latter approach because of its simplicity. It is not necessary to use either approach, because the conjugate property of temperature and entropy is important. In the sense of molecular physics, both the temperature and entropy are an aspect of kinetic movement and the energy level of molecules. 

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