Perturbation theory basic principles

The purpose of this chapter is to provide an introduction to tlie basic framework of quantum mechanics, with an emphasis on aspects that are most relevant for the study of atoms and molecules. After siumnarizing the basic principles of the subject that represent required knowledge for all students of physical chemistry, the independent-particle approximation so important in molecular quantum mechanics is introduced. A significant effort is made to describe this approach in detail and to coimnunicate how it is used as a foundation for qualitative understanding and as a basis for more accurate treatments. Following this, the basic teclmiques used in accurate calculations that go beyond the independent-particle picture (variational method and perturbation theory) are described, with some attention given to how they are actually used in practical calculations. 

Tompkins (1978) concentrates on the fundamental and experimental aspects of the chemisorption of gases on metals. The book covers techniques for the preparation and maintenance of clean metal surfaces, the basic principles of the adsorption process, thermal accommodation and molecular beam scattering, desorption phenomena, adsorption isotherms, heats of chemisorption, thermodynamics of chemisorption, statistical thermodynamics of adsorption, electronic theory of metals, electronic theory of metal surfaces, perturbation of surface electronic properties by chemisorption, low energy electron diffraction (LEED), infra-red spectroscopy of chemisorbed molecules, field emmission microscopy, field ion microscopy, mobility of species, electron impact auger spectroscopy. X-ray and ultra-violet photoelectron spectroscopy, ion neutralization spectroscopy, electron energy loss spectroscopy, appearance potential spectroscopy, electronic properties of adsorbed layers. 

In what follows we shall not derive any of the details of perturbation theory. The reader who wishes to know more is referred to the set of references at the end of the chapter. Our aim here is to show how the basic principles may be used in orbital construction. 

In this chapter we shall present a necessarily partial review of the main theoretical approaches so far developed to treat liquid systems in terms of physical frmctions. We shall restrict ourselves to two basic theories, integral equation and perturbation theories, to keep the chapter within reasonable bounds. In addition, only the basic theoretical principles imderly-ing the original methods will be discussed, because the progress has been less rapid for theory than for numerical applications. The latter are in fact developing so fast that it is an impossible task to try to give an exhaustive view in a few pages. 

Theoretical determinations are mainly based on the assumption that the initial perturbation of the orbital of interacting species determines the course of a reaction or an interaction. In terms of equation of state, the perturbation theory was developed first. In terms of energy gap between HOMO and LUMO, acids and bases were defined by their hardness and softness. The Hard-Soft Acid-Base principle (Pearson 1963) describes some basic rules about kinetics and equilibrium of the acid-base interactions. The HSAB principle will be described as it has evolved in recent years on the basis of the density-functional theory (Parr and Yang 1989). For organic interactions, the following statements were proposed ... 

For the case of weak anharmonicity, the basic principle of solution is the following one uses the solution of the harmonic lattice as a basis set and treats the nonlinearity in perturbation theory. This leads to a shift in the energy of the phonons and to a finite lifetime of them. We shall discuss this theory in Sect.5.5 and confine ourselves to a short review of its development here. 

An attempt has actually been made to subject to the theory of perturbations the second simplest atom, that of helium, with its one nucleus and two electrons. The result, however, was entirely negative the discrepancies between theory and observation were much too large to be accounted for by the inaccuracy of the calculations. This indicates that there is some basic error in the principles of our atomic mechanics. 

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