The many-body problem in atoms and molecules

This monograph is concerned with the application of Brillouin-Wigner methods to the many-body problem in atoms and molecules. 

In order to gain some understanding of the nature of the many-body problem in atoms and molecules, let us consider an array of well-separated systems, a Unear array of helium atoms, for example. By weU-separated we mean that the systems are not interacting. For simplicity, let us begin by considering just two weU-separated systems. The total Hamiltonian operator for the supersystem may be written... 

The purpose of this book is to provide a detailed description of Brillouin-Wigner methods and their application to the many-body problem in atomic and molecular physics and quantum chemistry. Recently there has been a renewal of interest in Brillouin-Wigner methods. This interest is fuelled by the need to develop robust, yet efficient multireference theoretical approaches to the electron correlation problem in molecules together with associated algorithms. Such theories are an essential ingredient of the quanmm mechanical description of most dissociative processes in molecules, of excited states, and of ionization and electron attachment processes. 

Of course, orbital models, such as the widely used Hartree-Fock approximation neglect the effects of electron correlation. One approximation which forms the basis of a computationally tractable approach to the electron correlation problem in atoms and molecules is the many-body perturbation... 

There are finally attempts to apply diagrammatic techniques of many-body perturbation theory S ), with the summation of certain diagrams to infinite order, to the correlation problem in atoms and molecules. A close relationship between this kind of approach and the independent electron-pair approximation has been demonstrated >. 

Today, many-body methodology underpins the most widely used ab initio approaches to the correlation problem in atoms and molecules. However, configuration interaction remains the most robust approach which can be invoked in difficult cases. 

During recent years, there has been much development in the other many-body problems of physics, e.g. nuclear matter (Brueckner theory) and the electron gas. > The possibility of applying these theories to atomic and molecular problems has been considered. It turns out, however, that in atoms and most molecules the many-body problem is physically very different from the other problems. 

Finite basis set Hartree-Fock calculations yield not only an approximation for the occupied orbitals but also a representation of the spectrum which can be used in the treatment of correlation effects. In particular, the use of finite basis sets facilitates the effective evaluation of the sum-over-states which arise in the many-body perturbation theory of electron correlation effects in atoms and molecules. Basis sets have been developed for low order many-body perturbation theoretic treatments of the correlation problem which yield electron correlation energy components approaching the suh-milliHartree level of accuracy [20,21,22]. 

Sessions dealt with atoms and small molecules, the many-body problem, density matrices, methods to deal with atoms in molecules, complex molecules, nature of the chemical bond, problems in stmcture and spectra, spectroscopy methods, reaction rates, and intermolecular forces. 

The reason we employ two rather distinct methods of inquiry is that neither, by itself, is free of open methodological issues. The method of molecular dynamics has been extensively applied, inter alia, to cluster impact. However, there are two problems. One is that the results are only as reliable as the potential energy function that is used as input. For a problem containing many open shell reactive atoms, one does not have well tested semiempirical approximations for the potential. We used the many body potential which we used for the reactive system in our earlier studies on rare gas clusters containing several N2/O2 molecules (see Sec. 3.4). The other limitation of the MD simulation is that it fails to incorporate the possibility of electronic excitation. This will be discussed fmther below. The second method that we used is, in many ways, complementary to MD. It does not require the potential as an input and it can readily allow for electronically excited as well as for charged products. It seeks to compute that distribution of products which is of maximal entropy subject to the constraints on the system (conservation of chemical elements, charge and... 

On the other hand, in the condensed phases the concept of supermolecules is not useful because every atom or molecule interacts simultaneously with many neighbors. The many-body nature of the induction process, combined with the statistical mechanics of liquids and a complex local field problem have been serious difficulties for a quantitative description of CILS in dense matter. Furthermore, for an accurate modeling, irreducible (i.e., the pairwise nonadditive) contributions of the intermolecular interaction and induction mechanisms may be significant, which complicate the problem even more. Most treatments of CILS in the dense phases have been undertaken in the time domain, based on correlation functions of the type... 

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