Atomic many-body theory, development

Lindgren, I., and Morrison, J., Atomic Many-Body Theory, Springer-Verlag, Berlin, 1982. Chapters 9-12 of this advanced textbook develop diagrammatic perturbation theory in a rigorous yet accessible way. The labels used for occupied and virtual orbitals are the same as ours. 

Moreover, for atoms with open shells, the difficulties in calculating the angular parts of the PT expansion grow very rapidly with the increase in the order of expansion terms. Even the methods of their calculations are not developed sufficiently, unlike the usual mathematical apparatus of the theory of atomic spectra. Therefore, in order to successfully apply the PT to complex atoms, further development of the many-body theory... 

Highly-ionized atoms DHF calculations on isoelectronic sequences of few-electron ions serve as the starting point of fundamental studies of physical phenomena, though many-body corrections are now applied routinely using relativistic many-body theory. Relativistic self-consistent field studies are used as the basis of investigations of systematic trends in ionization energies [137-144], radiative transition probabilities [145-148], and quantum electrodynamic corrections [149-151] in few-electron systems. Increased experimental precision in these areas has driven the development of many-body methods to model the electron correlation effects, and the inclusion of Breit interaction in the evaluation of both one-body and many-body corrections. 

One of the aims of this chapter, then, is to discuss the problem of calculating a property of a many-electron atom with suflicient precision so that the new physics of radiative corrections can be studied. The challenge to many-body theory is quite specific. As will be discussed below, properties of cesium, the atom in which the most accurate PNC measurement has been made [5] must be calculated to the fraction of a percent level to accurately study PNC and radiative corrections to it can this level in fact be reached by modern many-body methods While great progress has been made, the particular nature of this problem, in which relativity has to be incorporated from the start, and a transition between two open-shell states calculated in the presence of a parity-nonconserving interaction, has not permitted solution of the many-body problem to the desired level. It may well be that a reader of this chapter has developed techniques for some other many-electron problem that are of sufficient power to resolve this issue this chapter is meant to clearly lay out the nature of the calculation so that the reader can apply those techniques to what is, after all, a relatively simple system by the standards of quantum chemistry, an isolated cesium atom. 

The first approximation to the many-electron theory of atoms and molecules was derived by solving Eq. (64) with the H.F. using operator techniques. The development of Brueckner s theory of nuclear matter and other many-body theories also made much use of perturbation formalism. 

Pure thermodynamics is developed, without special reference to the atomic or molecular structure of matter, on the basis of bulk quantities like internal energy, heat, and different types of work, temperature, and entropy. The understanding of the latter two is directly rooted in the laws of thermodynamics— in particular the second law. They relate the above quantities and others derived from them. New quantities are defined in terms of differential relations describing material properties like heat capacity, thermal expansion, compressibility, or different types of conductance. The final result is a consistent set of equations and inequalities. Progress beyond this point requires additional information. This information usually consists in empirical findings like the ideal gas law or its improvements, most notably the van der Waals theory, the laws of Henry, Raoult, and others. Its ultimate power, power in the sense that it explains macroscopic phenomena through microscopic theory, thermodynamics attains as part of Statistical Mechanics or more generally Many-body Theory. 

Using the F ion as a prototype, the convergence of the many-body perturbation theory second-order energy component for negative ions is studied when a systematic procedure for the construction of even-tempered btisis sets of primitive Gaussian type functions is employed. Calculations are reported for sequences of even-tempered basis sets originally developed for neutral atoms and for basis sets containing supplementary diffuse functions. 

The many-body perturbation theory [39] [40] [41] was used to model the electronic structure of the atomic systems studied in this work. The theory developed with respect to a Hartree-Fock reference function constructed from canonical orbitals is employed. This formulation is numerically equivalent to the M ler-Plesset theory[42] [43]. 

Since his appointment at the University of Waterloo, Paldus has fully devoted himself to theoretical and methodological aspects of atomic and molecular electronic structure, while keeping in close contact with actual applications of these methods in computational quantum chemistry. His contributions include the examination of stability conditions and symmetry breaking in the independent particle models,109 many-body perturbation theory and Green s function approaches to the many-electron correlation problem,110 the development of graphical methods for the time-independent many-fermion problem,111 and the development of various algebraic approaches and an exploration of convergence properties of perturbative methods. His most important... 

Wilson reviews in detail many-body perturbation theory of molecules, which is one very useful technique for the inclusion of electron correlation in molecular calculations for small molecules. Ladik and Suhai at the other extreme describe the important advances which have recently been made in the study of the electronic structure of polymers, with emphasis on the use of ab initio methods, which have become practicable in recent years following the development of new computational schemes. Finally, March surveys the current status of the density functional approach, which gives an alternative approach to the description of atoms and molecules. 

The earliest quantitative theory to describe van der Waals forces between two colloidal particles, each containing a statistically large number of atoms, was developed by Hamaker, who used pairwise summation of the atom-atom interactions. This approach neglects the multi-body interactions inherent in the interaction of condensed phases. The modem theory for predicting van der Waals forces for continua was developed by Lifshitz who used quantum electrodynamics [19,20] to account for the many-body molecular interactions and retardation within and between materials. Retardation is a reduction of the interaction because of a phase lag in the induced dipole response that increases with distance. 

---