Atomic theory many-electron atoms

Sinanoglu O 1961 Many-electron theory of atoms and molecules Proc. US Natl Acad. Sc/. 47 1217-26... 

Sinanoglu O 1962 Many-electron theory of atoms and moleoules I. Shells, eleotron pairs vs many-eleotron oorrelatlons J. Chem. Phys. 36 706-17... 

Bohr s treatment gave spectacularly good agreement with the observed fact that a hydrogen atom is stable, and also with the values of the spectral lines. This theory gave a single quantum number, n. Bohr s treatment failed miserably when it came to predictions of the intensities of the observed spectral lines, and more to the point, the stability (or otherwise) of a many-electron system such as He. 

Sinanoglu, 0. [1961] Many-Electron Theory of Atoms and Molecules, Proceedings of the National Academy of Sciences of the United States of America, 47(8), p. 1217. 

Table II shows clearly the large differences between various theories for many-electron systems. The Kirkwood-Muller equation always yields somewhat too large coefficients for the atoms which are the only spherical systems but the London equation deviates by a greater amount on the low side. The Slater-Kirkwood equation gives a high value for He but yields coefficients smaller than the empirical ones for all other cases.

In recent years the old quantum theory, associated principally with the names of Bohr and Sommerfeld, encountered a large number of difficulties, all of which vanished before the new quantum mechanics of Heisenberg. Because of its abstruse and difficultly interpretable mathematical foundation, Heisenberg s quantum mechanics cannot be easily applied to the relatively complicated problems of the structures and properties of many-electron atoms and of molecules in particular is this true for chemical problems, which usually do not permit simple dynamical formulation in terms of nuclei and electrons, but instead require to be treated with the aid of atomic and molecular models. Accordingly, it is especially gratifying that Schrodinger s interpretation of his wave mechanics3 provides a simple and satisfactory atomic model, more closely related to the chemist s atom than to that of the old quantum theory. 

Most of the commonly used electronic-structure methods are based upon Hartree-Fock theory, with electron correlation sometimes included in various ways (Slater, 1974). Typically one begins with a many-electron wave function comprised of one or several Slater determinants and takes the one-electron wave functions to be molecular orbitals (MO s) in the form of linear combinations of atomic orbitals (LCAO s) (An alternative approach, the generalized valence-bond method (see, for example, Schultz and Messmer, 1986), has been used in a few cases but has not been widely applied to defect problems.)... 

See for example, Jones, R., and Gunnarsson, O. Rev. Mod. Phys. 61, 689 (1990) Parr, R.G., and Yang, W. (1990), Density Functional Theory of Atoms and Molecules, Oxford University Press, New York Kryachko, E.S., and Ludena, E.V. Energy Density Functional Theory of Many Electron Systems Kluwer Academic Publishers, 1990 Callaway, J., and March, N.H. Solid State Phys. 38, 135 (1984). 

During the last five decades, an alternative way of looking at the quantum theory of atoms, molecules, and solids in terms of the electron density in three-dimensional (3D) space, rather than the many-electron wave function in the multidimensional configuration space, has gained wide acceptance. The reasons for such popularity of the density-based quantum mechanics are the following ... 

The study of behavior of many-electron systems such as atoms, molecules, and solids under the action of time-dependent (TD) external fields, which includes interaction with radiation, has been an important area of research. In the linear response regime, where one considers the external held to cause a small perturbation to the initial ground state of the system, one can obtain many important physical quantities such as polarizabilities, dielectric functions, excitation energies, photoabsorption spectra, van der Waals coefficients, etc. In many situations, for example, in the case of interaction of many-electron systems with strong laser held, however, it is necessary to go beyond linear response for investigation of the properties. Since a full theoretical description based on accurate solution of TD Schrodinger equation is not yet within the reach of computational capabilities, new methods which can efficiently handle the TD many-electron correlations need to be explored, and time-dependent density functional theory (TDDFT) is one such valuable approach. 

Density functional theory (DFT) uses the electron density p(r) as the basic source of information of an atomic or molecular system instead of the many-electron wave function T [1-7]. The theory is based on the Hohenberg-Kohn theorems, which establish the one-to-one correspondence between the ground state electron density of the system and the external potential v(r) (for an isolated system, this is the potential due to the nuclei) [6]. The electron density uniquely determines the number of electrons N of the system [6]. These theorems also provide a variational principle, stating that the exact ground state electron density minimizes the exact energy functional F[p(r)]. 

Many-Electron Theory of Atoms, Molecules, and their Interactions (Sinanoglu). ... 

The possibility of adsorption on a virtual exciton was indicated by E. L. Nagayev (.14) on the simplest example of the adsorption of a one-electron atom. This problem is an example of the many-electron approach in chemisorption theory. Recently, V. L. Bonch-Bruevich and V. B. Glasko (16) have treated adsorption on metal surfaces by the many-electron method. 

D. A. Mazziotti, Variational two-electron reduced-density-matrix theory for many-electron atoms and molecules implementation of the spin- and symmetry-adapted Z2 condition through first-order semidefinite programming. Phys. Rev. A 72, 032510 (2005). 

T. Yanai and G. K. L. Chan, Canonical transformation theory for dynamic correlations in multireference problems, in Reduced-Density-Matrix Mechanics With Application to Many-Electron Atoms and Molecules, A Special Volume of Advances in Chemical Physics, Volume 134 (D.A. Mazziotti, ed.), Wiley, Hoboken, NJ, 2007. 

J. Paldus, J. Cizek, and 1. Shavitt, Correlation problems in atomic and molecular systems. IV. Extended coupled-pair many-electron theory and its application to the BHs molecule. Phys. Rev. A 5, 50 (1972). 

---