Electronic Structure of Atoms and Molecules

An atom must be at least as complex as a grand piano. 

Everything that counts in chemistry is related to the electronic structure of atoms and molecules. The formation of molecules from atoms, their behavior and reactivity all depend on the electronic structure. What is the role of symmetry in all this In various aspects of the electronic structure, symmetry can tell us a good deal why certain bonds can form and others cannot, why certain electronic transitions are allowed and others are not, and why certain chemical reactions occur and others do not. Our discussion of these points is based primarily on some monographs listed in References [2-8], 

To describe the electronic structure, the electronic wave function W(x, y, z, t) is used, which depends, in general, on both space and time. Here, however, only its spatial dependence will be considered, M (x, y, z). For detailed discussions of the nature of the electronic wave function, we refer to texts on the principles of quantum mechanics [9-12], For a one-electron system the physical meaning of the electronic wave function is expressed by the product of F with its complex conjugate F. The product F - M di gives the probability of finding an electron in the volume di = dx dydz about the point (x, y, z). 

A many-electron system is described by a similar but multivariable wave function 

Hargittai, I. Hargittai, Symmetry through the Eyes of a Chemist, 3rd ed., 

The symmetry properties of the electronic wave function and the energy of the system are two determining factors in chemical behavior. The relationship between the wave function characterizing the behavior of the electrons and the energy of the system—atoms and molecules—is expressed by the Schro-dinger equation. In its general and time-independent form, it is usually written as follows  

A fundamental property of the wave function is that it can be used as basis for irreducible representations of the point group of a molecule [6-4]. This property establishes the connection between the symmetry of a molecule and its wave function. The preceding statement follows from Wigner s theorem which says that all eigenfunctions of a molecular system belong to one of the symmetry species of the group [6-8]. 

In the expression of the energy of a system the following type of integral appears  

Depending on the problem, i i, and may be atomic orbitals used to construct molecular orbitals, or they may represent two different electronic states of the same atom or molecule, etc. The energy, then, expresses the extent of interaction between the two wave functions i[ . and As was shown in Chapter 4, an integral will have a nonzero value only if the integrand is invariant to the symmetry operations of the point group, i.e., belongs to the totally symmetric irreducible representation. 

The above energy integral contains the H operator, which always belongs to the totally symmetric irreducible representation. Therefore, the symmetry of the whole integrand depends on the direct product of il , and l/y. As was also 

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The relative strengths and weaknesses of perturbation theory and the variational method, as applied to studies of the electronic structure of atoms and molecules, are discussed in Section 6. 

Freed, K. F. [1971] Many-Body Theories of the Electronic Structure of Atoms and Molecules , Annual Review of Physical Chemistry, 22, p. 313. 

Along with code breakers, weather forecasters, and molecular biologists, chemists are now among the heaviest users of computers, which they use to calculate the detailed electronic structures of atoms and molecules (see Major Technique 5, following Chapter 13). 

H. F. Schaefer, III, Electronic Structure of Atoms and Molecules, Addison-Wesley, Reading, Mass., 1972, and Quantum Chemistry, Clarendon Press, Oxford, 1984. 

Schaefer, H. F., III. The electronic structure of atoms and molecules. Reading, Mass. Addison-Wesley 1972. 

Chemical reactions take place when the reacting atoms, molecules or ions collide with each other. Therefore the outer electrons are Involved when different substances react together and we need to understand the electronic structure of atoms to explain the chemical properties of the elements. Much of the information about the electronic structure of atoms and molecules is obtained using spectroscopic techniques based on different types of electromagnetic radiation. 

THE MOMENTUM DENSITY PERSPECTIVE OE THE ELECTRONIC STRUCTURE OF ATOMS AND MOLECULES... 

The importance of symmetry in the study of the electronic structure of atoms and molecules depends on the fact that wave functions must transform according to one of the symmetry species of the symmetry group of the molecule. Stated precisely, the eigenfunctions of a Hamiltonian form bases for irreducible representations of the symmetry group of the Hamiltoirian. This principle allows wave functions to be classified according to symmetry species it assists... 

Mean-field models are obviously approximations whose accuracy must be determined so scientists can know to what degree they can be "trusted". For electronic structures of atoms and molecules, they require quite substantial corrections to bring them into line with experimental fact. Electrons in atoms and molecules undergo dynamical motions in which their coulomb repulsions cause them to "avoid" one another at every instant of time, not only in the average-repulsion manner that the mean-field models embody. The inclusion of instantaneous spatial correlations among electrons is necessary to achieve a more accurate description of atomic and molecular electronic structure. 

The Dirac-Pauli representation is most commonly used in all applications of the Dirac theory to studies on electronic structure of atoms and molecules. Apart of historical reasons, there are several features of this representation which make its choice quite natural. Probably the most important is a well defined symmetry of and in the case of spherically-symmetric potentials V. The Dirac Hamiltonian... 

Simon Fraser University, founded in 1964, was one of many new universities established in Canada in the 1960s. It appears that Natalia Solony (a student of Fraser Birss) was the first theoretician at SFU, but she left after a year or two. In 1966 Margaret Benston, Gulzari Malli, and John Walkley joined the Department of Chemistry. Benston carried out research on the electronic structures of atoms and molecules for a few years, often in collaboration with Chong at UBC, before moving to the Department of Computing Science and then later to the Department of Women s Studies. She died prematurely in 1981. John... 

Parr, R. G. Quantum theory of molecular electronic structure. New York Benjamin 1963 Schaefer III, H. F. The electronic structure of atoms and molecules. A survey of rigorous quantum mechanical results. Reading, Massachusetts Addison-Wesley 1972... 

The OBS-GMCSC method offers a practical approach to the calculation of multiconfiguration electronic wavefunctions that employ non-orthogonal orbitals. Use of simultaneously-optimized Slater-type basis functions enables high accuracy with limited-size basis sets, and ensures strict compliance with the virial theorem. OBS-GMCSC wavefunctions can yield compact and accurate descriptions of the electronic structures of atoms and molecules, while neatly solving symmetry-breaking problems, as illustrated by a brief review of previous results for the boron anion and the dilithium molecule, and by newly obtained results for BH3. 

Dulak M, Kevorkiants R, Tran F, Wesolowski TA (2005) Applications of the orbital-free embedding formalism to study electronic structure of atoms and molecules in condensed phase, CHIMIA, 59 488 192... 

This correlation between symmetry and degeneracy of energy levels is fundamental to understanding the electronic structure of atoms and molecules. This relationship is valid not only when increasing symmetry renders the energy levels degenerate but also when energy levels are split as molecular symmetry decreases. 

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