Orbital symmetry basic concept

In this chapter we will familiarize ourselves with basic concepts in molecular symmetry [17]. The presence or absence of symmetry has consequences on the appearance of spectra, the relative reactivity of groups, and many other aspects of chemistry, including the way we will make use of orbitals and their interactions. We will see that the orbitals that make up the primary description of the electronic structure of molecules or groups within a molecule have a definite relationship to the three-dimensional structure of the molecule as defined by the positions of the nuclei. The orientations of the nuclear framework will determine the orientations of the orbitals. The relationships between structural units (groups) of a molecule to each other can often be classified in terms of the symmetry that the molecule as a whole possesses. We will begin by introducing the basic termi-... 

Chemi- and bio-luminescence phenomena have been attractive not only from the scientific interest concerning with their molecular mechanisms but also from analytical, clinical, and for other various useiul applications. Many theoretical studies have been performed to elucidate detailed mechanisms of chemi- and bio-luminescence reactions. In past decades, our group has carried out both broken-symmetry (BS) and symmetry-adapted (SA) molecular orbital (MO) studies to clarify the electronic mechanisms of these reactions. Here, our basic concepts and methodologies, together with computational results, are briefly summarized. 

The fundamental fixed-nuclei approximation, in which the nuclei are treated as distinguishable classical particles with positions in physical space, allows for the electronic structure of ground and excited states of both atoms and molecules to be ruled by the same principles, concepts, and approximations, such as the occupation of symmetry-adapted atomic or molecular orbitals by electrons, subject to the Pauli exclusion principle. The resulting basic interpretative and computational tool is the N-electron symmetry-adapted configuration (SAC), be it atomic or molecular. It is denoted here by i. When the SAC is adopted as a conceptual and computational tool, it is possible to use the same concepts and theoretical methods in order to treat the electronic eigenfunctions of states of both atoms and small molecules for each fixed geometry. 

In their now classic monograph [1], Wooodward and Hoffmann concentrate on three basic types of no mechanism reaction Electrocyclic reactions -notably polyene cyclizations, cycloadditions, and sigmatropic rearrangements. These three reaction types will be taken up in this and the next two chapters from the viewpoint of Orbital Correspondence Analysis in Maximum Symmetry (OCAMS) [2, 3, 4], the formalism of which follows naturally from that developed in Chapter 4. The similarities to the original WH-LHA approach [5, 6], and the points at which OCAMS departs from it, will be illustrated. In addition, a few related concepts, such as allowedness and forbiddenness , global vs. local symmetry, and concertedness and synchronicity , will be taken up where appropriate. 

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