MICHAEL KASHA 39 



in ihc ben/cne molecule, but in pyridine the electronegativity of the 

 N-atoni makes tto lo\ver in energy than tt-.^; an analogous result holds 

 for the orbitals tj-*^ and 77*5. This TT-orbital order is in accord with 

 the theoretical calculations of McWeeny and Peacock (24) . In the 

 diagrams of Fig. 4 the orbital distortion due to the electronegativity 

 of the N-atom is not shown. 



The n-orbital is an approx. sp~ hybrid lone-pair orbital on the 

 N atom, and is symmetric with respect to reflection in the molecular 

 plane. 



In the section which follows the symmetry classification of molecu- 

 lar orbitals will be considered. This will be done in order that the 

 full electronic state configurations may be described. From the state 

 symmetries it will be a simple matter to deduce electronic selection 

 rules and polarizations for the electronic transitions. The results will 

 have some important applications to biologically important N-hetero- 

 cyclics. 



III. Symmetry Classifications of Molecular Orbitals 

 AND Electronic States 



A. The Symmetry Requirement 



One of the fundamental quantum mechanical theorems requires 

 that proper wavefunctions for a system should conform to the sym- 

 metry operations of the system. It is w^orthwhile to apply this theorem 

 to classification of the electronic orbitals, configurations, and states 

 of a molecule. Not only will this lead to a concrete picture of the 

 nature of molecular electronic transitions, but the results will be 

 directly useful in our further discussion. 



The concept of symmetry is a loose one in ordinary usage. The 

 proper use of molecular symmetry involves the rather abstract 

 subject of Finite Point Groups, the utilization of which assures one 

 that a full closed set of symmetry operations is considered, with which 

 there is associated a complete set of symmetry species suitable for the 

 classification of molecular wavefunctions. In this presentation only 

 the role of symmetry operators will be stressed, circumventing the 

 development of the formal basis of the subject. This will suffice to 

 illustrate the methods used in some simple cases, and to permit some 

 analysis of the main molecules of interest. 



B. Classification of Molecules According to Point Groups 

 Coordinate axes are chosen for the molecules of interest, as shown 



