Symmetry of the pentacene molecule and classification of electron states studied in the frame of group action on a set

Pentacene have recently become the subject of intense studies due to their physical properties which follow from the states of their outer-shell electrons that are able to take part in molecule bonding. The symmetry of these molecules provides the classification of quantum states according to the group theory method. In this paper, we apply a molecular state-space factorization scheme for the classification of pentacene molecules based on the structure of their electron states.

Similarity Solutions: A Group-Theoretic Approach for Students

One of the most powerful methods for generating similarity solutions to problems in fluid mechanics and heat transfer is the group-theory method; it is also one of the easiest to apply. However, because of the apparent difficulty and obscurity of the underlying mathematics it is rarely mentioned in anything but advanced graduate seminars in these areas. This is unfortunate, as it is actually one of the most physically based and computationally simple of the methods available for obtaining such solutions. In this paper we give a presentation of this method which will make these group-theoretic techniques accessible and useful to advanced undergraduates and beginning graduate students. Several examples, both standard and unusual, are also given.