On the representation of atoms and molecules as self-interacting field with internal structure

The nonlinear Schrödinger equation with Gaussian convolution kernel K₂ induces the group SU₃ with reference to the classification of the multiplet structure of the eigenstates. Such a field can be used to describe some atoms (where the outermost electrons are related tos-orbitals) as a self-interacting, extended particle with an internal structure. In the case of those atoms, where the valence electrons are described byp-orbitals, and almost all molecules the Gaussian kernel K₂ has to be generalized by Hermite polynomials. By that, we can formulate a nonlinear field theory, establishing the spatial symmetry of a system via basis structure functions. Thus the symmetry represents the most essential starting-point for treating molecules as quasi-particles with an internal structure. It will be shown that there is some connection with the concept of chirality functions and the Ginzburg — Landau theory of super-conductivity. The latter theory indicates that we can consider the nonlinear Schrödinger equation and its generalizations as a classical field theory being associated with phase transitions.