We would like to dedicate this article to Prof. Peter Gill, whose elegant and masterly applications of simple and advanced mathematical tools in the field of quantum chemistry have been a great inspiration to Y.S. and other authors. To a large extent, our work is an attempt to follow Peter's example and develop simple mathematical tools to advance the chemical understanding. However, as will become obvious, our grid mapping has a serious shortcoming in that it does not conserve the number of electrons. Hopefully, more rigorous procedures will be developed in the future by readers of this special issue.