Stereographic Projection of Density Functions (DF) and the Holographic Electronic Density Theorem (HEDT)

Mezey's holographic electronic density theorem is discussed from the point of view of stereographic projection techniques. Such a mathematical procedure is analyzed in depth from the point of view of first-order density functions; the procedure is then extended to any relevant quantum chemical function. This endeavor provides the background to construct a Holographic General Function Theorem (HGFT) for multivariate well-behaved functions. Stereographic projections, applied first as a way to obtain pictures of molecular quantum chemical functions, are shown to provide a flexible and original vantage point for visualizing, from any location and any chosen perspective, the form of any well-behaved function, irrespective of the number of variables involved. The pictographic possibilities of the HGFT are explored and exploited in several examples.