Supramolecular Holographic Electron Density Theorem

Since molecular recognition typically involves two or more molecules, it is useful to phrase the problem in terms of a generalization of the Holographic Electron Density Theorem to supermolecular and supramolecular structures involving several interacting, but formally individual molecules. Such a generalization is the Supramolecular Holographic Electron Density Theorem. 

The Supramolecular Holographic Electron Density Theorem [27] states the following ... 

In order to apply the Holographic Electron Density Theorem to both the independent molecules and the supramolecular object, consider a nonzero volume part P of the electron density of independent molecule E. For example, select a spherical volume about a specific nucleus X of molecule E. As what follows from the Holographic Electron Density Theorem, this volume P contains all the information about the independent molecule E, assumed to be infinitely removed from any other molecule. 

In the next step, bring the two molecules into some mutual position where some interaction occurs between them, and consider the same nonzero volume part P in the supramolecular object ED, for example, the spherical volume of the same radius about the same nucleus X. Whereas this volume P was originally specified for the independent molecule E, nevertheless, by applying the Holographic Electron Density Theorem to the entire supramolecular object ED, now, this volume P now contains all the information about the supramolecular object. 

This result is a rather trivial consequence of the original Holographic Electron Density Theorem nevertheless, it can be viewed as a basic aspect of supramolecular chemistry, where the components of the supramolecular structure may retain a sufficient degree of their original, individual autonomy to justify a reference to their original electron density. 

---

See also in sourсe #XX -- [ ]

---