The Source Function Descriptor as a Tool to Extract Chemical Information from Theoretical and Experimental Electron Densities

  • Carlo GattiEmail author
Part of the Structure and Bonding book series (STRUCTURE, volume 147)


This chapter deals with the source function (SF) descriptor, originally put forth by Bader and Gatti back in 1998. After a brief review on how this descriptor is defined and what it physically represents, the various forms through which the SF may be analyzed are presented in some detail. The relationships between atomic SF contributions and chemical bond nature are analyzed in some prototypical cases, and the capability of the SF to neatly reveal π-electron conjugation directly from the electron distribution and independently from any MO scheme or decomposition is introduced. Applications of the SF to chemistry from the literature are reviewed and critically discussed, including the use of the SF to assess chemical transferability or to describe chemical bonding in challenging situations, like for instance the short-strong hydrogen bonds in π-conjugated frameworks or the metal–metal and metal–ligand interactions in the organometallic complexes. Comparison with the insight obtained from other bond topological descriptors is given, emphasizing the special role the SF has of being directly derivable from experimental electron density distributions and to so provide an ideal tool to compare experiment and theory. The robustness of the SF descriptor against changes in the models used to derive electron densities from theory of experiment is detailed. First results on using the SF to define an unambiguous full population analysis are outlined. The possible ways of further decomposing the atomic SF in chemically meaningful additive pieces, such as core and valence atomic contributions, are analyzed in view of their potential insight and degree of arbitrariness.


Chemical transferability Electron conjugation Local and nonlocal bonding descriptors Metal–metal and metal–ligand bonds Population analysis Short-strong hydrogen bonds Source function and chemical bonding Theoretical and experimental electron densities 



Positively(negatively) charge-assisted hydrogen bond


Bond critical point (in RFW Bader’s theory)


Bond path (in RFW Bader’s theory)




Charge concentration


Critical point (in RFW Bader’s theory)


Domain-averaged Fermi hole


Density functional theory


Electron localization function


Hydrogen bond




Hirshfeld surfaces (M Spackman’s definition)


Independent atom model


Interatomic surface (in RFW Bader’s theory)


Interchanged population


Isolated hydrogen bond


Ignored population


Interacting quantum atoms


Low-barrier hydrogen bond


Local source function


Multipole model


Multipole model experimental density


Multipole-modeled primary density


Midpoint (along an internuclear axis)


Mulliken’s population analysis


Natural bond order




Polarization-assisted hydrogen bond


Primary density (usually from ab initio computations)


Quantum theory of atoms in molecules (RFW Bader’s theory)


Resonance-assisted hydrogen bond


Ring critical point (in RFW Bader’s theory)


Reference point


Source function


Short-strong hydrogen bond


Trimethylenemethane complex


Valence shell charge concentration (RFW Bader’s theory)



I am deeply indepted to and warmly thank Richard Bader for his fundamental contribution to the seminal work on the Source Function. I also thank Luca Bertini, Fausto Cargnoni, Davide Lasi, and Leonardo Lo Presti for their precious collaboration in developing and applying the SF. I thank the Danish National Research Foundation for partial funding of this work through the Center for Materials Crystallography (CMC).


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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Istituto di Scienze e Tecnologie Molecolari del CNR (CNR-ISTM) e Dipartimento di Chimica Fisica ed ElettrochimicaUniversità di MilanoMilanoItaly
  2. 2.Center for Materials CrystallographyAarhus UniversityAarhus CDenmark

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