Journal of Molecular Modeling

, Volume 18, Issue 2, pp 541–548 | Cite as

σ-Holes, π-holes and electrostatically-driven interactions

  • Jane S. Murray
  • Pat Lane
  • Timothy Clark
  • Kevin E. Riley
  • Peter Politzer
Original Paper


A positive π-hole is a region of positive electrostatic potential that is perpendicular to a portion of a molecular framework. It is the counterpart of a σ-hole, which is along the extension of a covalent bond to an atom. Both σ-holes and π-holes become more positive (a) in going from the lighter to the heavier atoms in a given Group of the periodic table, and (b) as the remainder of the molecule is more electron-withdrawing. Positive σ- and π-holes can interact in a highly directional manner with negative sites, e.g., the lone pairs of Lewis bases. In this work, the complexes of 13 π-hole-containing molecules with the nitrogen lone pairs of HCN and NH3 have been characterized computationally using the MP2, M06-2X and B3PW91 procedures. While the electrostatic interaction is a major driving force in π-hole bonding, a gradation is found from weakly noncovalent to considerably stronger with possible indications of some degree of coordinate covalency.


Computed molecular surface electrostatic potential of SeO2 showing the π-hole above the selenium atom (middle). The position of the most positive electrostatic potential associated with the π-hole is indicated by a black hemisphere. Color ranges, in kcal mol-1, are: red, greater than 33; yellow, from 33 to 20; green, from 20 to 0; blue, less than 0 (negative).


Electrostatic potentials Interaction energies π-holes σ-holes 



TC gratefully acknowledges the generous support of the Deutsche Forschungsgemeinschaft as part of SFB583 (Sonderforschungsbereich 583) “Redox-Active Metal Complexes: Control of Reactivity in Molecular Architecture” and KER the NSF (National Science Foundation) EPSCOR (Experimental Program to Stimulate Competitive Research) Program (Grant number EPS-0701525) and the NSF PREM (Partnership for Research & Education in Materials) Program (Grant number DMR-0934115).


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Jane S. Murray
    • 1
  • Pat Lane
    • 2
  • Timothy Clark
    • 3
    • 4
  • Kevin E. Riley
    • 5
  • Peter Politzer
    • 1
  1. 1.CleveTheoComp, 1951 WClevelandUSA
  2. 2.Department of ChemistryUniversity of New OrleansNew OrleansUSA
  3. 3.Computer-Chemie-Centrum and Interdisciplinary Center for Molecular MaterialsFriedrich-Alexander-Universität, Erlangen-NürnbergErlangenGermany
  4. 4.Centre for Molecular DesignUniversity of Portsmouth, Mercantile HousePortsmouthUK
  5. 5.Department of ChemistryUniversity of Puerto RicoRio PiedrasUSA

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