Advertisement

Introduction: The Role of the Electrostatic Potential in Chemistry

  • Peter Politzer
  • Donald G. Truhlar

Abstract

The electrostatic potential at a point \(\vec r\) in the vicinity of an atomic or molecular system having an electronic density function ρ(\(\vec r\) ) is given, in atomic units,* by
$${V^{ES}}\left( {\overrightarrow r } \right) = \sum\limits_A {\frac{{{Z_A}}}{{\left| {{{\overrightarrow R }_A} - \overrightarrow r } \right|}}} - \int {\frac{{\rho \left( {\overrightarrow {r'} } \right)\overrightarrow {dr'} }}{{\left| {\overrightarrow {r'} - \overrightarrow r } \right|}}}$$
(1)
where ZA is the charge on nucleus A, located at \({\vec R_A}\) A. The two terms on the right side of equation (1) correspond, respectively, to the nuclear and electronic contributions to the potential. As can be seen, they have opposite signs and accordingly opposite effects; VES (\(\vec r\)) represents the net result at any point \(\vec r\). The electrostatic potential is a real physical property, which is rigorously defined by equation (1). It is exactly equal in magnitude to the electrostatic (coulombic) interaction energy between the static (i.e., unperturbed) charge distribution of the system and a positive unit point charge located at \(\vec r\).

Keywords

Electrostatic Potential Electrostatic Molecular Potential Electronic Density Function Positive Unit Atomic Electron Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    P. Ilohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136: B864 (1964).CrossRefGoogle Scholar
  2. 2.
    P. Gombas, “Die Statistische Theorïe des Atoms und ihre Anwendungen,” Springer, Vienna (1949); N. M. March, The Thomas-Fermi approximation in quantum mechanics, Advan. Phys. 6:1 (1957); J. Goodisman, On the partitioning of energy for atoms, ions and molecules, Theoret. Chim. Acta 15:165 (1973); J. Goodisman, Modified quantum-statistical calculations for atomic electron densities, Phys. Rev. A 2:1193 (1970); E. H. Lieb and B. Simon, The Thomas-Fermi theory of atoms, molecules and solids, Advan. Math. 23:22 (1977). See also J. Schwinger, Thomas-Fermi model: The leading correction, Phys. Rev. A 22: 1827 (1980).Google Scholar
  3. 3.
    C. Moller and M. S. Plesset, Note on an approximation treatment for many-electron systems, Phys. Rev. 46:618 (1934); M. Cohen and A. Dalgarno, Stationary properties of the HartreeFock approximation, Proc. Phys. Soc. (London) 77:748 (1961); W. A. Goddard III, Improved quantum theory of many-electron systems. IV. Properties of GF wave functions, J. Chem. Phys. 48: 5337 (1968).Google Scholar
  4. 4.
    G. Blyholder and C. A. Coulson, Basis of extended-Hückel formalism, Theoret. Chinn. Acta 10:316 (1968); J. Goodisman, The isoelectronic principle and the accuracy of binding energies in the Mickel method, J. Am. Chem. Soc. 91:6552 (1969); P. Politzer, R. K. Smith and S. D. Kasten, Energy calculations with the extended-Hückel method, Chem. Phys. Lett. 15: 226 (1972).Google Scholar
  5. 5.
    E. Scrocco and J. Tomasi, The electrostatic molecular potential as a tool for the interpretation of molecular properties, Top. Curr. Chem. 42:95 (1973); E. Scrocco and J. Tomasi, Electronic molecular structure, reactivity and intermolecular forces: An heuristic interpretation by means of electrostatic molecular potentials, Advan. Quantum Chem. 11:116 (1978); J. Tomasi, On the use of electrostatic molecular potentials in theoretical investigations on chemical reactivity, in: “Quantum Theory of Chemical Reactions,” R. Daudel, A. Pullman, L. Salem and A. Veillard, eds., D. Reidel Publishing Co., Dordrecht, Reidel Publishing Co., (1979), Vol. I, p. 191.Google Scholar
  6. 6.
    P. Politzer and K. C. Daiker, Models for chemical reactivity, in: “The Force Concept in Chemistry,” B. M. Deb, ed., Van Nostrand-Reinhold, Princeton, NJ (1981), in press.Google Scholar

Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Peter Politzer
    • 1
  • Donald G. Truhlar
    • 2
  1. 1.Department of ChemistryUniversity of New OrleansNew OrleansUSA
  2. 2.Department of Chemistry and Chemical Physics ProgramUniversity of MinnesotaMinneapolisUSA

Personalised recommendations