# Atomic Multipole Expansions of Molecular Charge Densities. Electrostatic Potentials

## Abstract

The molecular electrostatic potential has been shown to be a very useful tool for understanding the reactivities of molecules with ions or polar molecules^{1} and the structure and energetics of intermolecular complexes, including hydrogen bonded complexes.^{2} The electrostatic potential can be obtained as the by-product of a molecular orbital calculation in the form of a large table of numbers.^{3} A considerable computational advantage would be obtained if this information could be compressed into analytical form, and a large amount of effort has gone into the search for appropriate representations. For instance, Bonaccorsi, Scrocco and Tomasi^{4} have shown how one can resolve molecular electrostatic potentials into sums of contributions from fragments within the molecule; the fragment contributions are approximately transferable, allowing one to construct the potential for a large molecule without first performing a molecular orbital calculation on that molecule. Kollman^{5} has also addressed the problem of obtaining the potential without a wave function and has produced a family of point-charge models for which the necessary inputs are experimental bond lengths, bond angles, and dipole moments, atomic electronegativities, and van der Waals radii. These point-charge distributions produce electrostatic potentials at suitable reference points which are in reasonable accord with the potentials obtained from wave functions.

### Keywords

Methyl Cyanide Fluoride Cyanide Hydride Fluorine## Preview

Unable to display preview. Download preview PDF.

### References

- 1.E. Scrocco and J. Tomasi, The electrostatic molecular potential as a tool for the interpretation of molecular properties, Top. Curr. Chem. 42: 95 (1973).Google Scholar
- 2.P. Kollman, A general analysis of noncovalent intermolecular interactions, J. Am. Chem. Soc. 99: 4875 (1977).CrossRefGoogle Scholar
- 3.For instance, A. C. Wahl and R. H. Land, Evaluation of multicenter integrals by polished brute-force techniques. II. A.curacy, timing, integral values, and general computational considerations, J. Chem. Phys. 50: 4725 (1969).Google Scholar
- 4.R. Bonaccorsi, E. Scrocco and J. Tomasi, Group contributions to the electrostatic molecular potential, J. Am. Chem. Soc. 98:4049 (1975); An approximate expression of the electrostatic molecular potential in terms of completely transferable group contributions, J. Am. Chem. Soc. 99: 4546 (1977).CrossRefGoogle Scholar
- 5.P. A. Kollman, A method of describing the charge distribution in simple molecules, J. Am. Chem. Soc. 100: 2974 (1978).CrossRefGoogle Scholar
- 6.For instance, J. H. Jeans, “The Mathematical Theory of Electricity and Magnetism,” 3rd ed., The University Press, Cambridge, UK (1915), p. 224.Google Scholar
- 7.A. Julg, On the description of molecules using point charges and electric moments, Top. Curr. Chem. 58: 1 (1975).CrossRefGoogle Scholar
- 8.R. F. Stewart, J. Bentley and G. Goodman, Generalized X-ray scattering factors in diatomic molecules, J. Chem. Phys. 63: 3786 (1975).CrossRefGoogle Scholar
- 9.R. F. Stewart, One-electron density functions and many-centered finite-multipole expansions, Israel J. Chem. 16:124 (1977); R. F. Stewart, On the mapping of electrostatic properties from Bragg diffraction data, Chem. Phys. Lett. 65: 335 (1979).Google Scholar
- 10.J. Bentley and R. F. Stewart, Diatomic generalized X-ray scattering factors: Results from Hartree-Fock electron density functions, J. Chem. Phys. 63: 3794 (1975).CrossRefGoogle Scholar
- 11.J. Bentley, Collision-induced atomic dipole moments, J. Chem. Phys. 70: 3125 (1979).CrossRefGoogle Scholar
- 12.L. C. Snyder and H.. Basch, “Molecular Wave Functions and Properties,” Wiley, New York (1972).Google Scholar
- 13.T. H. Dunning, Jr., R. M. Pitzer and S. Aung, Near Hartree-Fock calculations on the ground state of the water molecule: Energies, ionization potentials, geometry, force constants, and one-electron properties, J. Chem. Phys. 57: 5044 (1972).CrossRefGoogle Scholar
- 14.P. E. Cade and W. M. Huo, Electronic structure of diatomic molecules. VI.A. Hartree-Fock wave functions and energy quantities for the ground state of the first-row diatomic hydrides, AH, J. Chem. Phys. 47: 614 (1967).CrossRefGoogle Scholar
- 15.R. D. Amos, MCSCF calculations of the properties of hydrogen fluoride, Mol. Phys. 35: 1765 (1978).Google Scholar
- 16.For instance, M. Cohen and A. Dalgarno, Stationary properties of the Hartree-Fock approximation, Proc. Phys. Soc. (London) 77: 740 (1961).Google Scholar
- 17.R. F. Stewart, E. R. Davidson and W. T. Simpson, Coherent X-ray scattering for the hydrogen atom in the hydrogen molecule, J. Chem. Phys. 42: 3175 (1965).CrossRefGoogle Scholar