Partial charge

A partial charge is a charge with an absolute value of less than one elementary charge unit (that is, smaller than the charge of the electron).

Partial charges are created due to the asymmetric distribution of electrons in chemical bonds. For example, in a polar covalent bond like HCl, the shared electron oscillates between the bonded atoms. The resulting partial charges are a property only of zones within the distribution, and not the assemblage as a whole. For example, chemists often choose to look at a small space surrounding the nucleus of an atom: When an electrically neutral atom bonds chemically to another neutral atom that is more electronegative, its electrons are partially drawn away. This leaves the region about that atom's nucleus with a partial positive charge, and it creates a partial negative charge on the atom to which it is bonded.

In such a situation, the distributed charges taken as a group always carries a whole number of elementary charge units. Yet one can point to zones within the assemblage where less than a full charge resides, such as the area around an atom's nucleus. This is possible in part because particles are not like mathematical points--which must be either inside a zone or outside it--but are smeared out by the uncertainty principle of quantum mechanics. Because of this smearing effect, if one defines a sufficiently small zone, a fundamental particle may be both partly inside and partly outside it.

Uses

Partial atomic charges are used in molecular mechanics force fields to compute the electrostatic interaction energy using Coulomb's law. They are also often used for a qualitative understanding of the structure and reactivity of molecules.

Determining partial atomic charges

Despite its usefulness, the concept of a partial atomic charge is somewhat arbitrary, because it depends on the method used to delimit between one atom and the next (in reality, atoms have no clear boundaries). As a consequence, there are many methods for estimating the partial charges. According to Cramer (2002), all methods can be classified in one of four classes:^[1]

• Class I charges are those that are not determined from quantum mechanics, but from some intuitive or arbitrary approach. These approaches can be based on experimental data such as dipoles and electronegativities.

• Class II charges are derived from partitioning the molecular wave function using some arbitrary, orbital based scheme.

• Class III charges are based on a partitioning of a physical observable derived from the wave function, such as electron density.

• Class IV charges are derived from a semiempirical mapping of a precursor charge of type II or III to reproduce experimentally determined observables such as dipole moments.

The following is a detailed list of methods, partly based on Meister and Schwarz (1994).^[2]

• Population analysis of wavefunctions
  • Mulliken population analysis
  • Coulson's charges
  • Natural charges
  • CM1, CM2, CM3 charge models

• Partitioning of electron density distributions
  • Bader charges (obtained from an atoms in molecules analysis)
  • Density fitted atomic charges
  • Hirshfeld charges
  • Maslen's corrected Bader charges
  • Politzer's charges
  • Voronoi Deformation Density charges

• Charges derived from density-dependent properties
  • Partial derived charges
  • Dipole charges
  • Dipole derivative charges, also called atomic polar tensor (APT) derived charges ^[3]
• Charges derived from electrostatic potential
  • Chelp
  • ChelpG (Breneman model)
  • Merz-Singh-Kollman (also known as Merz-Kollman, or MK)

• Charges derived from spectroscopic data
  • Charges from infrared intensities
  • Charges from X-ray photoelectron spectroscopy (ESCA)
  • Charges from X-ray emission spectroscopy
  • Charges from X-ray absorption spectra
  • Charges from ligand-field splittings
  • Charges from UV-vis intensities of transition metal complexes
  • Charges from other spectroscopies, such as NMR, EPR, EQR

• Charges from other experimental data
  • Charges from bandgaps or dielectric constants
  • Apparent charges from the piezoelectric effect
  • Charges derived from adiabatic potential energy curves
  • Electronegativity-based charges
  • Other physicochemical data, such as equilibrium and reaction rate constants, thermochemistry, and liquid densities.
  • Formal charges

References

• Frank Jensen. Introduction to Computational Chemistry (2nd Edition ed.). Wiley. ISBN 978-0-470-01187-4. 

1. ^ C. J. Cramer (2002). Essentials of Computational Chemistry: Theories and Methods. Wiley. pp. 278-289. 
2. ^ J. Meister; W. H. E. Schwarz (1994). "Principal Components of Ionicity". J. Phys. Chem. 98: 8245-8252. 
3. ^ P. J. Stephens; K. J. Jalkanen; R. W. Kawiecki (1990). "Theory of vibrational rotational strengths: comparison of a priori theory and approximate models". J. Am. Chem. Soc. 112 (18): 6518–6529. doi:10.1021/ja00174a011.