# Charge equilibration for molecular dynamics simulations

**Charge equilibration** (QEq) for molecular dynamics simulations ^{[1]} ^{[2]} is a technique for calculating the distribution of charges
within a (large) molecule. This distribution can change with time to match changes in the local environment.

## Electronegativity and electronic hardness[edit]

The atomic electronegativity is given by ^{[3]}

where IP is the ionisation potential, and EA is the electron affinity. The electronic hardness is given by ^{[4]}

## Charge equilibration energy[edit]

Using the above expressions one has the following second order approximation for the total electrostatic energy (^{[2]} Eq. 6)

The last term is a "shielded" Coulombic interaction, where

where represents a normalised *ns* Slater-type orbital.

## Split-charge formalism[edit]

^{[5]}

## Fluctuating-charge formalism[edit]

#### QTPIE[edit]

^{[6]}

## See also[edit]

## References[edit]

- ↑ Wilfried J. Mortier, Karin Van Genechten, Johann Gasteiger "Electronegativity equalization: application and parametrization", Journal of the American Chemical Society
**107**pp. 829-835 (1985) - ↑
^{2.0}^{2.1}Anthony K. Rappe and William A. Goddard III "Charge equilibration for molecular dynamics simulations", Journal of Physical Chemistry**95**pp. 3358-3363 (1991) - ↑ Robert S. Mulliken "A New Electroaffinity Scale; Together with Data on Valence States and on Valence Ionization Potentials and Electron Affinities", Journal of Chemical Physics
**2**pp. 782-793 (1934) - ↑ Robert G. Parr and Ralph G. Pearson "Absolute hardness: companion parameter to absolute electronegativity", Journal of the American Chemical Society
**105**pp. 7512-7516 (1983) - ↑ Razvan A. Nistor, Jeliazko G. Polihronov, Martin H. Müser, and Nicholas J. Mosey "A generalization of the charge equilibration method for nonmetallic materials", Journal of Chemical Physics
**125**094108 (2006) - ↑ Jiahao Chen and Todd J. Martínez "QTPIE: Charge transfer with polarization current equalization. A fluctuating charge model with correct asymptotics", Chemical Physics Letters
**438**pp. 315-320 (2007)