Charge equilibration for molecular dynamics simulations

Charge equilibration (QEq) for molecular dynamics simulations 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

The atomic electronegativity is given by

\[\chi = \frac{\mathrm{IP + EA} }{2} \approx \frac{\partial E}{\partial Q}\]

where IP is the ionisation potential, and EA is the electron affinity. The electronic hardness is given by

\[\eta = \mathrm{IP - EA} \approx \frac{\partial^2 E}{\partial Q^2} \]

Charge equilibration energy

Using the above expressions one has the following second order approximation for the total electrostatic energy ( Eq. 6)

\[E = \sum_i \left( q_i\chi_i + \frac{q_i^2}{2} \eta_i \right) + \sum_{i \neq j} q_i q_j J_{ij}\]

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

\[J_{ij} ({\mathbf{r}}_{ij}) = \left\langle \phi_i \phi_j \left\vert \frac{1}{| {\mathbf{r}}_{i} - {\mathbf{r}}_{j} |} \right\vert \phi_i \phi_j \right\rangle\]

where \(\phi\) represents a normalised ns Slater-type orbital.

See also

• Drude oscillators
• Polarizable point dipoles