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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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)

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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

Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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