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

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 expression 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.

See also

• Drude oscillators