Charge equilibration for molecular dynamics simulations

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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]

\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 [4]

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

Charge equilibration energy[edit]

Using the above expressions one has the following second order approximation for the total electrostatic energy ([2] 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.

Split-charge formalism[edit]


Fluctuating-charge formalism[edit]



See also[edit]