Editing Charge equilibration for molecular dynamics simulations

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'''Charge equilibration''' (QEq) for [[molecular dynamics]] simulations <ref>[http://dx.doi.org/10.1021/ja00290a017 Wilfried J. Mortier, Karin Van Genechten, Johann Gasteiger "Electronegativity equalization: application and parametrization", Journal of the American Chemical Society '''107''' pp. 829-835 (1985)]</ref> <ref>[http://dx.doi.org/10.1021/j100161a070 Anthony K. Rappe and William A. Goddard III "Charge equilibration for molecular dynamics simulations", Journal of Physical Chemistry '''95''' pp. 3358-3363 (1991)]</ref> 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.
==Split-charge formalism==
<ref>[http://dx.doi.org/10.1063/1.2346671 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)]</ref>
==References==
<references/>
'''Related reading'''

[[category: molecular dynamics]]
[[category: electrostatics]]
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 {{stub-general}}
-'''Charge equilibration''' (QEq) for [[molecular dynamics]] simulations <ref >[http://dx.doi.org/10.1021/ja00290a017 Wilfried J. Mortier, Karin Van Genechten, Johann Gasteiger "Electronegativity equalization: application and parametrization", Journal of the American Chemical Society '''107''' pp. 829-835 (1985)]</ref> <ref name="GoddardIII">[http://dx.doi.org/10.1021/j100161a070 Anthony K. Rappe and William A. Goddard III "Charge equilibration for molecular dynamics simulations", Journal of Physical Chemistry '''95''' pp. 3358-3363 (1991)]</ref> is a technique for calculating the distribution of charges
+'''Charge equilibration''' (QEq) for [[molecular dynamics]] simulations <ref>[http://dx.doi.org/10.1021/ja00290a017 Wilfried J. Mortier, Karin Van Genechten, Johann Gasteiger "Electronegativity equalization: application and parametrization", Journal of the American Chemical Society '''107''' pp. 829-835 (1985)]</ref> <ref>[http://dx.doi.org/10.1021/j100161a070 Anthony K. Rappe and William A. Goddard III "Charge equilibration for molecular dynamics simulations", Journal of Physical Chemistry '''95''' pp. 3358-3363 (1991)]</ref> 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 <ref>[http://dx.doi.org/10.1063/1.1749394 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)]</ref>
-:<math>\chi  = \frac{\mathrm{IP + EA} }{2} \approx \frac{\partial E}{\partial Q}</math>
-where IP is the ionisation potential, and EA is the electron affinity. The  electronic hardness is given by <ref>[http://dx.doi.org/10.1021/ja00364a005 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)]</ref>
-:<math>\eta = \mathrm{IP - EA} \approx  \frac{\partial^2 E}{\partial Q^2} </math>
-==Charge equilibration energy==
-Using the above expressions one has the following second order approximation for the  total electrostatic energy (<ref name="GoddardIII"> </ref> Eq. 6)
-:<math>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}</math>
-The last term is a "shielded" [[Coulomb's law | Coulombic interaction]], where
-:<math>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</math>
-where <math>\phi</math> represents a normalised ''ns'' Slater-type orbital.
 ==Split-charge formalism==
 <ref>[http://dx.doi.org/10.1063/1.2346671 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)]</ref>
-==Fluctuating-charge formalism==
-====QTPIE====
-<ref>[http://dx.doi.org/10.1016/j.cplett.2007.02.065 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)]</ref>
-==See also==
-*[[Drude oscillators]]
-*[[Polarizable point dipoles]]
 ==References==
 <references/>
+'''Related reading'''
 [[category: molecular dynamics]]
 [[category: electrostatics]]