Charge equilibration for molecular dynamics simulations - Revision history

Carl McBride: /* See also */ Added an internal link

2010-12-16T13:54:04Z

Carl McBride: /* Charge equilibration energy */

2010-05-05T15:22:47Z

Charge equilibration energy

← Older revision		Revision as of 17:22, 5 May 2010
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	:<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>		:<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 Slater-type ~~orbitals~~.		where <math>\phi</math> represents a normalised ''ns'' Slater-type orbital.

	==Split-charge formalism==		==Split-charge formalism==

Carl McBride: /* Charge equilibration energy */ A little more

2010-05-05T14:44:52Z

Charge equilibration energy: A little more

← Older revision		Revision as of 16:44, 5 May 2010
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	:<math>\eta = \mathrm{IP - EA} \approx \frac{\partial^2 E}{\partial Q^2} </math>		:<math>\eta = \mathrm{IP - EA} \approx \frac{\partial^2 E}{\partial Q^2} </math>
	==Charge equilibration energy==		==Charge equilibration energy==
	Using the above expressions one has the following ~~expression~~ for the total electrostatic energy (<ref name="GoddardIII"> </ref> Eq. 6)		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>		:<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]].		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 Slater-type orbitals.

	==Split-charge formalism==		==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>		<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>

Carl McBride: Added a little more

2010-05-05T14:27:01Z

Added a little more

← Older revision		Revision as of 16:27, 5 May 2010
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	{{stub-general}}		{{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>[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 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
	within a (large) molecule. This distribution can change with time to match changes in the local environment.		within a (large) molecule. This distribution can change with time to match changes in the local environment.
	==Electronegativity and electronic hardness==		==Electronegativity and electronic hardness==
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	:<math>\eta = \mathrm{IP - EA} \approx \frac{\partial^2 E}{\partial Q^2} </math>		:<math>\eta = \mathrm{IP - EA} \approx \frac{\partial^2 E}{\partial Q^2} </math>
	==Charge equilibration ~~potential~~ energy==		==Charge equilibration energy==
			Using the above expressions one has the following expression 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]].
	==Split-charge formalism==		==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>		<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>

Carl McBride at 16:03, 27 April 2010

2010-04-27T16:03:28Z

← Older revision		Revision as of 18:03, 27 April 2010
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	<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>		<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]]
	==References==		==References==
	<references/>		<references/>
	~~'''Related reading'''~~

	[[category: molecular dynamics]]		[[category: molecular dynamics]]
	[[category: electrostatics]]		[[category: electrostatics]]

Carl McBride: partial save.

2010-04-27T15:55:03Z

partial save.

@@ Line 2: / Line 2: @@
 '''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/>

Carl McBride at 14:00, 27 April 2010

2010-04-27T14:00:49Z

← Older revision		Revision as of 16:00, 27 April 2010
Line 2:		Line 2:
	'''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		'''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.		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==
	<references/>		<references/>
	'''Related reading'''		'''Related reading'''
	*[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)]

	[[category: molecular dynamics]]		[[category: molecular dynamics]]
	[[category: electrostatics]]		[[category: electrostatics]]

Carl McBride at 13:48, 27 April 2010

2010-04-27T13:48:36Z

← Older revision		Revision as of 15:48, 27 April 2010
Line 1:		Line 1:
	{{stub-general}}		{{stub-general}}
	'''Charge equilibration''' (QEq) for [[molecular dynamics]] simulations <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		'''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.		within a (large) molecule. This distribution can change with time to match changes in the local environment.
	==References==		==References==

Carl McBride at 13:36, 27 April 2010

2010-04-27T13:36:13Z

← Older revision		Revision as of 15:36, 27 April 2010
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	==References==		==References==
	<references/>		<references/>
			'''Related reading'''
			*[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)]

	[[category: molecular dynamics]]		[[category: molecular dynamics]]
	[[category: electrostatics]]		[[category: electrostatics]]

Carl McBride: New page: {{stub-general}} '''Charge equilibration''' (QEq) for molecular dynamics simulations [http://dx.doi.org/10.1021/j100161a070 Anthony K. Rappe and William A. Goddard III "Charge equ...

2010-04-27T13:12:29Z

New page: {{stub-general}} '''Charge equilibration''' (QEq) for molecular dynamics simulations <ref>[http://dx.doi.org/10.1021/j100161a070 Anthony K. Rappe and William A. Goddard III "Charge equ...

New page

{{stub-general}}
'''Charge equilibration''' (QEq) for [[molecular dynamics]] simulations <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.
==References==
<references/>

[[category: molecular dynamics]]
[[category: electrostatics]]

← Older revision		Revision as of 15:54, 16 December 2010
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	==See also==		==See also==
	*[[Drude oscillators]]		*[[Drude oscillators]]
			*[[Polarizable point dipoles]]

	==References==		==References==
	<references/>		<references/>