Hierarchical network model - Revision history

en>Gilliam: Reverted edits by 41.204.187.12 (talk) to last version by Yobot

2014-10-31T12:39:09Z

Reverted edits by 41.204.187.12 (talk) to last version by Yobot

← Older revision		Revision as of 14:39, 31 October 2014
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	~~The~~ '~~''reaction field method''' is used in molecular simulations to simulate the effect of long range dipole-dipole interactions for simulations with~~ [[periodic boundary conditions]]. Around each molecule there is a 'cavity' or sphere within which the Couloumb interactions are treated explicitly. Outside of this cavity the medium is assumed to have a uniform dielectric constant. The molecule induces polarization in this media which in turn creates a reaction field, sometimes called the '''Onsager reaction field'''. Although [[Lars Onsager\|Onsager]]'s name is often attached to the technique, because he considered such a geometry in his theory of the dielectric constant,<ref>{{cite journal\|last=Onsager\|first=Lars\|journal=Journal of the American Chemical Society\|date=1 August 1936\|volume=58\|issue=8\|pages=1486–1493\|doi=10.1021/ja01299a050\|accessdate=20 May 2012}}</ref> the method was first introduced by Barker and Watts in 1973.<ref>{{cite journal\|last=Barker\|first=J.A.\|coauthors=Watts, R.O.\|title=Monte Carlo studies of the dielectric properties of water-like models\|journal=Molecular Physics\|date=1 September 1973\|volume=26\|issue=3\|pages=789–792\|doi=10.1080/~~00268977300102101\|accessdate=20 May 2012\|bibcode = 1973MolPh..26..789B }}<~~/~~ref><ref>{{cite journal\|last=Watts\|first=R~~.O.~~\|title=Monte Carlo studies of liquid water\|journal=Molecular Physics\|date=1 October 1974\|volume=28\|issue=4\|pages=1069–1083\|doi=10.1080~~/~~00268977400102381\|accessdate~~=~~20 May 2012\|bibcode = 1974MolPh..28.1069W }}</ref>~~		My name's Jessica Eady but everybody calls me [http://Browse.deviantart.com/?q=Jessica Jessica]. I'm from Italy. I'm studying at the university (final year) and I play the Lap Steel Guitar for 4 years. Usually I choose music from my famous films ;). <br>I have two brothers. I like Conlanging, watching movies and Volleyball.<br><br>my web blog ... using sanyo lcd tv as computer monitor ([http://www.rockiefresh.com/forum/5-incredible-using-42-lcd-tv-computer-monitor-transformations-780141 just click the following article])

	~~The effective pairwise potential becomes:~~
	~~:<math> U_{AB} = q_A q_B \left[\frac{1}{r_{AB}} + \frac{(\varepsilon_{RF} - 1) r_{AB}^2}{(2\varepsilon_{RF} + 1) r_c^3} \right~~]~~</math>~~
	~~where <math>r_c</math> is the cut-off radius~~.

	~~The reaction field in the center of the cavity is given by :~~
	~~:<math> E_{RF} = \frac{2(\varepsilon_{RF} - 1)}{2\varepsilon_{RF} + 1} \frac{\vec{M}}{r_c^3}</math>~~
	~~where <math>\vec{M} = \sum \mu_i</math> is the total dipole moment of all the molecules in the cavity~~. ~~The contribution to the potential energy of the molecule <math>i</math>~~ at the ~~center of the cavity is <math>-1/2 \mu_i \cdot E_{RF}</math> and the torque on molecule <math>i</math> is simply <math>\mu_i \times E_{RF}</math>.~~

	When a molecule enters or leaves the sphere defined by the cut-off radius, there is a discontinuous jump in energy.<ref name=allen>{{cite book\|last=Tildesley\|first=M. P. Allen ; D. J.\|title=Computer simulation of liquids\|year=1997\|publisher=Clarendon Press [u.a.]\|location=Oxford [u.a.]\|isbn=0198556454\|pages=162\|edition=Repr.}}</ref> When all of these jumps in energy are summed, they do not exactly cancel, leading to poor energy conservation, a deficiency found whenever a spherical cut-off is used. The situation can be improved by tapering the potential energy function to zero near the cut-off radius. Beyond a certain radius <math>r_t</math> the potential is multiplied by a tapering function <math>f(r)~~</math>. A simple choice is linear tapering with <math>r_t = .95 r_c</math>, although better results may be found with more sophisticated tapering functions.~~

	Another potential difficulty of the reaction field method is that the dielectric constant must be known a priori. However, it turns out that in most cases dynamical properties are fairly insensitive to the choice of <math>\varepsilon_{RF}</math>. It can be put in by hand, or calculated approximately using any of a number of well-known relations between the dipole fluctuations inside the simulation box and the ~~macroscopic dielectric constant.<ref name=allen/>~~

	~~Another possible modification is to take into account the finite time required~~ for the reaction field to respond to changes in the cavity. This "delayed reaction field method" was investigated by van Gunsteren, Berendsen and Rullmann in 1978.<ref>{{cite journal\|last=van Gunsteren\|first=Wilfred F.\|coauthors=Berendsen, Herman J. C.; ~~Rullmann, Johan A. C.\|title=Inclusion of reaction fields in molecular dynamics~~. ~~Application to liquid water\|journal=Faraday Discussions of the Chemical Society\|date=1 January 1978\|volume=66\|pages=58\|doi=10.1039/DC9786600058}}~~<~~/ref~~> ~~It was found to give better results—this makes sense, as without taking into account the delay, the reaction field is overestimated~~. ~~However~~, ~~the delayed method has additional difficulties with energy conservation~~ and ~~thus is not suitable for simulating an NVE ensemble.~~

	~~==Comparison with other techniques==~~
	~~The reaction field method is an alternative to the popular technique of [[Ewald summation]]~~. Today, Ewald summation is the usual technique of choice, but for many quantities of interest both techniques yield equivalent results. For example, in [[Monte Carlo]] simulations of liquid crystals, (using both the [[hard spherocylinder]]<~~ref~~>{{cite journal\|last=Gil-Villegas\|first=By Alejandro\|coauthors=McGrother and George Jackson, Simon C.\|title=Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals\|journal=Molecular Physics\|date=1 November 1997\|volume=92\|issue=4\|pages=723–734\|doi=10.1080/002689797170004\|accessdate=20 May 2012\|bibcode = 1997MolPh..92..723G }}<~~/ref~~> and Gay-Berne models<ref>{{cite journal\|last=MOHAMMED HOUSSA ABDELKRIM OUALID LU\|title=Reaction field and Ewald summation study of mesophase formation in dipolar Gay-Berne model\|journal=Molecular Physics\|date=1 June 1998\|volume=94\|issue=3\|pages=439–446\|doi=10.~~1080/002689798167944\|accessdate=20 May 2012}}</ref>) the results from the reaction field method and Ewald summation are consistent~~. ~~However, the reaction field presents a considerable reduction in the computer time required~~. ~~The reaction field should be applied carefully, and becomes complicated or impossible to implement for non-isotropic systems, such~~ as ~~systems dominated by large biomolecules or systems with liquid-vapour or liquid-solid coexistence.<ref>~~[http://dx.~~doi~~.~~org~~/~~10.1016~~/~~0009~~-~~2614(94)01298~~-9 Benito Garzón, Santiago Lago and Carlos Vega "Reaction field simulations of the vapor-liquid equilibria of dipolar fluids: Does the reaction field dielectric constant affect the coexistence properties?", Chemical Physics Letters '''231''' pp. 366-372 (1994)]</ref>

	In section 5.5.5 of his book, Allen<ref name=allen /> compares the reaction field with other methods, focusing on the simulation of the [[Stockmayer system]] (the simplest model for a dipolar fluid, such as water). The work of Adams, et al. (1979) showed that the reaction field produces results with thermodynamic quantities (volume, pressure and temperature) which are in good agreement with other methods, although pressure was slightly higher with the reaction field method compared to the Ewald-~~Kornfeld method (1.69 vs 1.52). The results show that macroscopic thermodynamic properties do not depend heavily on how long~~-range forces are treated. Similarly, single particle correlation functions do not depend heavily on the method employed. Several other results also show that the dielectic constant <math>\epsilon</math> can be well estimated with either the reaction field or a lattice summation technique.<ref name=allen />

	~~==References==~~
	~~{{reflist}}~~

	~~==Further reading==~~
	*[http://dx.doi.org/10.1080/00268978000100361 Martin Neumann and Othmar Steinhauser "The influence of boundary conditions used in machine simulations on the structure of polar systems", Molecular Physics '''39''' pp. 437-~~454 (1980)]~~
	*[http://dx.doi.org/10.1080/00268978400101081 Martin Neumann, Othmar Steinhauser and G. Stuart Pawley "Consistent calculation of the static and frequency-~~dependent dielectric constant in~~ computer ~~simulations", Molecular Physics '''52''' pp. 97~~-~~113 (1984)]~~
	*[http://dx.doi.org/10.1063/1.3081138 Andrij Baumketner "Removing systematic errors in interionic potentials of mean force computed in molecular simulations using reaction-~~field~~-~~based electrostatics", Journal of Chemical Physics '''130''' 104106 (2009~~)]
	*[http://wanglab.bu.edu/DLPOLY2/node68.html Reaction Field method]

	~~[[Category:Molecular modelling]]~~

en>Mogism: Cleanup/Typo fixing, typo(s) fixed: peripherial → peripheral, world wide web → World Wide Web using AWB

2013-12-01T20:56:51Z

Cleanup/Typo fixing, typo(s) fixed: peripherial → peripheral, world wide web → World Wide Web using AWB

← Older revision		Revision as of 22:56, 1 December 2013
Line 1:		Line 1:
	Hi, ~~everybody!~~ <br>~~I'm Japanese female~~ :D. <br>~~I really love Shortwave listening!~~<br><br>~~Feel free~~ to ~~surf~~ to ~~my web blog~~ [http://~~languageclick~~.co.kr/~~zbxe~~/?~~mid~~=~~hrd_qna&amplistStyle~~=~~webzine&ampdocument_srl~~=~~6103080&document_srl~~=~~10776706 laptop deals~~]		The '''reaction field method''' is used in molecular simulations to simulate the effect of long range dipole-dipole interactions for simulations with [[periodic boundary conditions]]. Around each molecule there is a 'cavity' or sphere within which the Couloumb interactions are treated explicitly. Outside of this cavity the medium is assumed to have a uniform dielectric constant. The molecule induces polarization in this media which in turn creates a reaction field, sometimes called the '''Onsager reaction field'''. Although [[Lars Onsager\|Onsager]]'s name is often attached to the technique, because he considered such a geometry in his theory of the dielectric constant,<ref>{{cite journal\|last=Onsager\|first=Lars\|journal=Journal of the American Chemical Society\|date=1 August 1936\|volume=58\|issue=8\|pages=1486–1493\|doi=10.1021/ja01299a050\|accessdate=20 May 2012}}</ref> the method was first introduced by Barker and Watts in 1973.<ref>{{cite journal\|last=Barker\|first=J.A.\|coauthors=Watts, R.O.\|title=Monte Carlo studies of the dielectric properties of water-like models\|journal=Molecular Physics\|date=1 September 1973\|volume=26\|issue=3\|pages=789–792\|doi=10.1080/00268977300102101\|accessdate=20 May 2012\|bibcode = 1973MolPh..26..789B }}</ref><ref>{{cite journal\|last=Watts\|first=R.O.\|title=Monte Carlo studies of liquid water\|journal=Molecular Physics\|date=1 October 1974\|volume=28\|issue=4\|pages=1069–1083\|doi=10.1080/00268977400102381\|accessdate=20 May 2012\|bibcode = 1974MolPh..28.1069W }}</ref>

			The effective pairwise potential becomes:
			:<math> U_{AB} = q_A q_B \left[\frac{1}{r_{AB}} + \frac{(\varepsilon_{RF} - 1) r_{AB}^2}{(2\varepsilon_{RF} + 1) r_c^3} \right]</math>
			where <math>r_c</math> is the cut-off radius.

			The reaction field in the center of the cavity is given by :
			:<math> E_{RF} = \frac{2(\varepsilon_{RF} - 1)}{2\varepsilon_{RF} + 1} \frac{\vec{M}}{r_c^3}</math>
			where <math>\vec{M} = \sum \mu_i</math> is the total dipole moment of all the molecules in the cavity. The contribution to the potential energy of the molecule <math>i</math> at the center of the cavity is <math>-1/2 \mu_i \cdot E_{RF}</math> and the torque on molecule <math>i</math> is simply <math>\mu_i \times E_{RF}</math>.

			When a molecule enters or leaves the sphere defined by the cut-off radius, there is a discontinuous jump in energy.<ref name=allen>{{cite book\|last=Tildesley\|first=M. P. Allen ; D. J.\|title=Computer simulation of liquids\|year=1997\|publisher=Clarendon Press [u.a.]\|location=Oxford [u.a.]\|isbn=0198556454\|pages=162\|edition=Repr.}}</ref> When all of these jumps in energy are summed, they do not exactly cancel, leading to poor energy conservation, a deficiency found whenever a spherical cut-off is used. The situation can be improved by tapering the potential energy function to zero near the cut-off radius. Beyond a certain radius <math>r_t</math> the potential is multiplied by a tapering function <math>f(r)</math>. A simple choice is linear tapering with <math>r_t = .95 r_c</math>, although better results may be found with more sophisticated tapering functions.

			Another potential difficulty of the reaction field method is that the dielectric constant must be known a priori. However, it turns out that in most cases dynamical properties are fairly insensitive to the choice of <math>\varepsilon_{RF}</math>. It can be put in by hand, or calculated approximately using any of a number of well-known relations between the dipole fluctuations inside the simulation box and the macroscopic dielectric constant.<ref name=allen/>

			Another possible modification is to take into account the finite time required for the reaction field to respond to changes in the cavity. This "delayed reaction field method" was investigated by van Gunsteren, Berendsen and Rullmann in 1978.<ref>{{cite journal\|last=van Gunsteren\|first=Wilfred F.\|coauthors=Berendsen, Herman J. C.; Rullmann, Johan A. C.\|title=Inclusion of reaction fields in molecular dynamics. Application to liquid water\|journal=Faraday Discussions of the Chemical Society\|date=1 January 1978\|volume=66\|pages=58\|doi=10.1039/DC9786600058}}</ref> It was found to give better results—this makes sense, as without taking into account the delay, the reaction field is overestimated. However, the delayed method has additional difficulties with energy conservation and thus is not suitable for simulating an NVE ensemble.

			==Comparison with other techniques==
			The reaction field method is an alternative to the popular technique of [[Ewald summation]]. Today, Ewald summation is the usual technique of choice, but for many quantities of interest both techniques yield equivalent results. For example, in [[Monte Carlo]] simulations of liquid crystals, (using both the [[hard spherocylinder]]<ref>{{cite journal\|last=Gil-Villegas\|first=By Alejandro\|coauthors=McGrother and George Jackson, Simon C.\|title=Reaction-field and Ewald summation methods in Monte Carlo simulations of dipolar liquid crystals\|journal=Molecular Physics\|date=1 November 1997\|volume=92\|issue=4\|pages=723–734\|doi=10.1080/002689797170004\|accessdate=20 May 2012\|bibcode = 1997MolPh..92..723G }}</ref> and Gay-Berne models<ref>{{cite journal\|last=MOHAMMED HOUSSA ABDELKRIM OUALID LU\|title=Reaction field and Ewald summation study of mesophase formation in dipolar Gay-Berne model\|journal=Molecular Physics\|date=1 June 1998\|volume=94\|issue=3\|pages=439–446\|doi=10.1080/002689798167944\|accessdate=20 May 2012}}</ref>) the results from the reaction field method and Ewald summation are consistent. However, the reaction field presents a considerable reduction in the computer time required. The reaction field should be applied carefully, and becomes complicated or impossible to implement for non-isotropic systems, such as systems dominated by large biomolecules or systems with liquid-vapour or liquid-solid coexistence.<ref>[http://dx.doi.org/10.1016/0009-2614(94)01298-9 Benito Garzón, Santiago Lago and Carlos Vega "Reaction field simulations of the vapor-liquid equilibria of dipolar fluids: Does the reaction field dielectric constant affect the coexistence properties?", Chemical Physics Letters '''231''' pp. 366-372 (1994)]</ref>

			In section 5.5.5 of his book, Allen<ref name=allen /> compares the reaction field with other methods, focusing on the simulation of the [[Stockmayer system]] (the simplest model for a dipolar fluid, such as water). The work of Adams, et al. (1979) showed that the reaction field produces results with thermodynamic quantities (volume, pressure and temperature) which are in good agreement with other methods, although pressure was slightly higher with the reaction field method compared to the Ewald-Kornfeld method (1.69 vs 1.52). The results show that macroscopic thermodynamic properties do not depend heavily on how long-range forces are treated. Similarly, single particle correlation functions do not depend heavily on the method employed. Several other results also show that the dielectic constant <math>\epsilon</math> can be well estimated with either the reaction field or a lattice summation technique.<ref name=allen />

			==References==
			{{reflist}}

			==Further reading==
			*[http://dx.doi.org/10.1080/00268978000100361 Martin Neumann and Othmar Steinhauser "The influence of boundary conditions used in machine simulations on the structure of polar systems", Molecular Physics '''39''' pp. 437-454 (1980)]
			*[http://dx.doi.org/10.1080/00268978400101081 Martin Neumann, Othmar Steinhauser and G. Stuart Pawley "Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations", Molecular Physics '''52''' pp. 97-113 (1984)]
			*[http://dx.doi.org/10.1063/1.3081138 Andrij Baumketner "Removing systematic errors in interionic potentials of mean force computed in molecular simulations using reaction-field-based electrostatics", Journal of Chemical Physics '''130''' 104106 (2009)]
			*[http://wanglab.bu.edu/DLPOLY2/node68.html Reaction Field method]

			[[Category:Molecular modelling]]

en>Rcsprinter123: Reverted edits by Rcsprinter123 (talk) to last version by Madcoverboy

2012-06-03T11:56:46Z

Reverted edits by Rcsprinter123 (talk) to last version by Madcoverboy

New page

Hi, everybody! <br>I'm Japanese female :D. <br>I really love Shortwave listening!<br><br>Feel free to surf to my web blog [http://languageclick.co.kr/zbxe/?mid=hrd_qna&amplistStyle=webzine&ampdocument_srl=6103080&document_srl=10776706 laptop deals]