MW model of water: Difference between revisions
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The '''mW''' model <ref>[http://dx.doi.org/10.1021/jp805227c Valeria Molinero and Emily B. Moore "Water Modeled As an Intermediate Element between Carbon and Silicon", Journal of Physical Chemistry B '''113''' pp. 4008-4016 (2009)]</ref> of [[water]] is an atom with tetrahedrality intermediate between [[carbon]] and [[silicon]]. mW mimics the hydrogen-bonded structure of water through the introduction of a nonbond angular dependent term that encourages tetrahedral configurations. | The '''mW''' model <ref>[http://dx.doi.org/10.1021/jp805227c Valeria Molinero and Emily B. Moore "Water Modeled As an Intermediate Element between Carbon and Silicon", Journal of Physical Chemistry B '''113''' pp. 4008-4016 (2009)]</ref> of [[water]] is an atom with tetrahedrality intermediate between [[carbon]] and [[silicon]]. mW mimics the hydrogen-bonded structure of water through the introduction of a nonbond angular dependent term that encourages tetrahedral configurations. The model is given by: | ||
:<math>E = \sum_i \sum_{j>i} \Phi_{ij}(r_{ij}) + \sum_i \sum_{j\neq i} \sum_{k>j} \Phi_{ijk}(r_{ij}, r_{ik}, \theta_{ijk}) </math> | |||
where | |||
:<math> \Phi_{ij}(r_{ij}) = A \epsilon \left[ B \left(\frac{\sigma}{r} \right)^{p}- \left( \frac{\sigma}{r}\right)^q \right] \exp \left( \frac{\sigma}{r- a\sigma} \right)</math> | |||
and | |||
:<math>\Phi_{ijk}(r_{ij}, s_{ik}, \theta_{ijk}) = \lambda \epsilon \left[ \cos \theta - \cos \theta_0 \right]^2 \exp \left( \frac{\gamma \sigma}{r- a\sigma} \right) \exp \left( \frac{\gamma\sigma}{s- a\sigma} \right)</math> | |||
where | |||
<math>A = 7.049556277</math>, <math>B = 0.6022245584</math>, <math>p = 4</math>, <math>q = 0</math>, and <math>\gamma = 1.2</math> | |||
==References== | ==References== | ||
<references/> | <references/> | ||
Revision as of 10:59, 25 June 2010
The mW model [1] of water is an atom with tetrahedrality intermediate between carbon and silicon. mW mimics the hydrogen-bonded structure of water through the introduction of a nonbond angular dependent term that encourages tetrahedral configurations. The model is given by:
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle E=\sum _{i}\sum _{j>i}\Phi _{ij}(r_{ij})+\sum _{i}\sum _{j\neq i}\sum _{k>j}\Phi _{ijk}(r_{ij},r_{ik},\theta _{ijk})}
where
- Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{ij}(r_{ij})=A\epsilon \left[B\left({\frac {\sigma }{r}}\right)^{p}-\left({\frac {\sigma }{r}}\right)^{q}\right]\exp \left({\frac {\sigma }{r-a\sigma }}\right)}
and
![{\displaystyle \Phi _{ijk}(r_{ij},s_{ik},\theta _{ijk})=\lambda \epsilon \left[\cos \theta -\cos \theta _{0}\right]^{2}\exp \left({\frac {\gamma \sigma }{r-a\sigma }}\right)\exp \left({\frac {\gamma \sigma }{s-a\sigma }}\right)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/1d0df148e37c8d07039eb2c3b63f90fa608508ac)
where
, Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle B=0.6022245584} , Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle p=4} , 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 q = 0} , and 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 \gamma = 1.2}
References
Related reading