Editing Carbon dioxide

{{Jmol_general|carbon_dioxide.pdb|Carbon dioxide}}
'''Carbon dioxide''' (CO<sub>2</sub>)
==Models==
====BBV====
The BBV (Bock, Bich and Vogel) model <ref>[http://dx.doi.org/10.1016/S0301-0104(00)00161-0  S. Bock, E. Bich and E. Vogel "A new intermolecular potential energy surface for carbon dioxide from ab initio calculations", Chemical Physics '''257''' pp. 147-156 (2000)]</ref>.
====EPM====
The elementary physical model (EPM) and EPM2 of  Harris and Yung <ref>[http://dx.doi.org/10.1021/j100031a034 Jonathan G. Harris and Kwong H. Yung "Carbon Dioxide's Liquid-Vapor Coexistence Curve And Critical Properties as Predicted by a Simple Molecular Model", Journal of Physical Chemistry '''99''' pp. 12021-12024 (1995)]</ref>
consists of [[Lennard-Jones model | 12-6 Lennard-Jones sites]] in conjunction with partial charges centred on each of these sites.

{| style="width:80%; height:100px" border="1"
|- 
| Model || <math>r_{\mathrm {OC}}</math> (&Aring;)||  <math>k_{\theta}</math>  kJ/mol/rad<sup>2</sup> ||<math>\sigma_{C-C}</math> (&Aring;)|| <math>\epsilon_{C-C}/K</math> (K)||<math>\sigma_{O-O}</math> (&Aring;)|| <math>\epsilon_{O-O}/K</math> (K)||<math>\sigma_{C-O}</math> (&Aring;)|| <math>\epsilon_{C-O}/K</math> (K)|| q(O) (e) || q(C) (e) 
|- 
| EPM  || 1.161  || 1275 ||  2.785 || 28.999 || 3.064 || 82.997 || 2.921 || 49.060  ||  -0.33225 || +0.6645 
|- 
| EPM2 || 1.149  || 1236 ||  2.757 || 28.129 || 3.033 || 80.507 || 2.892 || 47.588  ||  -0.32560 || +0.6512 
|}

The bond bending potential is given by 
:<math>
\Phi_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2 
</math>
where <math>\theta_0 = 180</math> degrees.

====GCPCDO====
Gaussian charge polarizable carbon dioxide (GCPCDO) model <ref>[http://dx.doi.org/10.1063/1.3519022 Rasmus A. X. Persson "Gaussian charge polarizable interaction potential for carbon dioxide", Journal of Chemical Physics '''134''' 034312 (2011)]</ref>.
====Murthy, Singer and McDonald====
Murthy, Singer and McDonald proposed four models <ref>[http://dx.doi.org/10.1080/00268978100102331 C. S. Murthy, K. Singer, and I. R. McDonald "Interaction site models for carbon dioxide", Molecular Physics '''44''' pp. 135-143 (1981)]</ref>, two models (A1 and A2) consisting of two [[Lennard-Jones model | 12-6 Lennard-Jones sites]] located roughly on the [[oxygen]] atoms, plus a point quadrupole located at the molecular centre of mass. Model B differed from models A1 and A2 in the use of the [[9-6 Lennard-Jones potential]], and model C was a three site model using the [[Combining rules#Lorentz-Berthelot rules| Lorentz-Berthelot combining rules]] for the C-O interactions.
====MYVPBMM====
The Mognetti ''et al.'' model <ref>[http://dx.doi.org/10.1063/1.2837291  B. M. Mognetti, L. Yelash, P. Virnau, W. Paul, K. Binder, M. Müller, and L. G. MacDowell "Efficient prediction of thermodynamic properties of quadrupolar fluids from simulation of a coarse-grained model: The case of carbon dioxide", Journal of Chemical Physics '''128''' 104501 (2008)]</ref>
<ref>[http://dx.doi.org/10.1080/00268970902755025 B. M. Mognetti,  M. Oettel, P. Virnau,  L. Yelash, and K. Binder "Structure and pair correlations of a simple coarse grained model for supercritical carbon dioxide",  Molecular Physics '''107''' pp. 331-341 (2009)]</ref>
is a [[Coarse graining|coarse–grained]] model having either explicit (point)
quadrupolar interactions or spherically averaged quadrupolar interactions, in conjunction with a  single [[Lennard-Jones model | 12-6 Lennard-Jones site]].
====Oakley and  Wheatley====
The Oakley and  Wheatley (OW) model <ref>[http://dx.doi.org/10.1063/1.3059008  Mark T. Oakley and Richard J. Wheatley "Additive and nonadditive models of vapor-liquid equilibrium in CO2 from first principles", Journal of Chemical Physics '''130''' 034110 (2009)]</ref>.
====SAPT-s====
SAPT (symmetry-adapted perturbation theory) <ref>[http://dx.doi.org/10.1063/1.479108  Robert Bukowski, Joanna Sadlej, Bogumil Jeziorski, Piotr Jankowski, Krzysztof Szalewicz, Stanislaw A. Kucharski, Hayes L. Williams, and Betsy M. Rice "Intermolecular potential of carbon dioxide dimer from symmetry-adapted perturbation theory", Journal of Chemical Physics '''110''' pp. 3785- (1999)]</ref>.
====SYM====
The SYM model <ref>[http://dx.doi.org/10.1021/jp204563n Kuang Yu, Jesse G. McDaniel, and J. R. Schmidt "Physically Motivated, Robust, ab Initio Force Fields for CO2 and N2", Journal of Physical Chemistry B '''115''' pp. 10054-10063 (2011)]</ref><ref>[http://dx.doi.org/10.1063/1.3672810 Kuang Yu and J. R. Schmidt "Many-body effects are essential in a physically motivated CO2 force field", Journal of Chemical Physics  '''136''' 034503 (2012)]</ref>.
====TraPPE====
Parameters for CO<sub>2</sub> for use in the [[TraPPE force field]] are C having <math>\epsilon/k_B= 27.0</math>K and <math>\sigma = 2.80</math>&Aring; with a partial charge of 0.70 e, and O having <math>\epsilon/k_B= 79.0</math>K and <math>\sigma = 3.05</math>&Aring; with a partial charge of -0.35 e  <ref>[http://dx.doi.org/10.1002/aic.690470719 Jeffrey J. Potoff and J. Ilja Siepmann "Vapor–liquid equilibria of mixtures containing alkanes, carbon dioxide, and nitrogen", AIChE Journal '''47''' pp. 1676-1682 (2001)]</ref>. The molecular geometry is rigid, linear, with a C-C bond length set at the experimental value of 1.16  &Aring;. Unlike interactions use the [[Combining rules#Lorentz-Berthelot rules| Lorentz-Berthelot combining rules]].
====Zhang and Duan====
Parameters for CO<sub>2</sub> for the Zhang and Duan model
<ref>[http://dx.doi.org/10.1063/1.1924700 Zhigang Zhang and Zhenhao Duan "An optimized molecular potential for carbon dioxide", Journal of Chemical Physics '''122'''  214507 (2005)]</ref>
<ref>[http://dx.doi.org/10.1063/1.2965899 Thorsten Merker, Jadran Vrabec, and Hans Hasse "Comment on “An optimized potential for carbon dioxide”", Journal of Chemical Physics '''129''' 087101 (2008)]</ref>
<ref>[http://dx.doi.org/10.1063/1.2965900 Zhigang Zhang and Zhenhao Duan "Response to "Comment on 'An optimized potential for carbon dioxide' "", Journal of Chemical Physics '''129''' 087102 (2008)]</ref>
are C having <math>\epsilon/k_B= 28.845</math>K and <math>\sigma = 2.7918</math>&Aring; with a partial charge of 0.5888 e, and O having <math>\epsilon/k_B= 82.656</math>K and <math>\sigma = 3.00</math>&Aring; with a partial charge of -0.2944 e. The molecular geometry is rigid, linear, with a C-C bond length set at the experimental value of 1.163  &Aring;. Unlike interactions use the [[Combining rules#Lorentz-Berthelot rules| Lorentz-Berthelot combining rules]].

==Phase diagram==
<ref>[http://www.jce.divched.org/Journal/Issues/2002/Jul/abs874.html L. Glasser "Equations of state and phase diagrams",   Journal of Chemical Education '''79''' 874 (2002)]</ref>
<ref>[http://jchemed.chem.wisc.edu/journal/issues/2009/May/abs566.html  A. Herráez, R. M. Hanson, and L. Glasser "Interactive 3D phase diagrams using Jmol" Journal of Chemical Education '''86''': 566 (2009)] and [http://biomodel.uah.es/Jmol/plots/phase-diagrams/ website]</ref>
<ref>[http://dx.doi.org/10.1063/1.4792443   G. Pérez-Sánchez, D. González-Salgado, M. M. Piñeiro, and C. Vega "Fluid-solid equilibrium of carbon dioxide as obtained from computer simulations of several popular potential models: The role of the quadrupole", Journal of Chemical Physics '''138''' 084506 (2013)]</ref>
==Transport properties==
<ref>[http://dx.doi.org/10.1063/1.4896538  C. G. Aimoli, E. J. Maginn and C. R. A. Abreu "Transport properties of carbon dioxide and methane from molecular dynamics simulations", Journal of Chemical Physics '''141''' 134101 (2014)]</ref>
<ref>[http://dx.doi.org/10.1063/1.4896965 Thuat T. Trinh, Thijs J. H. Vlugt and Signe Kjelstrup "Thermal conductivity of carbon dioxide from non-equilibrium molecular dynamics: A systematic study of several common force fields", Journal of Chemical Physics '''141''' 134504 (2014)]</ref>

==References==
<references/>
'''Related reading'''
*[http://dx.doi.org/10.1063/1.1680756 Trevor G. Gibbons and Michael L. Klein "Thermodynamic properties for a simple model of solid carbon dioxide: Monte Carlo, cell model, and quasiharmonic calculations", Journal of Chemical Physics '''60''' pp. 112-126 (1974)]
*[http://dx.doi.org/10.1080/00268979100100341  R. Eggenberger, S. Gerber, and H. Huber "The carbon dioxide dimer", Molecular Physics '''72''' pp. 433-439 (1991)]
*[http://dx.doi.org/10.1063/1.4974995 Robert Hellmann "Nonadditive three-body potential and third to eighth virial coefficients of carbon dioxide", Journal of Chemical Physics '''146''' 054302 (2016)]

==External resources==
*[http://biomodel.uah.es/Jmol/plots/phase-diagrams/ 3D phase diagram of carbon dioxide]
[[category: models]]
[[category:phase diagrams]]
[[category: Contains Jmol]]
{{Numeric}}
@@ Line 10: / Line 10: @@
 {| style="width:80%; height:100px" border="1"
 |-
-| Model || <math>r_{\mathrm {OC}}</math> (&Aring;)||  <math>k_{\theta}</math>  kJ/mol/rad<sup>2</sup> ||<math>\sigma_{C-C}</math> (&Aring;)|| <math>\epsilon_{C-C}/k_B</math> (K)||<math>\sigma_{O-O}</math> (&Aring;)|| <math>\epsilon_{O-O}/k_B</math> (K)||<math>\sigma_{C-O}</math> (&Aring;)|| <math>\epsilon_{C-O}/k_B</math> (K)|| q(O) (e) || q(C) (e)
+| Model || <math>r_{\mathrm {OC}}</math> (&Aring;)||  <math>k_{\theta}</math>  kJ/mol/rad<sup>2</sup> ||<math>\sigma_{C-C}</math> (&Aring;)|| <math>\epsilon_{C-C}/K</math> (K)||<math>\sigma_{O-O}</math> (&Aring;)|| <math>\epsilon_{O-O}/K</math> (K)||<math>\sigma_{C-O}</math> (&Aring;)|| <math>\epsilon_{C-O}/K</math> (K)|| q(O) (e) || q(C) (e)
 |-
 | EPM  || 1.161  || 1275 ||  2.785 || 28.999 || 3.064 || 82.997 || 2.921 || 49.060  ||  -0.33225 || +0.6645
@@ Line 25: / Line 25: @@
 ====GCPCDO====
 Gaussian charge polarizable carbon dioxide (GCPCDO) model <ref>[http://dx.doi.org/10.1063/1.3519022 Rasmus A. X. Persson "Gaussian charge polarizable interaction potential for carbon dioxide", Journal of Chemical Physics '''134''' 034312 (2011)]</ref>.
-====Merker,  Engin,  Vrabec and  Hasse====
-The Merker,  Engin,  Vrabec and  Hasse model
-<ref>[http://dx.doi.org/10.1063/1.3434530  Thorsten Merker, Cemal Engin, Jadran Vrabec and Hans Hasse "Molecular model for carbon dioxide optimized to vapor-liquid equilibria", Journal of Chemical Physics '''132''' 234512 (2010)] </ref>
-consists of three [[Lennard-Jones model | 12-6 Lennard-Jones sites]] along with a point quadrupole (<math>Q=4.0739</math> D&Aring;) placed on the carbon site. The model is given by
-<math>r_{\mathrm {OC}}</math>  = 1.2869 &Aring;, <math>\sigma_{C}=</math> 2.8137 &Aring; <math>\epsilon_{C}/k_B=</math> 12.3724 K and <math>\sigma_{O}=</math> 2.9755 &Aring;, <math>\epsilon_{O}/k_B=</math> 100.493 K.
 ====Murthy, Singer and McDonald====
 Murthy, Singer and McDonald proposed four models <ref>[http://dx.doi.org/10.1080/00268978100102331 C. S. Murthy, K. Singer, and I. R. McDonald "Interaction site models for carbon dioxide", Molecular Physics '''44''' pp. 135-143 (1981)]</ref>, two models (A1 and A2) consisting of two [[Lennard-Jones model | 12-6 Lennard-Jones sites]] located roughly on the [[oxygen]] atoms, plus a point quadrupole located at the molecular centre of mass. Model B differed from models A1 and A2 in the use of the [[9-6 Lennard-Jones potential]], and model C was a three site model using the [[Combining rules#Lorentz-Berthelot rules| Lorentz-Berthelot combining rules]] for the C-O interactions.