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| {{Jmol_general|carbon_dioxide.pdb|Carbon dioxide}}
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| '''Carbon dioxide''' (CO<sub>2</sub>)
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| ==Models==
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| ====BBV====
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| 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>.
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| ====EPM====
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| 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>
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| consists of [[Lennard-Jones model | 12-6 Lennard-Jones sites]] in conjunction with partial charges centred on each of these sites.
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|
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| {| style="width:80%; height:100px" border="1"
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| | Model || <math>r_{\mathrm {OC}}</math> (Å)|| <math>k_{\theta}</math> kJ/mol/rad<sup>2</sup> ||<math>\sigma_{C-C}</math> (Å)|| <math>\epsilon_{C-C}/k_B</math> (K)||<math>\sigma_{O-O}</math> (Å)|| <math>\epsilon_{O-O}/k_B</math> (K)||<math>\sigma_{C-O}</math> (Å)|| <math>\epsilon_{C-O}/k_B</math> (K)|| q(O) (e) || q(C) (e)
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| |-
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| | EPM || 1.161 || 1275 || 2.785 || 28.999 || 3.064 || 82.997 || 2.921 || 49.060 || -0.33225 || +0.6645
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| | EPM2 || 1.149 || 1236 || 2.757 || 28.129 || 3.033 || 80.507 || 2.892 || 47.588 || -0.32560 || +0.6512
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| |}
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|
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| The bond bending potential is given by
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| :<math>
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| \Phi_{bend}(\theta) = \frac{1}{2} k_{\theta} \left( \theta - \theta_0 \right)^2
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| </math>
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| where <math>\theta_0 = 180</math> degrees.
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|
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| ====GCPCDO====
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| 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>.
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| ====Merker, Engin, Vrabec and Hasse====
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| The Merker, Engin, Vrabec and Hasse model
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| <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>
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| consists of three [[Lennard-Jones model | 12-6 Lennard-Jones sites]] along with a point quadrupole (<math>Q=4.0739</math> DÅ) placed on the carbon site. The model is given by
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| <math>r_{\mathrm {OC}}</math> = 1.2869 Å, <math>\sigma_{C}=</math> 2.8137 Å <math>\epsilon_{C}/k_B=</math> 12.3724 K and <math>\sigma_{O}=</math> 2.9755 Å, <math>\epsilon_{O}/k_B=</math> 100.493 K.
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| ====Murthy, Singer and McDonald====
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| 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.
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| ====MYVPBMM====
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| 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>
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| <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>
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| is a [[Coarse graining|coarse–grained]] model having either explicit (point)
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| quadrupolar interactions or spherically averaged quadrupolar interactions, in conjunction with a single [[Lennard-Jones model | 12-6 Lennard-Jones site]].
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| ====Oakley and Wheatley====
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| 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>.
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| ====SAPT-s====
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| 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>.
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| ====SYM====
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| 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>.
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| ====TraPPE====
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| 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>Å 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>Å 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 Å. Unlike interactions use the [[Combining rules#Lorentz-Berthelot rules| Lorentz-Berthelot combining rules]].
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| ====Zhang and Duan====
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| Parameters for CO<sub>2</sub> for the Zhang and Duan model
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| <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>
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| <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>
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| <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>
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| are C having <math>\epsilon/k_B= 28.845</math>K and <math>\sigma = 2.7918</math>Å 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>Å 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 Å. Unlike interactions use the [[Combining rules#Lorentz-Berthelot rules| Lorentz-Berthelot combining rules]].
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|
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| ==Phase diagram==
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| <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>
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| <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>
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| <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>
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| ==Transport properties==
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| <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>
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| <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>
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| ==References== | | ==References== |
| <references/>
| | #[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)] |
| '''Related reading'''
| | #[http://dx.doi.org/10.1080/00268979100100341 Rolf Eggenberger, Stefan Gerber and Hanspeter Huber "The carbon dioxide dimer", Molecular Physics '''72''' pp. 433 - 439 (1991)] |
| *[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)]
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| *[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)]
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| *[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)]
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| ==External resources==
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| *[http://biomodel.uah.es/Jmol/plots/phase-diagrams/ 3D phase diagram of carbon dioxide]
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| [[category: models]] | | [[category: models]] |
| [[category:phase diagrams]]
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| [[category: Contains Jmol]]
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| {{Numeric}}
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