Carbon dioxide: Difference between revisions

Revision as of 14:11, 26 May 2014

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Carbon dioxide

Carbon dioxide (CO₂)

Models

BBV

The BBV (Bock, Bich and Vogel) model ^[1].

EPM

The elementary physical model (EPM) and EPM2 of Harris and Yung ^[2] consists of 12-6 Lennard-Jones sites in conjunction with partial charges centred on each of these sites.

Model	$r_{\mathrm {OC} }$ (Å)	$k_{\theta }$ kJ/mol/rad²	$\sigma _{C-C}$ (Å)	$\epsilon _{C-C}/K$ (K)	$\sigma _{O-O}$ (Å)	$\epsilon _{O-O}/K$ (K)	$\sigma _{C-O}$ (Å)	$\epsilon _{C-O}/K$ (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

\Phi _{bend}(\theta )={\frac {1}{2}}k_{\theta }\left(\theta -\theta _{0}\right)^{2}

where $\theta _{0}=180$ degrees.

GCPCDO

Gaussian charge polarizable carbon dioxide (GCPCDO) model ^[3].

Murthy, Singer and McDonald

Murthy, Singer and McDonald proposed four models ^[4], two models (A1 and A2) consisting of two 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 Lorentz-Berthelot combining rules for the C-O interactions .

Oakley and Wheatley

The Oakley and Wheatley (OW) model ^[5].

SAPT-s

SAPT (symmetry-adapted perturbation theory) ^[6].

SYM

The SYM model ^[7]^[8].

TraPPE

Parameters for CO₂ for use in the TraPPE force field are C having $\epsilon /k_{B}=27.0$ K and $\sigma =2.80$ Å with a partial charge of 0.70 e, and O having $\epsilon /k_{B}=79.0$ K and $\sigma =3.05$ Å with a partial charge of -0.35 e ^[9]. 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 Lorentz-Berthelot combining rules.

References

Related reading

External resources

3D phase diagram of carbon dioxide

[1] 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)

[2] 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)

[3] Rasmus A. X. Persson "Gaussian charge polarizable interaction potential for carbon dioxide", Journal of Chemical Physics 134 034312 (2011)

[4] C. S. Murthy, K. Singer, and I. R. McDonald "Interaction site models for carbon dioxide", Molecular Physics 44 pp. 135-143 (1981)

[5] 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)

[6] 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)

[7] 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)

[8] 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)

[9] 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)

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@@ Line 5: / Line 5: @@
 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====
-A series of popular models for CO<sub>2</sub> are those 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>, namely the '''EPM Rigid''', the '''EPM Flexible''' and the '''EPM2''' models.
+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>.