Carbon dioxide

<jmol> <jmolApplet> <script>set spin X 10; spin on</script> <size>200</size> <color>lightgrey</color> <wikiPageContents>carbon_dioxide.pdb</wikiPageContents> </jmolApplet> </jmol>

Carbon dioxide

Carbon dioxide (CO₂)

Models

BBV

The BBV (Bock, Bich and Vogel) model .

EPM

The elementary physical model (EPM) and EPM2 of Harris and Yung 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)	$\epsilon _{C-C}/k_{B}$ (K)	$\sigma _{O-O}$ (Å)	$\epsilon _{O-O}/k_{B}$ (K)	$\sigma _{C-O}$ (Å)	$\epsilon _{C-O}/k_{B}$ (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 .

Merker, Engin, Vrabec and Hasse

The Merker, Engin, Vrabec and Hasse model consists of three 12-6 Lennard-Jones sites along with a point quadrupole ($Q=4.0739$ DÅ) placed on the carbon site. The model is given by $r_{\mathrm {OC} }$ = 1.2869 Å, $\sigma _{C}=$ 2.8137 Å $\epsilon _{C}/k_{B}=$ 12.3724 K and $\sigma _{O}=$ 2.9755 Å, $\epsilon _{O}/k_{B}=$ 100.493 K.

Murthy, Singer and McDonald

Murthy, Singer and McDonald proposed four models , 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.

MYVPBMM

The Mognetti et al. model is a coarse–grained model having either explicit (point) quadrupolar interactions or spherically averaged quadrupolar interactions, in conjunction with a single 12-6 Lennard-Jones site.

Oakley and Wheatley

The Oakley and Wheatley (OW) model .

SAPT-s

SAPT (symmetry-adapted perturbation theory) .

SYM

The SYM model .

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 . 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.

Zhang and Duan

Parameters for CO₂ for the Zhang and Duan model are C having $\epsilon /k_{B}=28.845$K and $\sigma =2.7918$Å with a partial charge of 0.5888 e, and O having $\epsilon /k_{B}=82.656$K and $\sigma =3.00$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 Lorentz-Berthelot combining rules.

References

Related reading

• 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)
• R. Eggenberger, S. Gerber, and H. Huber "The carbon dioxide dimer", Molecular Physics 72 pp. 433-439 (1991)

External resources

• 3D phase diagram of carbon dioxide