Carbon Dioxide

Carbon Dioxide (CO2)

The MO Calculations for Carbon Dioxide (CO2)

For Carbon Dioxide, the best calculated bond length was determined from the 6-21G and the 6-31G levels of theory. Both yielded a 1.81% error in comparison to the literature values found on the NIST website.⁵ Therefore, we adopted the 6-21G level for the following calculations.

Table 1: Bond length for all ab initio levels of theory and the literature value.

Theory	Bond length (nm)	Percent error (%)
Literature⁵	.11621	---
6-21G	.116	1.81
6-31G	.116	1.81
DZV	.117	6.80

The geometry of CO₂ under 6-21G, 6-31G, and DZV are shown in Figures 1-3. The bond angles are not shown because the molecule is linear.

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Figure 1: Geometry of CO2 using 6-21G calculation

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Figure 2: Geometry of CO2 using 6-31G calculation

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Figure 3: Geometry of CO2 using DZV calculation

Figure 4 shows the Highest Occupied Molecular Orbital (HOMO); it found at orbital 11 by dividing the sum of the total number of electrons in the molecule by 2. The Lowest Unoccupied Molecular Orbital (LUMO), shown in Figure 5, was found at the next orbital - orbital 12. The LUMO is filled by the excited valence electron(s) from the HOMO if the proper excitation occurs.

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Figure 4: Highest Occupied Molecular Orbital for CO2 using 6-21G calculation

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Figure 5: Lowest Unoccupied Molecular Orbital for CO2 using 6-21G calculation

        Figure 6 shows the electrostatic potential calculated using the 6-21G level of theory. A rainbow colored spectrum is used to distinguish between the lowest potential (red) to the highest potential (blue). The electrostatic potential shows the distribution of electrons in the molecule.⁷

        Figure 7 shows the partial atomic charges for CO₂ using the 6-21G level of theory. The oxygen atoms should have the more negative partial charge because they are more electronegative than carbon.

        Figure 8 and Figure 9 show possible primary motions associated with the peaks in the IR Spectrum shown in Figure 10. Oscillation for CO₂ in Figure 8 is found at 716.99 nm, while bond stretching in Figure 9 is found at 2384.1 nm on the spectrum.

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Figure 6: Electrostatic Potential for CO2 using 6-21G calculation

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Figure 7: Partial Atomic Charge for CO2 using 6-21G calculation

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Figure 8: Oscillation for CO2 using 6-21G calculation

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Figure 9: Bond Stretch for CO2 using 6-21G calculation

You can find this image at http://webbook.nist.gov/cgi/cbook.cgi?ID=C124389&Type=IR-SPEC&Index=1#IR-SPEC

Figure 10: Infrared Spectrum for Carbon Dioxide.

Because CO₂ is a non-polar moleculre, our calculations gave us 0.0 Db for a dipole moment.

Based on template by A. Herráez as modified by J. Gutow

Page skeleton and JavaScript generated by export to web function using Jmol 14.2.12_2015.01.22 2015-01-22 21:48 on Mar 3, 2015.

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