Di-Nitrogen Results
Figure 1: Geometry optimization of N2 using DZV basis set. The optimized bond length was calculated to be 1.10Ǟ at this basis set.
Geometry Results

The geometry of N2 was calculated using several basis sets. Of the basis sets used, Double Zeta Valence (DZV) was chosen as the most optimal geometry configuration since those calculations resulted in the lowest energy, which correlates to the most accurate representation of the actual molecule. Below is a comparison of the bond lengths and calculated energies calculated by other basis sets and literature values is shown.

Comparison of Bond Lengths of Di-nitrogen for Varying Basis Set Calculations and Comparison to Literature Values.
Basis Set Calculated Length (Ǟ)
AMI
 1.12
6-21G 1.08
6-31G 1.09
DZV
 1.10
Literature1
 1.0975 ±0.0008

From Table 1, one can see that the DZV optimization resulted in a bond length that had the smallest difference from the literature value; however the DZV value is not within the error of the literature value. To gain a more accurate value, a basis set with higher computations should be used.
 
Vibrational1

At the DZV theory level, the vibrational frequency of N2 was calculated as 2590.35cm-1 and literature values place the vibrational frequency of N2 to be 2359cm-1 .

To see an animation of molecular vibrational states, click here.
Potential Energy of Bond Stretching


Below is a graph showing the potential energy of bond stretching for a N2 molecules at different basis sets. It is easily seen that the higher the basis set, the better the calculated bond length. The red line shows that the DZV calculations resulted in the lowest energy value, thus meaning it is the most accurate basis set to use when determining the potential energy of bond length.
Molecular Orbitals2

The valence energy level diagram for dinitrogen, which is shown below, shows the bonding model for the valence eletrons around the two nitrogen atoms. The different labels for the molecular orbitals denotes the type of bond formed. The letter and number denote which orbital and energy level the valence shell is located, and simply, a sigma (σ) denotes a sigma bond, and pi (π) bond. Electrons are placed inside the molecular orbital diagram starting from lowest energy and following electron filling procedures.

After filling the molecular orbitals, there are some orbitals left unfilled. The difference between the last filled and the first filled orbital leads to the HOMO and LUMO terms, respectively. Highest Occupied Molecular Orbital (HOMO) and Lowest Unoccupied Molecular Orbital (LUMO) transitions are highly studied to better understand molecular properties.

To see the HOMO and LUMO states, click here.
Figure 2: A cartoon of the valence energy level diagram for di-nitrogen.
It is easily shown how the 2s and 2p orbitals split to form the 8 molecular orbitals.2


References:
(1) Weast, Robert C., Melvin J. Astle, and William H. Beyer. "Element Properties." CRC Handbook of Chemistry and Physics: A Ready-reference Book of Chemical and Physical Data. 60th ed.        Boca Raton, FL: CRC, 1984. N. pag. Print.

(2) "Molecular Orbitals - Energy Diagrams of N2 and O2." Molecular Orbitals -. N.p., n.d. Web. 03 Mar. 2013.






HOME



Based on template by A. Herráez as modified by J. Gutow
Page skeleton and JavaScript generated by export to web function using Jmol 13.0.12 2013-01-23 21:55 on Feb 25, 2013.