Diatomic Oxygen

Diatomic Oxygen

When applying the basis sets to diatomic oxygen, two different electron configurations were available; singlet and triplet. The triplet state always appeared to yield the lowest energy geometries of the diatom, and was continually used and referenced throughout the course of later calculations.

Molecular geometry optimizations were calculated for diatomic oxygen using several different basis sets. The first and most basic basis set was AM1, a MOPAC2 semi-empirical method. This optimization can be visualized using the button below.

AM1 Basis Set:

The next three molecular geometry optimizations were calculated on diatomic oxygen using ab initio methods.

6-21G Basis Set:

The 6-21G basis set was calculated from AM1 results.

6-31 Basis Set:

The 6-31G basis set was calculated from the 6-21G results.

Double Zeta Valence Basis Set:

The DZV basis set was calculated from the 6-31G results.

The DZV set, as seen above, gave a bond length of 1.21 Å. This value was the closest approximation to the experimental bond length found, which was 1.208 Å.1

There are two HOMO orbitals in triplet diatomic oxygen both identical, yet orthogonal to each other with respect to the linearity of the molecule. The two buttons below iterate the orthogonality of the two HOMO states with respect to each other. Observing the animation shows that this orbital is a bonding orbital as the occupied region is shared between the nuclei.

HOMO Orbital 1:

HOMO orbital calculated from the DZV basis set.

HOMO Orbital 2:

HOMO orbital calculated from the DZV basis set.

The LUMO state of the diatom is an antibonding orbital.

LUMO Orbital:

LUMO orbital calculated from the DZV basis set.

There was only one available mode of vibration for the diatomic oxygen molecule.

Vibrational Frequency:

Vibrational frequency calculated from DZV basis set.

The valence energy levels of diatomic oxygen were calculated using the DZV basis set. Diagrams of these energy levels can be seen below in Table 1.

Table 1: Valence Energy Level Diagram for Diatomic Oxygen
Energy (a.u.)	Bond Type	Molecular Orbital Diagram (from DZV)
-20.7604	Bonding
-20.7598	Anti-bonding
-1.761	Bonding
-1.2029	Anti-Bonding
-0.857	Bonding
-0.857	Bonding
-0.7544	Bonding
-0.5715	Anti-bonding
-0.5715	Anti-bonding
0.3561	Anti-bonding
0.7458	Bonding
0.7458	Bonding
0.7935	Anti-bonding
0.8415	Anti-bonding
0.8512	Anti-bonding
0.8512	Anti-bonding
1.2101	Bonding
1.8882	Anti-bonding

A plot of the potential energy of bond stretching for the three ab initio calculations can be seen below in Figure 1. The three basis sets gave nearly identical values for the potential energy, but the 6-21G basis set had the lowest energy initially.

Figure 1: Potential energy of bond stretching of diatomic oxygen for the three ab initio calculations

References

1. Lide D. R., Kehiaian, H.V. CRC Handbook of Chemistry and Physics Data,

CRC Press, Boca Raton, FL, 1992, p F-217.

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