Molecular Orbital Calculations

Molecular Orbital Calculations of Potassium Oxide (KO)

This page contains the optimized geometry, HOMO and LUMO orbital representations, molecular electrostatic potential and the partial atomic charges of this potassium oxide molecule. Each calculation or representation is based upon the data gathered from the JMol, MacMolPlt and GAMESS software.


	Basic representation of KO molecule. The length between the two atoms is 2.47 Angstroms.

The picture at the right represents a basic model of Potassium Oxide (KO). The length between the two molecules is approximately 2.47 Angstroms. The purple molecule represents Potassium, as it has a larger molecular mass, as the red molecule represents oxygen.


	Pictoral representation of the electrostatic potential between potassium and oxygen. The red represents higher electrostatic potential, the blue represents a lower electrostatic potential.

The picture to the left is a representation of the electrostatic potential of KO. Electrostatic potential directly correlates to the electronegativity of each atom. The red corresponds to a negative electrostatic potential meaning that the attraction of a proton is greater because it is concentrated around a higher electron density, or the ability to attract electrons.Electron density is also in which it notes which molecular orbitals are occupied.² Hence, the blue corresponds to a weaker proton attraction and a positive electrostatic potential.


	Pictoral representation of the LUMO orbital of KO.

The picture to the right is a display of the LUMO orbitals of KO.


	Basic graphical representation of the HOMO orbitals of KO.

This picture highlights the HOMO orbital in comparison to the LUMO as shown above. The HOMO is based upon the number of electrons in the molecule. For this particular case the HOMO is calculated by dividing the total number of electrons (19+8=27) divided by the total number of atoms (2) which equals 14.


	Display of the partial atomic charges of both oxygen and potassium in KO. The partial atomic charge of K is 0.9524 and that of O is -0.9522.

The partial atomic charges are displayed in the figure to the right. Due to the fact that KO is basically a nonexistent molecule, there is no bond between K and O. Therefore each partial atomic charge is nearly 1.

Figure 1: Plot of Potential Energy versus bond stretching for KO in Hartrees vs Angstroms. The results vary with the basis set size as the 3-21G is the value in between TZV and STO-3G.

The graph of potential energy versus bond stretching is very similar to the expected result of the graph. The dipole moments of the 3-21G calculations were a median range between the TZV and the STO-3G calculations. This then helps to explain the trend of the potential energy curve respectively. The plot however, is dissimilar to other potential energy plots for various reasons. Primarily, due to the lack of ability to perform the 6-31G, 6-21G and the DZV calculations based on the propeties of KO, the resultant curve is different than other diatomic potential energy versus bond stretching graphs.

Figure 2: Pictoral representation of valence electron energy diagram of KO. Levels are 2sigma (bonding) 2pi bonding, 2pi antibonding and 2sigma antibonding. There are 5 valence electrons of KO indicating that electrons occupy the 2sigma, and 2pi orbitals.

Table 1: Experimental values for the Dipole Moments of KO. KO rarely exists naturally therefore no literature value was found.

	TZV	STO-3G	3-21G	MINI	AM1	PM3
Dx	8.862614	-0.536175	7.166588	-0.0400584	0.008608	0.008171
Dy	-2.929484	0.182247	-2.435939	0.013795	1.02681	1.027852
Dz	-.345739	0.213430	-2.852742	0.016155	1.529298	1.451647
\|D\|	9.952694	0.605186	8.0890000	0.045808	1.873772	1.778714

KO is a molecule that rarely occurs naturally and therefore there is a very weak, if any, bond between the potassium and the oxygen. No literature was found for the dipole moments of KO. However, the values calculated from the AM1 and the PM3 runs are the most accurate in relevance to the literature data. This can be concluded because using both water and phenol as a reference, the values from these runs were closest to those that would have been found on NIST.

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

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