Difluromethane

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Nitric Oxide

The geometry optimizations for the three highest levels of theory are shown below. The bond angle is not included because it is 180 degrees. The literature³ value of 1.0619 angstroms for bond length was most closely found by the 6-31G level of theory which gave an error of 10.2%.

6-21G was the lowest level of theory used for the geometry optimization.

6-31G was the next highest level of theory used for the geometry optimization. This proved to be the best level of theory for geometry optimization as the value came closest to the the literature³ value of 1.0619 angstroms.

DZV was the highest level of theory used to determine geometry optimization.

This is the highest occupied molecular orbital at orbital 8. The orbitals were calculated by summing the amount of electrons in the molecule and dividing by two. In this case the result was a half-integer so the value was rounded up.

This is the lowest unoccupied molecular orbital at orbital 9. This would become occupied if the molecule was excited with the proper amount of energy.

This is the electrostatic potential of the molecule. The red area represents the lowest electrostatic potential and blue represents the highest electrostatic potential. Intermediate colors represent intermediate potentials.

The partial atomic charge on each atom is shown in this diagram. They are created by the asymmetric distribution of electrons in a chemical bond.

Table 1 shows the different orbitals for the NO molecule starting with the S bonding orbitals and going down to the highest energy orbital. The two P orbitals represent the p_x and p_y orbitals that contribute to pi bonding.

Table 1: Orbitals corresponding to the type of bonding occurring at that level.

Type of Bonding	Orbital
S sigma bonding
S sigma anti-bonding
P bonding
P anti-bonding
P² bonding
P² anti-bonding

The following graph, figure 1, shows the different potential energies of bond stretching at different levels of theory. The higher the level of theory the lower in energy the theory calculates for the lowest potential energy. The "bump" as the potential energy comes out of the well is due to interactions between the electrons that are not accounted for in the theories. The experimental graph for the potential energy would not have these "bumps."

Figure 1: Potential energy curves at different levels of theory. Note the "bumps" as the curve comes out of the well. This graph was generated by IGOR.

The final calculated value for the vibrational frequency using DZV theory came out to be 1158.13 cm^-1. The NIST website³ for nitric oxide gave a value of 1904 cm^-1, which is a percentage error of 39%.

The molecules were calculated at the different levels of theory to determine their dipole moments. They were then compared to the literature value found on NIST website of .153 debyes. The calculated results are shown in table 2.

Table 2: Calculated dipole moments using different levels of theory. The percent error was based off the literature value of .153 debyes.

Theory	Dipole Moment in Debyes (Db)	Percent error (%)
AM1	.090731	40.7
6-21G	.321852	110.4
6-31G	.131573	14.0
DZV	.136853	10.6

As can be seen in the table the higher level of theory gives the best calculated dipole moment. The 6-21G error should not have been larger than the AM1 theory and could be due to starting from the incorrect guess. The factor then that leads to better dipole moments is that the higher theories user progressively larger basis sets.

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

Page skeleton and JavaScript generated by export to web function using Jmol 14.1.8 2014-02-10 21:43: on Mar 4, 2014.

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