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Nitric Oxide (NO)

This page contains live displays of various geometry optimizations, molecular orbitals, and electrostatic potential, as well as other molecular information for the NO diatomic molecule.

Geometry optimizations were performed at different levels of theory, yielding slight variations in bond lengths and energies.

Bond lengths for different levels of theory

Level of Theory	Length (Angstrom)
AM1	1.16
PM3	1.11
621-G	1.21
631-G	1.17
DZV	1.20
Experimental¹	1.154

Click the button below to view the NO 621-G geometry optimization.

Click the button below to view the NO 631-G geometry optimization.

Click the button below to view the NO DZV geometry optimization.

The geometry optimization from the double zeta valence (DZV) geometry optimization was selected as the best model. The DZV optimization is made from the highest level of theory, and therefore the largest basis set, so it is expected to give the best model. This assumption is supported by the dipole moment data and the plot of potential bond stretching energy, although not entirely by the calculated bond lengths.
As can be seen in the table above, the bond length given by the DZV model is further from the experimental value than the 631-G model. However, the dipole moment results from the DZV model are better than those of the 631-G model. Additionally, and most importantly for determining the best model, the potential energy of bond stretching (shown below) is the lowest for DZV basis set. It is known that the lowest potential energy calculated will give the best model because of the variation principle: "If an arbitrary wavefunction is used to calculate the energy, the value calculated is never less than the true energy."²

Dipole moments

Level of Theory	Dipole Moment (Debye)
Experimental¹	0.159
621-G	0.322
631-G	0.389
DZV	0.331

Note that in the table of dipole moments, the values from all three levels of theory are quite high in comparison to the experimental value. While 621-G (a lower basis set) has a slightly closer value for the dipole moment than DZV, it is not significantly so in comparison to the overall margin of error. In general, larger basis sets will give dipole moments closer to the experimental values.

Dipole moments from diffuse functions of DZV basis set

# D Heavy Atoms	# F Heavy Atoms	# Light Atoms	Dipole Moment (D)
1	1	1	.211746
2	1	1	.136853
2	1	2	.136853
3	1	2	.124532
1	1	3	.211746

Diffuse functions can be used in an attempt to improve the calculated dipole moments. When using diffuse functions, the wavefunctions of the basis set are expanded to spread out more in space. The three types of atoms displayed in the table above are the polarization functions that are increased to values greater than zero in order to get different diffuse functions. For the NO molecule, the number of D heavy atoms are the only parameters which influence the dipole moment: the F heavy atoms could not be changed above one, and changing the number of light atoms did not affect the value.

Click the button below to view the highest occupied molecular orbital (HOMO) of NO.

Click the button below to view the lowest unoccupied molecular orbital (LUMO) of NO.

Click the button below to view a map of the NO electrostatic potential.

Click the button below to view the partial atomic charges of NO.

The vibrational frequency of NO calculated using the DZV basis set was found to be 1157.91 cm^-1. The experimental value for vibrational frequency is 1904.2 cm^-1. ¹ Therefore the error in the calculated value is significantly large.

Plot of the potential energies of bond stretching correlating to different levels of theory.

In the plot above, as the size of the basis set increases, the potential energy of the bond stretching decreases. This also means that as the basis set size increases, the calculated potential energies get closer to the actual value, as explained by the variation principle above.

Valence Energy Level Diagram

Non-bonding Lone Pair
Non-bonding Lone Pair
Bonding 2 electrons
Anti-bonding 2 electrons
Bonding 2 electrons
Bonding 2 electrons
Bonding 2 electrons
Anti-bonding 1 electron
Anti-bonding unoccupied
Bonding unoccupied
Anti-bonding unoccupied
Anti-bonding unoccupied

References

1. CCCBDB Computational Chemistry Comparison and Benchmark Database. http://cccbdb.nist.gov/. (accessed 2/28/12).

2. Atkins, P. and de Paula, J. Physical Chemistry, 9th ed.; W.H. Freeman and Company: New York, 2010.

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

Page skeleton and JavaScript generated by export to web function using Jmol 12.2.16 2011-12-13 21:20 on Mar 4, 2012.

Using directory E:/kelly/web page
  adding JmolPopIn.js
  ...jmolApplet0
      ...adding NO_621G_geometry.png
      ...adding NO_621G_geometry.spt
  ...jmolApplet1
      ...adding NO_631G_geometry.png
      ...adding NO_631G_geometry.spt
  ...jmolApplet2
      ...adding NO_DZV_geometry.png
      ...adding NO_DZV_geometry.spt
  ...jmolApplet3
      ...adding NO_HOMO.png
      ...adding NO_HOMO.spt
  ...jmolApplet4
      ...adding NO_LUMO.png
      ...adding NO_LUMO.spt
  ...jmolApplet5
      ...adding NO_electrostatic_potential.png
      ...adding NO_electrostatic_potential.spt
  ...jmolApplet6
      ...adding NO_partial_atomic_charges.png
      ...adding NO_partial_atomic_charges.spt