The calculated bond length
for each level of theory is presented below. The bond angles are not
show because they are all 180
o since disodium has a linear
geometry. It should be noted that triple zeta valence calculations (TZV)
were performed rather than double zeta valence (DZV) due to the
electronic character of disodium.
6-21G was the lowest level of theory used for geometry calculations.
Both the 6-31G and the TZV models calculated the bond length most closely matching the literature
7 value of 0.3079nm.
The highest occupied molecular
orbital (HOMO) is shown below. This is the orbital geometry that
represents the valence electrons in their ground state.
This was calculated by summing the total number of electrons for the
molecule and dividing by two.
The lowest unoccupied molecular
orbital (LUMO) is show below. This is the orbital that the valence
electrons occupy once they have been excited by some form of energy.
This was calculated by selecting the molecular orbital that was adjacent
to the HOMO orbital but with a differing sign associated with the
energy.
The electrostatic potential
graphic shown below, represents the probability density of where the
bonding electrons are located in a given molecule. Red colors represent
regions of greater probability density, while blue colors represent
regions of lower density. Colors between red and blue represent
intermediate probability densities.
The partial atomic charges for
disodium is shown in the graphic below. The atomic charges are 0 since
disodium is composed of two of the same atom, so the charge separation
is zero.
The different molecular bonding orbitals for disodium are shown in Table 1 below.
Table 1: Graphical representations of disodium's bonding and anti-bonding orbitals.
Type of Bonding
|
Graphical Representation
|
Sigma bonding
|
|
Sigma anti-bonding
|
|
The potential energy graph, Figure
2, shown below graphs the total potential energy of disodium as the
atoms move apart a given distance in nm. These potential energies were
calculated at every level of theory. As the number of basis sets
increased the calculated potential energy at each distance decreased.
This is why the TZV calculation has the lowest potential energy curve.
Figure 1: Potential energy curves generated at each level of theory.
As disodium is a symmetric
molecule it does not absorb in the IR region. Because of this there are
no vibrational frequencies to compared to. The TZV level of theory was
able to calculate a single vibration at 153.84cm
-1.
Additionally, since disodium is a
symmetric molecule composed of the same atom there is no dipole moment. So there are no literature
values to reference, nor were there any calculated values.
You may look at any of these intermediate views again by clicking on the appropriate button.
Based on template by A. Herráez as modified by J. Gutow
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