View source for Rep:Mod:IMM2RWL4015

__TOC__

== Computational Analysis of an Ammonia Molecule, NH<sub>3</sub> ==

=== Optimising the NH<sub>3</sub> Molecule ===

The following commands were used to calculate the optimal NH<sub>3</sub> structure using Gaussian:

{| class="wikitable" border="1"
! Calculation Type
| OPTF
|-
! Calculation Method
| B3LYP
|-
! Basis Set
| 6-31G(d,p)
|}

The following information about the optimised NH<sub>3</sub> molecule was found using the "Summary" window and the "Inquire" tool in GaussView. Experimentally determined values for the N-H bond distance and the H-N-H bond angle were also found and added to the table below:

{| class="wikitable" border="1"
|+ Ammonia, NH<sub>3</sub>
|-
| colspan="2" align="center"|[[File:WLIM_KEE_CHANG_NH3_OPTF_POP.png|thumb|center|Image of an optimised ammonia molecule using GaussView. The nitrogen atom is the central blue atom, and the smaller white atoms are hydrogens.]]
|-
! Final Energy, E(RB3LYP) (au)
| -56.55776873
|-
! RMS Gradient (au)
| 0.00000485
|-
! Point Group
| C<sub>3V</sub>
|-
! Optimised N-H Bond Distance (Å)
| 1.01798
|-
! Experimental N-H Bond Distance (Å)
|1.012<ref name="Experimental NH3 Data" />
|-
! Optimised H-N-H Bond Angle (°)
| 105.741 
|-
! Experimental H-N-H Bond Angle (°)
|106.7<ref name="Experimental NH3 Data" />
|}

From the "Item" table for the lowest energy molecule shown below, it can be seen that optimisation of the molecule has been performed successfully, with all forces and displacements having converged.

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000004     0.000450     YES
 RMS     Force            0.000004     0.000300     YES
 Maximum Displacement     0.000072     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES
</pre>

The link to the *.log file from which the "Item" table is taken is [[Media:WLIM_KEE_CHANG_NH3_OPTF_POP.LOG|here]].

A Jmol dynamic image has been added below to allow the optimised structure of NH<sub>3</sub> to be visualised in 3D and magnified and rotated.

<jmol><jmolApplet>
  <title>Optimised ammonia molecule</title>
  <color>black</color>
  <size>300</size>
  <uploadedFileContents>WLIM_KEE_CHANG_NH3_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.22;spin on</script>
</jmolApplet></jmol>

=== Vibrational Analysis of the NH<sub>3</sub> Molecule ===

The following vibrational modes and their corresponding frequencies and intensities were found for the optimised NH<sub>3</sub> molecule:

[[File:WLIM_KEE_CHANG_NH3_OPTF_POP_VIB.png|thumb|none|Screenshot of "Display Vibrations" window in GaussView showing the vibrational modes for an ammonia molecule]]

The absence of any negative frequency values is further evidence that the obtained structure is the fully optimised, lowest energy one.<ref name="Frequency Analysis" /> 

Using the 3N-6 rule for non-linear molecules, I would expect NH<sub>3</sub> to have 6 modes of vibration as 3(4)-6 = 6.<ref name="Elements of Physical Chemistry" /> The "Display Vibrations" window shows that modes 2 and 3, and 5 and 6 are degenerate, with each pair having the same frequency and therefore the same energy.<ref name="Elements of Physical Chemistry" /> The vibration animations show that modes 1-3 are "bending" vibrations, while modes 4-6 are "bond stretch" vibrations.<ref name="Chemguide IR Spectroscopy" /> Mode 4 in particular vibrates in a highly symmetric manner and mode 1 is known as the "umbrella" mode due to the way this bending vibration occurs and the appearance of the molecule as a result. As the molecule has 4 distinct vibrational modes with different energies, you would expect to see 4 bands in an experimental spectrum of gaseous ammonia, with absorptions occurring at 4 different wavenumbers.<ref name="Chemguide IR Spectroscopy" />

=== Atomic Charge Analysis of the NH<sub>3</sub> Molecule ===

Since nitrogen is more electronegative than hydrogen (χ<sub>P</sub> values for N and H are 3.04 and 2.20 respectively), I would expect the nitrogen atom to attract electron density in the N-H covalent bonds towards itself, making it negatively charged and leaving the hydrogen atoms positively charged.<ref name="Inorganic Chemistry" />

The distribution of charge across the NH<sub>3</sub> molecule is illustrated below, with charge values for the individual atoms also displayed in the table below.

[[File:WLIM_KEE_CHANG_NH3_OPTF_POP_CHARGE.png|thumb|none|Atomic charge distribution for the ammonia molecule displayed using GaussView. Note that the nitrogen atom is coloured red and the hydrogen atoms are green.]]

{| class="wikitable" border="1"
! Atom !! Charge
|-
| N || -1.125
|-
| H || 0.375
|}

The overall charge on the molecule is zero and so the charges on the individual atoms must total zero.

== Investigating the Haber-Bosch Process ==

Computational methods are extremely useful in predicting the energy of a reaction and therefore whether the energy is likely to be endothermic or exothermic and how readily it is likely to occur.<ref name="Computational Methods" /> Here, the reaction between nitrogen gas, N<sub>2</sub>, and hydrogen gas, H<sub>2</sub>, to form ammonia, NH<sub>3</sub>, as part of the Haber-Bosch process is investigated using the previously optimised NH<sub>3</sub> molecule and optimising N<sub>2</sub> and H<sub>2</sub> molecules.

=== Optimisation Procedure for N<sub>2</sub> and H<sub>2</sub> ===

The optimised structures of N<sub>2</sub> and H<sub>2</sub> were obtained using the same commands in Gaussian as for NH<sub>3</sub>:

{| class="wikitable" border="1"
! Calculation Type
| OPTF
|-
! Calculation Method
| B3LYP
|-
! Basis Set
| 6-31G(d,p)
|}

=== Nitrogen, N<sub>2</sub> ===

==== Optimising the N<sub>2</sub> Molecule ====

The following information about the optimised N<sub>2</sub> molecule was found:

{| class="wikitable" border="1"
|+ Nitrogen, N<sub>2</sub>
|-
| colspan="2" align="center"|[[File:WLIM_KEE_CHANG_N2_OPTF_POP.png|thumb|center|Image of an optimised nitrogen molecule using GaussView]]
|-
! Final Energy, E(RB3LYP) (au)
| -109.52412868
|-
! RMS Gradient (au)
| 0.00000060
|-
! Point Group
| D<sub>∞h</sub>
|-
! Optimised N≡N Bond Distance (Å)
| 1.10550
|}

The molecule has been optimised successfully, with the "Item" table for the lowest energy molecule indicating that all forces and displacements have converged.

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000001     0.000450     YES
 RMS     Force            0.000001     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000000     0.001200     YES
</pre>

The link to the *.log file from which the "Item" table is taken is [[Media:WLIM_KEE_CHANG_N2_OPTF_POP.LOG|here]].

A Jmol dynamic image has been added below to allow the optimised structure for N<sub>2</sub> to be visualised in 3D and magnified and rotated.

<jmol><jmolApplet>
  <title>Optimised nitrogen molecule</title>
  <color>black</color>
  <size>300</size>
  <uploadedFileContents>WLIM_KEE_CHANG_N2_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.11;spin on</script>
</jmolApplet></jmol>

==== Vibrational Analysis of the N<sub>2</sub> Molecule ====

As expected using the 3N-5 rule for linear molcules, a single vibrational mode was found for the optimised N<sub>2</sub> molecule:<ref name="Elements of Physical Chemistry" />

[[File:WLIM_KEE_CHANG_N2_OPTF_POP_VIB.png|thumb|none|Screenshot of "Display Vibrations" window in GaussView showing the single vibrational mode for a nitrogen molecule]]

Again, the absence of any negative frequency values provides further evidence of a fully optimised, lowest-energy structure.<ref name="Frequency Analysis" /> Note that the infrared intensity value for the vibration is zero due to N<sub>2</sub> being homonuclear and symmetric and therefore not having a dipole moment and being IR inactive.<ref name="Inorganic Chemistry" />

=== Hydrogen, H<sub>2</sub> ===

==== Optimising the H<sub>2</sub> Molecule ====

The following information about the optimised H<sub>2</sub> molecule was found:

{| class="wikitable" border="1"
|+ Hydrogen, H<sub>2</sub>
|-
| colspan="2" align="center"|[[File:WLIM_KEE_CHANG_H2_OPTF_POP.png|thumb|center|Image of an optimised hydrogen molecule using GaussView]]
|-
! Final Energy, E(RB3LYP) (au)
| -1.17853936
|-
! RMS Gradient (au)
| 0.00000017
|-
! Point Group
| D<sub>∞h</sub>
|-
! Optimised H-H Bond Distance (Å)
| 0.74279
|}

The molecule has been optimised successfully, with the "Item" table for the lowest energy molecule indicating that all forces and displacements have converged.

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000000     0.000450     YES
 RMS     Force            0.000000     0.000300     YES
 Maximum Displacement     0.000000     0.001800     YES
 RMS     Displacement     0.000001     0.001200     YES
</pre>

The link to the *.log file from which the "Item" table is taken is [[Media:WLIM_KEE_CHANG_H2_OPTF_POP.LOG|here]].

A magnifiable and rotatable Jmol dynamic image of the optimised H<sub>2</sub> structure in 3D is shown below:

<jmol><jmolApplet>
  <title>Optimised hydrogen molecule</title>
  <color>black</color>
  <size>300</size>
  <uploadedFileContents>WLIM_KEE_CHANG_H2_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.13;spin on</script>
</jmolApplet></jmol>

==== Vibrational Analysis of the H<sub>2</sub> Molecule ====

As with N<sub>2</sub>, the 3N-5 rule for linear molcules predicts a single vibrational mode for the optimised H<sub>2</sub> molecule:<ref name="Elements of Physical Chemistry" />

[[File:WLIM_KEE_CHANG_H2_OPTF_POP_VIB.png|thumb|none|Screenshot of "Display Vibrations" window in GaussView showing the single vibrational mode for a hydrogen molecule]]

Since the frequency is positive, the optimisation process has been successful.<ref name="Frequency Analysis" /> Again, the absence of a dipole moment results in an infrared intensity of zero.<ref name="Inorganic Chemistry" />

=== Determining the Energy of the Haber-Bosch Process ===

The following energy values were used to calculate the energy for the reaction between nitrogen and hydrogen gas to form ammonia, N<sub>2 (g)</sub> + 3H<sub>2 (g)</sub> → 2NH<sub>3 (g)</sub> :<ref name="Haber-Bosch Process" />

{| class="wikitable" border="1"
! !! Energy, E(RB3LYP) (au)
|-
! E(NH<sub>3</sub>)
| -56.55776873
|-
! 2E(NH<sub>3</sub>)
| -113.1155375
|-
! E(N<sub>2</sub>)
| -109.52412868
|-
! E(H<sub>2</sub>)
| -1.17853936
|- 
! 3E(H<sub>2</sub>)
| -3.53561808
|-
! ΔE
| -0.05579074
|}

Note that ΔE = 2E(NH<sub>3</sub>) - [E(N<sub>2</sub>) + 3E(H<sub>2</sub>)].<ref name="Frequency Analysis" />

The energy difference, ΔE, can be expressed in kJ mol<sup>-1</sup> as follows:

ΔE = -0.05579074 au × 2625.5 = <b>-146.48 kJ mol<sup>-1</sup></b>

A negative ΔE value indicates that the reaction is exothermic and so the release of energy results in the ammonia, NH<sub>3</sub> product being energetically more stable than the hydrogen, H<sub>2</sub> and nitrogen, N<sub>2</sub> reactants from which it is formed.<ref name="Elements of Physical Chemistry" />

== Computational Analysis of a Cyanide Anion, CN<sup>-</sup> ==

=== Optimising the CN<sup>-</sup> Anion ===

The following commands were used to calculate the optimised CN<sup>-</sup> structure using Gaussian:

{| class="wikitable" border="1"
! Calculation Type
| OPTF
|-
! Calculation Method
| B3LYP
|-
! Basis Set
| 6-31G(d,p)
|}

The following information about the optimised CN<sup>-</sup> anion was found using the "Summary" window and the "Inquire" tool in GaussView:

{| class="wikitable" border="1"
|+ Cyanide anion, CN<sup>-</sup>
|-
| colspan="2" align="center"|[[File:WLIM_KEE_CHANG_CN-_OPTF_POP.png|thumb|center|Image of an optimised cyanide anion using GaussView]]
|-
! Final Energy, E(RB3LYP) (au)
| -92.82453153
|-
! RMS Gradient (au)
| 0.00000704
|-
! Point Group
| C<sub>∞v</sub>
|-
! Optimised C≡N Bond Distance (Å)
| 1.18409
|}

As shown by the "Item" table below, the forces and the displacements are converged. Optimisation has therefore been successful.

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000012     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000005     0.001800     YES
 RMS     Displacement     0.000008     0.001200     YES
</pre>

The link to the *.log file from which the "Item" table is taken is [[Media:WLIM_KEE_CHANG_CN-_OPTF_POP.LOG|here]].

A Jmol dynamic image of the optimised structure of CN<sup>-</sup> can be found below:

<jmol><jmolApplet>
  <title>Optimised cyanide anion</title>
  <color>black</color>
  <size>300</size>
  rotate Y +90
  <uploadedFileContents>WLIM_KEE_CHANG_CN-_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.11;spin on</script>
</jmolApplet></jmol>

=== Vibrational Analysis of the CN<sup>-</sup> Anion ===

The following vibrational modes and their corresponding frequencies and intensities were found for the optimised CN<sup>-</sup> molecule:

[[File:WLIM_KEE_CHANG_CN-_OPTF_POP_VIB.png|thumb|none|Screenshot of "Display Vibrations" window in GaussView showing the vibrational modes for a cyanide anion]]

The presence of only 1 vibrational mode matches the prediction from the 3N-5 rule for linear molecules.<ref name="Elements of Physical Chemistry" />
 
The absence of any negative frequency values is again evidence that the obtained structure is the fully optimised, lowest energy one.<ref name="Frequency Analysis" /> There is also a non-zero intensity as CN<sup>-</sup> is heteronuclear and asymmetric and so has a dipole moment.<ref name="Inorganic Chemistry" />

=== Atomic Charge Analysis of the CN<sup>-</sup> Anion ===

Since nitrogen is more electronegative than carbon, I would expect the nitrogen atom to attract electron density in the C≡N covalent bonds towards itself, making it negatively charged and leaving the hydrogen atoms positively charged.<ref name="Inorganic Chemistry" />

The distribution of charge across the CN<sup>-</sup> anion is illustrated and the charge values for the individual atoms are tabulated below:

[[File:WLIM_KEE_CHANG_CN-_OPTF_POP_CHARGE_2.png|thumb|none|Atomic charge distribution across the cyanide anion displayed using GaussView. Note that the carbon atom is on the left and appears in a darker shade of red, while the nitrogen atom is on the right.]]

{| class="wikitable" border="1"
! Atom !! Charge
|-
| C || -0.246
|-
| N || -0.754
|}

Since the overall charge on the anion is -1, the individual charges must add up to -1.

=== Molecular Orbital Analysis of the CN<sup>-</sup> Anion ===

The shapes and energies of the molecular orbitals of the CN<sup>-</sup> anion were investigated using GaussView.

The energies for the first 12 molecular orbitals CN<sup>-</sup> are displayed below:

{| class="wikitable" border="1" style="text-align: center"
|+ Molecular Orbital Energies of CN<sup>-</sup>
! MO !! Energy (au) !! Electrons
|-
| 1 || -14.00393 || ↿⇂ 
|-
| 2 || -9.86720 || ↿⇂
|-
| 3 || -0.56195 || ↿⇂
|-
| 4 || -0.10626 || ↿⇂
|-
| 5 || -0.01696 || ↿⇂
|-
| 6 || -0.01696 || ↿⇂
|-
| 7 || 0.01859 || ↿⇂
|-
| 8 || 0.35435 ||
|-
| 9 || 0.35435 ||
|-
| 10 || 0.59206 ||
|-
| 11 || 0.84601 ||
|-
| 12 || 0.84601 ||
|}

The shapes of 5 CN<sup>-</sup> molecular orbitals are depicted below:

{| class="wikitable" border="1"
|+ Molecular Orbital Shapes of CN<sup>-</sup>
! MO Number
| 3
| 4
| 5
| 7
| 8
|-
! Image from GaussView
| [[File:WLIM_KEE_CHANG_CN-_OPTF_POP_MO3.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_CN-_OPTF_POP_MO4.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_CN-_OPTF_POP_MO5.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_CN-_OPTF_POP_MO7.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_CN-_OPTF_POP_MO8.png|150px|240px|none]]
|}

Molecular orbital 3 (3σ) is occupied by a pair of electrons and is formed from the overlap of the 2s atomic orbitals, which are both in the same phase, on the carbon and the nitrogen atoms. Note that the nitrogen atom has a greater electron density around it due to its greater electronegativity relative to carbon as well as the decreased Z<sub>eff</sub> due to the extra electron on the carbon atom.<ref name="Inorganic Chemistry" /> Although this MO is a combination of valence AOs, it sits deep in energy, indicated by a negative energy value.

Molecular orbital 4 (4σ<sup>*</sup>) is also occupied by a pair of electrons. However, since the two atomic orbitals are out-of-phase and destructive interference occurs,, indicated by the differently coloured electron density clouds, the MO is the σ<sup>*</sup> antibonding orbital and has a higher energy.<ref name="Inorganic Chemistry" /> Again, the electron density is skewed towards the more electronegative nitrogen atom and the extra electron associated with the carbon atom.

Molecular orbital 5 (1π) is formed from the in-phase overlap of the occupied 2p atomic orbitals, with the same orientation, on the carbon and nitrogen atoms, resulting in constructive the formation of a π-bond.<ref name="Inorganic Chemistry" /> Note that the AOs are both perpendicular to the bond formed. The overlapping AOs are larger and so the electrons are further from the nuclei, hence a higher energy.

Molecular orbital 7 (5σ) is the highest occupied molecular orbital, HOMO, and has a distorted shape due to mixing and is the bonding molecular orbital formed by the overlap of the 2p atomic orbitals parallel to the σ-bond formed.<ref name="Frequency Analysis" />

Molecular orbital 8 (2π<sup>*</sup>) is the lowest unoccupied molecular orbital, LUMO, and is the π<sup>*</sup> antibonding orbital formed by the out-of-phase overlap of the perpendicular 2p orbitals.<ref name="Inorganic Chemistry" /> This MO has the highest energy of the MOs discussed here.

== Computational Analysis of a Borohydride Ion, BH<sub>4</sub><sup>-</sup> ==

=== Optimising the BH<sub>4</sub><sup>-</sup> Anion ===

The following commands were used to calculate the optimised BH<sub>4</sub><sup>-</sup> structure using Gaussian:

{| class="wikitable" border="1"
! Calculation Type
| OPTF
|-
! Calculation Method
| B3LYP
|-
! Basis Set
| 6-31G(d,p)
|}

The following information about the optimised BH<sub>4</sub><sup>-</sup> anion was found using the "Summary" window and the "Inquire" tool in GaussView:

{| class="wikitable" border="1"
|+ Borohydride anion, BH<sub>4</sub><sup>-</sup>
|-
| colspan="2" align="center"|[[File:WLIM_KEE_CHANG_BH4-_OPTF_POP.png|thumb|center|Image of an optimised borohydride anion using GaussView. The boron atom at the centre of the anion is pink, with the hydrogen atoms in white.]]
|-
! Final Energy, E(RB3LYP) (au)
| -27.24992701
|-
! RMS Gradient (au)
| 0.00000671
|-
! Point Group
| T<sub>d</sub>
|-
! Optimised B-H Bond Distance (Å)
| 1.23933
|-
! Optimised H-B-H Bond Angle (°)
| 109.471
|}

As shown by the "Item" table below, convergence has occurred for all parameters and so optimisation has been successful.

<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000013     0.000450     YES
 RMS     Force            0.000007     0.000300     YES
 Maximum Displacement     0.000065     0.001800     YES
 RMS     Displacement     0.000035     0.001200     YES
</pre>

The link to the *.log file from which the "Item" table is taken is [[Media:WLIM_KEE_CHANG_BH4-_OPTF_POP.LOG|here]].

A Jmol dynamic image of the optimised BH<sub>4</sub><sup>-</sup> structure can be found below:

<jmol><jmolApplet>
  <title>Optimised borohydride anion</title>
  <color>black</color>
  <size>300</size>
  rotate Y +90
  <uploadedFileContents>WLIM_KEE_CHANG_BH4-_OPTF_POP.LOG</uploadedFileContents>
  <script>frame 1.21;spin on</script>
</jmolApplet></jmol>

=== Vibrational Analysis of the BH<sub>4</sub><sup>-</sup> Anion ===

Borohydride is formed of 5 atoms. According to the 3N-6 rule, I would expect there to be 9 vibrational modes.<ref name="Elements of Physical Chemistry" />

The following vibrational modes and their corresponding frequencies and intensities were found for the optimised BH<sub>4</sub><sup>-</sup> anion:

[[File:WLIM_KEE_CHANG_BH4-_OPTF_POP_VIB.png|thumb|none|Screenshot of "Display Vibrations" window in GaussView showing the vibrational modes for a borohydride anion]]

All the frequency values are positive and so BH<sub>4</sub><sup>-</sup> has been successfully optimised.<ref name="Frequency Analysis" /> The tetrahedral structure results in BH<sub>4</sub><sup>-</sup> being symmetrical and therefore not having a dipole moment.<ref name="Inorganic Chemistry" /> As observed, the symmetrical vibrational modes therefore have an infrared intensity of zero.

=== Atomic Charge Analysis of the BH<sub>4</sub><sup>-</sup> Anion ===

Since boron is much more electronegative than hydrogen, a large proportion of the electron density would be attracted towards the boron atom, resulting in it having a greater negative charge than the hydrogen atoms.<ref name="Inorganic Chemistry" />

The distribution of charge as well as the charge values associated with the individual atoms making up the BH<sub>4</sub><sup>-</sup> anion are shown below.

[[File:WLIM_KEE_CHANG_BH4-_OPTF_POP_CHARGE.png|thumb|none|Atomic charge distribution across the borohydride anion displayed using GaussView]]

{| class="wikitable" border="1"
! Atom !! Charge
|-
| B || -0.615
|-
| H || -0.096
|}

Again, the overall charge on the anion is -1 and so the total charge that can be distributed across the individual atoms is -1.

=== Molecular Orbital Analysis of the BH<sub>4</sub><sup>-</sup> Anion ===

The shapes and energies of the molecular orbitals of the BH<sub>4</sub><sup>-</sup> anion were investigated using GaussView.

The energies for the first 12 molecular orbitals of BH<sub>4</sub><sup>-</sup> are displayed below:

{| class="wikitable" border="1" style="text-align: center"
|+ Molecular Orbital Energies of BH<sub>4</sub><sup>-</sup>
! MO !! Energy (au) !! Electrons
|-
| 1 || -6.42128 || ↿⇂
|-
| 2 || -0.22587 || ↿⇂
|-
| 3 || -0.03183 || ↿⇂
|-
| 4 || -0.03183 || ↿⇂
|-
| 5 || -0.03183 || ↿⇂
|-
| 6 || 0.41617 ||
|-
| 7 || 0.41617 ||
|-
| 8 || 0.41617 ||
|-
| 9 || 0.43601 ||
|-
| 10 || 0.67306 ||
|-
| 11 || 0.67306 ||
|-
| 12 || 0.67306 ||
|}

The shapes of 5 BH<sub>4</sub><sup>-</sup> molecular orbitals are depicted below:

{| class="wikitable" border="1"
|+ Molecular Orbital Shapes of BH<sub>4</sub><sup>-</sup>
! MO Number
| 1
| 2
| 3
| 4
| 9
|-
! Image from GaussView
| [[File:WLIM_KEE_CHANG_BH4-_OPTF_POP_MO1.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_BH4-_OPTF_POP_MO2.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_BH4-_OPTF_POP_MO3.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_BH4-_OPTF_POP_MO4_2.png|150px|240px|none]]
| [[File:WLIM_KEE_CHANG_BH4-_OPTF_POP_MO9.png|150px|240px|none]]
|}

Molecular orbital 1 is very deep in energy, having an extremely large negative energy in comparison to the other molecular orbitals. Since the pair of electrons in this very small orbital take no part in bonding and are held very tightly to the boron atom, with no overlap with the orbitals of the hydrogen atoms, this MO is described as non-bonding.<ref name="Inorganic Chemistry" />

Molecular orbital 2 (σ<sub>g</sub>) is a bonding orbital occupied by a pair of electrons and is formed from the overlap of the 2s orbital on the central boron atom with the 1s orbitals of the hydrogen atoms to form 4 sigma bonds.<ref name="Inorganic Chemistry" />

Molecular orbitals 3 and 4 (σ<sub>g</sub>) are also bonding orbitals occupied by electrons but in this case are formed from the overlap of the 2p orbital on the boron atom and the 1s orbitals of the hydrogen atoms and have a slightly higher energy than molecular orbital 2. The two orbitals have the same shape, being formed by the 2p orbital in different orientations and so are degenerate, being 2 of the 3 degenerate MOs for each of the 3 possible orientations of the 2p atomic orbital.<ref name="Inorganic Chemistry" /> The different phases on the p orbital and the bonding nature of the MO gives rise to the formation of a nodal plane through the centre of the boron atom.<ref name="Inorganic Chemistry" />

Molecular orbital 9 (σ<sub>g</sub><sup>*</sup>) is very high in energy, having a positive value, and is therefore unoccupied. This MO is the antibonding MO that corresponds to molecular orbital 1 and is the result of the out-of-phase overlap of the 2s atomic orbital on boron and the 1s orbitals on the 4 hydrogen atoms, with all 4 hydrogen AOs having the same phase in this case.

== References ==

<references>
<ref name="Experimental NH3 Data">M. R. Chacon-Taylor and M. I. McCarthy, <I>J. Phys. Chem.</I>, 2011, <b>115</b>, 7610-7616.</ref>
<ref name="Frequency Analysis">Hunt Research Group, http://www.huntresearchgroup.org.uk/teaching/year1_lab_start.html, (accessed March 2017).</ref>
<ref name="Elements of Physical Chemistry">P. Atkins and J. de Paula, <I>Elements of Physical Chemistry</I>, Oxford University Press, Oxford, 7th edn., 2017.</ref>
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