ChemWiki - User contributions [en]

Rep:Mod:st6218

2019-03-15T01:05:36Z

St6218: /* Molecular Orbital */

== Chemistry ==

==NH3==

=== Optimization Results Summary ===

Molecule: NH3 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP): -56.55776873 a.u. 
RMS Gradient: 0.00000323 a.u. 
Point Group: C3V 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000014 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
</pre>

<jmol><jmolApplet>
<title>NH3</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SHIAU_NH3_OPT1.LOG</uploadedFileContents>
<script>frame 7</script>
</jmolApplet></jmol>

Optimised N-H Bond Distance: 1.02Å 
Optimised H-N-H Bond Angle: 106° 

The optimisation file is linked [[Media:SHIAU_NH3_OPT1.LOG| here ]]

===Vibrations===

[[File:NH3_vib_display.png]]

{| class="wikitable" border="1"
|+ Mode #1
|-
! colspan="18" style="text-align: left;"|Information
|-
| colspan="18" |[[File:Shiaunh3modes.png]]
|-
! style="text-align: center;"|wavenumber/ cm-1
! style="text-align: center;"|symmetry
! style="text-align: center;"|intensity/a.u.
! style="text-align: center;"|wavenumber/ cm-1
! style="text-align: center;"|symmetry
! style="text-align: center;"|intensity/a.u.
! style="text-align: center;"|wavenumber/ cm-1
! style="text-align: center;"|symmetry
! style="text-align: center;"|intensity/a.u.
! style="text-align: center;"|wavenumber/ cm-1
! style="text-align: center;"|symmetry
! style="text-align: center;"|intensity/a.u.
! style="text-align: center;"|wavenumber/ cm-1
! style="text-align: center;"|symmetry
! style="text-align: center;"|intensity/a.u.
! style="text-align: center;"|wavenumber/ cm-1
! style="text-align: center;"|symmetry
! style="text-align: center;"|intensity/a.u.
|-
| style="text-align: center;"|1090
| style="text-align: center;"|A1
| style="text-align: center;"|145
| style="text-align: center;"|1694
| style="text-align: center;"|E
| style="text-align: center;"|14
| style="text-align: center;"|1694
| style="text-align: center;"|E
| style="text-align: center;"|14
| style="text-align: center;"|3461
| style="text-align: center;"|A1
| style="text-align: center;"|1
| style="text-align: center;"|3590
| style="text-align: center;"|E
| style="text-align: center;"|0
| style="text-align: center;"|3590
| style="text-align: center;"|E
| style="text-align: center;"|0

|}

how many modes do you expect from the 3N-6 rule?
Answer: 6

which modes are degenerate (ie have the same energy)?
Answer: The modes at 1694 cm-1 and 3590 cm-1.

which modes are "bending" vibrations and which are "bond stretch" vibrations?
Answer: bend-1090 and 1694 cm-1 stretch-3461 and 3590 cm-1.

which mode is highly symmetric?
Answer: stretch with wavenumber of 3461 cm-1.

one mode is known as the "umbrella" mode, which one is this?
Answer: bend with wavenumber of 1090 cm-1.

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?
Answer: I expect to see at least 3 bands at low temperature.

=== Charge Analysis ===

Charge of N in NH3 = -1.125
Charge of H in NH3 = +0.375

The charges are expected as N is more electronegative than H and hence it will draw the electron density away from H, causing it to be more negatively charged since electrons are negative charges.

==N2==

=== Optimization Results Summary ===

Molecule: N2 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP): -109.52412868 a.u. 
RMS Gradient: 0.00000060 a.u. 
Point Group: D*H 

<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>

<jmol><jmolApplet>
<title>N2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SHIAU_N2_OPT1.LOG</uploadedFileContents>
<script>frame 7</script>
</jmolApplet></jmol>

Optimised N-N Bond Distance: 1.11 Å 

The optimisation file is linked [[Media:SHIAU_N2_OPT1.LOG| here ]]

===Vibration===

[[File:Shiau_n2_vib_display.png]]

{| class="wikitable" border="1"
|+ N2
|-
! colspan="3" style="text-align: left;"|Information
|-
| colspan="3" align="center"|[[File:Shiau n2 vector.png|256px]]
|-
! colspan="3" style="text-align: left;"|More Info
|-
| style="text-align: center;"|wavelength/cm-1
| style="text-align: center;"|symmetry
| style="text-align: center;"|intensity/a.u.
|-
| style="text-align: center;"|2457
| style="text-align: center;"|SGG
| style="text-align: center;"|0
|}

=== Charge Analysis ===

Charge of N in N2 = 0

This is expected as N2 is made up of the same atoms and hence no dipole moment between the two atoms. This meant that they have to share the electron density evenly, leading to zero charge on either atoms.

===Bond length comparison===

The bond length of N2 is 1.12 Å and 1.13 Å in the structure of AFUXAD (https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=AFUXAD&DatabaseToSearch=Published)

The bond length is longer than the one in just N2 because when the bond is formed, the electrons from the non-bonding d orbital of the transition metal is added to the lowest unoccupied molecular orbital of N2, which is an anti-bonding orbital (π*). This results in a lowering of the bond order and hence the bond between N-N is weakened and is reflected in the longer bond length in the structure of AFUXAD.

==H2==

=== Optimization Results Summary ===

Molecule: H2 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP): -1.17853936 a.u. 
RMS Gradient: 0.00000017 a.u. 
Point Group: D*H 

<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>

<jmol><jmolApplet>
<title>H2</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SHIAU H2 OPT1.LOG</uploadedFileContents>
<script>frame 7</script>
</jmolApplet></jmol>

Optimised H-H Bond Distance: 0.74 Å 

The optimisation file is linked [[Media:SHIAU H2 OPT1.LOG| here ]]

===Vibration===

[[File:Shiau h2 vector.png]]

{| class="wikitable" border="1"
|+ H2
|-
! colspan="3" style="text-align: left;"|Information
|-
| colspan="3" align="center"|[[File:Shiau h2 vector2.png|256px]]
|-
! colspan="3" style="text-align: left;"|More Info
|-
| style="text-align: center;"|wavelength/cm-1
| style="text-align: center;"|symmetry
| style="text-align: center;"|intensity/a.u.
|-
| style="text-align: center;"|4466
| style="text-align: center;"|SGG
| style="text-align: center;"|0
|}

=== Charge Analysis===

Charge of H in H2 = 0

This is expected as H2 is made up of the same atoms and hence no dipole moment between the two atoms. This meant that they have to share the electron density evenly, leading to zero charge on either atoms.

== Haber-Borsh Process ==

N2 + 3H2 → 2NH3

E(NH3)= -56.5577687 a.u.

2*E(NH3)= -113.1155375 a.u.

E(N2)= -109.5241287 a.u.

E(H2)= -1.1785394 a.u.

3*E(H2)= -3.5356181 a.u.

ΔE = 2*E(NH3) - [E(N2) + 3*E(H2)] = -0.0557907 a.u.

since 0.000038 a.u. = 0.1 kJ/mol

-0.0557907 a.u. = 146.8 kJ/mol

== CO ==
=== Optimization Results Summary ===

Molecule: N2 
Calculation Method: RB3LYP 
Basis Set: 6-31G(d,p) 
Final Energy E(RB3LYP): -113.30945314 a.u. 
RMS Gradient: 0.00000433 a.u. 
Point Group: C*V 

<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000004 0.001200 YES
</pre>

<jmol><jmolApplet>
<title>CO</title>
<color>black</color>
<size>200</size>
<uploadedFileContents>SHIAU CO OPT1.LOG</uploadedFileContents>
<script>frame 7</script>
</jmolApplet></jmol>

Optimised C-O Bond Distance: 1.14 Å 

The optimisation file is linked [[Media:SHIAU CO OPT1.LOG| here ]]

===Vibration===

[[File:Shiau co vibdis.png]]

{| class="wikitable" border="1"
|+ CO
|-
! colspan="3" style="text-align: left;"|Information
|-
| colspan="3" align="center"|[[File:Shiau co vector.png|256px]]
|-
! colspan="3" style="text-align: left;"|More Info
|-
| style="text-align: center;"|wavelength/cm-1
| style="text-align: center;"|symmetry
| style="text-align: center;"|intensity/a.u.
|-
| style="text-align: center;"|2209
| style="text-align: center;"|SG
| style="text-align: center;"|68.0
|}

=== Charge Analysis ===

Charge of C in CO = +0.506
Charge of O in CO = -0.506

This is expected as O is more electronegative than C and hence negatively charged electron density will be drawn to O, resulting in the above observation.

===Bond length comparison===

The bond length of CO is 1.15 Å in the structure of ACAVOS (https://www.ccdc.cam.ac.uk/structures/Search?Ccdcid=acavos&DatabaseToSearch=Published)

The bond length is longer than the one in just CO because when the bond is formed, the electrons from the non-bonding d orbital of the transition metal is added to the lowest unoccupied molecular orbital of CO, which is an anti-bonding orbital (π*). This results in a lowering of the bond order and hence the bond between CO is weakened and is reflected in the longer bond length in the structure of ACAVOS.

Additionally, the literature value of the CO bond is 1.13 Å<ref name="Literature value of CO bond length" /> , which is in good agreement with our bond length. The difference in length could be resulted by different value of equilibrium position taken.

=== Molecular Orbital===

{| class="wikitable" border="1"
! style="text-align: center;"|Molecular Orbital|| style="text-align: center;"|Description
|-
| style="text-align: center;"|[[File:Shiau co mo12s.png]]|| style="text-align: center;"|2s orbitals from C and O contributed to this bonding MO which is fully occupied. This is deep in energy (-1.16 a.u.) as s orbitals penetrate deep into the core electron shells, stabilising the orbital. The electron density leans towards O as O has a greater contribution to the bonding MO ( it's orbital is closer in energy level to the bonding MO).
|-
| style="text-align: center;"|[[File:Shiau co mo2 2s.png]] || style="text-align: center;"|2s orbitals from C and O contributed to this anti-bonding MO from destructive interference. This orbital is fully occupied.The electron density leans towards C as C has a greater contribution to the anti-bonding MO. This is because the 2s orbital from C is higher in energy than O as it has a lower atomic number but similar core shielding. This makes the energy level of C's 2s orbital closer to the anti-bonding 2s orbital, allowing greater contribution, reflected by the skew in electron density towards C.
|-
| style="text-align: center;"|[[File:Shiau co mo4 2px.png]] || style="text-align: center;"| 2p orbitals from C and O contribute to this bonding MO from constructive inference. This orbital is fully occupied and is the Highest Occupied Molecular Orbital (HOMO) with an energy level of -0.37 a.u. and hence likely to react well with Lowest Unoccupied Molecular Orbital (LUMO) of other molecules with similar energy level. The electron density is again skewed towards O as it has a greater contribution to this bonding MO.
|-
| style="text-align: center;"|[[File:Shiau co mo5 2px.png]] || style="text-align: center;"|2p orbitals from C and O contribute to this anti-bonding MO from destructive inference. This orbital is unoccupied and is the Lowest Unoccupied Molecular Orbital (LUMO) of the molecule with an energy level of -0.0218 a.u. and has another degenerate orbital perpendicular to this orbital. Addition of electron density into this orbital will lower the overall bond order of the bond.
|-
| style="text-align: center;"|[[File:Shiau co mo3 2p.png]]|| style="text-align: center;"|This orbital has a lower energy than the sigma orbital due to mixing (factors such as a good aligned overlap helps to improve mixing), which given more s character, have more penetration and thus a lower energy.
|}

== References ==

<ref name="Literature value of CO bond length">Jean Demaison, Atilla G., Journal of molecular structure, 2012, vol 1023, p7-14 </ref>

2019-03-14T22:42:27Z

St6218: /* H2 */

2019-03-14T22:30:39Z

St6218:

File:Shiau co vibdis.png

2019-03-14T22:30:04Z

St6218:

File:SHIAU CO OPT1.LOG

2019-03-14T22:26:02Z

St6218:

Rep:Mod:gxf12345678