View source for Cute yd3717

== NH<sub>3</sub> ==



=== General information ===


Molecule name: NH<sub>3</sub>

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy: E(RB3LYP) = -56.55776873 a.u.

RMS gradient norm: 0.00000485 a.u.

Point group: C<sub>3V</sub>

N-H bond distance: 1.01798

Experimental N-H bond distance: 1.0124 <sup>[1]</sup>

H-N-H bond angle: 105.741

Experimental H-N-H bond angle: 106.670 <sup>[1]</sup>

<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>


[[File:YD3717_PHUNT_NH3_OPTF_POP.LOG]]

<jmol><jmolApplet>
  <title>NH3 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YD3717_PHUNT_NH3_OPTF_POP.LOG</uploadedFileContents>
</jmolApplet></jmol>



=== Frequency analysis ===


[[File:yd3717_frequency_nh3.JPEG|thumb|Displayed frequencies of NH3]]

From 3N-6 rule, 6 modes are expected

Mode #2 & #3, also #5 & #6 are degenerate

Mode #1 & #2 & #3 are bending vibrations

Mode #4 & #5 & #6 are bond stretching vibrations

Mode #4 is highly symmetric

Mode #1 is known as the 'umbrella' mode

2 bands are expected to see in an experimental spectrum of gaseous ammonia, one is #1 and #2 & #3 (they are degenerate). These two are shown because they have a large change in dipole moment.



=== Atomic charges ===



Charge on each N atom : -1.125 e

Charge on each H atom : +0.375 e

H atom was expected to be +1 e, and N atom was expected to be -3 e, so that NH<sub>3</sub> would be neutral.

However, due to shielding effect of inner electrons, effective nuclear charge is smaller.

[[File:yd3717_nh3_charge.png|thumb|Charge distribution on NH3 molecule]]



=== Reaction energies ===



==== N<sub>2</sub> ====

Molecule name: N<sub>2</sub>

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy: E(RB3LYP) = -109.52412868 a.u.

RMS gradient norm: 0.00000060 a.u.

Point group: D*H

N-N bond distance: 1.10550

Literature value of N-N bond distance: 1.10 <sup>[2]</sup>

N-N bond angle: 180

<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>


[[File:yd3717_n2_frequency.JPEG|thumb|Displayed frequencies of N2]]

Frequency #1 : 2457.33


[[File:YD3717_N2.LOG]]

<jmol><jmolApplet>
  <title>N2 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YD3717_N2.LOG</uploadedFileContents>
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==== H<sub>2</sub> ====



Molecule name: H<sub>2</sub>

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy: E(RB3LYP) = -1.17853936 a.u.

RMS gradient norm: 0.00000017 a.u.

Point group: D*H

H-H bond distance: 0.74279

Literature value of H-H bond distance: 0.74 <sup>[2]</sup>

H-H bond angle: 180

<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>


[[File:yd3717_h2_frequency.JPEG|thumb|Displayed frequencies of H2]]

Frequency #1 : 4465.68


[[File:YD3717_H2.LOG]]

<jmol><jmolApplet>
  <title>H2 molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YD3717_H2.LOG</uploadedFileContents>
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==== Reaction ====


Haber-Bosch process : N<sub>2</sub> + 3H<sub>2</sub> -> 2NH<sub>3</sub>

E(NH<sub>3</sub>)= -56.55776873 a.u.

2*E(NH<sub>3</sub>)= -113.1155375 a.u.

E(N<sub>2</sub>)= -109.52412868 a.u.

E(H<sub>2</sub>)= -1.17853936 a.u.

3*E(H<sub>2</sub>)= -3.53561808 a.u.

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]= -0.05579074 a.u. = -146.478599028 kJ/mol

The ammonia product is more stable than the gaseous reactants

== HCl ==


=== General information ===

Molecule name: HCl

Calculation method: RB3LYP

Basis set: 6-31G(d,p)

Final energy: E(RB3LYP) = -460.80077875 a.u.

RMS gradient norm: 0.00005211 a.u.

Point group: C*V

H-Cl bond distance: 1.28599

Literature value of H-Cl bond distance: 1.27 <sup>[2]</sup>

H-Cl bond angle: 180
<pre>
         Item               Value     Threshold  Converged?
 Maximum Force            0.000090     0.000450     YES
 RMS     Force            0.000090     0.000300     YES
 Maximum Displacement     0.000139     0.001800     YES
 RMS     Displacement     0.000197     0.001200     YES
</pre>


[[File:YD3717_HCL.LOG]]

<jmol><jmolApplet>
  <title>HCl molecule</title>
  <color>black</color>
  <size>200</size>
  <uploadedFileContents>YD3717_HCL.LOG</uploadedFileContents>
</jmolApplet></jmol>



=== Frequency analysis ===

[[File:yd3717_hcl_frequency.JPEG|thumb|Displayed frequencies of HCl]]

[[File:yd3717_hcl_vibration.png|thumb|HCl molecule in vibration with displacement vector shown]]


Only one frequency : 2956.80

According to 3N-5 rule, one peak is expected for HCl molecule in the IR spectrum



=== Atomic charges ===


Charge on H atom : +0.284 e

Charge on Cl atom : -0.284 e

H atom was expected to be +1 e, and Cl atom was expected to be -1 e, so that HCl would be neutral.

However, due to shielding effect of inner electrons, effective nuclear charge is smaller.

[[File:yd3717_hcl_charge.png|thumb|Charge distribution on HCl molecule]]


=== Molecular orbitals ===

[[File:yd3717_hcl_mo.png|thumb|center|Molecular orbital energies of HCl]]


==== 5th MO ====

[[File:yd3717_hcl_5.png|thumb|center|5th molecular orbital of HCl]]

This is a molecular orbital of Cl derived from the 2p atomic orbital and it is non-bonding. There should be three degenerate 2p orbital : 3p<sub>x</sub>, 3p<sub>y</sub> and 3p<sub>z</sub>, each have the same dumbbell shape but orient in different direction. However, the GaussView MO diagram shows there are two degenerate 2p orbitals (#4 & #5) and one 2p orbital slightly lower in energy (#3). This is because #3 2p orbital align with the bond and stabilized by the bond. 


==== 6th MO ====

[[File:yd3717_hcl_6.png|thumb|center|6th molecular orbital of HCl]]

This is a bonding molecular orbital derived from 1s AO of H and 3s AO of Cl. The two AOs overlap in phase to form this sigma garade orbital. It is occupied by two electrons and there is no node.


==== 7th MO ====

[[File:yd3717_hcl_7.png|thumb|center|7th molecular orbital of HCl]]

This is a bonding molecular orbital derived from 1s AO of H and 3p<sub>z</sub> AO of Cl. The two AOs overlap in phase to form this sigma orbital. It is occupied by two electrons and there is one node on the Cl atom.


==== 9th MO ====

[[File:yd3717_hcl_9.png|thumb|center|9th molecular orbital of HCl]]

This is a molecular orbital of Cl derived from the 3p AO and it is non-bonding. There are two degenerate 3p orbital : 3p<sub>x</sub> and 3p<sub>y</sub> which corresponds to #8 & #9. 3p<sub>z</sub> is not degenerate because it is used in bonding (7th MO). The 9th orbital is the HOMO and it is occupied by two electrons.


==== 10th MO ====

[[File:yd3717_hcl_10.png|thumb|center|10th molecular orbital of HCl]]

This is an anti-bonding sigma* orbital derived from 1s AO of H and 3p<sub>z</sub> AO of Cl. The two AOs overlap out of phase and there are two nodes. This is the LOMO molecular orbital.

== References ==

1. [https://cccbdb.nist.gov/exp2x.asp?casno=7664417 Experimental values of NH<sub>3</sub>]

2. [http://www.wiredchemist.com/chemistry/data/bond_energies_lengths.html Common bond lengths]