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Toms Page

NH₃ Molecule

NH₃ Data
variable	Result
Molecule	NH₃
Calculation method	RB3LYP
Basis set	6-31(d.p)
Final energy (au)	-56.6
RMS gradient	0.00000485
Point group	C₃V
Bond distance	1.01798
Bond angle	105.741

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
 Predicted change in Energy=-5.986283D-10
 Optimization completed.

NH3 molecule

The optimisation file is liked to here

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

Using the 3N-6 rule there is an expected 6 vibrational frequencies which matches the data.

which modes are degenerate (ie have the same energy)?

Modes 2 and 3 are degenerate and also 5 and 6.

which modes are "bending" vibrations and which are "bond stretch" vibrations?

Type of Vibration
Bend	Stretch
1	4
2	5
3	6

which mode is highly symmetric?

Mode 4 is highly symmetric

one mode is known as the "umbrella" mode, which one is this?

The Umbrella stretch is mode 4 as it gives an umbrella stretch shape.

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

There would be 2 bands. There are three values with a high enough absorption to register a peak in the infrared spectrum. However 2 of the bends have the same frequency and absorption making the bands indistinguishable leaving 2 distinct bands.

Charge on ammonia

Atom/Charge
Atom	Charge
Hydrogen	0.375
Nitrogen	-1.125

Explanation of the charges

The Nitrogen atom is more electronegative and has a drawing affect on the electrons pulling them close to its nucleus. This polar character in the band towards the nitrogen means it picks up a slight negative charge. The electrons are therefore pulled further from the hydrogen nucleus resulting in a small positive charge on each Hydrogen.

N₂ Molecule

N₂ Data
variable	Result
Molecule	N₂
Calculation method	RB3LYP
Basis set	6-31(d.p)
Final energy (au)	-109.5
RMS gradient	0.0247
Point group	Dinf
Bond distance	1.10550
Bond angle	180.00

         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
 Predicted change in Energy=-3.400871D-13
 Optimization completed.

N2 molecule

The optimisation file is liked to here

H₂ Molecule

H₂ Data
variable	Result
Molecule	H2
Calculation method	RB3LYP
Basis set	6-31(d.p)
Final energy (au)	-1.178
RMS gradient	0.00000017
Point group	Dinf
Bond distance	0.6
Bond angle	180.00

         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
 Predicted change in Energy=-1.164080D-13
 Optimization completed.
    -- Stationary point found.

H2 molecule

The optimisation file is liked to here

N₂ + 3H₂ -> 2NH₃

Energy Of Molecules
Molecule/Function	Energy (au)
E(NH₃)	-56.557768
2*E(NH₃)	-113.115536
E(N₂)	-109.52412868
E(H₂)	-1.17853936
3*E(H₂)	-3.53561808
ΔE = 2E(NH₃) -[E(N₂)+3(H₂)]	0.634

Energy Of Process
uni	Energy
au	-0.05578924
KJ/mol	-146.475

Identify which is more stable the gaseous reactants or the ammonia product?

The Reactants are more stable than the products in this reaction. For the reaction to go forward there must be a positive increase in energy meaning the reactants where lower in energy and more stable. Energy is required to be put into the system to gain the products which have a higher energy.

Methane Molecule (Own Molecule)

CH₄ Molecule

CH₄ Data
variable	Result
Molecule	CH₄
Calculation method	RB3LYP
Basis set	6-31(d.p)
Final energy (au)	-40.524
RMS gradient	0.00003263
Point group	T_d
Bond distance	1.09197
Bond angle	109.47


         Item               Value     Threshold  Converged?
 Maximum Force            0.000063     0.000450     YES
 RMS     Force            0.000034     0.000300     YES
 Maximum Displacement     0.000179     0.001800     YES
 RMS     Displacement     0.000095     0.001200     YES
 Predicted change in Energy=-2.256043D-08
 Optimization completed.
    -- Stationary point found.

CH4 molecule

The optimisation file is liked to here

I would expect 2 bands in the infrared spectrum of this molecule as there are 6 modes which have an infrared intensity. But these go into 2 sets of 3 modes each identical.

CH₄ Bands
Frequency	Infrared 10^-40esu²cm²
1356.2	14.1008
3162.33	25.3343

CH₄ frequencies
Bend	Stretch
1	6
2	7
3	8
4	9
5

CH₄ Charges
Atom	Charge
Carbon	-0.93
Hydrogen	0.233

CH₄ Orbitals

CH₄ Data
Orbital	Representation
1S orbital of the Carbon, very low in Energy in comparison to the following orbitals due to it being closer to the nucleus. Filled with 2 spin paired electrons both from the carbon.
σ 2s electron from the Carbon combining with a 1s from Hydrogen forms a much higher energy MO compared to that of just the carbon. The electrons feel less force from the nucleus as they are in the valence shell.
σ Hydrogen 1s with Carbon 2p. The next 3 shells are all degenerate meaning they have the same energy but differing on the axis on which they are formed. These are higher Energy MO's because the p electron is further and more shielded from the nucleus. This increases the energy of the MO it forms.
σ Hydrogen 1s with Carbon 2p
σ Hydrogen 1s with Carbon 2p

Independent Investigation into Acetone

optimization first ran with a torsion angle of 0 degrees.

0 degrees dihedral

Acetic Acid data
variable	Result
Molecule	C₂H₄O₂
Calculation method	RB3LYP
Basis set	6-31(d.p)
Final energy (au)	-229.081
RMS gradient	0.0001307
Point group	CS
Dihedral Angle	0

         Item               Value     Threshold  Converged?
 Maximum Force            0.000322     0.000450     YES
 RMS     Force            0.000118     0.000300     YES
 Maximum Displacement     0.001823     0.001800     NO 
 RMS     Displacement     0.000801     0.001200     YES

<pre>
NOTE its acceptable for the max deisplacement not to converge in organic molecules

Acetic

The optimisation file is liked to here

The fact that all the infrared are evidence that the structure is optimized.

90° Torsion angle

Acetic Acid data
variable	Result
Molecule	C₂H₄O₂
Calculation method	RB3LYP
Basis set	6-31(d.p)
Final energy (au)	-229.081
RMS gradient	0.00001289
Point group	C₁
Dihedral Angle	90

         Item               Value     Threshold  Converged?
 Maximum Force            0.000018     0.000450     YES
 RMS     Force            0.000008     0.000300     YES
 Maximum Displacement     0.001389     0.001800     YES
 RMS     Displacement     0.000660     0.001200     YES
 Predicted change in Energy=-1.108190D-08
 Optimization completed.
    -- Stationary point found.

Acetic

Note structure was made mol file due to error in position when log used.

The optimization file is liked to here

The Molecule has been optimized and matches the structure when the dihedral is 0

Toms Page

NH3 Molecule

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

which modes are degenerate (ie have the same energy)?

which modes are "bending" vibrations and which are "bond stretch" vibrations?

which mode is highly symmetric?

one mode is known as the "umbrella" mode, which one is this?

how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

Charge on ammonia

Explanation of the charges

N2 Molecule

H2 Molecule

N2 + 3H2 -> 2NH3

Identify which is more stable the gaseous reactants or the ammonia product?

Methane Molecule (Own Molecule)

CH4 Molecule

CH4 Orbitals

Independent Investigation into Acetone

0 degrees dihedral

90° Torsion angle

NH₃ Molecule

N₂ Molecule

H₂ Molecule

N₂ + 3H₂ -> 2NH₃

CH₄ Molecule

CH₄ Orbitals