Felix Introduction to Molecular Modelling - Dr. Hunt

Optimisation, Vibrations and Charges, Reactions and Orbitals

After being introduced to ChemWiki and GaussView, we learnt the basics of optimisation, using NH₃ as our test molecule.

NH₃ Optimisation

Optimised NH₃ Molecule
Molecule	NH₃
Calculation Method	RB3LYP
Basis Set	6-31G(d.p.)
Final Energy E(RB3LYP) (au)	-56.557769
RMS Gradient	0.00000485
Point Group	C_3V
Optimised Bond Distance (Å)	1.01798
Optimised Bond Angle (°)	105.741

The following is an excerpt from the 'real' output, which is the file that Gaussian generates. The fact that the the Maximum force of any of the items does not exceed 0.00045 au and the RMS does not exceed 0.0003 au.


     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

Ammonia Molecule

This screenshot shows the vibrational modes of the NH₃ molecule calculated by GuassView. File:FD915 HUNT MOLMOD NH3 OPT POP.LOG

Questions on the Vibrational Modes of the Optimised NH₃ Molecule
How many modes do you expect from the 3N-6 rule?	6
Which modes are degenerate (ie have the same energy)?	Modes 2/3 and modes 5/6 are degenerate
Which modes are "bending" vibrations and which are "bond stretch" vibrations?	Modes 1,2,3 are bending, and modes 4,5,6 are stretching.
Which modes are highly symmetric?	Modes 1 and 4 are highly symmetric
One mode is known as the "umbrella" mode, which one is this?	The first mode
How many bands would you expect to see in an experimental spectrum of gaseous ammonia?	2, due to the low intensity of modes 4,5,6.

This thumbnail shows the nitrogen of ammonia in red to highlight its negative charge of -1.125, and the hydrogens in green with a positive charge of 0.375.

N₂ Optimisation:

FD915_Nitrogen_Optimisation
Molecule	N₂
Calculation Method	RB3LYP
Basis Set	6-31G(d.p.)
Final Energy E(RB3LYP) (au)	-109.5241
RMS Gradient	0.0000006
Point Group	D_∞h
Optimised Bond Distance (Å)	1.1055
Optimised Bond Angle (°)	180

Again, the values for the Maximum Displacement and the RMS show that the molecule has been properly optimised.

    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

The table shows that the molecule has only one vibrational mode.

Nitrogen Molecule

File:FD915 NITROGEN OPTIMISATION.LOG

H₂ Optimisation:

FD915_Hydrogen_Optimisation
Molecule	H₂
Calculation Method	RB3LYP
Basis Set	6-31G(d.p.)
Final Energy E(RB3LYP) (au)	-1.17854
RMS Gradient	0.00000017
Point Group	D_∞h
Optimised Bond Distance (Å)	0.74279
Optimised Bond Angle (°)	180

Note the especially low value for the final energy of the hydrogen molecule.

 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

Hydrogen Molecule

File:FD915 HYDROGEN OPTIMISATION.LOG

Energies Involved in Production of NH₃ (au):

Energies Involved In Production of NH₃ (au)
E(NH3)= -56.55776873
2*E(NH₃)= -113.1155375
E(N₂)=-109.52412868
E(H₂)=-1.17853936
3*E(H₂)= -3.53561808
ΔE=2E(NH₃)-[E(N₂)+3E(H₂)] = -0.0557907
In kJ/mol = -146.4784829

The ammonia is more stable than the gaseous reactants, due to the large negative energy value.

My Own Molecule

Optimised H₂O Molecule
Molecule	H₂O
Calculation Method	RB3LYP
Basis Set	6-31G(d.p.)
Final Energy E(RB3LYP) (au)	--76.41973740
RMS Gradient	0.000046276
Point Group	C_2V
Optimised Bond Distance (Å)	0.96522
Optimised Bond Angle (°)	103.745

The value for the Maximum Force/RMS show that the molecule has been optimised properly,
and that the angle for the water molecular is apparently 103.75°, 
whereas I thought the value was supposed to be around 104.5°.

  Item               Value     Threshold  Converged?
 Maximum Force            0.000099     0.000450     YES
 RMS     Force            0.000081     0.000300     YES
 Maximum Displacement     0.000115     0.001800     YES
 RMS     Displacement     0.000120     0.001200     YES

Water Molecule

Molecular Orbitals of the Optimised Water Molecule

Optimised H₂O Molecular Orbitals
Name:	Energy (au):	Description:
1Õ	-19.13799	The oxygen 1s orbital is too low in energy to interact with the 1s orbital of the hydrogen, and so forms a non-bonding molecular orbital.
3Õ	-0.51503	This molecular orbital shows contribution from the 2s and 2p orbitals of the oxygen and the 1s orbitals of the hydrogen. It is occupied and low lying as there is an occupied molecular orbital between it and the HOMO.
1π*	-0.37102	This fourth molecular orbital is occupied, showing contribution from the hydrogens and the oxygen molecule due to the wavefunction having areas of high density around all three atoms. It is only slightly lower in the energy than the HOMO.
HOMO	-0.29197	The HOMO here appears to be one of the p orbitals from oxygen which has formed a molecular orbita; the shape implies that there is no contribution from the hydrogen 1s orbitals.
LUMO - Angle 1	0.06538	The LUMO of water shows contribution from the 2s and 2p orbitals of the oxygen as well as the hydrogen 1s orbitals. It is large and diffuse, especially compared with some of the lower lying molecular orbitals in the molecule.
LUMO - Angle 2	0.06538