Rep:Mod:AW2415report

Molecule: NH₃

Below is shown information about the NH₃ molecule. The molecule was initially optimized using the program Gaussview. The data shown is after the optimization and covers bond length, vibrations and charge.

The following table shows information about the calculation method, bond lengths and angles.

Summary Table

Property
Calculation method	RB3LYP
Basis Set	6-31G(d,p)
Final Energy	-56.55776873 au
RMS gradient	0.00000485 au
Point Group	C3V
Optimized N-H bond length	1.01798 Å
Optimized H-N-H angle	105.74116o

Item Table

         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

Gallery

Optimised NH₃ molecule

test molecule

File:NH3 - 2 (FIRST OPTIMISATION).LOG

Vibrations

Questions

How many modes do you expect from the 3N-6 rule? No. modes=3(4)-6

Which modes are degenerate (ie have the same energy)? 2&3 and 5&6

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

Bends: 1,2,3

Stretch: 4,5,6

Which mode is highly symmetric? 4

One mode is known as the "umbrella" mode, which one is this? 1

How many bands would you expect to see in an experimental spectrum of gaseous ammonia? 4, however you will only see 2 because 2 have such a low intensity that they are likely to get lost in the spectrum.

Charge Analysis

Charge distribution on optimized NH₃ molecule

The charge distribution as expected because nitrogen is more electronegative than hydrogen. It therefore attracts electron density towards itself and so is more negative.

Charge on N: -1.125

Charge on H: 0.375

Molecule: H₂

The following data is about an H₂ molecule. It was obtained by using the program Gaussview after the molecule has been optimized.

Summary Table

Property
Calculation method	RB3LYP
Basis Set	6-31G(d,p)
Final Energy	-1.17853936 au
RMS gradient	0.00000017 au
Point Group	Dooh
Optimised H-H bond length	1.01798 Å

Item Table

         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

Gallery

H₂

test molecule

File:AW2415 H2 (FIRST OPTIMISATION).LOG

Vibrations

Vibrational anaysis for optimised H₂ molecule showing there are no negative frequencies

Charge Analysis

The two atoms are identical so there is an even charge distribution over the molecule. There is therefore no dipole within the molecule.

Molecule: N₂

The following data is about an N₂ molecule. It was obtained by using the program Gaussview after the molecule has been optimized.

Summary Table

Property
Calculation method	RB3LYP
Basis Set	6-31G(d,p)
Final Energy	-109.524128686 au
RMS gradient	0.00000060 au
Point Group	Dooh
Optimised N-N bond length	1.10550 Å

Item Table

         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

Gallery

test molecule

File:AW2415-N2 (OPTIMISED).LOG

Vibrations

Vibrational anaysis for optimised N₂ molecule showing there are no negative frequencies

Reaction Energies

E(NH₃)= -56.55776873 au

2*E(NH₃)= -113.1155375 au

E(N₂)= -109.524128686 au

E(H₂)= -1.17853936 au

3*E(H₂)= -3.53561808 au

ΔE=2*E(NH₃)-[E(N₂)+3*E(H₂)]= -0.055790734 au = -146.8177211 KJmol^-1

The enthalpy change for the reaction is negative therefore the products are more stable than the reactants.

Molecular Orbital Gallery

Charge Analysis

The two atoms are identical so there is an even charge distribution over the molecule. There is therefore no dipole within the molecule.

CO

Below is shown information about the carbon monoxide (CO) molecule. The molecule was initially optimized using the program Gaussview. The data shown is after the optimization and cover bond length, vibrations and charge.

Summary Table

Property
Calculation method	RB3LYP
Basis Set	6-31G(d,p)
Final Energy	-113.30945314 au
RMS gradient	0.00001828 au
Point Group	Dooh
Optimised C-O bond length	1.13793 Å

Item Table

         Item               Value     Threshold  Converged?
 Maximum Force            0.000032     0.000450     YES
 RMS     Force            0.000032     0.000300     YES
 Maximum Displacement     0.000012     0.001800     YES
 RMS     Displacement     0.000018     0.001200     YES

Gallery

Optimized CO molecule

test molecule

File:AW2415-CO (FIRST OPTIMISATION).LOG

Vibrations

IR spectrum of the CO molecule

Vibrational analysis of the CO molecule

Vibrational analysis for optimized CO molecule shows there are no negative frequencies. The only vibration is a symmetrical stretch, therefore there will only be one peak in the IR spectrum of CO.

Charge Analysis

Charge distribution in a CO molecule

Carbon and oxygen have different electronegativities and therefore there is an uneven charge distribution over the molecule. Oxygen is the more electronegative of the atoms due to having a higher effective nuclear charge on the valence electrons. Therefore it is the negative ens of the molecule.

Charge on oxygen: -0.506 au

Charge on Carbon: 0.506 au

Molecular Orbitals

Picture	Energy	Orbitals which form the MO	Description
	-19.25805 au	C:1s, O:1s	This orbital is a σ orbital. The orbital is deep in energy and hence will have little effect on the bonding of the molecule. Essentially it is just the oxygen 1s.
	-10.30433	C:1s, O:1s	This orbital is a σ* orbital. The orbital is very deep in energy and hence will have little effect on the bonding of the molecule. This is in reality just the carbon 1s.
	-1.15791	C:2s, O:2s	This orbital is the σ bonding orbital formed from the carbon and oxygen 2s orbitals. The 2s orbital of oxygen is lower in energy than the 2s of carbon, it is therefore closer to this, the bonding MO than the carbon 2s. As a result the orbital has more of the oxygen 2s character and hence is polarized towards oxygen. This orbital is filled and hence will contribute to the bonding of the molecule.
	-0.57004	C:2s, O:2s	This orbital is the σ* (antibonding) orbital formed from the carbon and oxygen 2s orbitals. The 2s orbital of carbon is higher in energy than the 2s of oxygen, it is therefore closer to the antibonding MO than the oxygen 2s. As a result the orbital has more of the carbon 2s character and hence is polarized towards carbon. This orbital is filled which means that it will cancel out the energy gain from putting electrons into the bonding orbital.
	-0.46743	C:2p, O:2p	This orbital is the π bonding orbital formed from the carbon and oxygen 2p orbitals. The 2p orbital of oxygen is lower in energy than the 2p of carbon, it is therefore closer to the bonding MO than the carbon 2s. As a result the orbital has more of the oxygen 2p character and hence is polarized towards oxygen. This orbital is filled and hence will contribute to the bonding of the molecule.
	-0.37145	C:2p, O:2p	This orbital is a σ bonding orbital formed from the head on overlap of two 2p atomic orbitals. It is also the HOMO of the molecule.
	-0.37145	C:2p, O:2p	This orbital is a π* (antibonding) orbital formed destructive side on overlap of two 2p atomic orbitals. It is also the LUMO of the molecule.