Rep:Mod:CET2016

NH₃ molecule

NH₃ optimisation

NH₃

Property	value
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)	-56.55776873 au
RMS gradient	0.00000485 au
Point group	C3v
Bond length	1.01798
Bond angle	105.741

Optimization results

         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

NH3

The optimisation file is liked to here

Vibrations

Vibrational frequencies of NH3.

For NH₃, following the 3N-6 rule, 6 vibrational modes would be expected. These include, symmetrical stretching, asymmetrical stretching, scissoring (bending), rocking, wagging and twisting. From our table, vibrations 2 and 3, and 5 and 6 are degenerate. Vibrations 1,2, and 3 are bending, and 4, 5, and 6 are stretching. Vibrational mode 4 is highly symmetric. Mode 1 is known as the "umbrella" mode, as it looks like an inversion. As an IR of gaseous ammonia, you would expect 4 peaks, however, the last peak would have a very small intensity (~0.2711) and is negligible.

Charge analysis

Charge analysis of the different atoms in NH3.

In NH₃, the nitrogen adopts a negative charge of -1.125, and hydrogen has a charge of +0.375. The nitrogen has a negative charge because it is more electronegative so draws the bonding electrons towards it to make the charge density negative. Nitrogen also has a lone pair of electrons, making it more negative. As the bonding electrons are drawn away from the hydrogen atoms, these adopt a positive charge. The net charge of the molecule is zero, as the positive hydrogen charge cancels out the negative charge on nitrogen. The molecule is not ionised.

N₂ optimisation

N₂

Property	value
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)	-109.52412868 au
RMS gradient	0.00000060 au
Point group	D*H
Bond length	1.10550
Bond angle	180

         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

There is only one vibrational frequency for N₂, which is a stretch at frequency of 2457.33 cm^-1. However, the intensity is 0, so this peak will not show on an IR spectra. N₂ is IR inactive.

The optimisation file is liked to here

H₂ optimisation

H₂

Property	value
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)	-1.17853936 au
RMS gradient	0.00000017 au
Point group	D*H
Bond length	0.74729
Bond angle	180

         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

There is only one vibrational frequency for H₂, which is a stretch at frequency of 4465.68 cm^-1. However, the intensity is 0, so this peak will not show on an IR spectra. H₂ is IR inactive.

The optimisation file is liked to here

Haber-Bosch process

N2 + 3H2 -> 2NH3

E(NH₃)= -56.55776873 au

2*E(NH₃)= -113.1155375 au

E(N₂)= -109.52412868 au

E(H₂)= -1.17853936 au

3*E(H₂)= -3.53591808 au

ΔE=2*E(NH₃)-[E(N₂)+3*E(H₂)]= -0.05549074 au = -145.6909489681 kJ/mol

The ammonia products are more stable as they have a more negative enthalpy than the reactants .

Project molecule CN^-

CN^-

Property	value
Calculation method	RB3LYP
Basis set	6-31G(d,p)
Final energy E(RB3LYP)	-92.82453153 au
RMS gradient	0.00000704 au
Point group	C*v
Bond length	1.18409
Bond angle	180

         Item               Value     Threshold  Converged?
 Maximum Force            0.000012     0.000450     YES
 RMS     Force            0.000012     0.000300     YES
 Maximum Displacement     0.000005     0.001800     YES
 RMS     Displacement     0.000008     0.001200     YES

CN molecule

The optimisation file is liked to here

Vibrations

Vibrational frequencies of CN.

There is one vibrational mode at 2139.19cm^-1, with an intensity of 7.7521. This is a bond stretch. There are no negative frequencies.

Charge Analysis

Charge analysis of CN.

In the CN^- molecule, the nitrogen atom adopts a charge of -0.750, and the carbon atom adopts a charge of -0.250. The overall charge of the atom is -1, and the substituent charges on the atoms add up to this value. The nitrogen has a more negative value because it is the more electronegative atom, so draws the bonding electrons and hence negative charge towards it. However, as the molecule is negative, there is still negative charges that reside on the carbon.

Molecular orbitals

Charge analysis of CN. This MO is asymmetrical d-orbital. This bond is not formed in CN^- because there are not enough electrons in CN^- to occupy the 3d AOs.

Charge analysis of CN. These two MO are of the two pi bonds found in CN^{-<, which are formed from the in phase overlap of p orbitals.}

Charge analysis of CN. These two MO are of the two pi bonds found in CN^{-<, which are formed from the in phase overlap of p orbitals.}

Charge analysis of CN. This MO shows p bonding character due to the appearance of nodes.

Charge analysis of CN. This MO shows distorted sigma bonding.