NH₃ Investigation

NH₃ Molecule

Summary

What is the molecule?: NH₃

What is the calculation method?: RB3LYP

What is the basis set?: 6-31G(d,p)

What is the final energy E(RB3LYP)(au)?: -56.55776873

What is the RMS gradient(au)?: 0.00000485

What is the point group of your molecule?: C_3V

What is the optimised N-H bond distance(Å)?: 1.01798

What is the optimised H-N-H bond angle(°)?: 105.741

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

Optimised NH₃ Molecule

Optimised NH3

The optimisation file is linked to here

Vibrations Display

What vibration does each mode correspond to?:

Mode 1 = N-H Wagging Bend (active - change in dipole moment)

Mode 2 = H-N-H Scissoring Bend (active - change in dipole moment)

Mode 3 = H-N-H Scissoring Bend (active - change in dipole moment)

Mode 4 = N-H Symmetric Stretch (active - change in dipole moment)

Mode 5 = N-H Asymmetric Stretch (active - change in dipole moment)

Mode 6 = N-H Asymmetric Stretch (active - change in dipole moment)

How many modes do you expect from the 3N-6 rule?: 3(4)-6 = 6

Which modes are degenerate (i.e. have the same energy)?: Using the mode numbers on the Display Vibrations window - 2&3 and 5&6

Which modes are "bending" vibrations and which are "bond stretch" vibrations?: Bending = 1,2,3 and Stretching = 4,5,6

Which mode is highly symmetric?: Mode 4

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

How many bands would you expect to see in an experimental spectrum of gaseous ammonia?: You would expect to see 4 bands.

Charge Distribution

What is the charge on the Nitrogen atom?: -1.125

What charge would you expect for the Nitrogen atom?: Negative charge

What is the charge on the Hydrogen atoms?: 0.375

What charge would you expect on the Hydrogen atoms?: Positive charge

N₂ Molecule

Summary

What is the molecule?: N₂

What is the calculation method?: RB3LYP

What is the basis set?: 6-31G(d,p)

What is the final energy E(RB3LYP)in atomic units(au)?: -109.52412868

What is the RMS gradient(au)?: 0.00000060

What is the point group of your molecule?: D_∞h

What is the optimised N-N bond distance(Å)?: 1.10550

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

Optimised N₂ Molecule

Optimised N2

The optimisation file is linked to here

Frequency of Vibration

The frequency of the vibrational mode is 2457.33 Hz. This is positive so the molecule is fully optimised.

H₂ Molecule

Summary

What is the molecule?: H₂

What is the calculation method?: RB3LYP

What is the basis set?: 6-31G(d,p)

What is the final energy E(RB3LYP)in atomic units(au)?: -1.17853936

What is the RMS gradient (au)?: 0.00000017

What is the point group of your molecule?: D_∞h

What is the optimised H-H bond distance (Å)?: 0.74279

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

Optimised H₂ Molecule

Optimised H2

The optimisation file is linked to here

Frequency of Vibration

The frequency of the vibrational mode is 4465.68 Hz. This is positive so the molecule is fully optimised.

Reaction Energies - The Haber-Bosch process

$E (N H 3) = - 56.55776873$

$2 \times E (N H 3) = - 113.1155375$

$E (N 2) = - 109.52412868$

$E (H 2) = - 1.17853936$

$3 \times E (H 2) = - 3.53561808$

$Δ E = 2 \times E (N H 3) - [E (N 2) + 3 \times E (H 2)] = - 0.05579074$

$Δ E (k J m o l^{- 1}) = 2625.5 \times - 0.05579074 = - 146.4785879 = - 146.479 k J m o l^{- 1}$

The energy change for the reaction is negative, meaning that the reaction is exothermic. This means that the product (gaseous ammonia) is more stable than the reactants (gaseous nitrogen and gaseous hydrogen)as the product is at a lower energy state.

F₂ Investigation

Summary

What is the molecule?: F₂

What is the calculation method?: RB3LYP

What is the basis set?: 6-31G(d,p)

What is the final energy E(RB3LYP)(au)?: -199.49825218

What is the RMS gradient(au)?: 0.00007365

What is the point group of your molecule?: D_∞h

What is the optimised F-F bond distance(Å)?: 1.40281

Item Table

         Item               Value     Threshold  Converged?
 Maximum Force            0.000128     0.000450     YES
 RMS     Force            0.000128     0.000300     YES
 Maximum Displacement     0.000156     0.001800     YES

Optimised F₂ Molecule

Optimised F2

The optimisation file is linked to here

Vibrations Display

This vibrational mode frequency refers to the symmetric stretch vibration. The value is positive and so the molecule is fully optimised.

Charge Distribution

What charge would you expect for the Fluorine atoms?: No charge, this is because the molecule is diatomic where both atoms are equally electronegative and have an equally strong pull on the electrons.

What is the charge on the atoms?: No charge

Molecular Orbitals

Molecular Orbital Diagram

Source:http://www.grandinetti.org/

**π^*2p**

What AOs contribute to the MO?: This MO is made up of the 2p AOs

Is the MO bonding, antibonding or a mixture?: This MO is antibonding

What is the energy of the MO?: -0.39190, this is the HOMO (highest occupied molecular orbital)

Is the MO occupied or unoccupied?: This MO is occupied

What effect will your MOs have on bonding?: The MO is antibonding and so will weaken the bonding. This cancels out the pi bonding orbitals and so no pi bond is formed.

**σ^*2p**

What AOs contribute to the MO?: This MO is made up of the 2p AOs

Is the MO bonding, antibonding or a mixture?: This MO is antibonding

What is the energy of the MO?: -0.12679

Is the MO occupied or unoccupied?: The MO is unoccupied, it is the LUMO (lowest unoccupied molecular orbital)

What effect will your MOs have on bonding?: The MO is antibonding and so would weaken the bonding if occupied. This is unoccupied and so a sigma bond can form.

π2p

What AOs contribute to the MO?: This MO is made up of the 2p AOs

Is the MO bonding, antibonding or a mixture?: This MO is bonding

What is the energy of the MO?: -0.52332

Is the MO occupied or unoccupied?: This MO is occupied

What effect will your MOs have on bonding?: This is a bonding orbital and so will contribute to the bonding and strengthen it. This would form part of the pi bond, however the antibonding is also filled and so no pi bond is formed.

σ2p

What AOs contribute to the MO?: This MO is made up of 2p AOs

Is the MO bonding, antibonding or a mixture?: This MO is bonding

What is the energy of this MO?: -0.58753

Is the MO occupied or unoccupied?: This MO is occupied

What effect will your MOs have on bonding?: This MO is responsible for the sigma bond, it is bonding and so strengthens the bond.

**σ^*2s**

What AOs contribute to the MO?: This MO is made up of 2s AOs

Is the MO bonding, antibonding or a mixture?: This MO is antibonding

What is the energy of the MO?: -1.09047

Is the MO occupied or unoccupied?: This MO is occupied

What effect will your MOs have on bonding?: This MO is antibonding and so weakens the bond. This cancels out the occupied 2s bonding orbital and so no sigma bond is formed from the 2s AOs.

ClF₃ Investigation

Summary

What is the molecule?: ClF₃

What is the calculation method?: RB3LYP

What is the basis set?: 6-31G(d,p)

What is the final energy E(RB3LYP)(au)?: -759.46531651

What is the RMS gradient(au)?: 0.00018431

What is the point group of your molecule?: C_S

What is the optimised Cl-F bond distance(Å)?: 1.65132, 1.72899 and 1.72765

What is the optimised F-Cl-F bond angle(°)?: 87.168 and 87.138

Item Table

        Item               Value     Threshold  Converged?
 Maximum Force            0.000333     0.000450     YES
 RMS     Force            0.000145     0.000300     YES
 Maximum Displacement     0.000851     0.001800     YES
 RMS     Displacement     0.000548     0.001200     YES

Optimised ClF₃ Molecule

Optimised ClF3

The optimisation file is linked to here

Vibrations Display

What vibration does each mode correspond to?:

Mode 1 = F-Cl-F Scissoring Bend (active - change in dipole moment)

Mode 2 = F-Cl-F Scissoring Bend (active - change in dipole moment)

Mode 3 = F-Cl-F Wagging Bend (active - change in dipole moment)

Mode 4 = Cl-F Symmetric Stretch (active - change in dipole moment)

Mode 5 = Cl-F Symmetric Stretch (active - change in dipole moment)

Mode 6 = Cl-F Asymmetric Stretch (active - change in dipole moment)

How many modes do you expect from the 3N-6 rule?: 3(4)-6=6

Which modes are "bending" vibrations and which are "bond stretch" vibrations?: Bending = 1,2,3 and Stretching = 4,5,6

One mode is known as the "umbrella" mode, which one is this?: Mode 2

How many bands would you expect to see in an experimental spectrum of ClF₃?: You would expect to see 6 bands.

Charge Distribution

What charge would you expect for the Chlorine atom?: Positive charge

What charge would you expect on the Fluorine atoms?: Negative charge as more electronegative so have a greater pull on the electrons in the bonds

What is the charge on the atoms?:

Chlorine = +1.225

Fluorine 1 = -0.455

Fluorine 2 = -0.316

Fluorine 3 = -0.454

NH3 Investigation

NH3 Molecule

Summary

Item Table

Optimised NH3 Molecule

Vibrations Display

Charge Distribution

N2 Molecule

Summary

Item Table

Optimised N2 Molecule

Frequency of Vibration

H2 Molecule

Summary

Item Table

Optimised H2 Molecule

Frequency of Vibration

Reaction Energies - The Haber-Bosch process

F2 Investigation

Summary

Item Table

Optimised F2 Molecule

Vibrations Display

Charge Distribution

Molecular Orbitals

Molecular Orbital Diagram

π*2p

σ*2p

π2p

σ2p

σ*2s

ClF3 Investigation

Summary

Item Table

Optimised ClF3 Molecule

Vibrations Display

Charge Distribution

NH₃ Investigation

NH₃ Molecule

Optimised NH₃ Molecule

N₂ Molecule

Optimised N₂ Molecule

H₂ Molecule

Optimised H₂ Molecule

F₂ Investigation

Optimised F₂ Molecule

**π^*2p**

**σ^*2p**

**σ^*2s**

ClF₃ Investigation

Optimised ClF₃ Molecule