Rep:Mod:Batman

Introduction to Milan's Modelling Emporium

When Analysing Molecules

The following criterion must be included:

what the molecule is
a rotable 3d JSmol image file
the molecular point group
the calculation method
the basis set
the RMS gradient
the final energy, E(RB3LYP), in atomic units
a link to the log file
the item table
the vibrational frequencies

NH₃ Molecule

ammonia molecule

The ammonia molecule, point group C_3v was optimised with calculation method RB3LYP, basis set 6-31G(d.p), giving an RMS gradient of 0.00000485au and a final energy of -56.55776873au. The optimised N-H bond length was 1.01798Å, with an H-N-H bond angle of 105.741°. The N atom bore a charge of -1.125, and each H atom a charge of +0.375. This is expected, as nitrogen is much more electronegative than hydrogen, with a ΔΧ value of 0.84. The log file can be found at Media:MilanK Ammonia OptF POP.LOG. The item table is below:

         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

From the 3N-6 rule, six modes of vibration are expected. Modes 2 and 3 are degenerate, as are modes 5 and 6. Modes 1 through 3 are 'bending' vibrations, and modes 4 through 6 are 'bond stretch' vibrations. Mode 4 is highly symmetric, and mode 1 is the umbrella mode. Therefore four total bands would be observed on an experimental infrared spectrum of ammonia in the gas phase. However, the high-wavenumber modes at 3589.82cm^-1 show extremely low intensity due to the negligible change in dipole moment.

H₂ Molecule

dihydrogen molecule

The dihydrogen molecule, point group D_∞h was optimised with calculation method RB3LYP, basis set 6-31G(D,P), giving an RMS gradient of 0.00000017au and a final energy of -1.17853936au. The optimised H-H bond length was 0.74279Å. There was no dipole moment. The log file can be found at Media:MILANK DIHYDROGEN OPTF POP.LOG. The item table is below:

         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

From the 3N-5 rule, one mode of vibration is expected, which has a frequency of 4465.68.

N₂ Molecule

dinitrogen molecule

The dinitrogen molecule, point group D_∞h was optimised with calculation method RB3LYP, basis set 6-31G(D,P), giving an RMS gradient of 0.00000124au and a final energy of -109.52412868au. The optimised N-N bond length was 1.10550Å. There was no dipole moment. The log file can be found at Media:MILANK DINITROGEN OPTF POP.LOG. The item table is below:

         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

From the 3N-5 rule, one mode of vibration is expected, which has a frequency of 2457.33.

Using Milan's Modelling Emporium to Calculate Reaction Energies

The enthalpy change for the reaction of the Haber Process can be computed using molecular energies. The equation for the reaction is N₂ + 3H₂ → 2NH₃

ΔE = 2 × E(NH₃) - [E(N₂) + 3 × E(H₂)]

E(NH₃) = -56.55776873au

2 × E(NH₃) = -113.11553746au

E(N₂) = -109.52412868au

E(H₂) = -1.17853936au

3 × E(H₂) = -3.53561808au

ΔE = -113.11553746au - (-109.52412868au + -3.53561808au) = -113.11553746au + 113.05974676au

ΔE = -0.0557907au = -146.47848285kJ/mol

Ammonia is more stable than the gaseous reactants.

Using Milan's Modelling Emporium to Model the Project Molecule Silane

silane molecule

The silane molecule, point group T_d was optimised with calculation method RB3LYP, basis set 6-31G(d.p), giving an RMS gradient of 0.00000003au and a final energy of -291.88802760au. There was no dipole moment. The optimised Si-H bond length was 1.48485Å, with an H-Si-H bond angle of 109.471°. The experimental bond lengths are 1.46Å (Ballinger, R.A and March, N.H. (1954): Bond-Lengths and Force Constants for Methane, Silane and Germane. Nature 174, p4421). The Si atom bore a charge of +0.629, and each H atom a charge of -0.157. This is expected, as hydrogen is slightly more electronegative than silicon, with a ΔΧ value of 0.3. The log file can be found at Media:MILANK SILANE OPTF POP.LOG. The item table is below:

         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     0.000000     0.001200     YES

From the 3N-6 rule, nine modes of vibration are expected. Modes 1, 2 and 3 are degenerate, as are modes 4 and 5, as well as modes 7, 8 and 9. Modes 1 through 5 are 'bending' vibrations, and modes 6 through 9 are 'bond stretch' vibrations. Modes 4 through 6 are symmetric, as they do not cause a change in the dipole moment of the molecule, therefore would not appear on the spectrum. Overall, therefore two total bands would be observed on an experimental infrared spectrum of silane in the gas phase.

The molecular orbital diagram for the main orbitals of silane is depicted below, along with the surface plots of six MOs formed using Gaussian. Figure 1 depicts the occupied silicon 2s orbital, which is too close to the silicon nucleus and too low in energy to interact with the hydrogen 1s orbitals. Figure 2 depicts the occupied silicon 2p orbital, which, for the same reasons, does not interact with the hydrogen 1s orbitals. Consequently, neither contribute to the bonding in silane, as they are too deep in energy. Figure 3 depicts the occupied silane 1a₁ orbital, which results from constructive overlap of the silicon 3s orbital and the four hydrogen 1s orbitals. It is a wholly bonding orbital that lies slightly below the HOMO in energy, and results in a strong sigma bonding interaction between the five atoms. Figure 4 depicts the occupied silane 1t₂ orbital, which results from constructive overlap of one of the silicon 3p orbitals and the four hydrogen 1s orbitals. It is a wholly bonding orbital and is one of the three HOMOs, as there are two more degenerate 1t₂ orbitals made up of the remaining silicon 3p orbitals. It results in a less strong sigma bonding interaction between the five atoms than than the 1a₁ orbital. Figure 5 depicts the unoccupied silane 2t₂* orbital, which results from destructive overlap of one of the silicon 3p orbitals and the four hydrogen 1s orbitals. It is a wholly antibonding orbital and is one of the three LUMOs, as there are two more degenerate 2t₂* orbitals made up of the remaining silicon 3p orbitals. It results in a less strong sigma antibonding interaction between the five atoms than than the 2a₁* orbital. Figure 6 depicts the unoccupied silane 2a₁* orbital, which results from destructive overlap of the silicon 3s orbital and the four hydrogen 1s orbitals. It is a wholly antibonding orbital that lies above the LUMO in energy, and results in a strong sigma antibonding interaction between the five atoms.