The Wiki page for Introduction to Molecular Modelling 2. Submitted by Peter Gobbett
NH3 Molecule
Calculation Data
Key Information
Common Name
Ammonia
Molecular Formula
NH3
Calculation Method
RB3LYP
Basis Set
6-31G(D.P)
Final Energy (RB3LYP)
-56.55776873 a.u.
RMS Gradient
0.00000485 a.u.
Point Group
C3v
Optimised N-H Bond Distance
1.01798A
Optimised H-N-H Bond Angle
105.741o
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
Gaussview vibration analysis window for an NH3 molecule.
Frequency Analysis
No. of Modes (3N-6)
6
Degenerate Modes
Modes 2&3, Modes 5&6
"Bending" vibration modes
1, 2, 3
"Bond Stretch" vibration modes
4, 5, 6
Mode of Highest Symmetry
4
"Umbrella" vibration mode
1
Bands in experimental spectrum
4 in therory (due to two degenerate pairs) but it is likely only modes 1 and 2&3 would be distinguishable above noise. 4 and 5&6 each have both high frequency and low intensity.
The above image shows the charge distribution in the optimised NH3 molecule. The Nitrogen is negatively charged and each Hydrogen atom has a slight partial positive charge. This difference is reinforced by theory, with the concept of electronegativity. Nitrogen is far more electronegative than Hydrogen, thus is better able to attract bonding electrons to itself. This accounts for the differences in charge. Thus, although the bonds are covalent, they have slight ionic character due to the difference in electronegativity. Thus they are polar bonds.
The calculated bond length is equal to the literature reference, so the Gaussian model is highly accurate.
Item Table
Item Value Threshold Converged?
Maximum Force 0.000211 0.000450 YES
RMS Force 0.000211 0.000300 YES
Maximum Displacement 0.000278 0.001800 YES
RMS Displacement 0.000393 0.001200 YES
The above image shows the charge distribution in the optimised H2 molecule. The molecule is diatomic and of the same element, thus there is no charge difference and the bond is fully covalent.
The calculated bond length is very close to the literature reference, so the Gaussian model is highly accurate.
Item Table
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000006 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000003 0.001200 YES
The above image shows the charge distribution in the optimised N2 molecule. The molecule is diatomic and of the same element, thus there is no charge difference and the bond is fully covalent.
Reaction Energies
Haber–Bosch process : 3H2 + N2 → 2NH3
Energy Data
E (NH3)
-56.55776873 a.u.
2x E (NH3)
-113.1155375 a.u.
E (N2)
-109.52412868 a.u.
E (H2)
-1.17853930 a.u.
3x E (H2)
-3.5356179 a.u.
ΔE
-0.05579092 a.u.
ΔE
-146.479071618 kJmol-1
Comments
The reaction is exothermic. Thus, the product (NH3) must be thermodynamically more stable than the reactants (H2 and N2).
The calculated bond length is very close to the literature reference, so the Gaussian model is highly accurate.
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
RMS Displacement 0.000221 0.001200 YES
The above image shows the charge distribution in the optimised F2 molecule. The molecule is diatomic and of the same element, thus there is no charge difference and the bond is fully covalent.
Molecular Orbitals
Molecular Orbital Energies
Respective energies of the molecular orbitals in a molecule of F2. The MOs formed from the 1s orbitals (1&2) are significantly deeper in energy than the higher order MOs. This is why they are rarely considered to have any effect on the bonding of fluorine. MO 10 is the LUMO as it is the lowest energy orbital that is not occupied. Similarly, MOs 8&9 are the HOMO, as the highest energy occupied orbitals (they are degenerate to one another).
1σg / 1σu*
1σ bonding MO made up of the 1s AOs. This MO is very deep in energy, so there is effectively no overlap hence this MO contributes little to the bonding in F2. The corresponding antibonding orbital is shown below.
2σg /2σu*
2σ bonding MO made up of the 2s AOs. The electrons in the MO are valence electrons, hence there is good overlap between the AOs. As F is too electronegative for mixing, the bonding orbital is cancelled out by the antibonding orbital also formed by the 2s electrons (below). As the antibonding orbital is filled, the bonding effect of the bonding orbital is not notable.
3σg / 3σu*
3σ bonding MO made up of the 2p AOs that are orientated along the line of the bond. The electrons in the MO are valence electrons, hence there is good overlap between the AOs. As the antibonding orbital (below) is not filled, the bonding effect of this MO is significant. The antibonding MO is the LUMO of the F2 molecule.
1πu / 1πg*
Both orientations of the pi MOs. Made up of the 2p AOs that are not orientated along the line of the bond, the electrons in the MO are valence electrons, hence there is good overlap between the AOs. As the antibonding orbital (below) is only partially filled, the bonding effect of this MO is significant. The antibonding MO is also the HOMO
The calculated bond length is fairly close to the literature reference, so the Gaussian model is accurate.
Item Table
Item Value Threshold Converged?
Maximum Force 0.000050 0.000450 YES
RMS Force 0.000028 0.000300 YES
Maximum Displacement 0.000204 0.001800 YES
RMS Displacement 0.000134 0.001200 YES
Gaussview vibration analysis window for a molecule of ClF3.
Frequency Analysis
No. of Modes (3N-6)
6
Degenerate Modes
None
"Bending" vibration modes
1-3
"Bond Stretch" vibration modes
4-6
Comment
Due to the bent T-shaped nature of the molecule, none of the stretches are degenerate. number 6 would have the strongest intensity in an experimental spectrum, while 3&4 may not show due to their poor intensity.
Clearly, the more electronegative fluorine molecules are more negatively charged than the central chlorine atom (comparatively, the more electropostive atom). The model also shows that there is a disparity between the charges of the axial fluorine atoms and the equatorial fluorine. I would hypothesize that this is due to the differing bond lengths, with the axial fluorines being further away from the electropostive chlorine. However, the method of charge analysis Gaussian uses is not based on electronegativity values, so no quantitative analysis can be made.
Sarin Molecule
Calculation Data
Key Information
Common Name
Sarin
Molecular Formula
(CH3)2CHOP(O)(CH3)F
Calculation Method
RB3LYP
Basis Set
6-31G(D.P)
Final Energy (RB3LYP)
-750.20043140 a.u.
RMS Gradient
0.00000766 a.u.
Point Group
None
Item Table
Item Value Threshold Converged?
Maximum Force 0.000026 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.001100 0.001800 YES
RMS Displacement 0.000250 0.001200 YES
The charge distribution for Sarin is very interesting.
All three CH3 group carbons have a slight negative charge, on account of each being bonded to three more electropositive hydrogen atoms. The CH3 carbon bonded to the central phosphorus atom is especially negative, on account of the significant (relative) electropositivity of the phosphorus atom.
The carbon of the CH group is slightly positively charged, on account of being bonded to three more electronegative atoms. The main contributor is likely the oxygen atom; oxygen is significantly more electronegative than carbon.
Both oxygen atoms are negatively charged. The fluorine atom is also negatively charged. This makes sense, as oxygen and fluorine are the two most electronegative elements known. The numerical disparity shown in the image is likely due to the functions Gaussian is using, as it does not account for electronegativity. Hence, no quantitative analysis is possible.
Molecular Orbitals
Bonding
The 13th MO is the first bonding orbital: all below are too deep in energy
Complexity increases
The complexity of the MOs rapidly increases for such a large molecule, with both bonding and antibonding characteristics. Pictured are MOs 16, 17 and 22.
↑Greenwood and Earnshaw (1984). "Chemistry of the Elements, pp. 412–6."
↑Brockway, L. O. (1938). "The Internuclear Distance in the Fluorine Molecule". Journal of the American Chemical Society. 60 (6): 1348–1349. http://pubs.acs.org/doi/abs/10.1021/ja01273a021 (Accessed at 11:53 on 10/03/2017)
↑Smith, D. F. (1953). "The Microwave Spectrum and Structure of Chlorine Trifluoride". The Journal of Chemical Physics. 21 (4): 609–614. http://aip.scitation.org/doi/10.1063/1.1698976 (Accessed at 11:44 on 10/03/2017)
