Rep:Mod:Introductiontomolecularmodelling2dt

Introduction to Molecular Modelling 2

NH₃ molecule

NH molecule

Geometric Information

N-H bond length = 1.01798 Å

H-N-H bong angle = 105.741°

Optimisation Information

Molecule Name	Ammonia (NH3)
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Final Energy E(RB3LYP)	-56.55776873 a.u.
RMS Gradient Norm	0.00000485 a.u.
Point Group	C_3v

"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
 Predicted change in Energy=-5.986273D-10
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.018          -DE/DX =    0.0                 !
 ! R2    R(1,3)                  1.018          -DE/DX =    0.0                 !
 ! R3    R(1,4)                  1.018          -DE/DX =    0.0                 !
 ! A1    A(2,1,3)              105.7412         -DE/DX =    0.0                 !
 ! A2    A(2,1,4)              105.7412         -DE/DX =    0.0                 !
 ! A3    A(3,1,4)              105.7412         -DE/DX =    0.0                 !
 ! D1    D(2,1,4,3)           -111.8571         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The table shows that the structure has converged and the optimisation process was therefore succesful.

Vibrations Results

It should be noted that all the frequencies are positive.

- how many modes do you expect from the 3N-6 rule?

 3 * 4 - 6 = 12 - 6 = 6 vibrational modes
 Those give all the stretching and bending combinations.

- which modes are degenerate (ie have the same energy)?

 Modes 2-3 and 5-6 respectively are degenerate as they have the same frequencies and, therefore, the same energies.

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

 "Bending" vibrations: 1, 2, 3
 "Bond stretch" vibrations: 4, 5, 6

- which mode is highly symmetric?

 Modes 1 and 4 are highly symmetric.

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

 Mode 1 is the "umbrella" mode.

- how many bands would you expect to see in an experimental spectrum of gaseous ammonia?

 Since there are 4 different frequencies, 4 peaks would be expected. However, the peaks corresponding to modes 4 and 5-6 respectively absorb very close to 0 so only 2 peaks are observed corresponding to Modes 1 and 2-3.

Charge analysis

Atom	Charge
N	- 1.125
H	+ 0.375

The atom charges are in accordance with the ones expected. N is more electronegative and therefore has a negative charge. The electrons are shared in a covalent bond as opposed to the ones in an ionic bond so it makes sense that the charges found are fractions.

Reactivity

Ammonia is made by reacting H₂ and N₂ gases industrially in the Haber-Bosch process. The reactivity of the two gases is be further studied and the reaction energy is calculated.

N₂ and H₂ molecules

Geometric Information

N-N bond length = 1.09200 Å

H-H bong length = 0.60000 Å

Optimisation Information

	N₂	H₂
Calculation Method	RB3LYP	RB3LYP
Basis Set	6-31G(d,p)	6-31G(d,p)
Final Energy E(RB3LYP)	-109.5235911 a.u.	- 1.17853936 a.u.
RMS Gradient Norm	0.02473091 a.u.	0.09719500 a.u.
Point Group	D_∞h	D_∞h

"Item" Tables

N₂

         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
 Predicted change in Energy=-3.401007D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  1.1055         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

H₂

         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
 Predicted change in Energy=-1.164080D-13
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.7428         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The tables show that the structures have converged and the optimisation process was therefore succesful.

Vibrations Results

N₂

H₂

It should be noted that all the frequencies are positive.

The IR spectrum shows no peak as the change in dipole is 0.

As far as the charge distribution is concerned, the atom charges for both N₂ and H₂ are 0.

Reaction Energy

N₂ + 3 H₂ ---> 2 NH₃

E(NH<sub>3</sub>)= -56.55776873 a.u.

2*E(NH<sub>3</sub>)= -113.11553746 a.u.

E(N<sub>2</sub>)= -109.5235911

E(H<sub>2</sub>)= -1.17853936 a.u.

3*E(H<sub>2</sub>)= -3.53561808 a.u.

ΔE=2*E(NH<sub>3</sub>)-[E(N<sub>2</sub>)+3*E(H<sub>2</sub>)]=  -0.05632828 a.u.

ΔE= -147.89 kJ/mol

The reaction energy is negative so the process is exothermic.

The gaseous reactants are lower in energy than the product so they are more stable.

The experimental value found for the reaction energy is ΔE_exp = −92.4 kJ·mol−1 ^[1]. The difference between the two values can be explained by the different conditions in which the two are calculated. The one found using the values given by Gaussview assumes standard pressure and temperature conditions, whereas the actual process is conducted with a metal catalyst and at high temperature and pressure.

H₂O molecule

H2O molecule

File:DT H2O POP.LOG

Geometric Information

O-H bond length = 0.96522 Å

H-O-H bong angle = 103.745°

Optimisation Information

Molecule Name	Water (H2O)
Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
Final Energy E(RB3LYP)	-76.41892999 a.u.
RMS Gradient Norm	0.00684281 a.u.
Point Group	C_2v

"Item" Table

         Item               Value     Threshold  Converged?
 Maximum Force            0.000099     0.000450     YES
 RMS     Force            0.000081     0.000300     YES
 Maximum Displacement     0.000115     0.001800     YES
 RMS     Displacement     0.000120     0.001200     YES
 Predicted change in Energy=-1.939669D-08
 Optimization completed.
    -- Stationary point found.
                           ----------------------------
                           !   Optimized Parameters   !
                           ! (Angstroms and Degrees)  !
 --------------------------                            --------------------------
 ! Name  Definition              Value          Derivative Info.                !
 --------------------------------------------------------------------------------
 ! R1    R(1,2)                  0.9652         -DE/DX =    0.0001              !
 ! R2    R(1,3)                  0.9652         -DE/DX =    0.0001              !
 ! A1    A(2,1,3)              103.7454         -DE/DX =    0.0                 !
 --------------------------------------------------------------------------------
 GradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGradGrad

The table shows that the structure has converged and the optimisation process was therefore succesful.

Vibrations Results

It should be noted that all the frequencies are positive.

IR Spectrum

The IR spectrum shows three peaks. The ones corresponding to modes 1 and 3 are easily observed, while the second one corresponds to a frequency for which the intensity is very close to 0 (1.6431 D). The peaks at 3914.23 cm-1 and 3801.05 cm-1 correspond to the O-H asymmetric and symmetric stretch respectively. The peak corresponding to the asymmetric stretch is higher in intensity because the change in the dipole moment is higher than the one in the symmetric stretch. The peak at 1665.00 cm-1 corresponds to the H-O-H scissoring bend.

The stretches can be seen in the following GIFs.

Charge analysis

Atom	Charge
O	- 0.953
H	+ 0.476

Similar to NH₃, the charge values are fractions as the electron density is shared between the atoms. Oxygen is more electronegative than Hydrogen and this is in accordance with the results found. When the Oxygen and Nitrogen charges are compared, N is more negative and this is due to the fact that it is bonded to three positive H atoms as oposed to two in water.

Molecular Orbitals

1s O AO.	2s AO(O) + σ MO(H).	2p_y AO(O) + σ* MO(H).	2p_z AO(O) + σ MO(H).	Nonbonding MO from 2p_x

The orbitals are displayed in order of increasing energy and they correspond only to the filled ones as the higher energy ones are not as reliable as the filled ones. This is explained by the fact that only the filled orbitals are well optimised in the procedure.

The first picture shows the AO orbital corresponding to the 1s O orbital and which is not interacting with the hydrogen orbitals as it is very low in energy. It can be noticed that this shows only the core electrons and the orbital does not cover the entire molecule. The descriptions show which are the atomic or molecular orbitals contributing to the resulting molecular orbitals.

When compared to the following MO Diagram, the orbitals can be easily matched by their increasing energy as well as their shape. The antibonding MOs show the characteristic nodal planes although for the first antibonding molecular orbital the shape is slightly distorted. This proves the point that sometimes the software does not give reliable results for unfilled orbitals.

^[2]

As far as the energy difference between the HOMO and the LUMO, this is higher than the difference between filled or unfilled molecular orbitals. Using the data from Gaussview, ΔE_filled ≈ 0.8 a.u. (last 2 filled orbitals) whereas ΔE_HOMO-LUMO ≈ 0.22 a.u.

References

[reaction_energy-1] ttps://dx.doi.org/10.1002%2F14356007.a02_143.pub2

[mo_diagram-2] ttps://commons.wikimedia.org/wiki/File:H2O-MO-Diagram.svg

[1]

[2]

Introduction to Molecular Modelling 2

NH3 molecule

Geometric Information

Optimisation Information

"Item" Table

Vibrations Results

Charge analysis

Reactivity

N2 and H2 molecules

Geometric Information

Optimisation Information

"Item" Tables

Vibrations Results

Reaction Energy

H2O molecule

Geometric Information

Optimisation Information

"Item" Table

Vibrations Results

IR Spectrum

Charge analysis

Molecular Orbitals

References

NH₃ molecule

N₂ and H₂ molecules

H₂O molecule