Rep:Mod:Molecular modelling 2

Ammonia

Summary Information

Here are the measurements for ammonia when optimised in GaussView

Optimisation measurements	Values
bond length	1.01798 Å
bond angle	105.741°
calculation method	B3LYP
basis set	6-31G(d.p)
RMS gradient	0.0000000485 (a.u)
final energy	-56.5578 (a.u)
point group	C3v

 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

This table shows the values at equilibrium when all the forces are at zero. Calculations show a non zero number due to rounding errors.

Optimised ammonia

Optimisation file for NH₃ is linked here

Vibrational Modes

Ammonia can absorb infrared, IR causes a dipole moment making ammonia IR active.

Modes 2/3 and 5/6 are degenerate, table shows they have the same value of energy. In the spectrum only visible modes are 1 and 2/3, however modes 4/5 and 6 are small values only visible by zooming in.

Table to show the types of vibrations associated with each mode:

Modes	Vibrations
1	bending, symmetric, also known as the umbrella mode
2	bending
3	bending
4	stretch, is highly symmetric
5	stretch
6	stretch

 

All other vibrations are asymmetric. In an experimental spectrum yo would see two peak intensities for mode 1 and 2/3. The values of the other modes relative to 1 and 2/3 are too small to be shown.

Charge Distribution

NH3 charge distribution

Nitrogen is the more electronegative species and so is expected to have negative dipole and therefore hydrogen is expected to have a positive dipole. Total charge is neutral the sum of all charges is 0.

Nitrogen

Summary Information

Values obtained for optimised nitrogen

Optimisation measurements	Values
bond length	1.10550Å
bond angle	180°
calculation method	B3LYP
basis set	6-31G(d.p)
RMS gradient	0.0000006 (a.u)
final energy	-109.5241 (a.u)
point group	D*H

         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=-3.400996D-13

Optimised Nitrogen

Optimisation file is linked here

Vibrational Modes

NO dipole moment therefore not IR active. No difference in charge because it is a diatomic molecule so both have the same electronegativity.

Hydrogen

Summary Information

Optimisation values for H₂

Optimisation measurements	Values
bond length	0.74279 Å
bond angle	180°
calculation method	RB3LYP
basis set	6-31G(d.p)
RMS gradient	-1.17853936 (a.u)
final energy	0.0000017 (a.u)
point group	D*H

 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.

Optimised Hydrogen

Optimisation file is linked here

Vibrational Modes

Symmetric vibrations, no dipole moment occurs therefore is IR inactive.

Hydrogen also has no difference in charge distribution.

Haber-Bosch Process

N₂+3H₂→2NH₃ This is the process used to make ammonia, using the values of energy calculated before we can create a Hess's cycle to work out the enthalpy of reaction.

E(NH3)= -56.5578
2*E(NH3)= -113.1156
E(H2)= -1.17853936
E(N2)= -109.5241
3*E(H2)= 3.53561808
ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.05579074

ΔE= -146.650 kj/mol

The standard value for the standard enthalpy of formation of ammonia is -45.910 kjmol-1 standard enthalpy changes form only one mole of product, therefore we will to multiply this value to compare to the Haber-Bosch process.

Using the standard enthalpy change, value for the process should be -91.82 kjmol-1. Differences in values are due to the optimisation as it takes into consideration the molecule at 0 K also standard enthalpy deals with moles while the optimisation only works with 1 molecule of ammonia.

Cyanide

Summary Information

Optimisation measurements	Values
bond length	1.18409Å
bond angle	180°
calculation method	RB3LYP
basis set	6-31G(d.p)
RMS gradient	-92.82453153 (a.u)
final energy	0.00000704 (a.u)
point group	C*V

         Item               Value     Threshold  Converged?
 Maximum Force            0.000005     0.000450     YES
 RMS     Force            0.000005     0.000300     YES
 Maximum Displacement     0.000002     0.001800     YES
 RMS     Displacement     0.000003     0.001200     YES
 

Predicted change in Energy=-6.650395D-11

Optimization completed.

-- Stationary point found.

Optimised Cyanide

optimisation for cyanide is here

Vibrational Modes

Is IR active, molecule has a dipole moment. The spectrum for cyanide is large only has one vibration mode due to the 3n-5 rule, and since cyanide has a bond order of 3 rotation is restricted and therefore unable to bend. Only stretching occurs.

Charge Distribution

CN charge distribution

Total molecule is negative however there is more negative charge on the nitrogen. This is due to the nitrogen's greater electronegativity

Molecular Orbitals

MOs
	Sigma bond Formed from the s atomic orbitals constructive interference. It is the deepest in energy and contributes mostly to nuclear shielding. You can see there is greater density on the nitrogen as it is more electronegative and contributes more to the bonding MO.
	This is the sigma* anti bonding MO. Formed by the destructive interference, carbon contributes more to the anti bonding orbital.
	This is the LUMO, lowest unoccupied molecular orbital, it is an anti bonding orbital that has nodes in the internuclear axis. Is formed by p AOs. LUMO is too high in energy to interact with other HOMOs.
	HOMO. This orbital is made by p and s AOs. Is a bonding orbital. The electron density is greatest on either side of the molecule. This is where the lone pairs of carbon and nitrogen exist. Lone pairs of electrons are highest in energy and are responsible for its nucleophilic character.
	π orbital, formed by p orbitals. Is one of the bonding orbitals that contribute to the triple bond of cyanide the other π orbital exists orthogonal to its plane.

 

Fluorine

Summary Information

Optimisation measurements	Values
bond length	1.40281Å
bond angle	180°
calculation method	RB3LYP
basis set	6-31G(d.p)
RMS gradient	0.00007365(a.u)
final energy	-199.49825218 (a.u)
point group	D*H

 

     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
 Predicted change in Energy=-1.995024D-08
 Optimization completed.
    -- Stationary point found.

Optimised Fluorine

Optimisation file is linked here

Vibrational Modes

Symmetric vibrations, no dipole moment occurs therefore is IR inactive.

Molecular Orbitals

MOs
	σ* anti bonding orbital
	π* anit bonding orbital
	π bonding orbital
	σ bonding orbital
	bonding orbital