Ferdiemodeling2:Modeling2

introduction to molecular modeling

NH₃

image of NH

NH₃

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-56.55776873 a.u.
RMS Gradient Norm	0.00000485 a.u.
Point Group	C3V
N-H bond length	1.01798Å
H-N-H Angel	105.741°

items table for NH₃

	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

display vibrations

mode	Frequency	Infrared	IR active	type
1	1089.54	145.3814	yes	bending
2	1693.95	13.5533	yes	bending
3	1693.95	13.5533	yes	bending
4	3461.29	1.0608	yes	stretching
5	3589.82	0.2711	yes	stretching
6	3589.82	0.2711	yes	stretching

• 6 modes are expected when using the 3N-6 rule
• modes 2 and 3 are degenerate and modes 5 and 6 are degenerate
• there will be 2 peaks in the absorbance spectrum as although all modes are IR active modes 4,5,6 have very low intensities which are proportional to the intensity in the spectrum and as they are so small they will be drowned out by noise in an experimental determined spectra as as modes 2 and 3 are degenerate they will occur at the same frequency
• modes 1, 2 ,and 3 are bending vibrations
• modes 4, 5, and 6 are bond stretching vibrations
• mode 1 is known as the umbrella mode
• mode 4 is the highly symmetric mode
• the N atom is predicted to have a charge of -1.125 and the H atoms have a charge of 0.375 which means that the molecule has an overall charge of 0
• we would expect that N has a negative change and so H has positive charge as it is more N is more electronegative than H and that the overall charge to be 0

data file

File:FERDIE KRAMMER NH3 3.LOG

N₂

image of N

N₂

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-109.52412868 a.u.
RMS Gradient Norm	0.00000060a.u.
Point Group	D*H
N-N bond length	1.10550Å

items table for 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

display vibrations

mode	Frequency	Infrared	IR active
1	2457.33	0.0000	no

there is no IR activity as it is a linear molecule

data file

File:FERDIE KRAMMER N2.LOG

molecular orbitals:

MO1

1s σ bonding orbitals E=-14.44676a.u.

MO2

1s σ^* anti-bonding orbitals E=-14.44512a.u.

MO3

2s σ bonding orbital E=-1.12383a.u.

MO4

2s σ^* anti-bonding orbital E=-0.55342a.u.

MO5

2p π bonding orbital degenerate with MO6 E=-0.462540a.u.

MO6

2p π bonding orbital degenerate with MO5 E=-0.462540a.u.

MO7

2p σ bonding orbital (HOMO) E=-0.42688a.u. (non degenerate as along the axis of the bond) this dose not exactly have the same shape as expected due to there being some s character due to mixing

MO8

2p π^* anti-bonding orbital (LUMO) degenerate with MO9 E=-0.02412a.u. this dose not exactly have the same shape as expected due to there being some d characteristic in the p orbitals due to the polarization function chosen

MO9

2p π^* anti-bonding orbital (LUMO) degenerate with MO8 E=-0.02412a.u. this dose not exactly have the same shape as expected due to there being some S character due to mixing

MO10

2p σ^* anti-bonding bonding orbital E=0.41366a.u. (non degenerate as along the axis of the bond) this dose not exactly have the same shape as expected due to there being some S character due to mixing however not as influential as in MO7 due to there being being destructive interference between the molecules

data file

File:FERDIE KRAMMER N2.LOG

H₂

image of H

H₂

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-1.17853936 a.u.
RMS Gradient Norm	0.00000017a.u.
Point Group	D*H
H-H bond length	0.74279Å

items table for 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

display vibrations

mode	Frequency	Infrared	IR active
1	4465.68	0.0000	no

this molecule is non IR active as it is linear and so has no dipole change

data file

File:FERDIE KRAMMER H2.LOG

Harbor-Bosh reaction

2N_{2 (g)} + 3H_{2 (g)} → 2NH_{3 (g)}

E(NH3)= -56.55776873 a.u.

2*E(NH3)= -113.11553746 a.u.

E(N2)=-109.52412868 a.u.

E(H2)=-1.17853936 a.u.

3*E(H2)=-3.53561808 a.u.

ΔE=2*E(NH3)-[E(N2)+3*E(H2)]= -0.0557907 a.u.

ΔE = -146.47848285 kJ/mol

therefore ΔE = -146.48 kJ/mol

the NH₃ is more stable than the gaseous reactants as ΔE is negative meaning that the reaction is exothermic, however there is an decrease in entropy meaning that this reaction will only occur below a certain temperature. As can be seen from the literature of -46210 J/mole the value that is calculated would be expected to be an exothermic.

[NH₄]⁺

image of [NH₄]⁺

[NH₄]⁺

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-56.90586436 a.u.
RMS Gradient Norm	0.00011991 a.u.
Point Group	TD
N-H bond length	1.02761Å
H-N-H Angle	109.47122°

items table for [NH₄]⁺

	Item	Value	Threshold	Converged?
Maximum	Force	0.000232	0.000450	YES
RMS	Force	0.000124	0.000300	YES
Maximum	Displacement	0.000537	0.001800	YES
RMS	Displacement	0.000287	0.001200	YES

display vibrations of [NH₄]⁺

mode	Frequency	Infrared	IR active	type
1	1496.46	181.0390	yes	bending
2	1496.46	181.0390	yes	bending
3	1496.46	181.0390	yes	bending
4	1726.51	0.0000	no	bending
5	1726.51	0.0000	no	bending
6	3366.56	0.0000	no	stretching
7	3491.44	197.7368	yes	stretching
8	3491.44	197.7368	yes	stretching
9	3491.44	197.7368	yes	stretching

charges on [NH₄]⁺ atoms

atoms	charges
N	-0.999
H	0.500

modes of vibration for [NH₄]⁺:

mode 1

mode 2

mode 3

mode 4

mode 5

mode 6

mode 7

mode 8

mode 9

Molecular orbitals

Molecular orbital energies

MO	occupancy	Energy (a.u.)
15	0	0.5405978170
14	0	0.5405978170
13	0	0.5405978170
12	0	0.3325906440
11	0	0.3325906440
10	0	0.3325906440
9	0	-0.1284344420
8	0	-0.1284344420
7	0	-0.1284344420
6	0	-0.2100277800
5	2	-0.8247061880
4	2	-0.8247061880
3	2	-0.8247061880
2	2	-1.2480757300
1	2	-14.7152516000

molecular orbital diagrams

MO1

in the first molecular orbital only the 1s orbital in the N is involved this is an anti bonding orbital

MO2

the nitrogen atom contributes an a 2s atomic orbital and the hydrogen atom contributes a 1s atomic orbital causing the formation of a σ bonding orbital

MO3-5

the nitrogen atom contributes an a 2p atomic orbital and the hydrogen atom contributes a 1s atomic orbital causing the formation of degenerate π bonding orbitals witch are the HOMO

MO6

the nitrogen atom contributes an a 2s atomic orbital and the hydrogen atom contributes a 1s atomic orbital causing the formation of a σ^* anti-bonding orbital which is the LUMO

MO7-9

the nitrogen atom contributes an a 2p atomic orbital and the hydrogen atom contributes a 1s atomic orbital causing the formation of degenerate π^* anti-bonding orbitals

MO10 and above

MO10 and above these are imaginary orbitals due to the linear fitting trying to produce results as can be seen for MO 15

data file

File:FERDIE KRAMMER -NH4-+ 1 2.LOG

CH₄

image of CH

CH₄+

Calculation Method	RB3LYP
Basis Set	6-31G(d,p)
E(RB3LYP)	-40.52401404 a.u.
RMS Gradient Norm	0.00003263a.u.
Point Group	TD
C-H bond length	1.09197Å
H-C-H Angle	109.47122°

items table for CH₄

	Item	Value	Threshold	Converged?
Maximum	Force	0.000063	0.000450	YES
RMS	Force	0.000034	0.000300	YES
Maximum	Displacement	0.000179	0.001800	YES
RMS	Displacement	0.000095	0.001200	YES

vibrations

display vibrations of CH₄

mode	Frequency	Infrared	IR active	type
1	1356.20	14.1008	yes	bending
2	1356.20	14.1008	yes	bending
3	1356.20	14.1008	yes	bending
4	1578.58	0.0000	no	bending
5	1578.58	0.0000	no	bending
6	3046.46	0.0000	no	stretching
7	3162.33	25.3343	yes	stretching
8	3162.33	25.3343	yes	stretching
9	3162.33	25.3343	yes	stretching

mode 1

mode 2

mode 3

mode 4

mode 5

mode 6

mode 7

mode 8

mode 9

Molecular orbitals

MO	Occupancy	Energy (a.u.)
15	0	0.8743736790
14	0	0.8743736790
13	0	0.8743736790
12	0	0.5291487570
11	0	0.5291487570
10	0	0.5291487570
9	0	0.1767699180
8	0	0.1767699180
7	0	0.1767699180
6	0	0.1182376210
5	2	-0.3883090690
4	2	-0.3883090690
3	2	-0.3883090690
2	2	-0.6904066760
1	2	-10.1670726000

MO1

like in ammonium ion only the 1s atomic orbital of the carbon atom is involved in the molecular orbital as is dose not mix forming a non-bonding orbital

MO2

like in ammonium ion this is a combination of the 2s atomic orbital form the carbon and the 1s atomic orbital form the Hydrogen forming a σ bonding orbital

MO3-5

like in ammonium ion this is a combination of the 2p atomic orbital form the carbon and the 1s atomic orbital form the Hydrogen which forms 3 degenerate Molecular orbitals forming the HOMO π bonding orbital

MO6

like in ammonium ion this is a combination of the 2s atomic orbital form the carbon and the 1s atomic orbital form the Hydrogen resulting in the formation of the LUMO σ^* anti-bonding orbital

MO7-9

like in ammonium ion this is a combination of the 2p atomic orbital form the carbon and the 1s atomic orbital form the Hydrogen which forms 3 degenerate Molecular orbitals forming an π^* anti-bonding orbital

MO10 and above

these are imaginary orbitals and are a result of the linear fitting trying to produce results as can be seen for MO 15

data file

File:FERDIE KRAMMER ME.LOG

comparison

as the ammonium ion is isoelectronic to the methane it is similar to it in every way with it having the same number of peaks in the IR spectra however they would be at different locations to those for the methane. the MO also have different Energies with the charge going from negative to positive between the HOMO and LUMO for methane however it changes from MO9-MO10 which is above the LUMO due to if being electron deficient as it is a positively changed molecule.