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Normal vibrational frequencies of water molecule

Question 1

Normal modes and vibrational frequencies of water molecule

HF/3-21* optimised geometry of the water molecule

H bond length

0.967

HOH bond angle

107.7˚

(ii) Energy of the HF/3-21G optimised water molecule = -75.58596 au

Cycle

Energy

Max. Grad.

Max. Dist.

1

75.58553

0.01246

0.00304

2

75.58589

0.00324

0.00025

3

75.58596

0.00001

0.00000

Frequency (cm-1)

Relative Motion

Stretch or Bend

Type

Symmetry (S or A)

1799.2

Bend

A1

S

3812.2

Stretch

A1

S

3945.8

r

Stretch

B1

A

HOD

Energy

75.58596 au

Geometry

Bond angle

107.7

Bond length

0.967

Vibrational frequencies

1578.7

H moves faster than D

symmetric

2815.3

D moves quickly whereas H moves slightly

asymmetric

3881.7

H moves quickly whereas D moves slightly - asymmetric

Normal modes and vibrational frequencies of the water dimmer (H2O)2

Hydrogen-Bond Acceptor

Hydrogen bond

Hydrogen Bond Donor

Hydrogen bond length (H''''O) = 1.808

Hydrogen bond angle (O-H''''O) = 174.9˚

Energy of the F/3.12G optimised water dimer = -151.18902 au

(a) Potential energy calculation:

ΔE = E(dimer) - 2xE(H2O)

= (-396 871.2KJ/mol) - 2x(-198 413.2KJ/mol)

= (-396 871.2) - (-396 826.3)

= - 44.9 KJmol-1

(b)As seen from the surface diagram for H2O, the oxygen has negative charge (δ-) whereas the hydrogens are positively charged (δ+).

In the water dimer molecule, the hydrogen atoms (on the H-bond donor oxygen) are δ+/blue region. The oxygen atom that is bonded to the hydrogen that is the H-bond acceptor has δ- charge/red region. Between in the H-bond, the positive(H) and negative(O) charges combine/green region.

The hydrogen bond is formed between one of the H atoms and one O, instead between the two oxygens, because the two oxygen atoms are negatively charged, and have δ-, and therefore repulsive interactions are formed between them. So, one H reacts with the O, which donates one of its lone pairs to form the H-bond.

In the structure of the molecule, the H''''O bond is almost linear, very close to 180˚ but it is distorted so it is about 175˚. Also, the distortion causes the bond H'''O to become longer.

(c) For the water molecule:

H bond length = 0.967

For the water dimer:

H bond length of H-bond donor = 0.965

H bond length of H-bond acceptor = 0.966, 0.974 (H of H-bond)

The H bond length of the hydrogen of the H-bond is bigger than the other O-H bonds in the molecule. This is because this H is bonded to the oxygen through the H-bond, and it is pulled towards the oxygen, causing its bond with the other oxygen to become a bit longer.

Question 2

The water dimer consists of two fragments, the H-bond acceptor (top OH2 group) and the H-bond donor (bottom OH2 group). When a vibration causes both fragments and H-bond to move, then it is considered to be the inter-monomer because it is a vibration between the two molecules. If only one of the fragments vibrates, then the vibration is only in one of the molecules (it is internal) and it is considered to be an intra-monomer.

The vibrational frequencies of the water dimer are the following:

Frequency = 81 cm-1

Type = A'

Bending Mode

Top part of the molecule moving slightly up and down, while the two bottom hydrogens move up and down as well

Inter-monomer: The vibration affects both molecules connected through the hydrogen bond.

Frequency = 133

Type = A''

Bending mode

Top part and bottom part moving right and left.

Inter monomer

Frequency = 172

Type = A''

Bending mode

Middle hydrogen moving right and left and two bottom H atoms moving up and down symmetrically (when one is up, other is down)

Inter Monomer

Frequency = 242

Type = A'

Stretching Mode

Inter monomer

Frequency = 425

Type = A'

Bending Mode

The H-bond acceptor fragment moves to the front and then back, and the H-bond donor fragment moves up and down as well.

Inter-monomer

Frequency = 826

Type = A''

Bending mode

The H of the H-bond (middle H) is moving to the right and left, causing the rest of the molecule to move in that way as well

Inter-monomer

Frequency = 1782

Type = A'

Bending Mode

The hydrogen atoms on the H-bond donor fragment move up and down to the sides going further away and then coming closer.

Intra-monomer

Frequency = 1854

Type = A'

Bending Mode

The hydrogen atoms on the H-bond acceptor fragment separate and go further away and then come closer together again.

Intra-monomer

Frequency = 3724

Type = A'

Stretching mode

The hydrogen forming the H-bond moves closer to the oxygen of the H-bond and then further from it, causing the O-H bond to come smaller and the H'''''O bond to become bigger, and the opposite.

Intra-monomer

Frequency = 3849

Type = A'

Stretching mode

The hydrogen atoms move symmetrically so that their bonds with the O of the H-bond donor are becoming bigger (stretch out) and then smaller.

Intra-monomer

Frequency = 3907

Type = A'

Stretching mode

The O-H bond of the H not involved in the H-bond acceptor fragment is stretching out, causing the bond to become longer, while the bond of the oxygen with the other H, which is involved in the H-bond, becomes shorter.

Intra-monomer

Frequency = 3982

Type = A''

Stretching mode

It is an unsymmetrical movement, where one O-H bond in the H-bond donor fragment becomes shorter and the other longer.

Intra-monomer

Question 3

Isotopic substitution in the water dimer

Free Energy (H-TS) = 37.8

ΔΗ Total = 127.5

Free Energy (H-TS) = 39.7

ΔΗ Total = 126.5

ΔG = G(B) - G(A) = 39.7KJmol-1 - 37.8KJmol-1 = 1.9 KJ/mol

K = e(-ΔG/RT) = exp(-1.9x10-3Jmol-1/8.314JK-1mol-1x298K) = 1.00000077

Deuterium prefers the position shown in B (connected to the oxygen of the H-bond acceptor fragment, but doesn't take part directly in the H-bond) because the molecule has higher free energy for this arrangement.

Question 4

Interconversion of water dimer structures

Frequency = i302

Type = B1

Frequency = 105

Type = B2

Frequency = 208

Type = A1

Frequency = 225

Type = B1

Frequency = 256

Type = A2

Frequency = 591

Type = B2

Frequency = 1785

Type = A1

Frequency = 1831

Type = A1

Frequency = 3829

Type = A1

Frequency = 3862

Type = A1

Frequency = 3952

Type = B1

Frequency = 3961

Type = B2

Acyclic water dimer Cyclic water dimer

Question 5

Syn-butane:

No imaginary frequencies à Valley à stable structure, highly favoured

Boat cyclohexane:

ne imaginary frequency à Hilltop à fairly unstable, exists but not preferred

All-syn cyclohexane:

More than one imaginary frequencies à Mountain Pass à does not exist, very unstable

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