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Normal vibrational frequencies of water molecule

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Question 1

Normal manners and vibrational frequences of H2O molecule

HF/3-21* optimised geometry of the H2O molecule

H bond length

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HOH bond angle

107.7 & A ; # 730 ;

( two ) Energy of the HF/3-21G optimised H2O molecule = -75.58596 gold



Max. Grad.

Max. Dist.













Frequency ( cm-1 )

Relative Gesture

Stretch or Bend


Symmetry ( S or A )
















75.58596 gold


Chemical bond angle


Chemical bond length


Vibrational frequences


H moves faster than D



D moves rapidly whereas H moves somewhat



H moves rapidly whereas D moves somewhat – asymmetric

Normal manners and vibrational frequences of the H2O 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 & A ; # 730 ;

Energy of the F/3.12G optimised H2O dimer = -151.18902 gold

( a ) Potential energy computation:

& A ; Delta ; E = 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 O has negative charge ( & A ; delta ; – ) whereas the Hs are positively charged ( & A ; delta ; + ) .

In the H2O dimer molecule, the H atoms ( on the H-bond giver O ) are & amp ; delta ; +/blue part. The O atom that is bonded to the H that is the H-bond acceptor has & A ; delta ; – charge/red part. Between in the H-bond, the positive ( H ) and negative ( O ) charges combine/green part.

The H bond is formed between one of the H atoms and one O, alternatively between the two Os, because the two O atoms are negatively charged, and have & amp ; delta ; – , and hence abhorrent interactions are formed between them. So, one H reacts with the O, which donates one of its lone brace to organize the H-bond.

In the construction of the molecule, the H ” ”O bond is about additive, really near to 180 & A ; # 730 ; but it is distorted so it is about 175 & A ; # 730 ; . Besides, the deformation causes the bond H ” ‘O to go longer.

( degree Celsius ) For the H2O molecule:

H bond length = 0.967

For the H2O dimer:

H bond length of H-bond giver = 0.965

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

The H bond length of the H of the H-bond is bigger than the other O-H bonds in the molecule. This is because this H is bonded to the O through the H-bond, and it is pulled towards the O, doing its bond with the other O to go a spot longer.

Question 2

The H2O dimer consists of two fragments, the H-bond acceptor ( top OH2 group ) and the H-bond giver ( bottom OH2 group ) . When a quiver causes both fragments and H-bond to travel, so it is considered to be the inter-monomer because it is a quiver between the two molecules. If merely one of the fragments vibrates, so the quiver is merely in one of the molecules ( it is internal ) and it is considered to be an intra-monomer.

The vibrational frequences of the H2O dimer are the undermentioned:

Frequency = 81 cm-1

Type = A ‘

Bending Mode

Top portion of the molecule traveling somewhat up and down, while the two underside Hs move up and down every bit good

Inter-monomer: The quiver affects both molecules connected through the H bond.

Frequency = 133

Type = A ”

Bending manner

Top portion and bottom portion traveling right and left.

Inter monomer

Frequency = 172

Type = A ”

Bending manner

Middle H traveling right and left and two underside H atoms traveling up and down symmetrically ( when 1 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 forepart and so back, and the H-bond giver fragment moves up and down every bit good.


Frequency = 826

Type = A ”

Bending manner

The H of the H-bond ( in-between H ) is traveling to the right and left, doing the remainder of the molecule to travel in that manner as good


Frequency = 1782

Type = A ‘

Bending Mode

The H atoms on the H-bond giver fragment travel up and down to the sides traveling farther off and so coming closer.


Frequency = 1854

Type = A ‘

Bending Mode

The H atoms on the H-bond acceptor fragment offprint and travel farther off and so come nearer together once more.


Frequency = 3724

Type = A ‘

Stretching manner

The H organizing the H-bond moves closer to the O of the H-bond and so farther from it, doing the O-H bond to come smaller and the H ” ‘ ” O bond to go bigger, and the antonym.


Frequency = 3849

Type = A ‘

Stretching manner

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


Frequency = 3907

Type = A ‘

Stretching manner

The O-H bond of the H non involved in the H-bond acceptor fragment is stretching out, doing the bond to go longer, while the bond of the O with the other H, which is involved in the H-bond, becomes shorter.


Frequency = 3982

Type = A ”

Stretching manner

It is an unsymmetrical motion, where one O-H bond in the H-bond giver fragment becomes shorter and the other thirster.


Question 3

Isotopic permutation in the H2O dimer

Free Energy ( H-TS ) = 37.8

& A ; Delta ; & A ; Eta ; Total = 127.5

Free Energy ( H-TS ) = 39.7

& A ; Delta ; & A ; Eta ; Total = 126.5

& A ; Delta ; G = G ( B ) – G ( A ) = 39.7KJmol-1 – 37.8KJmol-1 = 1.9 KJ/mol

K = vitamin E ( – & A ; Delta ; G/RT ) = exp ( -1.9×10-3Jmol-1/8.314JK-1mol-1x298K ) = 1.00000077

Deuterium prefers the place shown in B ( connected to the O of the H-bond acceptor fragment, but does n’t take portion straight in the H-bond ) because the molecule has higher free energy for this agreement.

Question 4

Interconversion of H2O dimer constructions

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 H2O dimer Cyclic H2O dimer

  • The acyclic H2O molecule energy is 3.969×10-5 KJmol-1 whereas the energy of the cyclic one is — — . The cyclic molecule is less stable than the acyclic one because its ability to travel about is efficaciously reduced compared to the acyclic one, due to the two bonds formed between the O of one molecule and the two H of the other molecule.
  • The fanciful frequence has the value of i306.9. One of the in-between Hs moves up while the other moves down, in an unsymmetrical motion as shown in the images above.
  • For the acyclic H2O dimer there are no fanciful frequences and it corresponds to the vale. This shows that it is really stable and this construction is preferred.
  • The cyclic molecule contains one vibrational frequence and this suggests that it is non every bit stable as the acyclic one. It corresponds to the brow of molecule-mountain.
  • If a molecule has more than one vibrational frequence it corresponds to the mountain base on ballss and it is a really unstable and unfavoured construction for the molecule to be at, which most likely does non be.
  • The cyclic construction is non really stable, and therefore it is non preferred over the acyclic one.

Question 5


No fanciful frequences & A ; agrave ; Valley & A ; agrave ; stable construction, extremely favoured

Boat cyclohexane:

ne fanciful frequence & A ; agrave ; Hilltop & A ; agrave ; reasonably unstable, exists but non preferable

All-syn cyclohexane:

More than one fanciful frequences & A ; agrave ; Mountain Pass & A ; agrave ; does non be, really unstable

Cite this Normal vibrational frequencies of water molecule

Normal vibrational frequencies of water molecule. (2017, Jul 17). Retrieved from https://graduateway.com/normal-vibrational-frequencies-of-water-molecule-essay/

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