Vibrational frequencies of water molecule

Vibrational frequencies of water shredQuestion 1 Normal dashs and vibrational frequencies of water blood cellHF/3-21* optimised geometry of the water moleculeH bond length0.967HOH bond angle107.7(ii) Energy of the HF/3-21G optimised water molecule = -75.58596 auCycleEnergyMax. Grad.Max. Dist.175.585530.012460.00304275.585890.003240.00025375.585960.000010.00000Frequency (cm-1)Relative Motion lead or Bend fictional characterSymmetry (S or A)1799.2BendA1S3812.2StretchA1S3945.8rStretchB1AHODEnergy75.58596 auGeometry stupefy angle107.7Bond length0.967Vibrational frequencies1578.7H moves faster than D symmetric2815.3D moves quickly whereas H moves slightly asymmetric3881.7H moves quickly whereas D moves slightly asymmetric Normal modes and vibrational frequencies of the water dimmer (H2O)2Hydrogen-Bond AcceptorHydrogen bondHydrogen Bond DonorHydrogen bond length (HO) = 1.808Hydrogen bond angle (O-HO) = 174.9Energy of the F/3.12G optimised water dimer = -151.18902 au(a) Potential energy calculationE = 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 (-) whereas the hydrogens are positively charged (+).In the water dimer molecule, the hydrogen atoms (on the H-bond donor oxygen) are +/blue region. The oxygen atom that is bonded to the hydrogen that is the H-bond acceptor has - charge/red region. Between in the H-bond, the positive(H) and negative(O) charges combine/green region.The hydrogen bond is formed between unitary of the H atoms and one O, instead between the two oxygens, because the two oxygen atoms are negatively charged, and have -, 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 HO bond is almost linear, very close to 180 but it is distorted so it is or so 175. Also, the distortion causes the bond HO to become longer.(c) For the water moleculeH bond length = 0.967For 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 new(prenominal) 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 2The water dimer consists of two fragments, the H-bond acceptor (top OH2 group) and the H-bond donor ( hind end 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 future(a)Frequency = 81 cm -1 typesetters case = ABending ModeTop part of the molecule paltry slightly up and mint, 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 typeface = A Bending mode Top part and bottom part moving right and left. Inter monomerFrequency = 172Type = ABending 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 MonomerFrequency = 242Type = AStretching Mode Inter monomer Frequency = 425Type = ABending 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 = 826Type = ABending modeThe H of the H-bond (middle H) is moving to the right and left, causing the rest of the molecule to move in that bearing as well Inter-monomer Frequency = 1782Type = A Bending Mode The hydrogen atoms on the H-bond donor fr agment move up and down to the sides breathing out gain away and then coming closer. Intra-monomer Frequency = 1854Type = A Bending Mode The hydrogen atoms on the H-bond acceptor fragment separate and go win away and then come closer together again. Intra-monomer Frequency = 3724Type = 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 HO bond to become bigger, and the opposite. Intra-monomer Frequency = 3849Type = 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 = 3907Type = A Stretching mode The O-H bond of the H non 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 = 3982T ype = 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-monomerQuestion 3Isotopic substitution in the water dimer Free Energy (H-TS) = 37.8 Total = 127.5 Free Energy (H-TS) = 39.7 Total = 126.5G = G(B) G(A) = 39.7KJmol-1 37.8KJmol-1 = 1.9 KJ/molK = e(-G/RT) = exp(-1.910-3Jmol-1/8.314JK-1mol-1x298K) = 1.00000077Deuterium prefers the position shown in B (connected to the oxygen of the H-bond acceptor fragment, but doesnt take part directly in the H-bond) because the molecule has higher free energy for this arrangement.Question 4Interconversion of water dimer structuresFrequency = i302Type = B1Frequency = 105Type = B2Frequency = 208Type = A1Frequency = 225Type = B1Frequency = 256Type = A2Frequency = 591Type = B2Frequency = 1785Type = A1Frequency = 1831Type = A1Frequency = 3829Type = A1Frequency = 3862Type = A1Frequency = 3952Type = B1Frequency = 3961Type = B2Acyclic water dimer Cyclic water dimer The acyclic water molecule energy is 3.96910-5 KJmol-1 whereas the energy of the cyclic one is -. The cyclic molecule is less constant than the acyclic one because its ability to move around is effectively cut compared to the acyclic one, due to the two bonds formed between the oxygen of one molecule and the two H of the other molecule. The ideational frequency has the value of i306.9. ace of the middle hydrogens moves up while the other moves down, in an unsymmetrical movement as shown in the pictures above. For the acyclic water dimer there are no imaginary frequencies and it corresponds to the valley. This shows that it is very stable and this structure is preferred.The cyclic molecule contains one vibrational frequency and this suggests that it is non as stable as the acyclic one. It corresponds to the hilltop of molecule-mountain.If a molecule has more than one vibrational frequency it corresponds to the mountain passes and it is a very unstable and unfavoured struc ture for the molecule to be at, which most probably does not exist. The cyclic structure is not very stable, and therefore it is not preferred over the acyclic one.Question 5Syn-butaneNo imaginary frequencies Valley stable structure, highly favouredBoat cyclohexanene imaginary frequency Hilltop fairly unstable, exists but not preferredAll-syn cyclohexaneMore than one imaginary frequencies Mountain convey does not exist, very unstable