Vibrational frequencies of water molecule

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 (HO) = 1.808 Hydrogen bond angle (O-HO) = 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 (ÃŽ ´-) whereas the hydrogens are positively charged (ÃŽ ´+). In the water dimer molecule, the hydrogen atoms (on the H-bond donor oxygen) are ÃŽ ´+/blue region. The oxygen atom that is bonded to the hydrogen that is the H-bond acceptor has ÃŽ ´- 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 ÃŽ ´-, 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 about 175. Also, the distortion causes the bond HO 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 HO 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 ΔÎâ€" Total = 127.5 Free Energy (H-TS) = 39.7 ΔÎâ€" Total = 126.5 ΔG = G(B) G(A) = 39.7KJmol-1 37.8KJmol-1 = 1.9 KJ/mol K = e(-ΔG/RT) = exp(-1.910-3Jmol-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 doesnt 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 The acyclic water molecule energy is 3.96910-5 KJmol-1 whereas the energy of the cyclic one is -. The cyclic molecule is less stable than the acyclic one because its ability to move around is effectively reduced 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 imaginary frequency has the value of i306.9. One 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 not 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 structure 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 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

Small scale embedded generation

Small graduated table air current energySmall graduated table embedded coevals is defined as â€Å" any beginning of electrical energy rated up to, and including, 16 A per stage, individual or multi-phase, 230/400V AC † [ 1 ] . In the instance of air current energy it is rather common to see little graduated table air current turbines as those rated less than 100kW. Small scale air current turbines offer several advantages over their large-scale opposite numbers although as a general regulation of pollex the entire cost of power coevals decreases with the size of the turbine. Large graduated table air current energy production requires a large capital investing non merely due to the equipment cost but besides due to the really big windy sites required for installing. This makes smaller air current turbines more suited for applications such as â€Å" stray islands, individual homes, remote cabins, and street visible radiations † necessitating much less capital investing although the cost of per generated W additions [ 2 ] . The low power evaluation of little air current turbines allows the usage of technologically advanced solutions which would be hard to implement in the instance of e.g. a 5MW air current turbine. This makes the usage of a figure of smaller air current turbines with important cumulative end product power much more attractive. Furthermore, the power evaluation of a air current turbine additions with size doing environmental jobs and important noise. This makes the installing of high power rated wind turbines unsuitable for urban countries but largely suited for distant countries where the connexion to the grid is weak [ 3 ] . In the White Paper on Energy published by the UK authorities it was estimated that at 2007, in UK entirely, there were 20000 installed little graduated table air current turbines with a entire end product power of 7MW. This shows the important proportion of little graduated table air current power coevals in the renewable sector compared to the estimated 1300 photovoltaic UK installings. Furthermore, the mean cost of 7p/kWh makes little wind engineering much more attractive than solar PV energy with an mean cost of 24p/kWh but still considerable expensive compared to big graduated table systems holding an mean cost of 3p/kWh [ 4 ] .Wind turbine typesThere are two basic types of little graduated table air current turbines depending on the place of the rotor: horizontal axis and perpendicular axis turbines. The advantage of the perpendicular axis, besides called Savonius or Darrieus rotor, over the horizontal type is the fact that it operates irrespective of the way of the air current. Although most big graduated table air current turbines presents use horizontal type air current turbines, in little graduated table systems the perpendicular axis orientation is still rather common. The horizontal types can be subdivided into axial and cross depending on their orientation with regard to the way of the air current. Axial air current turbines are widely used in both little and big graduated table systems. Small air current turbines are offered with 2, 3 or more blades. Orientation is provided via either a tail or shaped blades [ 5 ] . The large difference of little graduated table air current turbines compared to big scale systems is that the blades are fixed and protection is offered through the aeromechanicss of the rotor. This is frequently referred to as stall control since the rotor stalls at high air current velocities offering the advantages of simpleness and less power fluctuations. The disadvantages over the pitch control method employed in big scale systems, where the angle of onslaught is controlled by altering the pitch angle of the blades, are that less power is extracted from the air current at low air current velocities while no aid is offered at start-up. Further, fluctuations in air denseness and the frequence of the grid can do fluctuations in the end product power [ 6 ] . In rural countries little graduated table air current turbines are normally mounted on a mast stopping point to a home. However in urban environments where non much infinite is available, they can be installed on the roof of a edifice. The disadvantage of this installing is the turbulency of the air created by the orientation of the infinite environing the edifice. This can be overcome by modifying the construction of the edifice in order to steer the air to flux through the turbine blades. Very little air current turbines are besides mounted on sailing boats. Finally note that with little graduated table air current turbines no connexion in the grid substation is required ; the turbine can straight be connected in the local distribution system [ 5 ] . Another categorization of air current turbines is made with regard to the velocity of the rotor. Most little graduated table systems nowadays use variable velocity turbines in which the rotational velocity of the generator alterations in order to maximize the power extracted from the air current. As a consequence, blasts of air current are largely absorbed by fluctuations of the rotational velocity of the generator maintaining the torsion, and therefore the end product power, comparatively changeless. In contrast, fixed velocity turbines maintain the rotational velocity of the rotor changeless irrespective of the air current velocity while commanding the extracted power by changing the weaving sets. Fixed velocity turbines use initiation generators and offer simpleness, dependability, hardiness and low cost at the disbursal of reactive power ingestion for the exhilaration of the generator and increased mechanical emphasis and line losingss. These losingss are caused by electromotive force fluctuations that may happen due to alterations in power as a consequence of air current velocity fluctuations. On the other manus variable velocity air current turbines use either synchronal or initiation generators and are connected to the grid via a convertor which controls the velocity of the generator. Although fluctuations in end product power are smaller and mechanical emphasis in the aerodynamic system is less than in the instance of fixed velocity turbines, the debut of power electronic devices increases the complexness and cost of the system while extra losingss occur in the convertor [ 6 ] .GeneratorsIn general two types of generators are used widely in air current turbines: initiation and synchronal generators each with its relevant advantages and disadvantages. Initiation generators have governed the industry particularly in big scale air current systems. However little graduated table air current turbines have started to be dominated by lasting magnet synchronal machines. The biggest difference of a synchronal and an initiation generator is that the former operates at the frequence of the grid while the latter at a higher frequence. In both generators the stator is made of a laminated Fe nucleus fitted with a three stage weaving bring forthing a revolving magnetic field with changeless velocity. However the rotors in the two machines are different. In a synchronal generator the field twist of the rotor is fed with a DC current making a magnetic field. The interaction between the two Fieldss causes the rotor to revolve in synchrony with the stator field. In an initiation generator the rotor is non fed with current but the currents are induced due to the comparative motion of the rotor with regard to the magnetic field of the stator. The difference between the synchronal velocity and the rotational velocity of the rotor is called faux pas [ 7 ] . Initiation generators can be either squirrel coop or lesion rotor type. Squirrel coop generators are really efficient and require small care but a gear box between rotor and generator must be used since they rotate at different velocities. Their ability to somewhat alter their rotational velocity for big fluctuations of air current velocities makes them ideal for usage in fixed velocity air current turbines. However their steep torque-speed characteristic together with the high inpouring currents can do terrible electromotive force depressions and do necessary the usage of a soft starting motor. The torsion velocity characteristic can be modified with the usage of a lesion rotor where the opposition of the rotor twist can alter but the overall cost of the rotor increases [ 5 page66 ] . If for illustration the generator has high inpouring currents, the opposition of the twist can be increased at start-up therefore bring forthing high get downing torsion with low current. However this opposition must be decreased at high velocities to forestall big fluctuations of velocity with relevant torsion alterations caused by the alteration of the torsion velocity characteristic. Wound rotor generators are normally used with variable velocity air current turbines and in concurrence with an optically controlled convertor that modifies the opposition of the rotor twist. In general initiation generators are efficient, although less efficient than synchronal generators, and robust while there are minimal demands for care. Furthermore their big production has dropped down the cost of industry. Another advantage is that they can merely be connected to the grid either by conveying the rotor to rated velocity and so link the generator to the grid or by linking the generator to the grid and utilize it as a motor to convey the rotor in the rated velocity [ 9 page 229 ] . Either instance synchrony is non required. The large disadvantage of initiation generators it the demand for reactive power to excite the stator nucleus which must be provided either by the grid or a power convertor. The corresponding decrease in burden power factor can be compensated with the usage of capacitance Bankss [ 6 page67 ] . Synchronous generators are expensive and require care but they are really efficient and have the large advantage of control over reactive power flow through control of the field weaving [ 8 p121 ] . This gives full control over the electromotive force at the terminuss of the generator. A disadvantage of synchronal machines is that when connected to the grid particular synchronism equipment is needed to fit the electrical angle of the AC power with the angular place of the rotor. Another disadvantage is that they are comparatively stiff machines compared to initiation generators due to their changeless velocity feature. As a consequence they respond to sudden blasts of air current or mistakes in an oscillating manner by changing merely the burden angle which can do instability and loss of synchrony.Permanent magnet Synchronous machinesPower electronicsOpen circuit mistakesAC and DC collection effects of small-scale air current generators p.124Suitable design†¦ p.1Comparison of po wer convertor topologies p.2359the feasibleness of edifice p.11little air current turbines in the built.. p.1air current power in power systems p.55air current energy engineering toilet f. Walker page 46Renewable energy in power systemsair current energy explained

A Case Against Deceptive Advertising

Verizon Wireless, a joint ownership of Verizon Communications Inc. and the Vodafone Group PLC, had sold laptop cards with limited capabilities for wireless Internet access.For $59.99 the company was offering an â€Å"unlimited monthly usage plan,† despite the fact that the service had limitations (Sharma & Cheng, 2007).   Customers were not able to use their laptop cards for â€Å"high bandwidth activities,† for example, to download movies (Sharma & Cheng).   Moreover, Verizon Wireless had not mentioned the limitations of its laptop cards in advertisements (Sharma & Cheng).Following an investigation by the State Attorney of New York, Verizon Wireless was required not only to agree to change its â€Å"‘unlimited’ advertising† of the wireless broadband service, but also to reimburse the customers with $1 million in all (Sharma & Cheng).   Besides, the company was required to pay $150,000 in fees and penalties to New York.   Verizon Wireless agr eed to meet all of the legal conditions (Sharma & Cheng).CritiqueThe case of the laptop cards sold by Verizon Wireless concerned deceptive advertising.   The company had referred to its service as an unlimited plan in spite of its limitations.   Customers should have been informed about the limitations before they purchased the service.Thankfully, the New York State Attorney intervened to compel the company to reimburse the customers.   As a matter of fact, this aspect of business law is vital for consumer protection against company fraud.Deceptive advertising includes misrepresentation and omission.   Perhaps Verizon Wireless had mistakenly omitted the limitations of its service in its advertising.   Nevertheless, it was required to pay for its mistake.This serves as a warning for all companies in the U.S.   Furthermore, the business regulatory departments around the country must continue to evaluate all advertisements seeing that imperfect information is a source of ma rket failure.ReferencesSharma, A., & Cheng, R. (2007, Oct 24). Verizon Wireless Reaches Deal in Marketing Probe.The Wall Street Journal, pp. B5.

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