Water molecule vibrations

Water molecules vibrate and rotate in the gas phase. In the liquid phase, the rotation is hindered (Ubration) because of the structure (intermolecular H bonds) and the vibrations are modified (Section 2.11.2). 

Dangling OH bonds exit, which are not included in hydrogen bonds. These entities persists far longer than water molecule vibrational periods, and hence may hold the key to the structurally sensitive band shapes that arise in infrared and Raman spectroscopy of water and its solutions. 

Figure 19.12 Examples of vibrational and rotational motion, illustrated for the water molecule. Vibrational motions involve periodic displacements of the atoms with respect to one another. Rotational motions involve the spinning of a molecule about an axis. 

In ice, the water molecules vibrate randomly about their po, sitions in the solid. Their motions are represented by arrows. 

Gragson D E and Richmond G I 1998 Investigations of the structure and hydrogen bonding of water molecules at liquid surfaces by vibrational sum frequency spectroscopy J. Phys. Chem. 102 3847... 

Consider now the aquo-complexes above, and let v be the distance of the centre of mass of the water molecules constituting the iimer solvation shell from the central ion. The binding mteraction of these molecules leads to vibrations... 

An important area that has yet to be fully explored is the effect of the flexibility of water molecules. The intennolecular forces in water are large enough to cause significant distortions from the gas-phase monomer geometry. In addition, the flexibility is cmcial in any description of vibrational excitation in water. 

Intensive use of cross-terms is important in force fields designed to predict vibrational spectra, whereas for the calculation of molecular structure only a limited set of cross-terms was found to be necessary. For the above-mentioned example, the coupling of bond-stretching (f and / and angle-bending (B) within a water molecule (see Figure 7-1.3, top left) can be calculated according to Eq. (30). 

Polyatomic molecules vibrate in a very complicated way, but, expressed in temis of their normal coordinates, atoms or groups of atoms vibrate sinusoidally in phase, with the same frequency. Each mode of motion functions as an independent hamionic oscillator and, provided certain selection rules are satisfied, contributes a band to the vibrational spectr um. There will be at least as many bands as there are degrees of freedom, but the frequencies of the normal coordinates will dominate the vibrational spectrum for simple molecules. An example is water, which has a pair of infrared absorption maxima centered at about 3780 cm and a single peak at about 1580 cm (nist webbook). 

Molecular Nature of Steam. The molecular stmcture of steam is not as weU known as that of ice or water. During the water—steam phase change, rotation of molecules and vibration of atoms within the water molecules do not change considerably, but translation movement increases, accounting for the volume increase when water is evaporated at subcritical pressures. There are indications that even in the steam phase some H2O molecules are associated in small clusters of two or more molecules (4). Values for the dimerization enthalpy and entropy of water have been deterrnined from measurements of the pressure dependence of the thermal conductivity of water vapor at 358—386 K (85—112°C) and 13.3—133.3 kPa (100—1000 torr). These measurements yield the estimated upper limits of equiUbrium constants, for cluster formation in steam, where n is the number of molecules in a cluster. 

It is well known, that in aqueous solutions the water molecules, which are in the inner coordination sphere of the complex, quench the lanthanide (Ln) luminescence in result of vibrations of the OH-groups (OH-oscillators). The use of D O instead of H O, the freezing of solution as well as the introduction of a second ligand to obtain a mixed-ligand complex leads to either partial or complete elimination of the H O influence. The same effect may be achieved by water molecules replacement from the inner and outer coordination sphere at the addition of organic solvents or when the molecule of Ln complex is introduced into the micelle of the surfactant. 

Solvation effects on the molecular vibrations of 128 were studied by SCRF methods and by supermolecular approaches of 128 with one water molecule [97JPC(B) 10923, 98JPC(A)6010]. Correlations between the N—H (uracil) and O—H (water) bond elongations and the corresponding frequency shifts of the stretching vibrations are reported as... 

Consider, for example, a dilute aqueous solution of KC1, in which a field of 1 millivolt/cm is maintained. From the mobilities given in Table 3 we calculate that, when, for example, -is second has elapsed, the average drift in either direction for the K+ and the Cl- ions will have been less than (0.0007 X 10 3)/25 cm, that is to say, less than 3 X 10- cm (which is the diameter of one water molecule). Clearly, this distance is nothing but an average drift of the ions for during the 5 5 second, the ions in their (almost) random motion will, of course, have moved in all directions. As mentioned above, periods of molecular vibration usually lie between 10"1 - and 10- 5 sec and in 3V second each ion may have shifted its position many thousand times. Owing to the presence of the applied field the motion of the ions will not be quite random as a result of their drift the solution will appear to carry a steady current. 

The internal structure of a liquid at a temperature near its freezing point has been discussed in Sec. 24. Each molecule vibrates in a little cage or cell, whose boundaries are provided by the adjacent molecules, as in Fig. 20, and likewise for each solute particle in solution in a solvent near its freezing point. It is clear that the question of the hydration of ions no longer arises in its original form. In aqueous solution an atomic ion will never be in contact with less than three or four water molecules, which in turn will be in contact with other water molecules, and so on. There is an electrostatic attraction, not only between the ion and the molecular dipoles in immediate contact with it, but also between the ion and molecular dipoles that are not in contact with it. For solvent dipoles that are in contact with a small doubly charged ion, such as Ca++,... 

Table 28 presents structural characteristics of compounds with X Me ratios between 6 and 5 (5.67, 5.5, 5.33, 5.25). According to data provided by Kaidalova et al. [197], MsNbsC Fu type compounds contain one molecule of water to form M5Nb303Fi4-H20, where M = K, Rb, Cs, NH4. Cell parameters for both anhydrous compounds [115] and crystal-hydrates [197] were, nevertheless, found to be identical. Table 28 includes only anhydrous compound compositions because IR absorption spectra of the above compounds display no bands that refer to vibrations of the water molecule... 

A nonlinear molecule consisting of N atoms can vibrate in 3N — 6 different ways, and a linear molecule can vibrate in 3N — 5 different ways. The number of ways in which a molecule can vibrate increases rapidly with the number of atoms a water molecule, with N = 3, can vibrate in 3 ways, but a benzene molecule, with N = 12, can vibrate in 30 different ways. Some of the vibrations of benzene correspond to expansion and contraction of the ring, others to its elongation, and still others to flexing and bending. Each way in which a molecule can vibrate is called a normal mode, and so we say that benzene has 30 normal modes of vibration. Each normal mode has a frequency that depends in a complicated way on the masses of the atoms that move during the vibration and the force constants associated with the motions involved (Fig. 2). 

Let us now improve our two-body model by allowing the molecule of water to vibrate. A rather straightforward way to achieve the goal is simply to consider the potential energy between the two molecules as a sum of two contributions, one arising from the intermolecular and the second from the intramolecular motions an approximate interaction potential has been reported by Lie and dementi rather recently, where the intramolecular potential was simply taken over from the many body perturbation computation by Bartlett, Shavitt, and Purvis. The potential will henceforth be referred to as MCYL. 

A water molecule can vibrate by internal motion of its atoms. 

Note that in the above diagram there are still vibrational states but that the rotational states are "smeeired" one into the other. There is little translational motion for the water molecules within the interior of the liquid unless they escape from the liquid phase. If they do so, we call this "evaporation (This may be contrasted to the escape of molecules from a solid which we call "sublimation"). 

Most liquids do have a defined vapor pressure which means that molecules can and do escape from the surface of the liquid to form a gas. This is another reason that the properties of a liquid vary from those of the gaseous state. Hence, we still have the vibrational and rotational degrees of freedom left in the liquid, but not those of the translational mode. A representation of water molecules in the liquid state is presented in the following diagram, shown as 1.2.4. on the next page. 

Before considering the details of the structure of liquid water, it is important to define precisely what is meant by the term structure as applied to this liquid. If we start from ice I, in which molecules are vibrating about mean positions in a lattice, and apply heat, the molecules vibrate with greater energy. Gradually they become free to move from their original... 

Let us now turn our attention to liquid water. Just as in ice I, molecular motions may be divided into rapid vibrations and slower diffusional motions. In the liquid, however, vibrations are not centred on essentially fixed lattice sites, but around temporary equilibrium positions that are themselves subject to movement. Water at any instant may thus be considered to have an I-structure. An instant later, this I-structure will be modified as a result of vibrations, but not by any additional displacements of the molecules. This, together with the first I-structure, is one of the structures that may be averaged to allow for vibration, thereby contributing to the V-structure. Lastly, if we consider the structure around an individual water molecule over a long time-period, and realize that there is always some order in the arrangement of adjacent molecules in a liquid even over a reasonable duration, then we have the diffusionally averaged D-structure. 

The increase in density on melting is assumed to arise from two competing effects that occur as water is heated. First, increasing translational freedom for the water molecules weakens the hydrogen-bonded network that exists in ice I. This network thus collapses, and reduces the volume. Second, increased vibrational energy for the molecules causes an effective increase in the volume occupied by any one molecule, thus enlarging the overall volume of the liquid. The first effect is considered to predominate below 4 °C, the second above 4 °C. 

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