Vibrational modes water molecule

The complexity of the physical properties of liquid water is largely determined by the presence of a three-dimensional hydrogen bond (HB) network [1]. The HB s undergo continuous transformations that occur on ultrafast timescales. The molecular vibrations are especially sensitive to the presence of the HB network. For example, the spectrum of the OH-stretch vibrational mode is substantially broadened and shifted towards lower frequencies if the OH-group is involved in the HB. Therefore, the microscopic structure and the dynamics of water are expected to manifest themselves in the IR vibrational spectrum, and, therefore, can be studied by methods of ultrafast infrared spectroscopy. It has been shown in a number of ultrafast spectroscopic experiments and computer simulations that dephasing dynamics of the OH-stretch vibrations of water molecules in the liquid phase occurs on sub-picosecond timescales [2-14],... 

A nonlinear molecule with n atoms generally has 3n — 6 fundamental vibrational modes. Water (3 atoms) has 3(3) -6 = 3 fundamental modes, as shown in the preceding figure. Methanol has 3(6) - 6 = 12 fundamental modes, and ethanol has 3(9) - 6 = 21 fundamental modes. We also observe combinations and multiples (overtones) of these simple fundamental vibrational modes. As you can see, the number of absorptions in an infrared spectrum can be quite large, even for simple molecules. 

The translatory vibrations of water molecules are mostly mixed with both H2O librations and translatory modes of other entities present in the structure. Lattice vibrations containing H2O motions are normally found in the spectral range from 100 to 350 cm . In the case of pure Th q bands, the isotopic shift ratio cohjo/wdzO is 1.054. However, pure ThjO modes are rarely observed. Therefore, only little work was done on structural and bonding implications of H2O translatory modes. 

A nonlinear molecule with n atoms generally has 3n — 6 fundamental vibrational modes. Water (3 atoms) has 3(3) — 6 = 3 Fundamental modes, as shown in the preced-... 

Figure 19. Velocity auto-correlation functions for the three intramolecular vibrations of water molecules at supercritical temperatures (a) 771 K, 1.284 g/cm (b) 673 K, 0.166 g/cm. Q, Q2, and Q3 denote the symmetric stretching, bending, and asyimnetric stretching modes, as illustrated on the inserts.

Caution During a sininlation, solvent temperature may increase wh ile th e so In te cools. This is particii larly true of sm all solven t molecules, such as water, that can acquire high translational and rotational energies. In contrast, a macromolecule, such as a peptide, retains most of its kinetic energy in vibrational modes. This problem rem ains un solved, an d this n ote of cau tion is provided to advise you to give special care to simulations using solvent. 

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). 

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. 

For die example of the water molecule it is of interest to calculate the forms of the vibrational modes, as obtained from the evaluation of the matrix L = UL. The results can be presented most simply as shown in Fig. 4. The calculation of the specific form of the normal modes is complicated, although with the aid of current computer programs it becomes routine - at least for relatively simple molecules. 

It is apparent from Fig. 4 that the normal modes of vibration of the water molecule, as calculated from the eigenvectors, can be described approximately as a symmetrical stretching vibration (Mj) and a symmetrical bending vibration... 

As the molecule vibrates it can also rotate and each vibrational level has associated rotational levels, each of which can be populated. A well-resolved ro - vibrational spectrum can show transitions between the lower ro-vibrational to the upper vibrational level in the laboratory and this can be performed for small molecules astronomically. The problem occurs as the size of the molecule increases and the increasing moment of inertia allows more and more levels to be present within each vibrational band, 3N — 6 vibrational bands in a nonlinear molecule rapidly becomes a big number for even reasonable size molecules and the vibrational bands become only unresolved profiles. Consider the water molecule where N = 3 so that there are three modes of vibration a rather modest number and superficially a tractable problem. Glycine, however, has 10 atoms and so 24 vibrational modes an altogether more challenging problem. Analysis of vibrational spectra is then reduced to identifying functional groups associated... 

Infrared (IR) spectroscopy, especially when measured by means of the Fourier transform method (FTIR), is another powerful technique for the physical characterization of pharmaceutical solids [17]. In the IR method, the vibrational modes of a molecule are used to deduce structural information. When studied in the solid, these same vibrations normally are affected by the nature of the structural details of the analyte, thus yielding information useful to the formulation scientist. The FTIR spectra are often used to evaluate the type of polymorphism existing in a drug substance, and they can be very useful in studies of the water contained within a hydrate species. With modem instrumentation, it is straightforward to obtain FTIR spectra of micrometer-sized particles through the use of a microscope fitted with suitable optics. 

FIG. 9 Diagram illustrating the three vibrational modes (31V— 6) of water in the gas phase. (A) The first mode is called bending, in which the water molecule moves in a scissors-like manner. (B) The second is the symmetric stretch, where the hydrogen atoms move away from (or toward) the central oxygen atom simultaneously—i.e., in-phase motion. (C) The third is the asymmetric stretch, in which one hydrogen atom approaches the central oxygen atom, while the other moves away—i.e., out-of-phase motion. 

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