Dipole moment 20 -movement

Although a diatomic molecule can produce only one vibration, this number increases with the number of atoms making up the molecule. For a molecule of N atoms, 3N-6 vibrations are possible. That corresponds to 3N degrees of freedom from which are subtracted 3 translational movements and 3 rotational movements for the overall molecule for which the energy is not quantified and corresponds to thermal energy. In reality, this number is most often reduced because of symmetry. Additionally, for a vibration to be active in the infrared, it must be accompanied by a variation in the molecule s dipole moment. 

From the framework depicted, it emerges that photocatalytic activity seems strictly related to the dipole moment generated by a distorted crystal structure, namely electron-hole separation upon photoexcitation is promoted by a local electric field due to a dipole moment and, in turn, this promotes vectorial movement of electron and holes. 

Two later sections (1.6.5 and 1.6.6) look at the crystalline structures of covalently bonded species. First, extended covalent arrays are investigated, such as the structure of diamond—one of the forms of elemental carbon—where each atom forms strong covalent bonds to the surrounding atoms, forming an infinite three-dimensional network of localized bonds throughout the crystal. Second, we look at molecular crystals, which are formed from small, individual, covalently-bonded molecules. These molecules are held together in the crystal by weak forces known collectively as van der Waals forces. These forces arise due to interactions between dipole moments in the molecules. Molecules that possess a permanent dipole can interact with one another (dipole-dipole interaction) and with ions (charge-dipole interaction). Molecules that do not possess a dipole also interact with each other because transient dipoles arise due to the movement of electrons, and these in turn induce dipoles in adjacent molecules. The net result is a weak attractive force known as the London dispersion force, which falls off very quickly with distance. 

Even if molecules do not possess a permanent dipole moment weak forces can exist between them. The movement of the valence electrons creates transient dipoles , and these in turn induce dipole moments in adjacent molecules. The transient dipole in one molecule can be attracted to the transient dipole in a neighbouring molecule, and the result is a weak, short-range attractive force known as the London dispersion force. 

A piezoelectric crystal is one that develops an electrical voltage when subject to mechanical stress for example if pressure is applied to it, and conversely develops strain when an electric field is applied across it. Application of an electric field causes a slight movement of atoms in the crystal so that a dipole moment develops in the crystal. For it to be piezoelectric, a crystal must be made up from units that are non-centrosymmetric (i.e., they do not possess a centre of symmetry). Of the 32 crystal classes (see Chapter 1), 11 possess a centre of symmetry and one other cannot be piezoelectric because of other symmetry elements it possesses. 

Dipolar ions like CN and OH can be incorporated into solids like NaCl and KCl. Several small dopant ions like Cu and Li ions get stabilized in off-centre positions (slightly away from the lattice positions) in host lattices like KCl, giving rise to dipoles. These dipoles, which are present in the field of the crystal potential, are both polarizable and orientable in an external field, hence the name paraelectric impurities. Molecular ions like SJ, SeJ, Nf and O J can also be incorporated into alkali halides. Their optical spectra and relaxation behaviour are of diagnostic value in studying the host lattices. These impurities are characterized by an electric dipole vector and an elastic dipole tensor. The dipole moments and the orientation direction of a variety of paraelectric impurities have been studied in recent years. The reorientation movements may be classical or involve quantum-mechanical tunnelling. 

Dispersion forces (instantaneous-dipole - induced-dipole interactions) even in atoms and molecules having no permanent dipole moment, the continuous movement of electrons results, at any instant, in a small dipole moments, which fluctuatingly polarize the electronic system of the neighboring atoms or molecules. This coupling causes the electronic movements to be synchronized in such... 

Movement of an electron from the ground electronic state of a molecule to an excited state creates a momentary dipole, called an electric transition dipole. Thus, associated with each electric transition is a polarization (electric transition dipole moment) that has both direction and intensity which vary according to the nature of the chromophore and the particular excitation. When two or more chromophores lie sufficiently close together, their electric transition dipoles may interact through dipole-dipole (or exciton) coupling. Exciton coupling arises from the interaction of two (or more) chromophores through... 

Two kinds of dipole moments are the induced and the permanent. The induced dipole is created by an electric field. Its value is temperature independent, because the molecule will reorient itself in the direction of the field after it is perturbed by a thermally agitated molecule. The permanent dipole is caused by the electric negativity differences of the atoms within the molecule and is temperature dependent. At higher temperatures, the random movement of molecules opposes their tendency to become oriented in the direction of the electric field (Lyman et al., 1982). 

In case of non-primitive lattices with different atoms in the elementary cell, the sub-lattices can vibrate against each other (optical modes, see Figure 1.10). A vibration with a frequency iv 0 becomes possible even for k = 0. The opposite movement of neighboring atoms evokes large dipole moments allowing a coupling to electromagnetic waves. 

The behavior of such a large system as a pore formed by a bacterial porine (E. coli OmpF) has been simulated in a lipid bilayer of palmitoyloleoylphosphatidylethanola-mine (POPE) [95]. Despite the use of united atoms, the final system of the trimeric porin embedded into 318 POPE molecules and solvated with water consisted of more than 65 000 atoms in total. During the 1 ns of the MD simulation the trimeric structure remained stable, with almost all flexibility in the loops and turns outside the 3-strands. The movement and orientation of the water molecules was investigated in detail. As found in case of the pore formed by the hexameric LS3 helix bundle [90], the diffusion of the water was decreased to about 10% of that of bulk water. Some ordering of the water molecules was evident from the average water dipole moments, which showed a strong dependence on the vertical position within the porine. 

In this framework, polarization of an ion leads to movement of the center of charge as charge density is redistributed. In some applications, it may be advantageous to work in an ion-fixed coordinate system and track the dipole moment as an indicator of the extent of polarization, as has been done [182]. But an increase in the dipole moment in such a fixed coordinate system does not make the ion more polar , it is simply an artifact of the choice of coordinate. 

Displacements in units of a. Positive values indicate movements in direction of outward normal. Direction and magnitude of dipole moments (debye units) indicated by arrows. For negative ions length of arrow corresponds to one tenth of dipole moment... 

In Exp. 29, the effect of a static or low-frequency electric field on a molecule was considered and it was seen that a dipole moment is induced because of movement of the charged electrons and nuclei. At high optical frequencies (—10 Hz), the nuclei cannot respond rapidly enough to follow the field, but polarization of the electron distribution can occur. For an isolated molecule, an oscillating radiation field of intensity E will induce a dipole moment of magnitude... 

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