Microscopic Electric Dipole Moment

Molecules having a dissymetric electron cloud distribution exhibit a permanent electric dipole moment. The electric dipole moment of a molecule, i, is a vector physical quantity, denoted by y. or p., with a modulus expressed in C.m. In some old textbooks, it was expressed in the obsolete unit called the debye (D)  

The electric dipole moment between two identical electric charges, q, in coulombs (C) separated by a distance d in meters (m), is given by the equation  

NB When an electric dipole is composed of two point charges +q and -q, separated by a distance r, the direction of the dipole moment vector is taken to be from the negative to the positive electric charge. However, the opposite convention was adopted in physical chemistry but is to be discouraged. Moreover, the dipole moment of an ion depends on the choice of the origin. 

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The macroscopic electrical dipole moment, p, expressed in C.m, is the summation of all the contributions of individual microscopic electric dipole moments ... 

The pseudovector four-potential B may still contribute to other effects in the microscopic domain. For example, it would predict that a particle, such as a neutron, would have an electric dipole moment, whose value is proportional to the term in the Dirac Hamiltonian 2,a E [12]. However, after much experimental investigation into the possibility of the neutron electric dipole moment, it has not been found [15]—that is, in the context of this theory, the parameter if it were nonzero, must be too small (the order of 10-13) for this effect to be observed. 

In the above discussion, we have only considered the effects due to the CTE-CTE repulsion, which contribute to the resonant nonlinear absorption (as well as to other resonant nonlinearities) by the CTE themselves. Here, however, we want to mention a more general mechanism by which the nonlinear optical properties of media containing CTEs in the excited state can be enhanced. This influence is due to the strong static electric field arising in the vicinity of an excited CTE, If, for example, the CTE (or CT complex) static electric dipole moment is 20 Debye, at a distance of 0.5 nm it creates a field Ecte of order 107 V/cm. Such strong electric fields have to be taken into account in the calculation of the nonlinear susceptibilities, because they change the hyperpolarizabilities a, / , 7, etc. of all molecules close to the CTE. For instance, in the presence of these CTE induced static fields, the microscopic molecular hyperpolarizabilities are modified as follows... 

The AFM creates atomic level resolution images of the surfaces of noncon-ductive specimens, using the quantum mechanical phenomenon of repulsive atomic force. The AFM records the repulsive forces that occur when electron clouds of two atoms, one in the microscope probe and the other at the sample surface, are in close proximity to each other. In most AFMs, the sample is mounted on the piezoelectric tube, so the sample moves in relation to a stationary tip. As the sample is very close to the probe, the fluctuations in electric dipole moment of the interacting atoms create a repulsive action between atoms of the specimen and atoms of the probe. As the probe is deflected by the atoms on the surface of the specimen, its movement is intercepted by a laser beam, which transmits the information to the computer for image generation. 

In (2.16), which is the microscopic analogue of (2.1), apices i, j, k, I etc. indicate (contravariant) components of the three vectors jx ed E, which are, respectively, the ground state electric dipole moment of the unperturbed molecule. 

P describes the electric dipole moment per unit volume inside the material, caused by the alignment of microscopic dipoles by the electric field. It is related to the bound charge density via ... 

It turns out that there is another branch of mathematics, closely related to tire calculus of variations, although historically the two fields grew up somewhat separately, known as optimal control theory (OCT). Although the boundary between these two fields is somewhat blurred, in practice one may view optimal control theory as the application of the calculus of variations to problems with differential equation constraints. OCT is used in chemical, electrical, and aeronautical engineering where the differential equation constraints may be chemical kinetic equations, electrical circuit equations, the Navier-Stokes equations for air flow, or Newton s equations. In our case, the differential equation constraint is the TDSE in the presence of the control, which is the electric field interacting with the dipole (pemianent or transition dipole moment) of the molecule [53, 54, 55 and 56]. From the point of view of control theory, this application presents many new features relative to conventional applications perhaps most interesting mathematically is the admission of a complex state variable and a complex control conceptually, the application of control teclmiques to steer the microscopic equations of motion is both a novel and potentially very important new direction. 

Light-matter interactions can be described via an induced polarization, i.e., the induced dipole moment per unit volume. Ultrafast laser pulses, which are used in laser scanning microscopes, have high enough intensity to induce a nonlinear polarization in various materials. For intense optical electric field E, the polarization vector P can be expanded in the power series (Boyd 1992)... 

The phenomenon of two-photon absorption (2 PA) can be presented as a process of simultaneous absorption of two photons under high intensity irradiation, resulting in one excited molecule [Ij. The investigations of 2PA previously undertaken are of great interest for a wide variety of emerging applications [3,36-42]. The nature of 2PA can be described based on the interaction of molecular electrons with an optical field. On a microscopic level the displacement of molecular electronic charge under the electric field, E, is related to the induced molecular dipole moment fi ... 

At the microscopic level, the nonlinearity of a molecular structure is described by the electric dipole interaction of the radiation field with the molecules. The resulting induced dipole moment and the Stark energy are given as (1,3)... 

In order to find a correlation between the macroscopic polarization and the microscopic properties of the material a single (polarizable) particle is considered. A dipole moment is induced by the electric field at the position of the particle which is called the local electric field Eloc... 

The nonlinearity may be of microscopic or macroscopic origin. The polarization density P = Np is a product of the individual dipole moment p, which is induced by the applied electric field E, and the density of dipole moments N. The nonlinear behavior may have its origin in either p or N. 

In organic materials, it is convenient to define microscopic nonlinear coefficients that relate the molecular dipole moment with the electric field applied to the molecule. Including the possibility of a permanent molecular dipole moment, /jlq, the molecular dipole moment is related to the electric field components in the frequency domain by ... 

Following the discussion on ionic conductivity in section 12.1, and protonic conduction in section 12.1.2, it can definitely be seen that overall conduction in gum Arabica belongs to the aforementioned category. The nature of the mentioned conductivity is analyzed from a.c. conduction. In the microscopic level mechanism in the solid, there is a particular pair of states between which jumps take place which are influenced by the electric field. A dielectric material of natural type gum containing permanent dipole moment g, when sandwiched between two plane parallel electrodes of area A, separation d, the conductivity a and dielectric constant e are connected to conductance G and capacitance C by <7 = G (d/A) and = C (d/Eg A). In the absence of an external electric field, dipoles are oriented at random and possess only electronic polarizability in the field direction. 

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