Dipole, defined

Because the orientations of the dipoles defined by the strings in generation 0 have been chosen at random, none of these strings is likely to have a high fitness. The initial points in any GA population will be scattered randomly across the fitness surface (Figure 5.13). 

In its most elementary form an electric dipole comprises two equal and opposite point charges separated by a distance 5x. The dipole moment p of the dipole, defined as... 

We also can make the corresponding computation using our test charge and dipole or two test dipoles defined in Section II of Ref. 4. Putting K= k s, we have by convolution (integration over s) KD = f 3... 

Chapter 6, devoted to dipoles, defines the exchange reversibility r ij which quantifies the behavior of the exchange by flows between pole / and pole j ... 

A strong retardation of the rotational motion of water is usually observed near surfaces of biomolecules. The rotational motion of water is usually analyzed through the reorientational dynamics of its electrical dipole defined as the vector pointing from the water oxygen to the middle point of the two hydrogen atoms. Two first- and second-rank autocorrelation functions Ti and Ti are the time average of the Legendre polynomials Pn(cos(6>)) ... 

Many methods for the evaluation of from equation ( Al.5.20) use moments of the dipole oscillator strength distribution (DOSD) defined, for molecule A, by... 

With this convention, we can now classify energy transfer processes either as resonant, if IA defined in equation (A3.13.81 is small, or non-resonant, if it is large. Quite generally the rate of resonant processes can approach or even exceed the Leimard-Jones collision frequency (the latter is possible if other long-range potentials are actually applicable, such as by pennanent dipole-dipole interaction). 

Before substiUitmg everything back into equation B1.2.6, we define the transition dipole moment between states 1 and 2 to be the integral... 

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

The first tenn is tire dipole force, sometimes called tire trapping force, Fj, because it is a conservative force and can be integrated to define a trapping potential for tire atom ... 

C3.4.13)). The dimer has a common ground state and excitation may temrinate in eitlier tire or excited state (see tire solid arrows in figure C3.4.3). The transition dipole moments of tliese transitions are defined as ... 

In contrast to the point charge model, which needs atom-centered charges from an external source (because of the geometry dependence of the charge distribution they cannot be parameterized and are often pre-calculated by quantum mechanics), the relatively few different bond dipoles are parameterized. An elegant way to calculate charges is by the use of so-called bond increments (Eq. (26)), which are defined as the charge contribution of each atom j bound to atom i. 

In stead, the electrostatic con tribn tion conies from definin g a set of bond dipole moments associated woth polar bonds. These bond moments are defined in the m m psir.LxL(dbf) file along with the bond stretching parameters and are given in units of Debyes. The cen ter of th e dipole Is defined to be th e m Idpoint of the bond an d two dipoles p. and pj. separated by Rjj. as shown beltnv ... 

Energy, geometry, dipole moment, and the electrostatic potential all have a clear relation to experimental values. Calculated atomic charges are a different matter. There are various ways to define atomic charges. HyperChem uses Mulliken atomic charges, which are commonly used in Molecular Orbital theory. These quantities have only an approximate relation to experiment their values are sensitive to the basis set and to the method of calculation. 

The permanent dipole moment of an isolated molecule depends on the magnitude of the charge and on the distance separating the positive and negative charges. It is defined as... 

Measured at 1.907 lm unless otherwise iadicated. 1 is the dipole moment and P is the molecular first hyperpolarizabiUty defined in equation 1. Measured at 1.3 lm Ref. 9. 

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