Center of charge

Centers of positive and negative charge that are separated from each other consti tute a dipole The dipole moment p- of a molecule is equal to the charge e (either the positive or the negative charge because they must be equal) multiplied by the distance between the centers of charge... 

Any given molecule has two centers of charge, one associated with the positive nuclei of the ion cores, the other associated with the negative valence electrons. For a spherically symmetric molecule (and others) these centers are coincident. When an electric field is applied to such a molecule (or to a solid containing such molecules), the centers of charge separate by some distance, x forming an electric dipole with a moment, p = qx where q is the amount of charge associated with each center, p and x are determined by the polarizability which will be considered later. 

Fig. 17.2. The distribution of charges at the internal wall of a silica capillary. x is the length in cm from the center of charge of the negative wall to a defined distance, 1 = the capillary wall, 2 = the Stern layer or the inner Helmholtz plane, 3 = the outer Helmholtz plane, 4 = the diffuse layer and 5 = the bulk charge distribution within the capillary.

Table 16. Shift of the centers of charge of the localized orbitals upon complex formation1)...

Figure 8 Plots of In H, 2 (cm-1) vs. distance R (A) from the center of the SS bond and the center of charge of the ground (left line) and excited (right line) Rydberg orbitals for the HjN-(CH2)n-S-S-CH3 model compounds having n = 1, 2, and 3 (appears as Figure 6 in ref. 3s).

F represents the contribution due to variations of intemuclear distances, say, R i instead of the reference value Rm, and to changes of electronic centers of charge... 

Finally, we must consider the contribution of the electrostatic work required to transfer one electron into free space. After overcoming the short range chemical forces, the electron must be moved a certain distance against the electric field in the surface. Under the assumption that the lines of force of the electric field are located between the ion defects in the boundary layer and the surface charges represented by the chemisorbed gas atom, we obtain the expression afi for this electrostatic work term. is the boundary field strength represented in Equation (11), and a is the distance between the surface of the oxide and the centers of charge of the chemisorbed atoms in the a-phase. 

Fig. 4.4. The vector S connects the centers of charge and R the centers of mass of the HD molecules, Eq. 4.44.

As briefly recollected by Ohanian [107], the mechanical origin of spin was mentioned as a possibility at the beginning of the twentieth century. Quantum theory adopted a point model for particles, which completely closed the door to a mechanical interpretation of spin. Corben [108-111] tried to develop a relativistic composite model for particles, where the basic components were punctual, but allowing for a separation between the center of mass and the center of charge. Corben argued that one of the components could have negative mass. 

Figure 3. The arrows indicate how the local dipoles of the H-bonds might interact with the local dipoles of the p- and m-nitroanilines to give head to tail and head to head interactions. The + and - signs indicate centers of charge. Unmarked carbon atoms are neutral.

Here, the phase factor e k R,x is associated with the wave vector of applied laser field and the center of mass (or the center of charge) position of the molecule. The density matrix operator can be then defined as... 

Such charge repulsion effects can operate either in homogeneous solution or in anisotropic media where appreciable centers of charge density develop. Two important classes of media in which these electrostatic effects appreciably influence chemical reactivity (in self-organizing assemblies and polymers) are treated in the following sections. 

The same approach may be applied to ionic systems using what is known as the center of charge framework [181]. In this case, the first (Coulomb) term in Eq. (7) is nonzero and dominates electrostatic interactions. It is the dipole term that is coordinate dependent and is eliminated by the choice of origin. This is accomplished by placing the origin Rcq... 

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. 

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